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Tools For Chemical Product Design  From Consumer Products to Biomedicine [1st Edition]
 9780444636843, 9780444636836

Table of contents :
Content:
Front MatterPage iii
CopyrightPage iv
List of ContributorsPages xvii-xviii
Chapter 1 - Mathematical Principles of Chemical Product Design and StrategiesPages 3-43L.Y. Ng, N.G. Chemmangattuvalappil, V.A. Dev, M.R. Eden
Chapter 2 - Integrated Consumer Preferences and Price/Demand–Driven Product Design: An Alternative to Stage-Gate ProceduresPages 45-59M. Bagajewicz
Chapter 3 - VPPD-Lab: The Chemical Product SimulatorPages 61-94S. Kalakul, S. Cignitti, L. Zhang, R. Gani
Chapter 4 - Development of a Multiscale Strategy and Application to Chemical Vapor DepositionPages 95-123L.E.K. Achenie, Y. Sharifi, D.G. Lee
Chapter 5 - Molecular Property Clustering TechniquesPages 125-149F. Eljack
Chapter 6 - Computer-Aided Molecular Design and Property PredictionPages 153-196R. Gani, L. Zhang, S. Kalakul, S. Cignitti
Chapter 7 - The Incorporation of Safety and Health Aspects as Design Criteria in a Novel Chemical Product Design FrameworkPages 197-220J.Y. Ten, M.H. Hassim, D.K.S. Ng, N.G. Chemmangattuvalappil
Chapter 8 - Molecular Design in the Pharmaceutical IndustriesPages 221-238K. Boone, F. Abedin, M.R. Anwar, K.V. Camarda
Chapter 9 - Ionic Liquid Product DesignPages 239-268A.T. Karunanithi, R. Farahipour
Chapter 10 - Integrated Multiobjective Molecular and Process Design: Operational and Computational FrontiersPages 269-313A.I. Papadopoulos, P. Linke, P. Seferlis
Chapter 11 - The Signature Molecular Descriptor in Molecular Design: Past and Current ApplicationsPages 315-343D.P. Visco Jr., J.J. Chen
Chapter 12 - Integrated Process and Product Design OptimizationPages 347-372F.P. Bernardo
Chapter 13 - Tools for Formulated Product DesignPages 373-392M. Martín, A. Martínez
Chapter 14 - Simulation-Based Food Process DesignPages 393-415T.E. Moxon, S. Bakalis
Chapter 15 - A Structured Approach for Product-Driven Process Synthesis in Foods ManufactureaPages 417-441C. Almeida-Rivera, P. Bongers, E. Zondervan
Chapter 16 - Managing Risk in the Design of Product and Closed-Loop Supply Chain StructurePages 443-474L.J. Zeballos, C.A. Méndez
Chapter 17 - Optimization of Blending-Based ProductsPages 475-486N.A. Yunus, Z.A. Manan
Chapter 18 - Decomposition-Based Optimization of Tailor-Made Green Diesel BlendsPages 487-505L.Y. Phoon, H. Hashim, R. Mat, A.A. Mustaffa
Chapter 19 - Strategies for Structured Particulate Systems DesignPages 509-579C. Amador, L. Martin de Juan
Chapter 20 - Computational Tools for the Study of BiomoleculesPages 583-648P.G. Jambrina, J. Aldegunde
Chapter 21 - Walk-In Brain: Virtual Reality Environment for Immersive Exploration and Simulation of Brain Metabolism and FunctionPages 649-658G. Hartung, A. Alaraj, A. Linninger
IndexPages 659-681

Citation preview

Computer Aided Chemical Engineering, 39

Tools for Chemical Product Design From Consumer Products to Biomedicine

Edited by Mariano Martı´n Universidad de Salamanca, Salamanca, Spain

Mario R. Eden Auburn University, Auburn, Alabama, United States

Nishanth G. Chemmangattuvalappil The University of Nottingham Malaysia Campus, Semenyih, Selangor, Malaysia

AMSTERDAM l BOSTON l HEIDELBERG l LONDON l NEW YORK PARIS l SAN DIEGO l SAN FRANCISCO l SINGAPORE l SYDNEY

l l

OXFORD TOKYO

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, USA Copyright © 2016 Elsevier B.V. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-444-63683-6 ISSN: 1570-7946 For Information on all Elsevier publications visit our website at https://www.elsevier.com/

Publisher: John Fedor Acquisition Editor: Kostas Marinakis Editorial Project Manager: Sarah Watson Production Project Manager: Anitha Sivaraj Designer: Mark Rogers Typeset by TNQ Books and Journals

List of Contributors F. Abedin, California State Polytechnic University, Pomona, CA, United States L.E.K. Achenie, Virginia Tech, Blacksburg, VA, United States A. Alaraj, University of Illinois at Chicago, Chicago, IL, United States J. Aldegunde, Universidad de Salamanca, Spain C. Almeida-Rivera, Unilever Research, Vlaardingen, The Netherlands C. Amador, P&G Technical Centres Limited, Newcastle Upon Tyne, United Kingdom M.R. Anwar, The University of Kansas, Lawrence, KS, United States M. Bagajewicz, University of Oklahoma, Norman, OK, United States S. Bakalis, University of Birmingham, Birmingham, United Kingdom F.P. Bernardo, University of Coimbra, Coimbra, Portugal P. Bongers, Unilever Research, Vlaardingen, The Netherlands K. Boone, The University of Kansas, Lawrence, KS, United States K.V. Camarda, The University of Kansas, Lawrence, KS, United States N.G. Chemmangattuvalappil, The University of Nottingham Malaysia Campus, Semenyih, Selangor, Malaysia J.J. Chen, The University of Akron, Akron, OH, United States S. Cignitti, Technical University of Denmark, Kongens Lyngby, Denmark V.A. Dev, Auburn University, Auburn, Alabama, United States M.R. Eden, Auburn University, Auburn, Alabama, United States F. Eljack, Qatar University, Doha, Qatar R. Farahipour, University of Colorado Denver, Denver, CO, United States R. Gani, Technical University of Denmark, Kongens Lyngby, Denmark G. Hartung, University of Illinois at Chicago, Chicago, IL, United States H. Hashim, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia M.H. Hassim, Universiti Teknologi Malaysia, Johor, Malaysia P.G. Jambrina, Universidad Complutense de Madrid, Spain S. Kalakul, Technical University of Denmark, Kongens Lyngby, Denmark A.T. Karunanithi, University of Colorado Denver, Denver, CO, United States D.G. Lee, Virginia Tech, Blacksburg, VA, United States xvii

xviii

List of Contributors

P. Linke, Texas A&M University at Qatar, Doha, Qatar A. Linninger, University of Illinois at Chicago, Chicago, IL, United States Z.A. Manan, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia M. Martı´n, Universidad de Salamanca, Salamanca, Spain L. Martin de Juan, P&G Technical Centres Limited, Newcastle Upon Tyne, United Kingdom A. Martı´nez, Procter and Gamble, Brussels Innovation Center, Strombeek-Bever, Belgium R. Mat, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia C.A. Me´ndez, INTEC (UNL-CONICET), Santa Fe, Argentina T.E. Moxon, University of Birmingham, Birmingham, United Kingdom A.A. Mustaffa, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia D.K.S. Ng, The University of Nottingham Malaysia Campus, Selangor D.E., Malaysia L.Y. Ng, Universiti Tunku Abdul Rahman Sungai Long Campus, Kajang, Selangor, Malaysia A.I. Papadopoulos, Centre for Research and Technology Hellas (CERTH), Thessaloniki, Greece L.Y. Phoon, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia P. Seferlis, Aristotle University of Thessaloniki, Thessaloniki, Greece Y. Sharifi, University of Connecticut, Storrs, CT, United States J.Y. Ten, The University of Nottingham Malaysia Campus, Selangor D.E., Malaysia D.P. Visco, Jr., The University of Akron, Akron, OH, United States N.A. Yunus, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia L.J. Zeballos, INTEC (UNL-CONICET), Santa Fe, Argentina L. Zhang, Hong Kong University of Science and Technology, Hong Kong, China; Technical University of Denmark, Kongens Lyngby, Denmark E. Zondervan, Bremen University, Bremen, Germany

Chapter 1

Mathematical Principles of Chemical Product Design and Strategies L.Y. Ng,* N.G. Chemmangattuvalappil,x V.A. Dev{ and M.R. Eden{, 1 *Universiti Tunku Abdul Rahman Sungai Long Campus, Kajang, Selangor, Malaysia; x The University of Nottingham Malaysia Campus, Semenyih, Selangor, Malaysia; { Auburn University, Auburn, Alabama, United States 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION In the period from 1980e2000, the chemical industry transformed itself from being process-centered to product-centered (Stephanopoulos and Reklaitis, 2011). In the former approach, the products were simple molecules and the research and development activities were not as complicated as in the latter approach. In the product-centered approach, the chemical industry moved towards the manufacture and sale of high value-added materials marketed on performance rather than compositional specifications (Hill, 2009). Thus, in agreement with the prediction of Grossmann and Westerberg (2000), there has been increased attention from the process systems engineering (PSE) community towards the design of chemical products that provide value to businesses and end consumers. This increased attention is part of a larger effort to integrate product design with process design as part of “molecular systems engineering” (Adjiman and Galindo, 2011). Klatt and Marquardt (2009) have alternately used the term “multi-scale product and process systems engineering.” Gani and Ng (2015) recently provided a holistic, multidisciplinary, and hierarchal framework to design products in an integrated manner. The aim of efforts of Gani and Ng (2015) is to win the customers’ appreciation by providing products with desirable properties in an optimal manner. Their very elaborate and detailed framework takes into account various factors, such as finance and economics, and sales and marketing decisions, which directly or indirectly impact the process and product performance. Sales and marketing decisions are based on direct contact and feedback from customers. Sales professionals are made aware of the customers’ needs through various Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00001-0 Copyright © 2016 Elsevier B.V. All rights reserved.

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SECTION j I Basic Concepts and General Tools

TABLE 1.1 Classification of Chemical Products Commodities

Molecular Products

Performance Products

Design key

Cost

Speed

Function

Design basis

Unit operations

Chemistry

Microstructure

Design risk

Feedstock

Discovery

Science

methods of survey. Hence, they are an important factor while deciding on the types and nature of products to be designed and manufactured. The chemical product design framework of Gani and Ng (2015) is in line with the expansion that has occurred in PSE, which now also includes the supply chain in its design considerations (Sargent, 2005). A chemical product can be defined as a system consisting of different chemical substances, which are designed and manufactured for one or more purposes (Cisternas and Ga´lvez, 2006). According to Cussler et al. (2010), chemical products can be generally categorized into three types as shown in Table 1.1. The first type is commodities, such as acids and alcohols. Most of these chemical products are relatively simple to produce, as the production processes are well established. Thus, the design goal is to produce these commodities at minimum cost. The second type is molecular products, such as pharmaceutical drugs. The selling point of molecular products is the speed in designing and introducing the products into the market. In order to stay competitive with companies in the same field, the rates of discovery and development of the products are more important than the production cost of the products. The third type is performance products. The value of this type of products highly depends on its functions, which are normally defined by the structure of the products. Although the key design steps, selling points, and possible risks encountered for these distinct categories of chemical products are different, the procedures for the design of these chemical products are similar. Chemical product design can be defined as the conversion of a conceptual idea into a tangible, manufactured object with a defined molecular structure. Moggridge and Cussler (2000) proposed that the entire process of chemical product design can be explained by four principal steps as follows: 1. 2. 3. 4.

needs: identify product needs ideas: generate ideas to meet the needs selection: select among ideas manufacture: manufacture products

Mathematical Principles of Chemical Product Design Chapter j 1

Throughout the years, various algorithms, approaches, methodologies, and strategies have been developed for different chemical product design problems. In this chapter, the advancement of these chemical product design strategies with the focus on their mathematical principles is discussed.

2. CHEMICAL PRODUCT DESIGN STRATEGIES 2.1 Initial Efforts Traditionally, the common practice in designing new chemical products is by using bottom-up approaches. According to Odele and Macchietto (1993), bottom-up approaches have been considered as iterative approaches, which rely heavily on design heuristics, experimental studies, and expert judgments while designing new chemical products. Most of the time, these traditional approaches require a search, which involves a large number of potential candidate molecules (Venkatasubramanian et al., 1994). During the product design process, the scientists or product designers first hypothesize a target molecule as the potential product that possesses the desired product needs. This is followed by the synthesizing of the product and testing for the desired product needs. Redesigning of the target molecule is required if the desired product needs are not met. Thus, in a bottom-up process, the starting point is a hypothesized molecule, and the end point is a designed molecule(s) with structure(s) matching the desired design objectives. As these approaches are iterative in nature, they are expensive and time-consuming and result in low performance in terms of efficiency and cost-effectiveness (Venkatasubramanian et al., 1994). Furthermore, these approaches are highly dependent on the available information and knowledge. Therefore, it is challenging to search for new chemical products that possess optimal properties without systematic selection tools (Churi and Achenie, 1996). A generalized framework of the traditional chemical product design approach is shown in Fig. 1.1.

2.2 Design of Experiment and Mixture Design of Experiments 2.2.1 Design of Experiment Design of experiments (DOE) is a statistical method to plan and execute experiments in a systematic manner so that maximum information can be gained from the experiments (Box et al., 1978). As the process of product design in actual practice is heavily dependent on the results obtained through experiments, DOE is a potential tool in chemical product design. The first step in developing a model for a system is to identify the factors that affect the system variable of interest. In the next step, a model is postulated to represent the effect of the factors on the response variable. The response variable is the one that is to be optimized. This is followed by the gathering of experimental points to which the model is to be fitted. Finally,

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SECTION j I Basic Concepts and General Tools

Design objectives

Designer

Hypothetisise a target molecule

Synthesise the molecule Revise design Test for desired properties

Meets design objectives?

No

Yes Solution FIGURE 1.1 Traditional molecular design approach.

the adequacy of the model is tested. A number of iterations may be required until a reliable accuracy is determined by the experimenter (Cornell, 2002). The focus of the experimenter is to determine the most effective choice of model and the location of the design points. In most cases, the polynomial model is the preferred model to represent a response surface, as it can be expanded through a Taylor series for accuracy enhancement (Cornell, 2002). According to Montgomery (2008), first or second order models are adequate to represent the response surface, as they require fewer observations. Third or higher ordered models are seldom selected since they need a higher number of experiments for the development of response surface. Also, overfitting may occur with higher order models. Eqs. (1.1) and (1.2) show the general form of fitted first order and second order equations, respectively.

Mathematical Principles of Chemical Product Design Chapter j 1

y ¼ bo þ

u X

bi xi þ ε

(1.1)

i¼1

y ¼ bo þ

u X

bi xi þ

u X u X

bij xi xj þ ε

(1.2)

i j ji

i¼1

In Eqs. (1.1) and (1.2), y is the response, xi and xj are the factors affecting the response, and bo, bi, and bij are the regression coefficients, while ε is the error observed in the response. The total number of i or j chemical constituents is u. Least-squares regression can be applied to determine the regression coefficients by maximizing the model sum of squares and minimizing the residual sum of squares to improve the model fit (Kramer, 1998). Some of the commonly used least-squares regression include classical least squares (CLS), inverse least squares, multiple linear regression, principal component regression (PCR), and partial least squares applied to latent surfaces (Solvason et al., 2009). For example, to derive the regressor solution for a first order model by using CLS, Eq. (1.1) can be written in terms of matrix notation: Y ¼ XB

(1.3)

In Eq. (1.3), Y is the matrix of predicted responses, X is the matrix of component fractions, and B is the matrix of estimated regression coefficients. The least squares solution can then be written as Eqs. (1.4) and (1.5) to determine the central result of CLS analysis: XT Y ¼ XT XB B ¼ XT YðXT XÞ

1

(1.4) (1.5)

The example above is demonstrated for first order model. The same method can be applied to second and third order models as well.

2.2.2 Mixture Design of Experiments Mixture DOE (MDOE) is an extension of DOE in which the factors are the chemical constituents. Scheffe´ developed the first simplex-lattice designs, which make it possible to represent the mixture data on a simplex (Scheffe´, 1958, 1963). To develop the designs, the location of the response of a mixture made up of zero constituent must be identically zero. In other words, the regression coefficient bo in Eqs. (1.1) and (1.2) is zero. In addition, the constituent fractions, xi will sum to one, and every constituent fraction must have a value between zero and one. This can be shown in Eqs. (1.6) and (1.7) u X

xi ¼ 1

(1.6)

0  xi  1

(1.7)

i¼1

7

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SECTION j I Basic Concepts and General Tools

According to Scheffe´ models (Scheffe´, 1958, 1963), the response surface can be represented in terms of only the pure component and interaction terms. However, due to the colinearity, the regressors will not provide the true interpretation of the pure component or interaction effects. Cox model (Cox, 1971) is introduced to address the limitations of Scheffe´ models. However, as discussed by Solvason et al. (2009), although Cox model removes the colinearities introduced by the relation between the mixture constituents, it leaves the secondary colinearities introduced by the constraints in the constituent ranges. Common approaches to solve this issue include the utilization of PCR, ordinary least squares (OLS), and property clustering techniques (Kettaneh-Wold, 1992; Solvason et al., 2009).

2.3 Computer-Aided Molecular Design Chemical product design problems can be defined as the identification of chemical products that satisfy a set of desired product needs. In most cases, performance and functionality of a product are better defined in terms of physical properties rather than chemical structure of the product. Therefore, chemical product design problems can be considered as inverse property prediction problems where the preferred product attributes are represented in terms of physical target properties. The objective for the inverse property prediction problems is to determine the molecule that matches the defined properties (Gani and O’Connell, 2001). As stated by Stephanopoulos (2003), one of the important sources of product specifications and requirements in product design is customer needs. Thus, it is required to translate descriptive customer requirements into measurable physical properties of a product (Achenie et al., 2003). After the required product attributes are represented with measurable product properties, a chemical product that meets the product needs can be designed based on the identified product properties. The design of chemical products based on product properties can be accomplished by using such top-down approaches. Compared to bottom-up approaches, the product design process in top-down approaches starts with the identification of properties the product needs to fulfill, followed by the searching of molecules which possess the properties which meet the product needs (Gani et al., 1991). The design of chemical product via top-down approaches can be carried out using computer-aided molecular design (CAMD) techniques.

2.3.1 Types of Properties and Estimation Techniques CAMD techniques are important for chemical product design problems for their ability in predicting, estimating, and designing molecules with a set of predefined target properties (Harper and Gani, 2000). According to Gani and Constantinou (1996), properties of a chemical product (pure compound and mixture) can be divided into different categories based on the nature of the property. Table 1.2 shows the classification of chemical product properties.

Mathematical Principles of Chemical Product Design Chapter j 1

TABLE 1.2 Classification of Chemical Product Properties Property Type

Property

Primary

Critical temperature, critical pressure, critical volume, normal boiling point, normal melting point, heat of vaporization at 298K, heat of fusion at 298K, Gibbs energy of formation at 298K

Secondary

Surface tension, vapor pressure, density, volume, viscosity, heat capacity

Functional

Vapor pressure, liquid density, conductivity, solubility

Mixture

Liquid density, saturation temperature, saturation pressure, liquid solubility, solid solubility

As shown in Table 1.2, chemical product properties are categorized into primary, secondary, functional, and mixture properties. Primary properties are properties that can be estimated from the molecular structure of the product. Secondary properties are pure component properties, which are dependent on other properties. Functional properties are pure component properties, which are dependent on the temperature and/or pressure of the system, such as density and vapor pressure. Mixture properties are properties of a mixture, which are dependent of the composition of the mixture constituents. Properties such as saturation temperature and saturation pressure are important for the estimation of mixture properties. Depending on the types of product properties and the required estimation accuracy, different types of property models can be utilized for chemical product design problems. In general, CAMD techniques predict and estimate the properties of molecules by using property models. Property models estimate product properties from structural descriptors, which are numerical values that contain chemical information of a molecule (Gani and Pistikopoulos, 2002). Some of the commonly used structural descriptors to quantify a molecular structure include chemical bonds and molecular geometry (Randic et al., 1994). According to Gani and O’Connell (2001), the importance of property models in design can be described via three distinct roles: service role; service plus advice role; and service, advice plus solve role. In the service role, property models provide estimations of properties to the design problem. In such cases, the users are looking for the accuracy and generality of property models. In the service plus advice role, other than the accuracy and reliability, the property models provide feedback (“advice”) to the users on the combinatorial and compositional feasibility of the design. In service, advice plus solve role, property models are utilized as an integral part of the design process to promote feasibility and convergence of a design problem.

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SECTION j I Basic Concepts and General Tools

Although property models are commonly utilized for their service and service plus advice roles, service, advice plus solve role is more powerful as it provides the opportunity to reduce the size of and solve integrated design problems (O’Connell et al., 2009). Property models can be classified in terms of reference and approximate methods (Gani and Constantinou, 1996). Reference methods are methods that can verify a theory and/or validate other simpler/approximate methods. These methods usually provide accurate property estimation. However, they are often computationally intensive. On the other hand, approximate methods estimate property by matching a theory within a limited range of experimental data. Though these approximate methods are less accurate, they are computationally inexpensive compared with reference methods (Gani and Constantinou, 1996). Property models can be further categorized into mechanical, semiempirical, and empirical models, each with its advantages and disadvantages. These models provide property estimation for different chemicals, such as pure compounds, mixtures, and polymers with varying degrees of accuracy. Achenie et al. (2003) arranged the classification of property models, which can be shown in Fig. 1.2. Selecting appropriate property models for a system is vital to good product design. It is important to balance accuracy and reliability against computational efficiency when identifying the appropriate property models. In general, the development of property models is an iterative process of theory/ hypothesis definition, model equations solving, validation of model against experimental data, and modification of theory/model parameters, if required (Kontogeorgis and Gani, 2004). As property models are generally developed from regression analysis over a set of compounds, the main feature of all property models is that regressed values for a set of model parameters are required to estimate the property from the model equations. The estimation

Classification of Estimation Methods

Reference

• • •

Mechanical Models Quantum Mechanics Molecular Mechanics Molecular Simulation

• • •

Appoximate

Semi-empirical Models Corresponding States Theory Topology/Geometry Group/Atom/Bond additivity

Empirical Models • Chemometrics • Pattern matching • Factor analysis • QSAR/QSPR

FIGURE 1.2 Classification of property estimation methods.

Mathematical Principles of Chemical Product Design Chapter j 1

Problem specification

Problem type System classification

Information sources Model construction Model calibration and validation

Model solution Model verification

Model development

Model application FIGURE 1.3 Illustration of steps in property model development.

can be done if there are parameters available in the regressed form. Otherwise, it is required to regress the unavailable model parameter values or select another property model (Kontogeorgis and Gani, 2004). When appropriate property models cannot be identified, an efficient property model development procedure proposed by O’Connell et al. (2009) can be utilized. This is shown in Fig. 1.3. As proposed by O’Connell et al. (2009), the process of property model development can be divided into problem specification and model development. The first step is to specify the problem type, system classification, and information sources. Based on the intended use, the accuracy requirements on the properties and the amount of effort in application are taken into consideration. The expected outcome of the problem is then measured. Next, the process of property model development is continued via the construction and solution for property model as well as the verification of property model for internal consistency. A property model is ready to be applied in design problems after the process of calibration and validation. The following sections discuss the details of some of the commonly utilized property models. 2.3.1.1 Group Contribution Methods One of the important classes of semiempirical property models is group contribution (GC) models. Currently, most of the CAMD techniques use property models based on GC methods to verify and ensure that the generated molecules possess the specified set of desirable properties (Harper et al., 1999). By utilizing molecular groups as structural descriptors, GC methods estimate the property of the molecule by summing up the contributions from the molecular groups in the molecule according to their appearance frequency

11

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SECTION j I Basic Concepts and General Tools

(Ambrose, 1978; Horvath, 1992; Joback and Reid, 1987). Property models based on GC methods are widely used for property estimation because these models are simple to apply, yet provide reasonably accurate predictions for many properties. Moreover, they can provide quick property estimations without significant errors and expensive computational effort (Constantinou et al., 1993). However, the early GC property models become less reliable as the complexity of the molecule increases. As molecular groups were assumed to be independent and nonoverlapping, resonance, conjugation, and proximity effects were not taken into account (Mavrovouniotis, 1990). Hence, the models cannot differentiate between isomers and capture the interactions among different molecular groups. Constantinou and Gani (1994) presented an improved GC approach by defining the molecular groups as first and second order molecular groups. The basic level is called as first order molecular groups, while the next higher level is known as second order molecular groups. Second order molecular groups are developed and defined by having the first order molecular groups as their building blocks. These second order molecular groups represent different types of interactions and the effect of these interactions among the first order molecular groups. Hence, isomers and compounds with functional groups can be distinguished. Later, GC methods have been further extended by Marrero and Gani (2001) by identifying and incorporating third order molecular groups into the property models. The formation of third order molecular groups is analogous to the second order molecular groups, but their contribution have been correlated to focus on molecular fragments or compounds whose description is insufficient through first and second order molecular groups. These include polyfunctional and structural groups, such as multiring compounds, fused ring compounds, and compounds, which consist of various functional groups. A general representation of property model by using GC methods can be shown with the following equation. X X X f ðXÞ ¼ Ni Ci þ zI Nj Cj þ zII Nk Ck (1.8) i

j

k

In Eq. (1.8), f(X) is a function of the target property X; zI and zII are binary coefficients depending on the levels of estimation; and Ni, Nj and Nk are the numbers of occurrence of first, second, and third order molecular groups, respectively, while Ci, Cj and Ck are the contributions of first, second, and third order molecular groups, respectively. 2.3.1.2 Topological Indices and Group Contributionþ Method In addition to GC methods, established methods in developing property models include the application of topological indices (TIs). TIs are molecular descriptors calculated based on principles in chemical graph theory

Mathematical Principles of Chemical Product Design Chapter j 1

(Trinajstic, 1992). In chemical graph theory, which considers the molecules as the vertices and edges in a graph, atoms in the graph are named vertices, while the bonds used to connect them are called edges (Wilson, 1986). This method allows the capture of molecular information such as types of atoms and bonds, total number of atoms, and bonding between the atoms. Hence, interactions among different atoms/molecular groups and their effects can be captured and utilized in describing a molecular graph as an index. This index is used to correlate the chemical structure to physical properties of a molecule. These correlated relationships are called quantitative structure property relationships (QSPR)/quantitative structure activity relationships (Kier and Hall, 1986). Some of the well-known Tis, which can correlate the chemical structure to physical properties of a molecule, are Wiener indices (Wiener, 1947), Randic’s molecular connectivity index (CI) (Randic, 1975), Kier’s shape indices (Kier, 1985), and edge adjacency indices (Estrada, 1995). Some of the properties, which can be estimated by using property models developed from Tis, include toxic limit concentration (Koch, 1982), soil sorption coefficient (Bahnick and Doucette, 1988), molar volume (Dai et al., 1998), octanolewater partition coefficient, melting point and water solubility (Siddhaye et al., 2004), and flash point (Patel et al., 2009). Knowing the shortcoming of GC methods that the required molecular groups to describe a chemical compound are not always available, Gani et al. (2005) utilized CI to develop a GCþ model in addressing the issue of unavailability of molecular groups and the respective contributions in the GC model. The model is able to create the unavailable molecular groups and create the respective contributions for the estimation of property. Zeroth and first order CIs are used in GCþ model to predict the contribution of the missing molecular groups, as shown in Eq. (1.9): X     f ðXÞ ¼ Ni Ci þ b v c0 þ 2c v c1 þ d (1.9) i

In Eq. (1.9), f(X) is a function of the target property X, Ni, is the number of ith-atoms occurring in the molecular structure, Ci is the contribution of atom i, v 0 c is the zeroth-order atom CI, vc1 is the first-order bond CI, and b and c are adjustable parameters, while d is a constant.

2.4 Molecular Signature Descriptors In some chemical product design problems, the desired target properties could not be estimated by using a single class of property model. Hence, different classes of property models are required for the estimation of different target properties in the design problem. Although property models are useful in estimating target product properties, applying different classes of property models together in an inverse molecular design problem is a computationally challenging task (Camarda and Maranas, 1999). As mathematical formulations

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are exclusive for different property models, it is difficult to utilize these different models by using a similar calculation method. This difficulty is addressed by utilizing a structural descriptor known as molecular signature descriptor (Visco et al., 2002). The signature is a systematic coding system to represent the atoms in a molecule by using the extended valencies to a predefined height. The relationship between a TI and its signature can be represented in Eq. (1.10): TIðGÞ ¼ kh xG $TI½ðrootðh SÞ

(1.10)

h

Here, xG is the occurrence number of each signature of height h in molecular graph G, TI[root (hS)] is the TI values for each signature root, and k is a constant specific to TI. Signature of a molecule can be obtained as a linear combination of its atomic signatures by representing a molecule with atomic signature. While signature descriptors represent individual building blocks for a complete molecule, they are related to the rest of the building blocks in the molecule, as they carry information of their neighboring atoms. Therefore, TIs can be described by using molecular signature (Faulon et al., 2003). Another significance of signature descriptors is their ability to take into consideration the contributions of second and third order molecular groups in property model developed based on GC methods (Chemmangattuvalappil and Eden, 2013). Hence, by writing a molecule in terms of signature, GC methods and TIs with different mathematical formulations can now be expressed and utilized on a common platform. As target properties in a product design problem might not be able to be estimated by using only a single class of property models, the application of molecular signature is important for chemical product design problem, which involves multiple property targets (Chemmangattuvalappil et al., 2010).

2.5 Enumeration Approach In general, a CAMD problem can be formulated as the process of identifying all compounds, which match a specified set of physical properties that give the required product needs. Throughout the years, various approaches have been developed, applied, and extended in solving a wide range of chemical product design problems. These methodologies and approaches for CAMD can be classified into different categories. One of the main categories is enumeration approaches. In enumeration approaches, molecular groups and target properties, which correspond to the product needs, are first identified. This is followed by the generation of feasible set of compound structures by using a combinatorial approach and the prediction of target properties of the generated compound structures. The desired product can then be designed and selected among the identified compounds with the predicted target properties. However, the traditional enumeration approaches can lead to combinatorial explosion while solving CAMD problems (Constantinou et al., 1996). Harper

Mathematical Principles of Chemical Product Design Chapter j 1

et al. (1999) developed a multilevel generate-and-search approach where only feasible molecules are generated from molecular building blocks by using rule-based combinatorial approach. The framework of the proposed multilevel generate-and-search approach used for chemical product design problem is illustrated in Fig. 1.4 (Harper et al., 1999).

“I want acyclic alcohols, ketones, aldehydes and ethers with solvent properties similar to benzene” Pre-design A set of building blocks: CH3, CH2, CH, C, OH, CH3CO, CH2CO, CHO, CH3O, CH2O, CHO + A set of numerical constraints

A collection of group vectors like: 3 CH3, 1 CH2, 1 CH, 1 CH2O All group vectors satisfy constraints

CH CH

CH

CH O

Design (Start)

CH CH

CH CH

CH O

CH

CH CH

Refined property estimation. Ability to estimate additional properties or use alternative methods

Design (Higher levels)

Rescreening against constraints

CH

CH CH

O

CH

Start of post-design

CH CH

CH CH CH

CH O

CH CH

FIGURE 1.4 Basic steps in generate-and-search CAMD approach.

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As shown in Fig. 1.4, the generate-and-search CAMD framework can be divided into predesign, design, and postdesign phases. In the predesign phase, product needs are determined. Required functionalities of the product and the basic molecular groups that form the product are identified in this stage. This information is used in the design phase to determine the feasible candidates. If necessary, property estimation and product analysis can be performed at a higher level in postdesign phase. The postdesign phase may also address the question of synthesis and manufacturing of the chemical product. Each level of the proposed approach has a generation and screening step. By controlling the generation and testing of molecules, the proposed multilevel generate-andsearch approach solves chemical product design problems without suffering from combinatorial explosion (Harper et al., 1999).

2.6 Mathematical Programming Approaches In addition to generate-and-test approaches, mathematical programming approaches are also among the well-known approaches for solving CAMD problems (Macchietto et al., 1990). In mathematical programming approaches, the chemical product design problem is formulated as a mathematical programming model defined by a list of objectives and constraints, which is solved to identify the molecule in terms of appropriate performance index. Depending on the nature of the design problem, constraints such as material balances, process, and design limitations can be incorporated during the generation of molecule. According to Gani (2004), the basic concept of mathematical programming approach can be shown by using the generic mathematical expression as shown in the following: Objective function: FOBJ ¼ maxfCT y þ f ðxÞg

(1.11)

h1 ðxÞ ¼ 0

(1.12)

h2 ðxÞ ¼ 0

(1.13)

h3 ðxÞ ¼ 0

(1.14)

l1  g1 ðxÞ  u1

(1.15)

l2  g2 ðxÞ  u2

(1.16)

l3  By þ Cx  u3

(1.17)

Subject to:

In Eqs. (1.11)e(1.17), the term f(x) represents a vector of objective functions, which can be linear or nonlinear, and x is a vector of continuous variables (e.g., operating conditions, design variables, mixture compositions, etc.), while y is a vector of binary integer variables of molecular descriptors

Mathematical Principles of Chemical Product Design Chapter j 1

identifying the presence of product architectures such as atoms and molecular groups. h1(x) are the set of equality constraints related to process design parameters (e.g., operation pressure, heat addition/reduction, reflux ratio etc.); h2(x) are the set of equality constraints that describe process model equations such as mass and energy balances; h3(x, y) are a set of equality constraints related to the feasibility rules for the generation of molecular structure, mixing of properties, and other information regarding the structure of the chemical product; and g1(x) are a set of inequality limits related to the process design specifications, while g2(x, y) are a set of inequality limits on the product composition and molecular structure, which can be related to the environmental constraints (e.g., toxicity, global warming potential etc.) and/or property constraints related to chemical product design (e.g., solubility parameter, octanolewater partition coefficient etc.). It should be noted that the binary variables in the mathematical formulation usually appear linearly, as described by Eq. (1.17). Depending on the requirements of the product design problem, modifications of the mathematical formulation can be done. A detailed description of the formulation variations is listed below (Gani, 2004): 1. Satisfy only Eq. (1.16): This type of mathematical formulation is used for property-based chemical product design problems. It represents a database search for chemical product, which satisfies the property constraints. Molecular structure generation is not necessary. 2. Satisfy only Eq. (1.14): This type of mathematical formulation is referred to as molecular structure enumeration. It represents the generation of the molecular structure of all candidate molecules. 3. Satisfy Eqs. (1.14) and (1.16): This type of mathematical formulation generates the molecular structures of the chemical product that satisfy the property constraints. There are two ways to identify feasible solutions for this type of formulation. This first is called as “generate-and-test” method, which applies Eq. (1.14) followed by Eq. (1.16). The second method applies Eqs. (1.14) and (1.16) simultaneously. 4. Satisfy Eqs. (1.11), (1.14), and (1.15): This type of mathematical formulation identifies the optimum candidate for the chemical product design problem. 5. Satisfy Eqs. (1.12)e(1.17): This type of mathematical formulation determines all molecules that satisfy both property attribute and process model constraints. 6. Satisfy all equations: This type of mathematical formulation identifies the optimum molecule that satisfies both property attribute and process model constraints. It should be noted that the computational expense rises with the level of detail required for the design of chemical product. This results in a trade-off between accuracy and consumed resources. Hence, the key in solving product design problems by using mathematical programming approaches is to

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achieve as much accuracy as possible using as little computational power as possible. Since in a CAMD problem we are concerned with constructing molecules from molecular fragments, the mathematical programming problem will always involve the variable y. Variable y is binary, and hence the programming problem to be formulated has to be an integer programming problem. If only a single objective function is involved, the mathematical programming problem is formulated as a mixed-integer linear programming (MILP) problem or a mixed-integer nonlinear programming (MINLP) problem, depending on the linearity or nonlinearity of objective and constraints. If multiple conflicting objectives are involved, then depending on the linearity or nonlinearity of objectives and constraints, a multiobjective MILP problem or a multiobjective MINLP problem will be formulated. The available techniques for solving optimization problems can be broadly classified into stochastic optimization techniques and deterministic optimization techniques. The stochastic optimization techniques make a random choice in the search direction as the algorithm iterates towards a solution (Spall, 2012). On the other hand, in deterministic optimization techniques, the search path and values of both design variables and the functions are repeatable (Yang, 2010). MILP problems are tractable compared to MINLP problems. Enormous advances in theory of solving MILP problems have led to implementation of solvers, both commercial and open-source, which are now routinely used to solve many industrial problems of large size (Bonami et al., 2012). Effective and robust commercial solvers that can solve MILP problems include CPLEX and Gurobi. Recently, Struebing et al. (2013) utilized the CPLEX solver for a case study involving CAMD of solvents that enhance reaction kinetics. Earlier, McLeese et al. (2010) utilized the CPLEX solver for a case study involving design of ionic liquids. While the formulation of a CAMD problem in terms of an MILP guarantees a global optimal solution, this is not the case with an MINLP formulation. However, a global optimal solution may not be necessary due to the limited accuracy of property models utilized in formulating the MINLP problem (McLeese et al., 2010). In practice, near-optimal solutions may suffice. Also, compared to MILP problems, MINLP problems can be computationally expensive to solve (Eljack and Eden, 2008). Out of the MINLP problems, the ones containing objective functions that are convex can be solved much more efficiently than the ones with nonconvex objective (Bonami et al., 2012). Also, exact methods are available to solve convex MINLP problems. Exact methods are those that terminate with a guaranteed optimal solution or prove that such a solution is nonexistent. In contrast, heuristic methods exist that can be considered as algorithms that explore only some possible states of the problem or those that begin by exploring the most likely ones (Shelokar et al., 2014). Heuristic methods are designed to quickly provide good but unprovably optimal solutions (Burer and Letchford, 2012). Heuristics can be incorporated in a solution methodology both in a deterministic and stochastic manner. Purely heuristics-based solutions may be

Mathematical Principles of Chemical Product Design Chapter j 1

inconsistent and often subjective (Shelokar et al., 2014). Hence, metaheuristics were introduced to address such shortcomings. These can be defined as master strategies that guide and modify other heuristics to produce solutions beyond those that are normally generated in a quest for local optimality (Glover, 1986). All modern nature-inspired search methods like genetic algorithms (GAs), simulated annealing (SA), ant colony optimization, etc., can be classified under metaheuristics (Shelokar et al., 2014). Some form of randomization is usually introduced in such search algorithms. In general, most deterministic MINLP solution methods utilize some form of tree search (Belotti et al., 2013). These methods can be broadly classified as single-tree and multitree methods. An example of the single-tree method is NLP-based branch and bound (Gupta and Ravindran, 1985). An example of the multitree method is the outer approximation method (Fletcher and Leyffer, 1994). The main concepts utilized by existing deterministic algorithms for solving MINLP problems include linear approximations of nonlinear functions, transformation of MINLP problems into continuous NLP problems, reformulation as a disjunctive program, etc. (Melo et al., 2014). To solve convex MINLP problems, many deterministic algorithms exist where linearization techniques have been adopted to provide globally optimal solutions. Some of these algorithms include NLP-based branch and bound (Gupta and Ravindran, 1985), generalized benders decomposition (Geoffrion, 1972), outer approximation (Fletcher and Leyffer, 1994), hybrid LP/NLPebased branch and bound (Quesada and Grossmann, 1992), and extended cutting plane method (Westerlund and Pettersson, 1995). To solve nonconvex MINLP problems, some of the approaches include utilizing piecewise linear approximations and obtaining convex relaxations (Belotti et al., 2013). A complex aspect of solving nonconvex MINLP problems is that their continuous relaxation, i.e., the problem obtained by relaxing the integrality requirement, has local optima (D’Ambrosio and Lodi, 2011). Thus, methods have to be designed such that they are able to navigate through these local optima to hopefully reach the global optima. Some real world problems cannot be solved to global optimality because the problems are too large, generate a huge search tree, or must be solved in real time (Belotti et al., 2013). In such situations, heuristic search techniques may be utilized and incorporated in order to obtain a good solution quickly rather than waiting for an optimal solution. While the term “deterministic” has been utilized to describe aforementioned optimization methods, these methods can benefit through introduction of randomness in certain iterations, so the category may not be as rigid (Belotti et al., 2013). Some of the algorithms utilized to solve nonconvex MINLP problems, deterministically, include spatial branch and bound, branch and reduce, and a-branch and bound (Burer and Letchford, 2012). Some of the commonly utilized solvers for MINLP problems include DICOPT, BARON, BONMIN, and SBB (D’Ambrosio and Lodi, 2011). Recently, Dev et al. (2015) utilized the DICOPT solver to obtain optimal

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structures of reactants and products for a case study where the standard Gibbs free energy of transesterification reaction was minimized. Earlier, Chavez-Islas et al. (2011) utilized CONOPT, SBB, and BARON solvers to design ionic liquids for separation of ethanolewater azeotrope. In general, a variety of approaches are utilized to solve CAMD problems, depending on the challenges posed by the problems. Some of the approaches include decomposition methods that use local optimizers for the NLP subproblem (Karunanithi et al., 2006), global optimization (Ostrovsky et al., 2002), interval analysis (Achenie and Sinha, 2003), dynamic optimization (Giovanoglou et al., 2003), metaheuristics like ant colony optimization (Gebreslassie and Diwekar, 2015), etc. In Sections 2.7 and 2.8, metaheuristics and decompositionbased approaches have been expanded upon. Also, the approaches to solve multiobjective counterparts of MILP and MINLP problems have been discussed in Section 2.9.

2.7 Metaheuristic Approaches Metaheuristics have gained a lot of popularity over the years as optimization methods. This is because they tend to be flexible, efficient, highly adaptable, and easy to implement. Among metaheuristics, evolutionary optimization (EO) algorithms additionally provide scope for parallelization. Also, EO algorithms do not require any derivative information (Deb, 2011). Some of the widely used metaheuristic techniques include GA, SA, and Tabu search (TS). These approaches are sometimes regarded as stochastic or random search methods, as they are based on the successive random generation method. Various metaheuristic approaches have been adopted in solving different chemical product design problems. Venkatasubramanian et al. (1994) solved a CAMD problem by utilizing GA to perform a guided stochastic search where improved solutions with preferred target properties are achieved. Marcoulaki and Kokossis (1998) presented an approach that combines stochastic optimization and group GC methods to select chemicals with optimized properties. Lin et al. (2005) proposed a detailed implementation of TS algorithm for CAMD of transition metal catalysts. Compared to the deterministic approach, the proposed approach showed that TS is able to provide a list of good candidate molecules while using a smaller amount of computational time. Heintz et al. (2014) adopted GA in developing a computer-aided product design tool for the design of sustainable chemical product. Other than being utilized to identify optimal solution in chemical product design problems, different stochastic approaches have been applied in addressing the accuracy and performing sensitivity in CAMD problems. This is discussed in Section 2.11. In general, metaheuristic search methods are applied for problems when deterministic approaches result in slow convergence or are difficult to apply. They are particularly useful when the information of the design problem is incomplete or the required computational effort is too high. Although

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metaheuristics have enjoyed continuous success, challenges still persist in their implementation. These are mostly concerned with finding a balance between exploration and exploitation (Yang, 2015). Other challenges involve fine-tuning of parameters and choice of selection methodology in deriving the population of feasible solutions. However, like in the case of GAs, opportunities for improvement exist especially in hybridization with other techniques (Younes et al., 2010). In the following subsections, the GA and SA have been expanded upon.

2.7.1 Genetic Algorithm Based on Darwinian models of natural selection and evolution, the basic concept behind GA is the evolutionary creation of a new population of entities from an earlier generation through process of evolution (Holland, 1975). The ultimate goal of GA is to generate better and fitter generations through evolution in achieving the design objective. In GA, the possible solutions to the search problem are represented in a “genetic” form called chromosome. These chromosomes are molecularly represented in terms of strings or symbols, which include a backbone chain and side chains. The process of evolution starts with a collection of chromosomes. Depending upon its proximity to the target, each chromosome is assigned a level of fitness. After the representation of possible solutions in terms of strings, a transition rule, which consists of a reproductive plan and genetic operators, is defined to mimic the evolution process. The reproductive plan identifies strings of the current population, which will be utilized to generate the next solution population. The genetic operators are used to modify the structure of the identified strings to produce the members of next generation according to the operation rate of the genetic operator. Two of the most commonly utilized genetic operators are crossover and mutation: l

l

Crossover: creates two offspring chromosomes by exchanging contiguous chunks of units from two parent chromosomes. Each parent chromosome is cut at the crossover point, and the parts between two parent chromosomes are exchanged. Mutation: modifies one or more units of a chromosome. Upon mutation, a unit of a chromosome changes from its current value to some other allowable value. In a string-wise mutation, every bit on a chromosome is mutated according to some probability. In comparison, the selection and mutation of a unit in a chromosome is carried out randomly in single-bit mutation.

During the evolution process, the fitter chromosomes are identified as “parents.” Only the parents are allowed to modify their genetic information to create offspring for the next generation by using genetic operators. Hence, by using reproductive plan and genetic operators, a new generation of offspring is created to replace the existing population. This evolution process is repeated

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for successive generations of the population until an acceptable solution is identified or a predecided number of generations have evolved. The solution in this generation with the highest level of fitness is the optimal solution of the problem. While using GA to determine the optimal solution for a design problem, the most commonly used selection method to identify the fittest chromosome is the fitness proportionate reproduction method. This is shown in the following equation. FðiÞ PðiÞ ¼ PN j¼1 FðjÞ

(1.18)

In Eq. (1.18), P(i) is the probability of selection of chromosome I, and F(i) is the fitness level of chromosome i, while N is the total number of individuals in the population. In fitness proportionate reproduction, individual with higher fitness level will have a higher expected number of offspring. Therefore, this selection method guides the searching process towards the identification of the most promising solution. In general, there are two cases during the identification of the fitness level of a chromosome: cases where the target property is bounded by both upper and lower bounds, and cases where the target property is bounded by only an upper or lower bound. During the design for a target property value bounded by both upper and lower bounds, Gaussian-like function as shown in Eq. (1.19) is employed 0 "  2 #1 n X Pi  Pi F ¼ exp@ a (1.19)  2 A i¼1 Pi;max  Pi;min where Pi is the ith property value, and Pi is the average of the maximum (Pi,max) and minimum (Pi,min) acceptable property values, which are used to normalize the property values, while a is the parameter for fitness decay rate that determines how the fitness values fall off as the solutions move away from the center of the target. In Eq. (1.19), the index i applies for all the property constraints that are utilized in the problem. It is to be noted that the function F ranges from zero to one, with one being the target molecule’s fitness. For the design, which involves property constraints that are bounded by only an upper or lower limit, sigmoidal function is the preferred function to determine the fitness level of a chromosome: (  !)1 n 1X Pi  PF¼0:5;i F¼ (1.20) 1 þ exp b n i¼1 PRange;i In Eq. (1.20), PF¼0.5,i is the property value for which the evaluated fitness is 0.5. This value can be taken to be the upper or the lower limit of the acceptable property constraints. PRange,i normalizes the property values to remove any bias of a single property on the overall fitness, which is taken as

Mathematical Principles of Chemical Product Design Chapter j 1

the mean of all individual property fitness values. Parameter b in Eq. (1.20) controls the slope of the sigmoid. GA investigates and explores the search space by using the principle and laws of natural selection. The search for the better and fitter solution is done by modifying the best solution of the population n to create the population n þ 1 using genetic operators. For crossover operator, it results in huge leaps from one point to another point while searching for optimal solution in the search space. Hence, the regions, which are far spread from one another in a search space, can be navigated rapidly. Compared to crossover, mutation operator results in small movements in a given region of the search space. Therefore, mutation is utilized as a local optimization operator. By using both operators, the exploratory power of crossover and the local search ability of mutation are combined. Thus, GA is able to quickly identify the promising areas of the search space and explore each of the areas in detail. Recently, Herring and Eden (2015) developed a GA for de novo molecular design such that a variety of property models could be treated on a single platform through the utilization of spatial signature descriptors. Dev et al. (2014) utilized a real coded GA in order to design multiple reactants and products using signature descriptors. The product molecules had their respective design objectives and sets of property and structural constraints. Venkatraman et al. (2016) utilized a GA for the molecular design of imidazole-based adsorbents for CO2 capture. Their QSPR-guided scheme drastically reduced the search time needed to find promising adsorbent structures.

2.7.2 Simulated Annealing SA is a combinatorial optimization technique for solving unconstrained and bound-constrained optimization problems. Based on the analogy between problem optimization and statistical physics, SA solves optimization problems based on random estimation of objective function and evaluation of the problems constraints. In the context of chemical product design, after the identification of an initial molecule, random modification is applied to the molecule to transform it into a molecule with better performance. Evaluation on the performance of the new molecule is carried out after each modification. The new molecule is retained for further modification if its performance is higher than the previous molecule. If higher performance is not achieved, an acceptance probability, which depends on the difference of performance, is utilized to decide if the new molecule is kept. The acceptance probability, which follows the metropolis criteria (Metropolis et al., 1953), is commonly used. According to the criteria, when the gain of performance between state i and j (DFi,j) is greater than zero, the acceptance probability for the move from state i to j under T [Bij(T)] can be determined as follows:   DFi; j Bij ðTÞ ¼ exp  (1.21) T

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In Eq. (1.21), T is the “annealing temperature,” which is a statistical cooling parameter than can be updated by a cooling schedule (Aarts and van Laarhoven, 1985). When DFi,j is equal or lesser than zero then the value of Bij(T) is equal to one. While requiring a great number of function evaluations to determine the optimal solution, the application of SA increases the possibility for the generation of global optimal solution, even for problems with multiple local minima. Recently, Song and Song (2008) presented an optimization approach for the design of environmentally friendly solvents for separation processes using the CAMD approach based on SA technique. By solving several case studies, it is shown that the presented optimization approach can solve the design problems with significantly reduced amount of computational time. Also, earlier, Kim and Diwekar (2002a,b,c) utilized SA to design solvents under uncertainty.

2.8 Decomposition-Based Approaches In chemical product design problems, there may be cases where all the desired properties cannot be met by a single component molecule. In such cases, the design of mixture/blend of chemicals would be an ideal solution. According to Churi and Achenie (1997), the main purpose of designing mixtures is that mixtures have the potential for giving a good mix of target properties, which is unattainable by individual chemical components. Generally, mixtures contain one (or more) liquid chemical as the main component and a set of additional chemicals, which acts as additive components. The main component performs the key functionalities of the mixture while the additive components enhance the quality of the mixture. Hence, by mixing the main component with additive components, a mixture, which possesses target properties that satisfy the product needs, can be designed. However, during the design of mixtures, the functions and properties of mixtures, which are required to be predicted, can be complicated. This results in challenging modeling effort for the design of mixtures. The complexity of the mixture design problems can be managed through decomposition of the mixture design problem into subproblems (Karunanithi et al., 2005). In decomposition-based approaches, the complexity of the mixture design problem is managed by decomposing the design problem into a series of solvable subproblems. Then, each subproblem is solved and analyzed at a reduced complexity. With the results and knowledge gained by solving the subproblems, an overall evaluation of the complex design problem is made. In order to apply decomposition-based approach, the general molecular/ mixture design problem is divided into two parts. For the design of optimal single-component product, the first part of the design problem is solved. For the design of mixture, which consists of multiple components, the design of single-component product is first carried out to identify the potential

Mathematical Principles of Chemical Product Design Chapter j 1

candidates as the main component. This is followed by the second part of the design problem, which is solved to determine the additive components. Thus, optimal mixture is designed by mixing the identified main and additive components (Karunanithi et al., 2005). By solving the design problem as a series of subproblems, the complexities associated with the initial subproblems can be solved in the early stages of the problem. This prevents the complexities to be brought to the final optimization problem. The solution to the final optimization problem is made easier as decomposition-based approaches systematically reduce the search space of design problems. Conte et al. (2011) presented decomposition-based virtual producteprocess design laboratory (virtual PPD-lab) software for the design of formulated liquid products. The potential of the presented PPD-lab in managing the complexity in the design and verification of formulated products is illustrated through a case study of the design of hairspray product. Yunus et al. (2014) developed a decomposition-based methodology for the design of tailor-made blended products. In the developed methodology, the tailor-made blended product design is decomposed into four main tasks: problem definition, property model identification, mixture/blend design, and model-based verification. By using the developed methodology, a large number of alternatives is filtered at each hierarchical step to reduce the search space, hence reducing the complexity for the design of blended products.

2.9 Multiobjective Chemical Product Design In order to design an optimal chemical product, there can be situations where multiple conflicting product properties are needed to be considered and optimized simultaneously. As more than one design objective is involved, the design problems have to be solved as multiobjective optimization (MOO) problem. In general, the result of an MOO problem is a set of Pareto optimal solutions, referred as the Pareto set. A solution for an MOO problem is Pareto optimal if no other solution that improves at least one of the objective functions without deteriorating the performance in any other objective function(s) can be found. Mathematically, each Pareto optimal solution is an equally acceptable solution of the MOO problem (Miettinen, 1999). However, it is desirable to choose one solution from the Pareto set. Thus, a decision-maker (DM) is needed who can provide preferences, which can be considered in evaluating various Pareto solutions. The DM is assumed to be adequately familiar with problem(s) under consideration. The MOO problem is solved in cooperation with an analyst. An analyst is a person or computer program responsible for the mathematical side of the solution process (Miettinen, 1999). The analyst is supposed to help the DM at various stages of the solution process, in particular, in eliciting preference information and in interpreting the information coming from the computations (Miettinen, 2008). Depending

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on what role the DM plays in the solution process, the available methods to solve MOO problems can be broadly classified into four classes (Hwang and Masud, 1979). These are: l

l

l

l

No-preference methods: These are used when there is no DM and the DM’s preference is unknown. The task in these methods is to find a neutral comprise solution. An example method in this category is the method of global criterion (Miettinen, 2008). The shortcoming of no-preference methods is that only one solution is obtained. A priori methods: In such methods, the DM provides preference(s) beforehand, and later, the solution process tries to find a Pareto optimal solution that meets the given preferences. An example method in this category is the weighted sum method (Miettinen, 1999). In the case of a priori methods, it is challenging for the DM to know beforehand and to accurately quantify his/her preferences. A posteriori methods: In such methods, a representative set of Pareto optimal solutions is generated, and then the DM makes a choice of the most preferred Pareto optimal solution. An example method in this category is the epsilon-constraint method (Mavrotas, 2009). Depending on the size of the representative set generated using a posteriori method, it may be computationally expensive for the method to generate the set. Interactive methods: In such methods, an iterative solution algorithm is utilized and repeated. After each iteration, some information is provided to the DM. Next, the DM is asked to specify preference information in the form that the method can utilize. Thus, by interacting with the method, the DM cannot only familiarize with the behavior of objective functions, but can also alter his preferences after each iteration. An example method in this category is the Nondifferentiable Interactive Multiobjective BUndle-based optimization System (NIMBUS) method (Ojalehto et al., 2014). The drawback with interactive methods is that the DM is not able to get the full picture of the Pareto set or the representative set of Pareto solutions.

In the following sections, Section 2.9.1, Section 2.9.2, Section 2.9.3, and Section 2.9.4, the weighted sum method, bi-level optimization approach, fuzzy optimization approaches, and ε-constraint method, respectively, have been expanded upon.

2.9.1 Weighted Sum Method According to Kim and de Weck (2006), the most commonly used approach in solving the MOO problem is the weighted sum method. This method can be explained mathematically as follows (Fishburn, 1967): Aweighted sum ¼ a1 A1 þ a2 A2 þ / þ ay Ay

(1.22)

In Eq. (1.22), Aweighted sum is the overall objective function, while ay is the weighting factor for the individual objective function Ay. This method

Mathematical Principles of Chemical Product Design Chapter j 1

converts multiple objectives into an aggregated scalar objective function by first assigning each objective function with a weighting factor and later summing up all the contributors to obtain the overall objective function. By using the weighted sum method, each objective is given a weight to differentiate their relative importance during the aggregation of the overall objective function. Papadopoulos and Linke (2006) proposed a multiobjective molecular design technique by using weighted sum method and SA. In the developed technique, the weighted sum method is adopted to explore the Pareto set of the design problem, while SA is utilized to identify the optimal molecule subjects to the design constraints. The multiobjective molecular design technique proposed by Papadopoulos and Linke (2006) is extended by Papadopoulos et al. (2013) in developing a CAMD method for the synthesis and selection of binary working fluid mixtures used in organic Rankine cycles. According to Ehrgott and Gandibleux (2002), the major drawback of weighted sum method is that a DM is required in finding the appropriate weighting factor to be assigned to each objective. As a result, these methods tend to be biased, as the weighting factors assigned to the objective are based on expert knowledge or personal subjective preferences of the DM (Korte, 2003). In the context of chemical product design, while considering the design problems as decision-making problems, the weighting factor for each property are assumed to be deterministic/crisp when the conventional MOO methods are used (Deckro and Hebert, 1989; Deporter and Ellis, 1990). However, the relative importance of each property to be optimized in chemical design problems is not always definable. Hence, the significance of each product property to design an optimal product in a design problem is normally uncertain/fuzzy. Furthermore, these objectives might be incomplete, unclear, or contradictory in nature.

2.9.2 Bi-Level Optimization Approach Bi-level optimization approach is another potential approach for solving MOO problems. Different from the general MOO approaches, which perform optimization of several objectives simultaneously, bi-level optimization approach orders and arranges the objectives in a MOO problem to a hierarchy and solves them in a hierarchical order (Caramia and Dell’Olmo, 2008). Introduced based on the static Stackelberg game with leaderefollower strategy, the concept of bi-level optimization is to obtain an optimized solution for the main optimization problem while independently optimizing the second-level optimization problem (von Stackelberg, 1952). In other words, in order to optimize the multiobjective decision-making problems, the objectives of the problems are categorized into upper-level objective (leader’s objective) and lower-level objectives (follower’s objective). The overall optimized solution for the problems can then be identified by first optimizing the lower-level objective,

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followed by the optimization of the upper-level objective. A general formulation of bi-level optimization problem can be written as follows: Objective function: Maximise=Minimise Fðp; nÞ

(1.23)

Gðp; nÞ  0

(1.24)

Maximise=Minimise f ðp; nÞ

(1.25)

gðp; nÞ  0

(1.26)

Subject to:

Subject to:

In Eqs. (1.23)e(1.26), the objective F(p, n) is the upper-level objective function, while f(p, n) is/are the lower-level objective function(s). G(p, n) and g(p, n) are sets of property and structural constraints for upper level and lower level, respectively. Problems that can be modeled by means of bi-level optimization approach are those for which the variables of the upper-level problem are constrained by the optimal solution(s) of the lower-level problem (Caramia and Dell’Olmo, 2008). In the MOO-based approach for optimal chemical product design developed by Ng et al. (2014), bi-level optimization approach is utilized to determine the property target ranges, which are undefined.

2.9.3 Fuzzy Optimization Approaches In addition to the weighted sum method and bi-level optimization approach, fuzzy optimization approach is another commonly utilized MOO approach in solving a multiobjective decision-making problem. In order to solve a decision-making problem, fuzzy set theory was developed by Zadeh (1965). As the theory systematically defines and quantifies vagueness and uncertainty, it is possible to solve problems, which require decision-making under a fuzzy environment. Bellman and Zadeh (1970) developed a fuzzy optimization approach that is able to select the preferred alternative in a fuzzy environment by solving an objective function on a set of alternatives given by constraints. Zimmermann (1976) then incorporated fuzzy set theory in linear programming problems by solving the problems under fuzzy goals and constraints. Later, Zimmermann (1978) extended the approach to address linear programming problems, which involve multiple objectives. This extended fuzzy optimization approach integrates several objective functions into a single objective function and solves the overall objective function based on the predefined fuzzy limits to obtain an optimized solution in a MOO problem. In order to utilize fuzzy optimization approaches, the objectives in a MOO problem can be written as fuzzy optimization models, which can be described by their membership function. These membership functions represent the relationships between the degree of satisfaction of the objectives (l) and the

Mathematical Principles of Chemical Product Design Chapter j 1

objective values within the target ranges. In general, the fuzzy membership functions can be categorized into maximum, minimum, trapezoidal, and triangular membership functions (Zimmermann, 2001). The different types of fuzzy membership functions are shown in Fig. 1.5. In Fig. 1.5, va, vb, vc, and vd are different values, which can be used to represent different target ranges for the objective V in chemical product design problems. As shown in Fig. 1.5A and B respectively, within a target range bounded by va and vb, the maximum fuzzy membership function is used for objectives where higher values are preferred, while minimum fuzzy membership function is utilized for objectives where lower values are desirable. Objectives where the values are preferred to fall within a certain target range can be modeled as trapezoidal fuzzy membership functions, as shown in Fig. 1.5C. The trapezoidal fuzzy membership function is characterized by its core and supports. The core (bounded by vb and vc) represents the target range of highly plausible values. On the other hand, the supports, which consist of lower support (bounded by va and vb) and upper support (bounded by vc and vd), cover the values that are at least marginally plausible. When the objective value of vb in a trapezoidal fuzzy membership function equals to the value of vc, the objective can be modeled as triangular fuzzy membership function, as shown in Fig. 1.5D. In fuzzy optimization approaches, by writing the objectives in a MOO problem as fuzzy membership functions, trade-off between the objectives can be introduced. Therefore, an optimal compromise solution can be obtained by solving the MOO problem. Fuzzy optimization approaches are useful to address the vagueness and ambiguity in MOO problems due to the incompleteness and unavailability of relevant information. There are two different fuzzy optimization approaches, which are commonly utilized for their advantages and suitability in solving chemical product design problems. These two approaches are discussed in detail in the following sections. 2.9.3.1 MaxeMin Aggregation Approach The objective of the maxemin aggregation approach is to make sure that every individual objective will be satisfied partially to at least the degree l. Therefore, each individual objective has an associated fuzzy membership function, and the optimum overall objective is obtained by maximizing the least satisfied objective (Zimmermann, 1978, 1983). The objective here is to optimize the least satisfied objective among all objectives to be optimized. In chemical product design problems, the objective can be the maximization/minimization of any target property for the product to be designed. Hence, the difference between the individual objectives can be minimized. This approach is suitable for multiobjective chemical product design problems where each target product property to be optimized is treated with equal importance. The maxemin aggregation approach makes sure that the objectives in a MOO

29

λ Acceptable

Partially acceptable

Unacceptable

1

0

va

λ Acceptable

V

vb

(A)

Unacceptable

Partially acceptable

1

0

va

λ

(B)

Partially acceptable

Unacceptable

V

vb Partially acceptable

Acceptable

Unacceptable

1

Lower support

0

va

λ

(C)

1

va

Upper support

vc Partially acceptable

Partially acceptable

Unacceptable

0

vb

Core

vb=vc

vd

V

Unacceptable

vd

V

(D) FIGURE 1.5 Fuzzy membership functions for: (A) maximizing, (B) minimizing, (C) trapezoidalshaped, (D) triangular constraints.

Mathematical Principles of Chemical Product Design Chapter j 1

approach will not be overimproved while neglecting the importance of the other objectives. Therefore, by utilizing the maxemin aggregation approach, a chemical product with multiple important target properties can be designed without overlooking the significance of any of the target properties to be optimized. The mathematical formulation for maxemin aggregation approach is shown as follows: l

Maximise l  lp

cp ˛P

(1.27) (1.28)

In Eqs. (1.27) and (1.28), l is the degree of satisfaction for the individual target property for the chemical product design problem. In order to optimize the least satisfied property among all target properties to be optimized lp, the least satisfied degree of satisfaction l is maximized, as shown in Eqs. (1.27) and (1.28). Maxemin aggregation approach aims to maximize the least satisfied property so that the disparity in degrees satisfaction among all target properties to be optimized would be lessen. However, it is to be noted that this approach is unable to discriminate between solutions that vary in attained levels of satisfaction other than the least satisfied goal (Dubois et al., 1996; Dubois and Fortemps, 1999). While the least satisfied goal is maximized, since the other goals might be overly curtailed or relaxed, there is still room to search for better solutions in terms of degree of satisfaction. Thus, other than the maxemin aggregation approach, the two-phase approach proposed by Guu and Wu (1999, 1997) is incorporated into the proposed MOO approach. 2.9.3.2 Two-Phase Approach In addition to the maxemin aggregation approach, the two-phase approach developed by Guu and Wu (1999, 1997) is also widely applied. In order to utilize the two-phase approach, the MOO problem is solved sequentially in two phases. In the first phase of the optimization problem, the problem is solved by using the maxemin aggregation approach to obtain the degree of satisfaction of the least satisfied property. In the second phase of the optimization problem, the two-phase approach is utilized to solve the problem. The overall objective for two-phase approach is maximizing the summation of all degrees of satisfaction. This means that all of the individual objectives for the chemical product design problem are optimized as a whole. Hence, the optimization objective of two-phase approach is set as the maximization of the summation of all degrees of satisfaction for every target properties to be maximized. This can be described by Eq. (1.29). X Maximise lp (1.29) p

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In Eq. (1.29), lp is the degree of satisfaction determined from the second phase by using the two-phase approach. The main purpose of utilizing the twophase approach is to distinguish the solutions with identical least satisfied objectives and search for an improved solution, if there is any. In order to achieve the goal in differentiating the solutions with similar least satisfied goal and identifying the better solution, it is required to ensure that the solution obtained in the second phase will not be of any worse than the solutions initially obtained in the first phase. Hence, the degree of satisfaction obtained by using two-phase approach should not be lower than the degree of satisfaction of the least satisfied goal determined by using the maxemin approach. This is achieved by adding Eq. (1.30) to the mathematical model. lp  lp

cp ˛P

(1.30)

In Eq. (1.30), lp is the degree of satisfaction of the least satisfied property obtained by using the maxemin aggregation approach. As shown in Eq. (1.30), the degrees of satisfaction of the target properties identified in the second stage lp will not be lower than the least satisfied property obtained in the first stage, lp. In the MOO-based approach discussed earlier (Ng et al., 2014), maxemin aggregation and two-phase fuzzy optimization approaches are applied to address the property weighting factors in a multiobjective chemical product design problem. In the developed approach, the product properties are first maximized by using maxemin aggregation approach. The two-phase approach is later employed to discriminate the products with similar least satisfied property to identify the optimal chemical product.

2.9.4 ε-Constraint Method The ε-constraint method was introduced by Haimes et al. (1971). In this method, one of the objective functions is selected to be optimized, and all other objective functions are converted into constraints by setting up an upper bound to each of them. Let the MOO problem be stated as follows: max½f1 ðxÞ; f2 ðxÞ; f3 ðxÞ.fp ðxÞ st x ˛S where x is the vector of decision variables. f1(x), f2(x),.fp(x) are p objective functions, and S is the feasible region. In the ε-constraint scheme, the MOO problem is transformed into the following problem: max½fn ðxÞ st

Mathematical Principles of Chemical Product Design Chapter j 1

f1 ðxÞ  e1 f2 ðxÞ  e2 . fn ðxÞ  en . fp ðxÞ  ep x ˛S By the variation in parameter on the right hand side of the constrained objective functions (ei), the efficient solutions of the problem are obtained. Compared to the widely utilized weighted sum method, the ε-constraint method offers many advantages (Mavrotas, 2009). One of the advantages is that almost every run of ε-constraint method can be exploited to produce a different efficient solution. Another advantage is that unsupported Pareto solutions can be generated in multiobjective mixed integer and integer programming problems. Unsupported Pareto solutions are those that do not lie on the boundary of the feasible objective space. However, the ε-constraint method has shortcomings, despite the offered advantages. Some of the generated solutions obtained from the method may be not be efficient solutions. Besides, it is challenging to calculate the range of the objective functions over the Pareto set. Additionally, the ε-constraint method can become computationally expensive when more than two objective functions are involved. These shortcomings, however, have been largely addressed in the recently developed augmented ε-constraint method (AUGMECON) (Mavrotas, 2009) and an improved version of the augmented ε-constraint method, AUGMECON2 (Mavrotas and Florios, 2013). With regards to product design, the ε-constraint method was recently utilized by Martin and Martinez (2013). They presented an optimization-based methodology for simultaneous formulas and process design in the consumer product business applied to the case of the laundry detergent business. Martin and Martinez (2015) later addressed the uncertainty in the sustainable formulated products and process design. The uncertainty in their work arose from the variability in the ingredient prices and lack of knowledge of product processability. Besides the ε-constraint method, its augmented version, AUGMECON, has been utilized for CAMD by Dev et al. (2016). In their work, the simultaneous design of reactants and products has been achieved by utilizing signature descriptors. The reactants and products are each subjected to a set of property constraints and have conflicting objective functions that need to be optimized.

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2.10 Chemical Product Design Under Property Prediction Uncertainty As previously discussed, CAMD techniques utilize property models to predict, estimate, and design molecules, which possess a set of required target properties (Harper and Gani, 2000). In general, property models are developed from regression analysis over a set of compounds. While providing relatively simple and accurate methods in property predictions, it should be noted that these property models are approximate in reality, and there are always some discrepancies between experimental measurements and model predictions. The disagreement between the prediction and experimental values applies to all property estimation methods, such as factor analysis, pattern recognition, molecular similarity, and different TIs and GC methods (Maranas, 1997a). From the cyclic process of property models, it can be said that the accuracy of a model is affected by the uncertainties, which can arise from deficiency in theories or models and their parameters and insufficient of knowledge of the systems. It is to be noted that the effectiveness and usefulness of these property models in estimating a property and eventually identifying the optimum molecule rely heavily on the accuracy of the property models. In general, the performance or accuracy of property models is evaluated and shown in terms of statistical performance indicators. Some of the commonly used pointers include standard deviation, average absolute error, average relative error, and coefficient of determination. Traditionally, the accuracy of property models is only used as an indicator of the models’ ability in predicting the product properties or the expected error that the model might produce. As long as the property models provide reasonable precision, the accuracy of the property models is seldom taken seriously. Few works have been published to address the issue of property prediction uncertainty. Attempt to analyze, address, and improve the uncertainty of property models have been carried out. For example, Maranas (1997b) presented a systematic methodology that quantifies property prediction uncertainty by using multivariate probability density distributions to model the likelihood of different realizations of the parameters of GC methods. The proposed work describes the disagreement between experimental measurements and GC predictions by recognizing that the contribution of molecular groups to various properties is dependent on molecular structure around some nominal value, depending on the particular molecular structure. By imposing chance constraints in the developed methodology, optimal molecule can be identified through stochastic property matching or stochastic property optimization formulation. The developed methodology is applied in solving different cases of polymer design problems (Maranas, 1996, 1997b). Kim et al. (2002) proposed the incorporation of uncertainty factor (UF) to define property

Mathematical Principles of Chemical Product Design Chapter j 1

prediction uncertainty of GC methods in solving a solvent selection problem. UF can be determined via the following equation: UF ¼

Vlit Vest

(1.31)

As shown in Eq. (1.31), UF is defined as the discrepancy percentage between literature (Vlit) and estimated values (Vest). The developed approach (Kim et al., 2002) utilizes the Hammersley stochastic annealing algorithm in tackling the problems of solvent selection under uncertainty and searching for reliable candidate solvents. The use UF for the quantification of uncertainties in property models is further extended by Xu and Diwekar (2005). The proposed optimization framework uses and compares the performance of efficient GA and Hammersley stochastic GA in solving the computer-aided solvent design problems. Folic et al. (2007) presented a method in assessing the impact of uncertainty in the developed hybrid experimental/computer-aided methodology for the design of solvents for reactions. The presented work applied global sensitivity methods to explore the uncertain parameter space in identifying the key parameters and the most likely solvent candidates in the solvent design problem. According to Bertsimas et al. (2011), although stochastic programming approach provides a comprehensive solution with consideration of probabilistically realized uncertainty, it often results in the formulation of a multistage problem, which can be computationally intensive. Therefore, in addition to the utilization of stochastic programming approach in addressing the property prediction uncertainty while solving the design problems, robust optimization approaches are used for design problems under uncertainty in which the uncertainty model is deterministic. As robust programming is a single-stage optimization where the uncertainties are expressed as userdefined probability, there are no recourse actions involved in the programming model. Hence, computational effort required in solving the design problem can be greatly reduced (Bertsimas et al., 2011). Ng et al. (2015) developed a robust chemical product design methodology for the design of optimum molecules by considering and optimizing property superiority and robustness. In the developed methodology (Ng et al., 2015), property superiority is quantified by property optimality, while the effect of property model accuracy (property robustness) is expressed in the form of standard deviation of the property model. Standard deviation is chosen as it is the measure of average variation between the measured and estimated values in regression analysis. After taking the allowance of property prediction model accuracy, target property ranges for the chemical product design problem are shifted and divided into three different regions to improve the estimation of target properties. The design problem is then formulated as MOO problem and solved by using fuzzy optimization approaches as discussed in Section 2.10.3.

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3. CONCLUSIONS AND FUTURE DIRECTIONS In this chapter, a review on the mathematical principles of chemical product design strategies is discussed. Traditionally, the approaches for the design of chemical product are mainly trial and errorebased. As the nature of chemical products and the end user requirements evolve, the traditional bottom-up approaches are unsatisfactory in terms of cost and time required as well as effectiveness in designing the product that suits the customer needs. In view of this, top-down approaches are developed where the design of chemical product aims to identify molecules that possess a set of properties, which fulfill customer requirements. Depending on the nature of the chemical product and the available resources, the chemical product can be designed through enumeration, metaheuristic, mathematical programming, visual or decomposition-based approaches, as discussed in the chapter. In general, mathematical programming approaches are widely utilized for their flexibility and simplicity to incorporate different design considerations during the design of an optimal chemical product. For cases where these approaches are difficult to apply or slow in providing results, random generationebased metaheuristic approaches can applied. For the design of complex chemical product such as formulated products, decomposition-based approaches, which break down the complicated design problem into solvable subproblems, can be utilized to reduce the complexity and solve the design problem. When visualization during the design process is preferred, visual approaches, which provide visualization for the design of chemical products, can be used. Chemical design strategies are developed for the solution of multiobjective chemical product design problems and chemical design problems with consideration of property prediction uncertainty as well. With the aid of various design strategies, chemical products can be designed in a more systematic, efficient, and sustainable way. Although there exists a wide range of strategies for the design of different chemical products, the development of newer property prediction models is the key in expanding the application of the current design techniques. In addition, advancement in modeling and optimization approaches for chemical product design is needed to be explored in order to achieve breakthrough. The advancement should be achieved with consideration of balance between required resources and result accuracy. Furthermore, frameworks that link design to synthesis of chemical products are required to provide systematic and efficient methods for the design and production of chemical products. It is to be noted that the development of different chemical product design strategies are built on the foundation of knowledge and understanding of the actual product behavior and conditions. Therefore, the importance of experiments on the synthesis and validation of chemical products in the design process should not be neglected.

Mathematical Principles of Chemical Product Design Chapter j 1

REFERENCES Achenie, L.E.K., Gani, R., Venkatasubramanian, V., 2003. Computer Aided Molecular Design: Theory and Practice, vol. 20. Elsevier, Amsterdam. Achenie, L.E.K., Sinha, M., 2003. Interval global optimization in solvent design. Reliable Computing 9, 317e338. Adjiman, C.S., Galindo, A., 2011. Front matter. In: Pistikopoulos, E.N., Georgiadis, M.C., Dua, V., Adjiman, C.S., Galindo, A. (Eds.), Process Systems Engineering: Molecular Systems Engineering, vol. 6. Wiley-VCH Verlag GmbH & Co. KGaA. Ambrose, D., 1978. Correlation and Estimation of Vapour-Liquid Critical Properties: I. In: Critical Temperatures of Organic Compounds, vol. 1. National Physical Laboratory, Teddington, United Kingdom. Arts, E.H.L., Van Laarhoven, P.J.M., 1985. A new polynomial-time cooling schedule. Proceedings of the IEEE International Conference on Computer-Aided Design 206e208. Bahnick, D.A., Doucette, W.J., 1988. Use of molecular connectivity indices to estimate soil sorption coefficients for organic chemicals. Chemosphere 17 (9), 1703e1715. Bellman, R.E., Zadeh, L.A., 1970. Decision-making in a fuzzy environment. Management Science 17 (4), 141e164. Belotti, P., Kirches, C., Leyffer, S., Linderoth, J., Luedtke, J., Mahajan, A., 2013. Mixed-integer nonlinear optimization. Acta Numerica 22, 1e131. Bertsimas, D., Brown, D.B., Caramanis, C., 2011. Theory and application of robust optimization. SIAM Review 53 (3), 464e501. Bonami, P., Kilinc¸, M., Linderoth, J., 2012. Algorithms and software for convex mixed integer nonlinear programs. In: Lee, J., Leyffer, S. (Eds.), Mixed Integer Nonlinear Programming. Springer, New York, pp. 1e39. Box, G.E.P., Hunter, W.G., Hunter, J.S., 1978. Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. Wiley. Burer, S., Letchford, A.N., 2012. Non-convex mixed-integer nonlinear programming: a survey. Surveys in Operations Research and Management Science 17 (2), 97e106. Camarda, K.V., Maranas, C.D., 1999. Optimization in polymer design using connectivity indices. Industrial and Engineering Chemistry Research 38 (5), 1884e1892. Caramia, M., Dell’Olmo, P., 2008. Multi-objective optimization. In: Multi-Objective Management in Freight Logistics: Increasing Capacity, Service Level and Safety with Optimization Algorithms. Springer, London, pp. 11e37. Chavez-Islas, L.M., Vasquez-Medrano, R., Flores-Tlacuahuac, A., 2011. Optimal molecular design of ionic liquids for high-purity bioethanol production. Industrial and Engineering Chemistry Research 50 (9), 5153e5168. Chemmangattuvalappil, N.G., Eden, M.R., 2013. A novel methodology for property-based molecular design using multiple topological indices. Industrial and Engineering Chemistry Research 52 (22), 7090e7103. Chemmangattuvalappil, N.G., Solvason, C.C., Bommareddy, S., Eden, M.R., 2010. Reverse problem formulation approach to molecular design using property operators based on signature descriptors. Computers and Chemical Engineering 34 (12), 2062e2071. Churi, N., Achenie, L.E.K., 1996. Novel mathematical programming model for computer aided molecular design. Industrial and Engineering Chemistry Research 35 (10), 3788e3794. Churi, N., Achenie, L.E.K., 1997. The optimal design of refrigerant mixtures for a two-evaporator refrigeration system. Computers and Chemical Engineering 21, S349eS354.

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SECTION j I Basic Concepts and General Tools Cisternas, L.A., Ga´lvez, E.D., 2006. Principles for chemical products design. Computer Aided Chemical Engineering 21 (C), 1107e1112. Constantinou, L., Gani, R., 1994. New group contribution method for estimating properties of pure compounds. AIChE Journal 40 (10), 1697e1710. Constantinou, L., Bagherpour, K., Gani, R., Klein, J.A., Wu, D.T., 1996. Computer aided product design: problem formulations, methodology and applications. Computers and Chemical Engineering 20 (6e7), 685e702. Constantinou, L., Prickett, S.E., Mavrovouniotis, M.L., 1993. Estimation of thermodynamic and physical properties of acyclic hydrocarbons using the ABC approach and conjugation operators. Industrial and Engineering Chemistry Research 32 (8), 1734e1746. Conte, E., Gani, R., Malik, T.I., 2011. The virtual Product-Process Design laboratory to manage the complexity in the verification of formulated products. Fluid Phase Equilibria 302 (1e2), 294e304. Cornell, J.A., 2002. Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data. Wiley. Cox, D.R., 1971. Biometrika Trust a note on polynomial response functions for mixtures. Biometrika 58 (1), 155e159. Cussler, E.L., Wagner, A., Marchal-Heussler, L., 2010. Designing chemical products requires more knowledge of perception. AIChE Journal 56 (2), 283e288. Dai, J., Jin, L., Wang, L., 1998. Prediction of molar volume of aliphatic compounds using edge adjacency index. Progress in Natural Science 8 (6), 760e761. D’Ambrosio, C., Lodi, A., 2011. Mixed integer nonlinear programming tools: a practical overview. 4OR 9 (4), 329e349. Deb, K., 2011. Multi-objective optimisation using evolutionary algorithms: an introduction. In: Wang, L., Ng, C.M.H., Deb, K. (Eds.), Multi-Objective Evolutionary Optimisation for Product Design and Manufacturing. Springer, London, pp. 3e34. Deckro, R.F., Hebert, J.E., 1989. Resource constrained project crashing. Omega 17 (1), 69e79. Deporter, E.L., Ellis, K.P., 1990. Optimization of project networks with goal programming and fuzzy linear programming. Computers and Industrial Engineering 19 (1e4), 500e504. Dev, V.A., Chemmangattuvalappil, N.G., Eden, M.R., 2014. Reactant structure generation by signature descriptors and real coded genetic algorithm. In: Eden, M.R., Siirola, J.D., Towler, G.P. (Eds.), Computer Aided Chemical Engineering, vol. 34. Elsevier B.V, pp. 291e296. Dev, V.A., Chemmangattuvalappil, N.G., Eden, M.R., 2015. Designing reactants and products with properties dependent on both structures. In: Gernaey, K.V., Huusom, J.K., Gani, R. (Eds.), Computer Aided Chemical Engineering, vol. 37. Elsevier B.V, pp. 1445e1450. Dev, V.A., Chemmangattuvalappil, N.G., Eden, M.R., 2016. Multi-Objective Computer-Aided Molecular Design of Reactants and Products. In: Kravanja, Z., Bogataj, M. (Eds.), Computer Aided Chemical Engineering, Vol. 38. Elsevier B.V., pp. 2055e2060. Dubois, D., Fortemps, P., 1999. Computing improved optimal solutions to max-min flexible constraint satisfaction problems. European Journal of Operational Research 118 (1), 95e126. Dubois, D., Fargier, H., Prade, H., 1996. Refinements of the maximin approach to decision-making in a fuzzy environment. Fuzzy Sets and Systems 81 (1), 103e122. Ehrgott, M., Gandibleux, X., 2002. Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Multiple Criteria Optimization. Kluwer Academic Publishers, USA. Eljack, F.T., Eden, M.R., 2008. A systematic visual approach to molecular design via property clusters and group contribution methods. Computers and Chemical Engineering 32 (12), 3002e3010. Estrada, E., 1995. Edge adjacency relationships in molecular graphs containing heteroatoms: a new topological index related to molar volume. Journal of Chemical Information and Computer Sciences 35 (4), 701e707.

Mathematical Principles of Chemical Product Design Chapter j 1 Faulon, J.-L., Churchwell, C.J., Visco, D.P., 2003. The signature molecular descriptor. 2. Enumerating molecules from their extended valence sequences. Journal of Chemical Information and Computer Sciences 43 (3), 721e734. Fishburn, P.C., 1967. Additive utilities with incomplete product sets: application to priorities and assignments. Operations Research 15 (3), 537e542. Fletcher, R., Leyffer, S., 1994. Solving mixed integer nonlinear programs by outer approximation. Mathematical Programming 66 (3), 327e349. Folic, M., Adjiman, C.S., Pistikopoulos, E.N., 2007. Design of solvents for optimal reaction rate constants. AIChE Journal 53 (5), 1240e1256. Gani, R., 2004. Chemical product design: challenges and opportunities. Computers and Chemical Engineering 28 (12), 2441e2457. Gani, R., Constantinou, L., 1996. Molecular structure based estimation of properties for process design. Fluid Phase Equilibria 116 (1e2), 75e86. Gani, R., Ng, K.M., 2015. Product design e molecules, devices, functional products, and formulated products. Computers and Chemical Engineering 81, 70e79. Gani, R., O’Connell, J.P., 2001. Properties and CAPE: from present uses to future challenges. Computers and Chemical Engineering 25 (1), 3e14. Gani, R., Pistikopoulos, E.N., 2002. Property modelling and simulation for product and process design. Fluid Phase Equilibria 194e197, 43e59. Gani, R., Harper, P.M., Hostrup, M., 2005. Automatic creation of missing groups through connectivity index for pure-component property prediction. Industrial and Engineering Chemistry Research 44 (18), 7262e7269. Gani, R., Nielsen, B., Fredenslund, A., 1991. A group contribution approach to computer-aided molecular design. AIChE Journal 37 (9), 1318e1332. Geoffrion, A., 1972. Generalized benders decomposition. Journal of Optimization 10, 237e260. Gebreslassie, B.H., Diwekar, U.M., 2015. Efficient ant colony optimization for computer aided molecular design: Case study solvent selection problem. Computers & Chemical Engineering 78, 1e9. Giovanoglou, A., Barlatier, J., Adjiman, C.S., Pistikopoulos, E.N., Cordiner, J.L., 2003. Optimal solvent design for batch separation based on economic performance. AIChE Journal 49, 3095e3109. Glover, F., 1986. Future paths for integer programming and links to artificial intelligence. Computers and Operations Research 13 (5), 533e549. Grossmann, I.E., Westerberg, A.W., 2000. Research Challenges in Process Systems Engineering. AIChE Journal 46 (9), 1700e1703. Gupta, O.K., Ravindran, A., 1985. Branch and bound experiments in convex nonlinear integer programming. Management Science 31 (12), 1533e1546. Guu, S., Wu, Y., 1997. Weighted coefficients in two-phase approach for solving the multiple objective programming problems. Fuzzy Sets and Systems 85 (1), 45e48. Guu, S., Wu, Y., 1999. Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets and Systems 107 (2), 191e195. Haimes, Y., Ladson, L., Wismer, D., 1971. On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man and Cybernetics 1, 296e297. Harper, P.M., Gani, R., 2000. A multi-step and multi-level approach for computer aided molecular design. Computers and Chemical Engineering 24 (2e7), 677e683. Harper, P.M., Gani, R., Kolar, P., Ishikawa, T., 1999. Computer-aided molecular design with combined molecular modeling and group contribution. Fluid Phase Equilibria 158e160, 337e347.

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SECTION j I Basic Concepts and General Tools Heintz, J., Belaud, J.-P., Pandya, N., Teles Dos Santos, M., Gerbaud, V., 2014. Computer aided product design tool for sustainable product development. Computers and Chemical Engineering 71, 362e376. Herring III, R.H., Eden, M.R., 2015. Evolutionary algorithm for de novo molecular design with multi-dimensional constraints. Computers and Chemical Engineering 83, 267e277. Hill, M., 2009. Chemical product engineeringdthe third paradigm. Computers and Chemical Engineering 33 (5), 947e953. Holland, J.H., 1975. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Ann Arbor, USA. Horvath, A.L., 1992. Molecular Design: Chemical Structure Generation from the Properties of Pure Organic Compounds. Elsevier Science, Amsterdam. Hwang, C.-L., Masud, A.S.M., 1979. Multiple Objective Decision Making e Methods and Applications: A State-of-the-Art Survey. Springer, Berlin. Joback, K.G., Reid, R.C., 1987. Estimation of pure-component properties from group-contribution. Chemical Engineering Communications 57 (1e6), 233e243. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2005. A new decomposition-based computer-aided molecular/mixture design methodology for the design of optimal solvents and solvent mixtures. Industrial and Engineering Chemistry Research 44 (13), 4785e4797. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2006. A computer-aided molecular design framework for crystallization solvent design. Chemical Engineering Science 61, 1247e1260. Kettaneh-Wold, N., 1992. Analysis of mixture data with partial least squares. Chemometrics and Intelligent Laboratory Systems 14 (1e3), 57e69. Kier, L.B., 1985. A shape index from molecular graphs. Quantitative Structure-Activity Relationships 4 (3), 109e116. Kier, L.B., Hall, L.H., 1986. Molecular Connectivity in Structure-Activity Analysis. Research Studies Press, Herefordshire. Kim, I.Y., de Weck, O.L., 2006. Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation. Structural and Multidisciplinary Optimization 31 (2), 105e116. Kim, K.J., Diwekar, U.M., Joback, K.G., 2002. Greener solvent selection under uncertainty. ACS Symposium Series 819, 224e237. Kim, K., Diwekar, U., 2002a. Efficient combinatorial optimization under uncertainty. 1. Algorithmic development. Industrial and Engineering Chemistry Research 41, 1276e1284. Kim, K., Diwekar, U., 2002b. Efficient combinatorial optimization under uncertainty. 2. Application to stochastic solvent selection. Industrial and Engineering Chemistry Research 41, 1285e1296. Kim, K., Diwekar, U., 2002c. Hammersley stochastic annealing: efficiency improvement for combinatorial optimization under uncertainty. IIE Transactions Institute of Industrial Engineers 34, 761e777. Klatt, K.-U., Marquardt, W., 2009. Perspectives for process systems engineeringdpersonal views from academia and industry. Computers and Chemical Engineering 33 (3), 536e550. Koch, R., 1982. Molecular connectivity and acute toxicity of environmental pollutants. Chemosphere 11 (9), 925e931. Kontogeorgis, G.M., Gani, R., 2004. Introduction to computer aided property estimation. In: Kontogeorgis, G.M., Gani, R. (Eds.), Computer Aided Chemical Engineering, first ed., vol. 19. Elsevier B.V, Amsterdam, The Netherlands, pp. 3e26. Korte, R.F., 2003. Biases in decision making and implications for human resource development. Advances in Developing Human Resources 5 (4), 440e457.

Mathematical Principles of Chemical Product Design Chapter j 1 Kramer, R., 1998. Chemometric Techniques for Quantitative Analysis. CRC Press. Lin, B., Chavali, S., Camarda, K., Miller, D.C., 2005. Computer-aided molecular design using Tabu search. Computers and Chemical Engineering 29 (2), 337e347. Macchietto, S., Odele, O., Omatsone, O., 1990. Design of optimal solvents for liquid-liquid extraction and gas absorption processes. Chemical Engineering Research and Design 68 (5), 429e433. Maranas, C.D., 1996. Optimal computer-aided molecular design: a polymer design case study. Industrial and Engineering Chemistry Research 35 (10), 3403e3414. Maranas, C.D., 1997a. Optimal molecular design under property prediction uncertainty. AIChE Journal 43 (5), 1250e1264. Maranas, C.D., 1997b. Optimization accounting for property prediction uncertainty in polymer design. Computers and Chemical Engineering 21, S1019eS1024. Marcoulaki, E.C., Kokossis, A.C., 1998. Molecular design synthesis using stochastic optimisation as a tool for scoping and screening. Computers and Chemical Engineering 22, S11eS18. Marrero, J., Gani, R., 2001. Group-contribution based estimation of pure component properties. Fluid Phase Equilibria 183e184, 183e208. Martin, M., Martinez, A., 2013. A methodology for simultaneous process and product design in the formulated consumer products industry: the case study of the detergent business. Chemical Engineering Research and Design 91, 795e809. Martin, M., Martinez, A., 2015. Addressing uncertainty in formulated products and process design. Industrial and Engineering Chemistry Research 54, 5990e6001. Mavrotas, G., 2009. Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied Mathematics and Computation 213 (2), 455e465. Mavrotas, G., Florios, K., 2013. An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems. Applied Mathematics and Computation 219 (18), 9652e9669. Mavrovouniotis, M.L., 1990. Estimation of properties from conjugate forms of molecular structures: the ABC approach. Industrial and Engineering Chemistry Research 29 (9), 1943e1953. McLeese, S.E., Eslick, J.C., Hoffmann, N.J., Scurto, A.M., Camarda, K.V., 2010. Design of ionic liquids via computational molecular design. Computers and Chemical Engineering 34 (9), 1476e1480. Melo, W., Fampa, M., Raupp, F., 2014. Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming. Journal of Global Optimization 60 (2), 373e389. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E., 1953. Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics 21 (6), 1087e1092. Miettinen, K., 1999. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston. Miettinen, K., 2008. Introduction to multiobjective optimization: noninteractive approaches. In: Branke, J., Deb, K., Miettinen, K., Słowi nski, R. (Eds.), Multiobjective Optimization: Interactive and Evolutionary Approaches. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 1e26. Moggridge, G.D., Cussler, E.L., 2000. An introduction to chemical product design. Chemical Engineering Research and Design 78 (1), 5e11. Montgomery, D.C., 2008. Design and Analysis of Experiments. John Wiley & Sons.

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SECTION j I Basic Concepts and General Tools Ng, L.Y., Chemmangattuvalappil, N.G., Ng, D.K.S., 2014. A multiobjective optimization-based approach for optimal chemical product design. Industrial and Engineering Chemistry Research 53 (44), 17429e17444. Ng, L.Y., Chemmangattuvalappil, N.G., Ng, D.K.S., 2015. Robust chemical product design via fuzzy optimisation approach. Computers and Chemical Engineering 83, 186e202. O’Connell, J.P., Gani, R., Mathias, P.M., Maurer, G., Olson, J.D., Crafts, P.A., 2009. Thermodynamic property modeling for chemical process and product engineering: some perspectives. Industrial and Engineering Chemistry Research 48 (10), 4619e4637. Odele, O., Macchietto, S., 1993. Computer aided molecular design: a novel method for optimal solvent selection. Fluid Phase Equilibria 82, 47e54. Ojalehto, V., Miettinen, K., Laukkanen, T., 2014. Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS. Computational Optimization and Applications 58 (3), 757e779. Ostrovsky, G.M., Achenie, L.E.K., Sinha, M., 2002. On the solution of mixed-integer nonlinear programming models for computer aided molecular design. Computers and Chemistry 26, 645e660. Papadopoulos, A.I., Linke, P., 2006. Multiobjective molecular design for integrated processsolvent systems synthesis. AIChE Journal 52 (3), 1057e1070. Papadopoulos, A.I., Stijepovic, M., Linke, P., Seferlis, P., Voutetakis, S., 2013. Toward optimum working fluid mixtures for organic Rankine cycles using molecular design and sensitivity analysis. Industrial and Engineering Chemistry Research 52 (34), 12116e12133. Patel, S.J., Ng, D., Mannan, M.S., 2009. QSPR flash point prediction of solvents using topological indices for application in computer aided molecular design. Industrial and Engineering Chemistry Research 48 (15), 7378e7387. Quesada, I., Grossmann, I.E., 1992. An LP/NLP based branch-and-bound algorithm for convex MINLP. Computers and Chemical Engineering 16, 937e947. Randic, M., 1975. Characterization of molecular branching. Journal of the American Chemical Society 97 (23), 6609e6615. Randic, M., Mihalic, Z., Nikolic, S., Trinajstic, N., 1994. Graphical bond orders: novel structural descriptors. Journal of Chemical Information and Computer Sciences 34 (2), 403e409. Sargent, R., 2005. Process systems engineering: a retrospective view with questions for the future. Computers and Chemical Engineering 29 (6), 1237e1241. Scheffe´, H., 1958. Experiments with mixtures. Journal of the Royal Statistical Society. Series B (Methodological) 20 (2), 344e360. Scheffe´, H., 1963. The simplex-centroid design for experiments with mixtures. Journal of the Royal Statistical Society. Series B (Methodological) 25 (2), 235e263. Shelokar, P., Kulkarni, A., Jayaraman, V.K., Siarry, P., 2014. Metaheuristics in process engineering: a historical perspective. In: Jayaraman, V.K., Siarry, P. (Eds.), Applications of Metaheuristics in Process Engineering. Springer International Publishing, pp. 1e38. Siddhaye, S., Camarda, K., Southard, M., Topp, E., 2004. Pharmaceutical product design using combinatorial optimization. Computers and Chemical Engineering 28 (3), 425e434. Solvason, C.C., Chemmangattuvalappil, N.G., Eljack, F.T., Eden, M.R., 2009. Efficient visual mixture design of experiments using property clustering techniques. Industrial and Engineering Chemistry Research 48 (4), 2245e2256. Song, J., Song, H., 2008. Computer-aided molecular design of environmentally friendly solvents for separation processes. Chemical Engineering and Technology 31 (2), 177e187. Spall, J.C., 2012. Stochastic optimization. In: Gentle, E.J., Ha¨rdle, K.W., Mori, Y. (Eds.), Handbook of Computational Statistics: Concepts and Methods. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 173e201.

Mathematical Principles of Chemical Product Design Chapter j 1 Stephanopoulos, G., 2003. Invention and innovation in a product-centered chemical industry: general trends and a case study. In: AIChE Annual Conference. San Francisco. Stephanopoulos, G., Reklaitis, G.V., 2011. Process systems engineering: from Solvay to modern bio- and nanotechnology: a history of development, successes and prospects for the future. Chemical Engineering Science 66 (19), 4272e4306. Struebing, H., Ganase, Z., Karamertzanis, P.G., Siougkrou, E., Haycock, P., Piccione, P.M., Armstrong, A., Galindo, A., Adjiman, C.S., 2013. Computer-aided molecular design of solvents for accelerated reaction kinetics. Nature Chemistry 5, 952e957. Trinajstic, N., 1992. Chemical Graph Theory. CRC Press, Boca Raton. Venkatasubramanian, V., Chan, K., Caruthers, J.M., 1994. Computer-aided molecular design using genetic algorithms. Computers and Chemical Engineering 18 (9), 833e844. Venkatraman, V., Gupta, M., Foscato, M., Svendsen, H.F., Jensen, V.R., Alsberg, B.K., 2016. Computer-aided molecular design of imidazole-based absorbents for CO2 capture. International Journal of Greenhouse Gas Control 49, 55e63. Visco, D.P., Pophale, R.S., Rintoul, M.D., Faulon, J.-L., 2002. Developing a methodology for an inverse quantitative structure-activity relationship using the signature molecular descriptor. Journal of Molecular Graphics and Modelling 20 (6), 429e438. von Stackelberg, H., 1952. The Theory of the Market Economy. William Hodge. Westerlund, T., Pettersson, F., 1995. A cutting plane method for solving convex MINLP problems. Computers and Chemical Engineering 19, 131e136. Wiener, H., 1947. Structural determination of paraffin boiling points. Journal of the American Chemical Society 69 (1), 17e20. Wilson, R.J., 1986. Introduction to Graph Theory, fourth ed. Pearson Education Limited, Harlow. Xu, W., Diwekar, U.M., 2005. Improved genetic algorithms for deterministic optimization and optimization under uncertainty. Part II. Solvent selection under uncertainty. Industrial and Engineering Chemistry Research 44 (18), 7138e7146. Yang, X.-S., 2010. Engineering Optimization. Engineering Optimization: An Introduction with Metaheuristic Applications. John Wiley & Sons, Inc, pp. 15e28. Yang, X.-S., 2015. Nature-inspired algorithms: success and challenges. In: Lagaros, N.D., Papadrakakis, M. (Eds.), Engineering and Applied Sciences Optimization: Dedicated to the Memory of Professor M.G. Karlaftis. Springer International Publishing, pp. 129e144. Younes, A., Elkamel, A., Areibi, S., 2010. Genetic algorithms in process engineering: developments and implementation issues. In: Rangaiah, G.P. (Ed.), Stochastic Global Optimization: Techniques and Applications in Chemical Engineering. World Scientific Publishing Co., Inc, River Edge, NJ, USA, pp. 111e146. Yunus, N.A., Gernaey, K.V., Woodley, J.M., Gani, R., 2014. A systematic methodology for design of tailor-made blended products. Computers and Chemical Engineering 66, 201e213. Zadeh, L.A., 1965. Fuzzy sets. Information and Control 8 (3), 338e353. Zimmermann, H.-J., 1976. Description and optimization of fuzzy systems. International Journal of General Systems 2 (4), 209e215. Zimmermann, H.-J., 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1 (1), 45e55. Zimmermann, H.-J., 1983. Fuzzy mathematical programming. Computers and Operations Research 10 (4), 291e298. Zimmermann, H.-J., 2001. Fuzzy Set Theory e and Its Applications, vol. 30. Springer Science & Business Media, Norwell, Massachusetts.

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Chapter 2

Integrated Consumer Preferences and Price/ DemandeDriven Product Design: An Alternative to Stage-Gate Procedures M. Bagajewicz University of Oklahoma, Norman, OK, United States E-mail: [email protected]

1. INTRODUCTION Product design requires the collaboration of marketing experts, economists, and engineers, and has been advocated to be one of the new frontiers opened for chemical engineers (Westerberg and Subrahmanian, 2000; Cussler and Morridge, 2001). Hill (2004) and Stephanopoulos (2003) argued that this renewed interest in products has obvious impact on research and education (Seider et al., 2004; Cussler, 2003), while others advocate that this is just an expansion of the competency that will include the commodity supply chain, and will incorporate the new performance-based constraints of a product (Joback and Stephanopoulos, 1995; Bagajewicz, 2005; Costa et al., 2006a,b; Ng et al., 2006; Siddhaye et al., 2000, 2004; among many others). Typically, while marketing experts identify consumer “needs and wants” and economists provide means to assess costs and profit, engineers try to advance a product structure/formulation that will achieve the product functionality that targets some of these needs and wants in some optimal way (in the current western economy, it is usually maximum profit). In other words, the needs and wants are not always fully met by the products marketed to these consumers. These needs and wants are usually expressed using consumer-related properties, in terms of properties defined in plain language that are not many times the same as the ones used by engineers to describe the product. Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00002-2 Copyright © 2016 Elsevier B.V. All rights reserved.

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Product design procedures, like the one proposed in the area of process systems engineering by Cussler and Moggridge (2001) or Seider et al. (2004), are the ones that insist on the identification of consumer wants and needs first using them as targets for the product design, while considering consumer response to price as well as optimality (profit or other objective) later. Similarly, the Stage-GateÔ Product Development Process (SGPDP) (Cooper, 2001, 2002, 2005) proceeds in a similar manner by using so-called phases sequentially (first concept, then feasibility, development, manufacturing, and finally product marketing). The first two help shape up the product based on consumer needs and wants using market surveys and tests. At this point, the SGPDP method also suggests building a business case for each product option. The main assumption is that once the concept and the feasibility have been tested, then one product, which could be later refined, emerges. The claim made in this chapter is that identifying the product first and determining its impact on economics of a company (or other societal areas) later prevents the design of achieving an optimal product. Instead, simultaneously treating product quality (measured by consumer preferences), behavior against price, as well as manufacturing costs, is the right way to identify such profit-optimal product structure (composition, form, functionalities, effectiveness, etc.), and prevents making decisions that can later face manufacturing roadblocks (especially cost) or marketing problems (lack of or smaller profitability or other societal impacts). To reinforce the idea, recent case studies (Street et al., 2008; Heflin et al., 2009) suggested answers where the innovation is discouraged because the market preferences and consumer behavior towards prices do not anticipate higher profitability. Then, the main idea is not to develop the best product as seen by the study of consumer needs and wants, but the optimal one, eventually (or not) balancing the wants and needs with the costs (company cost and/or societal costs), as well as projected revenues. The most obvious objective in our current western economic system is profit, and we will use it here without loss of generality. When and if one wants to add societal objectives, those ought to be treated as constraints or “costs.” Otherwise, if profit is confronted with societal objectives, the problems become multiobjective. By contrast, we claim that in the SGPDP context, the (many times) wrong product would continue to be developed until the lack of optimality (profitability or other) is discovered at later stages.

2. PRODUCT DESIGN INTEGRATED MODEL We consider the following to be the key elements: l

Product identification: type and functionality. This requires identifying consumer needs and wants first, as in SGPDP. We keep in mind that there are products that can be introduced in the market without them being wants

Stage-Gate Procedures Chapter j 2

l

l

l

l

and/or not even perceived needs, generating artificially, so to speak, new wants and needs that did not exist before. Examples of this artificial generation of needs and wants abound. Identification of product attributes: These are typically the functionalities that are given value by consumers. For example, in the specific case of skin lotions (Bagajewicz et al., 2011), an example we use frequently in this chapter, one would identify its effectiveness, thickness, smoothness, color, creaminess, scent, etc. In devices such as cars, one talks about power, acceleration, comfort, accessories, etc. In medical devices, one talks about its accuracy, its false positives/false negative. We claim that such a list can be made for every product! Consumer preferences: Establish a quantitative measure of how much a consumer prefers a product (regardless of its price) given the attributes. This is where we depart slightly from what economists call “hedonic value” and “hedonic pricing,” started by studies like those on “revealed preference theory” pioneered by Samuelson (1938) and continued through time (see Baltas and Freeman, 2001). In all these cases, the underlying idea is that the consumer makes choices that are influenced by (1) perceived preference of one product versus others, (2) price(s), and (3) budget. In other words, when price and affordability are not considered, consumers will almost always declare preference for the product that has their bestperceived quality, but when price and budget are included, the choice is different. Thus, consider cars: asked what car would one like, one may, for example, choose a fancy sport car; when budget is considered, the choices are based on the car type and model they can afford (accessible range of prices), and within that range, preferences play a role, so many times, one “pays for quality.” Consumer buying behavior: A price demand relationship that incorporates the consumer preferences. Optimization: A procedure that is capable of identifying the attributes that achieve the “right” product to manufacture given a certain criteria [we use the maximization of profit here, but it could be as stated above any other (set of) criteria].

Fig. 2.1 shows the linkage between the components. Consumer preferences, prices, demands, and budget feed the consumer model as parameters. The optimization variables are the product structure/composition/design, which, in turn, are used to compute the cost. Both the cost and the consumer model are then used to evaluate the profit. An optimization procedure, be it mathematical programming, stochastic procedures, genetic algorithms, or other ad hoc procedures, can be used to find the optimal product. In a model that is more amenable to readers that prefer mathematical programming schemes, one can summarize (and generalize) the scheme of Fig. 2.1 by maximizing net present value as a function of all marketing decisions made together with the product structure.

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SECTION j I Basic Concepts and General Tools

FIGURE 2.1 Integrated product design procedure.

3. CONSUMER SATISFACTION SCORE We first start with defining the consumer satisfaction score of product candidate, i (Hi), as a function of certain parameters (ri,j) and normalized scores of different consumer-related “properties” (yi,j):   Hi ¼ f ri; j ; yi; j (2.1) We believe that satisfaction (and later preferences) ought to be established without incorporating prices in the analysis first, and then use relative preferences in a price/demand model of choice. Until now, we used the simplest form for satisfaction, a linear one, as follows: X wi; j yi; j (2.2) Hi ¼ where wi,j are weights (Bagajewicz, 2007). The weights represent how much a specific attribute contributes to the overall satisfaction. To determine those, one needs to perform marketing surveys on products without factoring the price. In turn, the scores, defined in the range from zero to one together with the weights, determine an overall score, Hi, in the range from zero to one. Consumer properties are defined in plain terms that the product user defines in plain language. In the case of a few published examples, these properties are shown in Table 2.1. In turn, these consumer properties have to be expressed in terms of engineering properties (xi,k). In unpublished work performed by several groups of undergraduate chemical engineering students, we have tested these ideas for a variety of products, using their corresponding attributes, later connected to engineering properties: hospital oxygen generators (ease of use, noise, appearance, maintenance frequency, reliability, durability, etc.), carbohydrate vaccines

TABLE 2.1 Consumer Properties of Selected Products Skin Lotion (Bagajewicz et al., 2011)

Wine (Whitnack et al., 2009)

Saliva Diagnostic Kit (Heflin et al., 2009)

Wine Nose (Linehan et al., 2011)

Effectiveness, durability

Acidity

Sensitivity

Accuracy

Scent type

Feel

Sweetness

False negative rate

Size

Greasiness

Scent intensity

Form

Bitterness

False positive rate

Weight

Smoothness

Fragrance duration

Toxicity

Clarity

Patient discomfort

Creaminess

Toxicity

Scent

Color

Carpet Deodorizer (Street et al., 2008)

Insect Repellent (Bagajewicz, 2007)

Effectiveness

Disinfecting power, odor elimination power

Thickness

Properties

Brightness

Absorption rate

Bouquet

Color

Body/texture

Scent

Finish/aftertaste

Associated EngineeringeManipulated Properties l

Composition

l l l

Composition Dose Material and radius particles

l

Composition

l l

l l

Grape Barrel type and burn Time Etc.

Sensor(s) type (MV) Geometry Materials

Engineering Properties Used for Assessment l l

l

Release time duration

l l

Size Weight

49

l

Diffusivities Viscosity Surface tension Density

Stage-Gate Procedures Chapter j 2

Spreadability

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SECTION j I Basic Concepts and General Tools

(efficacy, side effects, delivery method, etc.), cholesterol inhibitor (efficacy, side effects, etc.), vodka (clarity, aroma, sensation, aftertaste), roach killers (durability, speed, odor, toxicity, etc.), automotive hydrophobic coating (texture, frequency of application, water retention, application method), flame retardants (retardancy time, number of applications, odor, setting time, biodegradability, toxicity), osteoarthritis alleviation treatment (frequency, pain upon application, etc.), cartilage tissue repair method seeding chondrocytes (long-term outcome, invasiveness, recovery time), anticavity toothpaste (effectiveness, thickness, cooling effect, abrasiveness, sweetness, foaminess, creaminess, etc.), new refrigerants (safety, global warming potential, ozone depletion impact, compatibility with existing system, stability, explosion potential, etc.), and polymer composite gasoline tank (weight, gasoline diffusion, potential spillage, emission tests, strength upon impact, rupture), each one presenting its own set of challenges, but adhering to the same concepts. Thus, in general, we write:   yi; j ¼ f xi; j

(2.3)

where xi,j are engineering properties. Thus, we can finally define a product using the aforementioned manipulated properties. We now present a procedure to determine this relationship for the case of the humidifying skin lotion (Bagajewicz et al., 2011). We first note that in this case, the composition is the manipulated variable, and all other properties are the result of this choice. Composition is described in this case by humectants (bind water), occlusives (prevent loss of water), exfoliants (dead skin removal), emollients (fillers of intercellular space), perfumes, and many other inactive ingredients (solvents, thickeners, preservatives, buffers, emulsifiers, colorants, etc.) that help achieve the desired degree of satisfaction through the manipulation of viscosity, density, diffusivity, and surface tension (Bagajewicz et al., 2011). To illustrate the connections between manipulated variables and satisfaction, we show how the consumer preference for effectiveness (the ability to humidify the stratum corneum) is related by consumers to skin appearance. To establish the preference score, one needs to poll a certain number of potential customers of the targeted market segment. Thus, in our example, the effectiveness is rated (Fig. 2.2A) and connected to the skin water content (Fig. 2.2B) and later to the presence of humectants in the skin (Fig. 2.2C). The resulting connection between preference and amount of humectants in the skin is seen in Fig. 2.2D. Thus, the amount of humectants per lotion application can later be defined in terms of the lotion composition of humectant compounds. Similar connections can be made for other properties. For example, for thickness, consumers are asked to rank how different mixtures flow (ketchup, mayonnaise, cream, etc.), and connections are made to the resulting viscosity

(A)

(B)

6

(C)

Frog Skin Baby’s Skin

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

Stratum Corneum Water Content

20.00%

10.00%

0

100

200

300

Humectants (nmol cm -2 )

400

500 Humectants (nmol cm -2 )

FIGURE 2.2 (A) Preference versus skin appearance, (B) skin appearance versus water content, (C) water content versus humectants, (D) preference versus humectants content.

Stage-Gate Procedures Chapter j 2

Consumer Preference

(D)

30.00%

0.00%

Velvet

0 0.00%

Skin Appearance

Stratum Corneum Water Content

Elderly Person’s Skin

Skin Appearance

Consumer Preference

Fish

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SECTION j I Basic Concepts and General Tools

obtained by the composition (thickness is proportional to the square root of viscosity). In turn, for greasiness, consumers are asked to rank several different products (grease, baby oil, suntan lotion, alcohol) regarding their perceived feeling of greasiness and connections are made to the fatty oil contents. Smoothness is related to greasiness and thickness (it is a metadescriptor, a descriptor composed of other descriptors); so is creaminess. Finally, spreadability identifies the ease of a fluid to displace another fluid on a given surface. Consumers are asked to rate their satisfaction to this product attribute by comparing to other substances (glue, syrup, detergent, ketchup, oil, water). This is connected to surface tension. Absorption rate, related to the ease or speed with which a product disappears on application, is related to diffusivity in the stratum corneum. We omit for reasons of space connections and derived engineering properties for other products in the above table. They are described in the associated papers. We now turn our attention to the weights in Eq. (2.2). To establish these, there are several marketing survey techniques that we omit discussing here in detail. In the simplest form, without loss of generality, one could ask several consumers to rate the product properties outlined in Table 2.1 as most important, second importance, third importance and so on, and then use this information to obtain the weights.

4. CONSUMER PREFERENCE MODEL We now turn into the determination of consumer preference score to quantify how much a consumer prefers one product, i, over another product, j. This is done by defining: bi; j ¼ f ðHi ; Hj Þ

(2.4)

Without loss of generality of the product design procedure, we used bi; j ¼ Hj Hi

so far. Thus, for example, bi, j ¼ 1 indicates that there is indifference, bi, j ¼ 0.5 indicates that product i provides the consumer twice the satisfaction of product j, and bi, j ¼ 0 that product j does not satisfy consumers at all (i.e., Hj ¼ 0), which is an extreme that is hardly found in practice. Finally, bi, j > 1 would indicate that product j is better than product i for the consumer.

5. MANUFACTURING AND DISTRIBUTION COSTS In our example, lotions are emulsions that can be either oil-in-water or waterin-oil. The choice is mainly dictated by practical considerations, such as ease of application and consumer perception (Wibowo and Ng, 2001). The oilin-water emulsions, which are less sticky on application, predominate in the market and are the choice for our study. Emulsifying agents are used to stabilize the oil-in-water mixture. The most common type of emulsifier are

Stage-Gate Procedures Chapter j 2

surfactants, which decrease the interfacial tension between the two phases. The actual manufacturing procedure is simple and consists of mixing the oil and water phases together. The following steps show how the lotion is made: 1. Heat and mix the aqueous and oil phases separately. 2. Combine both phases into one batch. 3. Perform posttreatment modifications (i.e., decrease drop size using a sonificator, followed by a colloid mill and homogenizer). As we shall see later, drop size plays a role in some properties.

6. PRICEeDEMAND CONSUMER MODEL To determine demand as a function of price, we use the constant elasticity of substitution demand model presented by Bagajewicz (2007)  r   a Y  p1 d1 1r r p2 d1 (2.5) p1 d1 ¼ b p2 d2 ¼

Y  p1 d1 p2

(2.6)

where b is the previously defined preference score and a is the level of awareness of the new product (zero when consumers are not aware of the new product and one when they are fully aware), p1 and p2 the new product and the competition prices, d1 and d2 the corresponding demands, Y the total budget of the consumers, and r is a parameter related to the elasticity. Without loss of generality, we use r ¼ 0.75 and consider a ¼ 1. We realize that the market in this case has a maximum demand (D) given by the number of people that would actually seek moisturizing lotions in the market in question. Thus, Eq. (2.5) can only be used if the market is unsaturated, i.e., when d1 þ d2 < D. In a saturated market, consumers have enough budget to buy either product, and the demand will be driven by preferences, not preferences and budget anymore. In such case, maximizing consumer utility, (Bagajewicz, 2007) renders: D ¼ d1 þ d2 D 1þg r  r1 a g¼ b d1 ¼

(2.7) (2.8)

(2.9)

Thus, the way we establish demand as a function of the rest of the parameters (a, b, g, D and r) by obtaining d1 and d2 using Eqs. (2.5) and (2.6). If these do not satisfy d1 þ d2 < D, then we use (7) through (9).

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4

β =1.04

β =1.07

β =0.97

3.5 Demand (106 bottles/year)

54

3 2.5

β =1.24 β =1.11

2

β =1.20 β =1.14

1.5

β =1.00

1 0.5 0

$5

$7

$9

$11 Price ($)

$13

$15

FIGURE 2.3 Demand as a function of prices and preference for lotions.

For our example of the skin lotion, the market was determined by looking at what areas of the US have signs and symptoms of xerosis and ichthyosis vulgaris that are the worst (see Bagajewicz et al., 2011 for more details). Also, for the example in question, a fixed capital investment, working capital, and total capital investment were determined as a function of total manufacturing capacity. The demand as a function of price was calculated for different values of b and is shown in Fig. 2.3 (we used D ¼ 500,000 bottles/month). It can be inferred that for prices less then $10, the consumer budget is not a limiting factor. At prices around $10, we reach the maximum demand we could have for our product, and it will not increase for lower prices. Then the total product cost for each value of b was computed by looking at what ingredients can match the selected value of b at minimum cost. They vary from $7.5/bottle for b ¼ 0.97 to $8.00/bottle for b ¼ 1.11. The competitor’s lotion cost is $9.40/bottle. One can also consider the possibility of multiple competitors; in such case, one can reformulate the consumer utility function and perform its maximization subject to the budget constraint,, assuming a ¼ one, one gets (Street et al., 2008): !1=ð1rÞ r=ð1rÞ p1 dj ¼ bj;1 d1 js1 (2.10) pj

Stage-Gate Procedures Chapter j 2

where (bj,1 ¼ Hj/H1), which, with the help of the (active) budget constraint X pj d j ¼ Y (2.11) j

provides the different demands as a function of all prices. Both equations are solved for different process, p1, and if the sum of the demands is larger than the natural maximum demand D (in our case, the total number of households that could use some carpet deodorizer), then the demands are no longer driven by the consumer budget and are only driven by preferences in which case the consumer preference function is maximized subject to the demand P constraint ð di ¼ DÞ. Using this model, Street et al. (2008), showed that a i

proposed carpet disinfectant/deodorizer that is superior to others is not worth pursuing.

7. PROFIT MODEL AND OPTIMIZATION In a very general form, one can pose the problem one of maximizing of expected profit, using a two-stage stochastic model P Max prs NPVRs  Fixed Capital Investment z;p

s

s:t: NPVRs ¼ Saless L Manufacturing Costss  Supply Chain Costss  Marketing Costss where prs is the probability of scenario s, which includes consumer budgets, total demands, and even preferences! The model has “here and now” decisions (first-stage variables) and “wait and see” or recourse decisions (second-stage variables). The former are decided upfront, and the latter are taken in response to certain scenario materializing as illustrated by Barbaro and Bagajewicz (2004). We also treated uncertainty in wine manufacturing (Whitnack et al., 2009). Instead of formalizing everything in a large numerical method, we realize that the problem can be nicely decomposed: if the value of b is fixed, one can calculate the net present worth (NPW) for all products that have that value of b. In principle, there might be more than one product corresponding to each value of b, a situation we believe is infrequent. For our illustrating example, with the cost computed and demand, one can now compute the profit (NPW) for a 10-year lifespan as a function of price for different values of b (Fig. 2.4). The “best lotion” (82% preference, b ¼ 0.97), is not the most profitable one, while a lotion with 80% of consumer preference would be more profitable, with a selling price between $9 and $10.

55

SECTION j I Basic Concepts and General Tools 400

β =1.0 4 β =1.00

350

β =1.0 7

300

NPW (106 $)

56

β =0.97

250 200

β =1. 14

150

β =1. 11

100

β =1. 20

50 0

$6

$7

$8

$9

$10

$11

$12

$13

$14

$15

Price ($)

FIGURE 2.4 Net present worth as a function of price for different preferences.

8. COMPETITIVE MARKETS Once our product is introduced to the existing market, some of the market will leave their current suppliers to use our product instead. This essentially takes the demand away from our competitors, decreasing their cash flow. The competitors can respond to the introduction of our product in four ways to earn some of their demand back: 1. 2. 3. 4.

change change change change

their their their their

amount of advertising composition production costs price

The first one, change in their amount of advertising, would affect the awareness function (a). The second competitor’s response, changing their composition, affects directly b. If the competitor changes his product in such a way that he will attract more of the market, our NPW will be also affected. We do not discuss these here either. The third action the competitor can take in response to our product is to minimize their manufacturing costs. This would not directly affect our product. The last action the competitor can take is to change their sales price to gain back some of the market. The new price the competitor is described by the function as follows:     d2;0  d2 a1 =a2 p2 ¼ p2;0  g p2;0  C2 b (2.12) d2;0

Stage-Gate Procedures Chapter j 2

FIGURE 2.5 Net present worth as a function of price and preference.

where p2,0 is the competitor’s original price, g is a proportionality constant (we use g ¼ 0.28), C2 is the competitor’s manufacturing cost per bottle, b is the usual relative preference, d2 is the new demand for the competitor’s product, d2,0 is the original demand of the competitor’s product, and ai is the respective awareness of the products (we assumed them to be equal to one). Thus, the new price is adjusted by multiplying the difference in cost and old price (p2,0  C2) by a function of the relative demand drop. After this is done, a new equilibrium is achieved and a new cycle is started. To assess this process, we built a discrete dynamic model that considers monthly price adjustments over a 10-year horizon. Finally, for the cases we looked at, the maximum demand D was never surpassed. The NPW was then calculated as a function of the initial price. Fig. 2.5 shows the NPW for each beta, indicating that a product of similar quality than the competition is now the most profitable, with the best starting price being $8. In Fig. 2.6, we plot both prices and show them reaching equilibrium within 1.5 years. In all cases, equilibrium is achieved within a 2-year period. All prices converged to the same equilibrium, regardless of the starting price. 16.00

Competitor’s Equilibrium Price

Price ($)

14.00 12.00 10.00 8.00

Our Equilibrium Price

6.00 0

6

12

18

24

Time (months)

FIGURE 2.6 Our and competitor’s selling price as a function of time for different starting prices (b ¼ 1.00).

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9. CONCLUSIONS This chapter presents an alternative approach to product design. We claim that one needs to use an integrated model, which looks over a time horizon and determines, simultaneously, the product. In several cases, we found that the best product is not necessarily the most profitable one. However, a product with slightly less of consumers’ preference is more profitable. We finished applying different strategies to predict selling price and demand in a competitive market, looking for the maximization of profit. We found that the equilibrium price in a competitive market depends on the preference and total product cost, but not on the starting selling price.

REFERENCES Bagajewicz, M., 2005. Integration of process systems engineering and business decision making tools: financial risk management and other emerging procedures. In: Galan, M., Martin del Valle, E. (Eds.), Chemical Engineering Trends and Developments. John Wiley, Chichester, England. Bagajewicz, M., 2007. On the role of microeconomics, multi-scale planning and finances in product design. AIChE Journal 53 (12), 3155e3170. Bagajewicz, M., Hill, S., Robben, A., Lopez, H., Sanders, M., Sposato, E., Baade, C., Manora, S., Coradin, J.H., 2011. Product design in price-competitive markets: a case study of a skin moisturizing lotion. AIChE Journal 57 (1), 160e177. Baltas, G., Freeman, J., 2001. Hedonic price methods and the structure of high-technology industrial markets: an empirical analysis. Industrial Marketing Management 30, 599e607. Barbaro, A.F., Bagajewicz, M., 2004. Managing financial risk in planning under uncertainty. AIChE Journal 50 (5), 963e989. Cooper, R.G., 2001. Winning at New Products: Accelerating the Process from Idea to Finish, third ed. Perseus Publ., Cambridge, Mass. Cooper, R.G., 2002. Product Leadership: Creating and Launching Superior New Products. Perseus Publ., Cambridge, Mass. Cooper, R.G., 2005. Product Leadership: Creating and Launching Superior New Products, second ed. Basic Books, Cambridge, Mass. Costa, R., Moggridge, G.D., Saraiva, P., April 2006a. Chemical product engineering: a future paradigm. CEP 10e13. Costa, R., Moggridge, G.D., Saraiva, P., 2006b. Chemical product engineering: an emerging paradigm within chemical engineering. AIChE Journal 52 (6), 1976e1986. Cussler, E.L., November, 2003. Chemical product design and engineering. (plenary talk). In: AIChE Annual Conference. San Francisco, Paper 430a. Cussler, E.L., Moggridge, G.D., 2001. Chemical Product Design. Cambridge University Press. Heflin, L., Walsh, S., Bagajewicz, M., 2009. Design of medical diagnostics products: a case-study of a saliva diagnosis kit. Computers and Chemical Engineering 33 (5), 1067e1076. Hill, M., 2004. Product and process design for structured products. AIChE Journal 8 (50), 1656e1661. Joback, K., Stephanopoulos, G., 1995. Searching spaces of discrete solutions: the design of molecules possessing desired physical properties. Advances in Chemical Engineering 21, 257e311.

Stage-Gate Procedures Chapter j 2 Linehan, S., Nizami, S.N., Bagajewicz, M., 2001. Design of monitoring instruments for wine fermentation using microeconomics and consumer preferences. Chemical Engineering Communications 198 (2), 255e272 (2011). Ng, K., Gani, R., Dahm-Johansen, K., 2006. Chemical Product Design: Towards a Perspective Through Case Studies. In: Computer Aided Chemical Engineering Series, vol. 23. Elsevier. Samuelson, P., 1938. A note on the pure theory of consumers’ behaviour. Economica 5 (17), 61e71. Seider, W.D., Seader, J.D., Lewin, D.R., 2004. Product and Process Design Principles. John Wiley, New York. Siddhaye, S., Camarda, K.V., Topp, E., Southard, M.Z., 2000. Design of novel pharmaceutical products via combinatorial optimization. Computers and Chemical Engineering 24, 701e704. Siddhaye, S., Camarda, K.V., Southard, M.Z., Topp, E., 2004. Pharmaceutical product design using combinatorial optimization. Computers and Chemical Engineering 28, 425e434. Stephanopoulos, G., November 2003. Invention and innovation in a product-centered chemical industry: general trends and a case study. In: AIChE Conference. 55th Institute Lecture. San Francisco. Street, C., Woody, J., Ardila, J., Bagajewicz, M., 2008. Product design: a case study of slow release carpet deodorizers/disinfectants. Industrial and Engineering Chemistry Research 47 (4), 1192e1200. Whitnack, C., Heller, A., Frow, M.T., Kerr, S., Bagajewicz, M., 2009. Financial risk management in the design of products under uncertainty. Computers and Chemical Engineering 33 (No 5), 1056e1066. Wibowo, C., Ng, K.M., 2001. Product-oriented process synthesis and development: creams and pastes. AIChE Journal 47 (12), 2746e2767. Westerberg, A.W., Subrahmanian, E., 2000. Product design. Computers and Chemical Engineering 24, 959e966.

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Chapter 3

VPPD-Lab: The Chemical Product Simulator S. Kalakul,* S. Cignitti,* L. Zhangx and R. Gani*, 1

*Technical University of Denmark, Kongens Lyngby, Denmark; xHong Kong University of Science and Technology, Hong Kong, China 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION Product design and development has become a key topic in the development of chemical engineering as a profession since chemical industries have entered into the era of increasing focus on high value-added products, green chemistry, and producteprocess sustainability (Hill et al., 2014). In chemical product design and development, it is not only important to find the chemical product that exhibits certain desirable properties and find the way to manufacture it, but improving product performance and making products more versatile have received increased attention in this decade. The design process for chemical products involves several steps, which may be incorporated in design methods that are applied for specific product design problems. Moggridge and Cussler (2000) proposed chemical product design as being comprised of four essential steps: (1) identification of consumer needs that should be met by the product, (2) generation of ideas that can satisfy the needs, (3) selection of the most promising product idea, and (4) development of a process to manufacture the desired product. While it is not stated how these steps should be performed, for steps 2 and 3, use of experiment-based trial and error approaches is common. For step 4, which is regarded as the process design problem, use of a wide range of methods and tools is already possible now. However, it is now generally accepted that application of computer-aided model-based methodologies helps to design/ improve products to reach the market faster by reducing some costly and timeconsuming experiments (Gani, 2004) and by employing valuable resources related to experiments only during the final (verification) stage. The initial design analysis of a chemical product design problem identifies product needs and translates them into physical and chemical property targets Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00003-4 Copyright © 2016 Elsevier B.V. All rights reserved.

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(for example, the product must be emulsified in water or must be miscible with oils). These targets are used to generate and evaluate chemical product candidates that may have different molecular structures, compositions, and/or forms, which also influence the selection of the processing operations for their production (such as the liquid compounds must be mixed with emulsifier at high speed or various additives must be blended into a product). In addition, in order to evaluate the sustainability of the designed product process, economic, environmental, health, and safety analyses must be performed. With the availability of validated and predictive models, all these steps may be performed through model-based computer-aided techniques. Recent efforts have focused on the development of computer-aided modelbased methodologies that are able to handle a large range of chemical product design problems. The concept of computer-aided molecular design (CAMD) has been extended to design polymers (Satyanarayana et al., 2009), solvents for separation (Hostrup et al., 1999; Chemmangattuvalappil et al., 2010), solvents for organic synthesis (Folic et al., 2008), and many more. Conte et al. (2011a,b) developed a systematic model-based methodology for the design of homogeneous formulated products, which has been adapted and extended by Yunus et al. (2014) for blend design and Mattei et al. (2014) for the design of emulsified products. Cignitti et al. (2015) and Zhang et al. (2015) utilized a mathematical programming approach for the design of novel pure, mixed, and blended products. The main feature for these methods and tools is that building blockebased methods are used to represent the molecular structures, and their contributions are used to model (estimate) the target properties. However, in order to cover a wider range of chemical-based products, there is a need for more data, property models, and a multidisciplinary approach because of the nature of many of these product design and evaluation problems. This is a challenging task requiring data acquisition, data testing, model development, and multiscale modeling that needs to be integrated within a product design framework. The objective of the framework is to provide the architecture through which various computer aided methods, tools, and data may be employed to design, analyze, and verify chemicals based products in a fast, efficient, reliable, and systematic manner. The architecture of the framework, which also becomes the basis for its implementation in the VPPD-Lab product design software (Kalakul et al., 2015), is presented in this chapter.

2. SYSTEMATIC FRAMEWORK FOR CHEMICAL PRODUCT DESIGN A versatile chemical product software would need a reasonably large knowledge base of data to design/analyze chemical products, such as solvents, microcapsule devices, fuel blends, homogeneous liquid products, and emulsified products; a large collection of models, such as property prediction models and product behavior models (controlled release models, mixing models, etc.); product design algorithms, such as methods for formulation

VPPD-Lab: The Chemical Product Simulator Chapter j 3

design, molecule design, and polymer design; and other tools, such as property prediction software, model generation software, process flow sheet design software, etc.). The data, methods, and tools need to be organized through a framework for efficient management of the complexity. The developed systematic framework (architecture) for implementation into the product design simulator (VPPD-Lab) is shown in Fig. 3.1, where it can be seen that the framework, and therefore VPPD-Lab, handles four main product design related problems (modules). Each module is characterized by its options, algorithms, and tools, thus allowing the needed workflow and data flow and associated with a specific product design task to be established. The framework allows the use of a suite of tools, such as: 1. property toolbox (see Fig. 3.2) 2. template generator toolbox 3. experiment toolbox for product verification and guidelines for design of experiments Furthermore, the framework allows the link and integration with other tools, such as: l

l l l

l l

modeling tools: ModDev (model development algorithms); ModTem (model template algorithms); MoT (modeling toolbox); ProCAMD (CAMD tool); Opt-CAMD (Optimal Computer-aided Molecular Design); SolventPro (special tool for solvent selection and design for various solvent-based applications); ProPred (pure compound property prediction tool); TML (thermodynamic model parameter estimation tool).

Property toolbox is the main recurrent toolbox within the framework (see Fig. 3.2), as different parts of it are needed by other tools. It consists of: 1. database: property data for a very wide range of chemicals found in different databases classified in terms of use in chemical products; the database also has a search engine with forward and backward search options; 2. property models: employs a library of property models (pure compound, mixture and phase equilibriumerelated properties) with associated model parameters that are linked to property prediction tools (such as, ProPred for pure compounds, TML for thermodynamic calculations, lipids toolbox for lipids pure and mixture properties, and a general property prediction toolbox covering a wide range of properties); 3. property prediction: employs a collection of property calculation algorithms for the needed properties (such as phase equilibrium, solvent selectivity, liquid mixture stability); and 4. consistency tests: checks the consistency of retrieved data from the database and/or predicted data through property models.

63

64 SECTION j I Basic Concepts and General Tools FIGURE 3.1 Architecture (framework) of the VPPD-Lab software. AI, Active ingredients; MoT, modeling toolbox; TML, thermodynamic model parameter estimation tool.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

FIGURE 3.2 Architecture of property toolbox in VPPD-Lab. AI, Active ingredient; TML, thermodynamic model parameter estimation tool.

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FIGURE 3.3 Template structure.

Each product design module within the framework employs a specific design template that provides the corresponding product design/evaluation workflow, the associated data flow, tools, models, and calculation algorithms. The structure of the template is shown in Fig. 3.3. Each step in the template is incorporated with auxiliary tools. Knowledge base stores information about product design needs, target properties, molecular structural constraints, list of experiments for verification, and many more. Property toolbox employs databases for different classes of compounds, property models (pure and mixture), product performance models, process models that are related to a specific product design/evaluation problem, etc.

2.1 Modeling Module This module is designed for generation, analysis, and validation of new models for product design and evaluation tasks that cannot be handled with those currently available in the models library. Examples of each option are shown in Fig. 3.4. Through the use of computer-aided tools (MoT, ModDev, and/or ModTem), it is possible to quickly create, validate, and add to the new models to the model library. MoT is used when the model equations are known and the model needs to be added to the model library and also to estimate the model parameters through data regression; ModDev is used to create the new model and save it as a MoT file; ModTem is used for model reuse, that is, take an existing model and modify it to match the objectives of the new model.

2.2 Product Design Module As highlighted through the generic workflow in Fig. 3.5, this module has options to design a wide range of chemical product types, as classified by Gani and Ng (2015): (1) single molecules, (2) formulations, (3) emulsions, (4) blends, and (5) devices. Each option consists of a number of problem specific

VPPD-Lab: The Chemical Product Simulator Chapter j 3

FIGURE 3.4 Modeling module.

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FIGURE 3.5 Product design module.

templates (methodologies) together with their corresponding database, solvers, product design algorithms, and analysis tools.

2.2.1 Molecular Design and Blend Design The design problems for these single molecule products are typically formulated by giving the specifications (properties) of the desired product (chemical) and solved by determining the molecular structures of the chemicals that satisfy the specifications, or by determining the mixtures (blends) that satisfy the desired product specifications. Blends are considered if single molecules are unable to satisfy all the desired product specifications (Gani, 2004). Common examples of single molecule products are solvents, ingredients, and refrigerants where the size and complexity of the design problem depends on the size and structure of the molecular product. Different options may be used to solve these problems: l

Database search: for small molecules such as solvents and refrigerants, using the database search template can help to find the molecular structures that match the desired target properties (See Fig. 3.5).

VPPD-Lab: The Chemical Product Simulator Chapter j 3

l

l

l

Generate-and-test approach: ProCAMD employs this approach (Harper and Gani, 2000). Solvent design template using SolventPro: several options that solve specific solvent selectionedesigneevaluation problems are available through this option, for example, solvent-based separations, solvents for organic synthesis, solvents for pharmaceutical applications, and ionic liquids selection and design as solvents (Mitrofanov et al., 2012). Mathematical programming approach: product design problem is formulated as a mixed integer linear and/or nonlinear programming problem and solved with an appropriate numerical solver. The template is able to generate novel pure, mixed, and blended chemical products (Yunus et al., 2014). In addition, process models can be integrated for the simultaneous solution of producteprocess problems. Through the template, needs and target properties are defined and translated to formulate as the mixed-integer nonlinear programming problems that include molecular structure constraints, property constraints, and process constraints. It employs optimization solvers to solve and obtain optimal product designs for the specified design problem (Cignitti et al., 2015; Zhang et al., 2015). The design templates follow the generic workflow, as shown in Fig. 3.6. Step 1: Problem definition The producteprocess design problem is defined through the definition of needs and their translation to target properties for the desired products. Step 2: Problem formulation The computer-aided product design problem is formulated through molecular structural constraints, mixture constraints, target property constraints, and process constraints. Here, knowledge base, property models, thermodynamic models, and process models are also available, if needed.

FIGURE 3.6 Generic workflow for molecular design and blend design.

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Step 3: Problem solution The design problem is formulated as a mathematical programming problem, which is usually of the mixed integer nonlinear programming (MINLP) type. Different solution strategies are available to solve the design problem, such as database search, generate-test approach (first generate candidates that satisfy the constraints and then order the feasible candidates in terms of their objective function values), simultaneous solution approach (use an appropriate optimization algorithm to solve the MINLP problem), and decomposition approach (decompose the main problem into subproblems and solve these subproblems according to a predefined solution order). Note that it is possible to consider economic, environmental, and sustainability issues through the addition of appropriate models. Step 4: Model-based verification/experimental verification In this step, each feasible product design is verified either through rigorous model-based tests or experimental tests suggested by the design of experiment toolbox. In this step, the stability of the product, the desired performance, the target properties, the color, the smell, etc., are verified.

2.2.2 Formulation Design Formulations are the products where different chemicals are mixed to obtain a desired set of target properties. They usually contain active ingredients (AIs) that provide the main function of the product, solvents that help to dissolve and/or deliver the AIs, and additives to improve the final product qualities, that is, enhance the end use properties of the product. Through a template implemented in the framework, it is possible to perform systematic design/verification of liquid formulated products such as insect repellent lotion, paint formulation, hairspray, and sunscreen. The template employs formulation the design methodology of Conte et al. (2011a,b), as shown in Fig. 3.7.

FIGURE 3.7 Generic workflow for formulation design. AIs, Active ingredients.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

Step 1: Problem definition The consumer needs are defined, which are then translated into target properties based on a formulation knowledge base. The formulation knowledge base stores product functions (needs) and their target properties based on common sense, literature data, and empirical rules suggested by experts. Step 2: AIs identification AIs database is searched to identify the most suitable AIs with respect to the main functions of the product. Step-3: Solvent mixture design Solvent mixture candidates (binary, ternar and multicomponent mixtures) are generated and screened to find the feasible candidates matching the predefined target properties. In this step, a linear programming problem is first solved to identify the solvent mixture candidates subject to linear target property constraints. The feasible mixtures and their compositions then are used to calculate nonlinear properties. Finally, a test for liquid phase stability of the feasible mixtures that satisfied all linear and nonlinear target properties is made to identify the set of feasible solvent mixtures. Information about the stability of a liquid mixture is obtained from the calculated Gibbs energy of mixing (DG/RT), and from its first and second derivatives. Step 4: Additive identification After the optimal solvent mixture is identified, the additive(s) are added in order to enhance the end use properties of the products, such as perfumes, moisturizing agents, and color and neutralizing agents. Step 5: Experimental verification The experimental toolbox in the framework suggests a list of experimental validation tests that need to be performed to determine the physicochemical properties of the various pure compounds and/or mixtures, and to test the formulation end use properties with respect to specific formulated products. Once the experimental validation is done, if the results do not match with the a priori defined target property constraints, step 2 to step 4 are repeated until all target properties are satisfied. A more practical option is to simply fine-tune (change the compositions of the additives or add a new additive) the formulation formula until all the specific constraints are satisfied.

2.2.3 Emulsion Design An emulsion is defined as a mixture of two or more liquids that are normally immiscible. It has suspension forms where insoluble chemicals disperse in the liquid with the help of a dispersant. Within the framework, the option for emulsions allows design of products, such as sunscreen lotion and liquid handwash detergent, where the solid constituents are emulsified through

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FIGURE 3.8 Generic workflow for emulsion design.

emulsifiers together with solvents and additives. The workflow is adopted from formulation design with additional new property models, databases, and knowledge base (Mattei et al., 2014). The design template follows the generic workflow, as shown in Fig. 3.8. Step 1: Problem definition The consumer main needs and secondary needs are converted into target properties using the emulsion knowledge base. The main needs are responsible for the product main functions (such as the protection from sunburns and UV radiations, which are the main needs for a sunscreen lotion), while the other consumer needs are classified as secondary needs. Step 2: AIs identification Chemical candidates for AIs are screened through rule-based selection criteria, based on databases, where the relevant properties, if not available, are predicted through dedicated pure compound property models. For the emulsion design problem, surfactants and co-emulsifiers are selected as active ingredients since they act simultaneously as emulsifiers and enhance the stability of the final emulsion, respectively. Step 3: Solvent mixture design The design of the solvents and of the emulsifiers, driven by selection criteria based on the functional properties of the chemicals as well as consideration of effectiveness, safety, toxicity, and cost, is done through a data modelebased CAMD technique. Once all the ingredients have been chosen, the recipe candidates are identified through a knowledge-based mixture design method, where economic considerations are included together with appropriate boundaries related to solubility, stability, toxicity, and safety issues.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

Step 4: Additive identification Additives are defined in this work as those chemicals responsible for the satisfaction of the secondary needs. A rule-base selection is applied based on the emulsion knowledge base and databases. Step 5: Composition calculation Once all appropriate ingredients have been chosen, the composition calculator is used to determine the overall composition of the product. In this step, the solubility of the different ingredients in the two solvents is quantified with UNIFAC-based (Universal quasichemical Functional-group Activity Coefficients) calculations. The a priori defined target property constraints are considered. The knowledge base is used to set feasible composition ranges of ingredients since some of them are known to be effective only in a certain range of compositions. Finally, the emulsified product is determined by minimizing the total cost. Step 6: Experimental verification Same as in step 5 of formulation design.

2.2.4 Device Design Examples of device products are fuel cells, microcapsules, a hemodialysis device, and many more. The basis of the design is to determine the device forms and constituent materials through which the desired product performances are satisfied. The challenging tasks are how to translate needs to product material properties and how constituent materials are configured since engineering science knowledge for many devices is not available. Therefore, using the knowledge base is very useful to store the information of each type of devices. The information can be product key ingredients, product structures, ingredient’s property models, and physicochemical phenomena models with respect to desired product performances. Device template employs a combination of different computational tools integrated within the framework: modeling tools, molecular and mixture design tool, and solvent selection tool to design various types of device products. Thus, multiscale modeling features and device design algorithms are included within the template, as illustrated in Fig. 3.9 (Morales-Rodriguez and Gani, 2009). Step 1: Problem definition In this step, the type of device, product performance specifications or functions, the product structure, key ingredients, and main compositions, as well as physicochemical phenomena models with respect to desired product performances are specified. For example, the type of a device can be microcapsule-controlled release of pharma products. Within the device knowledge base, the function of the product to keep an effective level of drug in the body for a specific period of time, and thereby side effects generated by drug overdosing and/or underdosing may be avoided. The product structure (see Fig. 3.10) contains: (1) AIs, which are drug

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FIGURE 3.9 Generic workflow for device design.

FIGURE 3.10 Schematic representation of a microcapsule (Morales-Rodriguez et al., 2011).

molecules such as antibodies, antioxidants, or probiotics that are placed in the core of the device; (2) donor medium which is a solvent that dissolve AIs; (3) microcapsule wall (for example, a polymer membrane) that encapsulate AIs and the solvent; and (4) release medium, which depends on the application field (for example, blood or some other medium found within the human body). Finally, the list of product phenomena/performance models, variables, and parameters for the mass transfer (by diffusion) calculation of the AI through the wall are retrieved from the databases, depending on classes of ingredients. Step 2: Calculation of primary and secondary properties Once the necessary variables are retrieved from the databases, if there are some missing primary or functional properties, property toolbox is employed to fill the gap.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

FIGURE 3.11 Comparison between the experimental values and models predictions of the release of codeine (AI) (Morales-Rodriguez et al., 2011).

Step 3: Calculation of product performances In this step, a simulation of product performances is performed. For example, if the product is a microcapsule for controlled release, the diffusion mass transfer phenomena in the micro-scale and the microcapsule-based controlled release in the meso-scale are performed. Meso-scale calculations involve number of microcapsule sizes, number of particles, and surface area of the microcapsule to name a few. This information is used in the micro-scale to calculate the mass of released AIs. Within the released mass of AIs, the calculation of the total amount released to the receiver medium as well as the percent of the AI released from the microcapsules can be calculated. Step 4: Experimental verification After product performances are calculated, the product is tested to verify if it satisfies the specifications. The calculation of the total amount released to the receiver medium of AI is compared with the experimental results (see Fig. 3.11). The three scenarios use different polymer wall thickness values (scenario 1 < scenario 2 < scenario 3).

2.3 Product Analysis This option is used for a known product whose properties and/or performance need to be tested and/or verified. Therefore, the methods and tools used here are the same as the ones used for the model-based verification step in the generic workflow to design single molecules and blends as well as calculations

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in the product performance step in the device design workflow. The property toolbox (see Fig. 3.2) is employed.

2.4 New Product Template The template generator (see Fig. 3.2) helps the user to create user templates for a new product design or product evaluation by giving the user freedom to modify an available template to match the needs of the user specific problems, or the user can follow the generic workflow for product design to create a new template where different models and/or data may be used.

3. VPPD-LAB SOFTWARE IMPLEMENTATION The systematic framework for chemical product design allows the user to solve the problems covering a wide range of problems in an easy and efficient manner. However, it requires a number of computational tools and methods that come from different sources and disciplines. Thus, an important issue is how they can be used simultaneously and efficiently for product designeanalysis. Therefore, the architecture (framework) presented in Section 2 has been implemented into the VPPD-Lab software. VPPD-Lab has the necessary feature for integration and merging of methods and tools from different sources. Through the use of COMObjects (Component Object Model), reusable pieces of code and data in binary form that is plugged to other software components from other sources with relatively little effort. Therefore, the software is able to accommodate models used for the prediction of the product property/behavior using modeling and related tools, which provide interactions with modeling engines, numerical solvers, and external software. It has an interface to identify templates (workflow) to guide users through the appropriate designeanalysis steps. A special product design ontology has been developed for knowledge representation. The knowledge within each product designeanalysis template is structured in terms of product needs, their translation into properties, the corresponding property/product performance models, and a wide range of data from different sources. This way, it provides a means to apply systematic framework for chemical product design for a large range of problems. In the same way as a typical process simulator, VPPD-Lab can be routinely used to systematically, efficiently, and robustly solve various types of product designeanalysis problems. A screen shot of the main VPPD-Lab interface is shown in Fig. 3.12. It can be noted that the same modules of the framework highlighted in Fig. 3.1 are available in this software. Available templates, options, and integrated tools corresponding to different product design-analysis scenarios are shown in the VPPD-Lab main user interface (see Fig. 3.12). In the modeling module, the modeling template is applied to generate/ develop models to study product the behavior of products, such as products

VPPD-Lab: The Chemical Product Simulator Chapter j 3

FIGURE 3.12 VPPD-Lab main user interface.

from oxidation of unsaturated fatty acid, crystallization models (Fedorova et al., 2015), and the spraying process of a fragrance product (Heitzig et al., 2011). The integrated software does not require the user to know any programming knowledge or language because the user interface systematically guides the user through the steps of the workflow. Generated mathematical models are translated into model objects and solved by through MoT. Furthermore, the created templates are combined or modified using ModTem (Fedorova et al., 2015). In the product design module, various product design problems are solved using templates available within the software. For molecular design, Mitrofanov et al. (2012) used a solvent selection template in SolventPro to design solvent mixture for pharmaceutical products. Gani et al. (2005) used the ProCAMD template to generate feasible solvent candidates and evaluate their target properties to find the most promising solvents. More details of molecular design problems, for example, for refrigerant design and lubricant design can be found in Cignitti et al. (2015) and Zhang et al. (2015) and for polymer design can be found in Sayanarayana et al. (2009). Blend design templates have be used for the design of gasoline blends, diesel blends, lubricant blends (Yunus et al., 2014), and for jet fuel blends (Kalakul et al., 2015). Formulation

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templates have been used for the design of an insect repellent lotion, paint formulation, hairspray, and sunscreen lotion (Conte et al., 2011a,b) have been solved using the formulation template. For emulsion design, such as cleaning detergent, handwash detergent (Mattei et al., 2014), and for device design (Morales-Rodriguez and Gani, 2009), the emulsion template needs to be used. In the product analysis module, various property prediction and product behavior/performance models have been implemented into the product analysis template, for example, models for pure compound and mixture property calculations, stability check of mixtures, uptake of AIs, control release of AI, and solvent evaporation rate calculations are available in the software. In the new product template module, the template generator is used to modify an existing module. For example, the blend template can be modified for diesel blend design and jet fuel blend design (Kalakul et al., 2015).

4. VPPD-LAB APPLICATION EXAMPLES In this chapter, the application of the product analysis module is highlighted with: l

stability check of solvent mixtures

The application of the product design module is highlighted with three case studies, involving: l l l

design of a lubricant blend (using GAMS-based tool template) design of a jet fuel blend (using blend template) design of an insect repellent lotion (using formulation template) Many more application examples can be found in Table 3.1.

4.1 Stability Check of Solvent Mixtures The objective of this case study is to create a list of binary solventemixture candidates that are water-soluble using solvents present in the database. The solvent mixture design template in the property toolbox is used. The objective of this case study is to find all miscible binary blends between water-soluble alcohols present in the solvents database. Liquid miscibility of all the binary mixtures of the selected solvents from the databases is verified. Solvent mixture design algorithm (Conte et al., 2011a,b) is launched, giving all the possible binary combinations between the water-soluble alcohols, as shown in Fig. 3.13. In a similar way, blends of solvents that are not soluble in water or binary mixtures of chemicals that form azeotropes, etc., can also be found. Additionally, mixture properties, such as density, viscosity, etc., may also be specified as target properties.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

TABLE 3.1 Product Design and Analysis Problems Solved Through VPPD-Lab Product Design Problem

Product

References

Solvent substitutes for separation of acetic acid from water, solvente antisolvent design for ibuprofen, prediction of multicomponent diffusion, solvent replacement for multistep organic synthesis, polymers, and refrigerants

Hostrup et al. (1999), Karunanithi et al. (2004, 2006), Bardow et al. (2008), Mitrofanov et al. (2012), Harper and Gani (2000), Gani et al. (2005), Satyanarayana et al. (2009), Cignitti et al. (2015), and Churi and Achenie (1997)

Blend design

Gasolines, lubricants, diesels, and jet fuels

Yunus et al. (2012, 2013), Phoon et al. (2015), and Kalakul et al. (2015)

Formulation design

Insect repellent lotion, sunscreen lotion, paint formulation, and skincare cream

Cheng et al. (2009), Conte et al. (2011a,b), and Conte et al. (2012)

Emulsion design

Tank cleaning detergent and handwash detergent

Mattei et al. (2013, 2014)

Device design

Direct methanol fuel cell, uptake of pesticides from water droplets to leaves, microcapsule controlled release of active ingredients

Morales-Rodriguez and Gani, 2009, Morales-Rodriguez, 2011 and Teixeira et al. (2012)

Product analysis l Product separation l Miscibility calculation l Phase equilibria calculation

Acetone/chloroform separation, lipids separation, ionic liquids separation, solvents separation, solvent stability tests, vapor-liquid equilibrium (VLE)/solidliquid equilibrium (SLE)/ liquid-liquid equilibrium (LLE) calculations

Hostrup et al. (1999) and Cunico et al. (2013, 2015)

Molecular design l Solvent mixture design l Chemical replacement l Polymer design l Refrigerant design

4.2 Design of a Lubricant Blend The objective of this case study is to find a lubricant blend for engine lubricants, which is the most common use of lubricants. Engine oils accounts for

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FIGURE 3.13 Results of stability check.

approximately 57% of lubricants used in the world, and 28% is used in passenger cars, for example, engines running on gasoline. Engine lubricants are used to lubricate compounds of an internal combustion engine, such as gasoline and diesel engines. Engine lubricants perform in an open atmosphere where it is highly oxidative and exposed to the combustion process in the internal engine. First a lubricant base oil design problem is developed and solved using the mathematical programming based template from the workflow (see Fig. 3.6). Step 1: Problem definition Input: Product type is lubricants Tools: Mathematical programming template (Fig. 3.6) and knowledge base of lubricant design Output: Product needs, target properties, and their constraints In this step, the product needs with respect to the selected type of product are retrieved from the knowledge base. The needs for blended products are primarily determined from the principal product function, which is the main reason for the products to be sold. A knowledge base, literature search, and legislation details are used to determine the product needs in this case study. The needs for base oil are defined using the knowledge base. The main function of a lubricant base oil is to lubricate and prevent wear between two moving surfaces. In addition, it must be able to resist a high temperature, flow continuously at a low temperature, and must be nonflammable. Besides, the density of base oils is considered for handling purposes. Once all needs are defined, the developed knowledge base for lubricants is used to transform the product needs into target properties. The translated properties and properties constraints are given in Table 3.2.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

TABLE 3.2 Base Oil Needs, Target Properties, and Target Values Need

Unit

Target Value

Viscosity, 100 C

cSt

n > 4.12

Friction coefficient

e

0.001 < mtot < 0.9

Ability to flow at the ambient temperature

Normal melting point

K

Tm < 293.15

Nonflammable

Flash point

K

Ability to lubricate and prevent wear

Property 

Tf > 493.15

Handling purpose

Density

g/cm

0.80 < r < 0.90

Heavy compound

Molecular weight

g/mol

Mw > 150

Not easily vaporized

Normal boiling point

K

Tb > 303.15

3

The lubricant base oil design is a mixture/blend design problem. In the molecule design problem, functional groups (building blocks) are the elements of the design problem through which the molecule is formed. However, in the mixture/blend design problem, molecules are the elements of the design problem through which mixture/blend is formulated. Thus, a candidate molecule database is needed before the blend design problem can be solved. For the sake of this case study, the molecules from esters, paraffins, iso-paraffins, and naphthenes database are selected. Step 2: Problem formulation Input: List of target properties and their constraints from step 1 Tools: CAMD tools Output: Set of lubricant candidates, objective function, property constraints and equations, process/process model equations 1. CAMD formulation: a set of lubricant candidates is generated using Opt-CAMD and ProCAMD with input data in Table 3.2. The BARON solver in GAMS is used to screen all feasible solutions. One-hundred seventy-seven compounds have been generated. In addition, the stability analysis is based on the trend of the Gibbs energy function of mixing (DGmix/RT) and its first and second derivatives as a function of composition (Conte et al., 2011a,b). All binary pairs in the database are tested in the full categories of the composition. In this case study, all mixtures are totally miscible. 2. Pure compound property model selection: pure compound property models are retrieved from the property model library employed in the property toolbox. The melting point (Tm), flash point (Tf), and total solubility parameter (dT) are estimated using Constantinou and Gani group

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contribution method (Constantinou and Gani, 1994). The kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with the fluid mass density (n ¼ m/r). The absolute viscosity is calculated using Joback and Reid group contribution method (Joback and Reid, 1987), and the liquid density is predicted using modified Rackett correlation (O’Connell et al., 2000). The estimation of friction coefficient is obtained from Bongaerts et al. (2007). 3. Mixture property model selection: the mixture property models are applied in product design to estimate the product’s performance. The models used in this case study are collected from a literature survey. Density: X r¼ x i ri (3.1) i

Kinematic viscosity ln n ¼

X

xi ln ni

(3.2)

i

Pour point 

PP 1000

Flash point ðln Tf  2:6287Þ2 exp  0:91725

12:5 ¼

! ¼

X  Tm;i 12:5 xi 1000 i

X i



ln Tf;i  2:6287 xi exp  0:91725

(3.3)

2 ! (3.4)

Step 3: Problem solution Input: Set of lubricant candidates, objective function, property constraints and equations, process/process model equations Tools: Solvers such as GAMS, MATLAB, etc. Output: List of promising candidates An optimization problem is formulated in this step. Based on consumer’s needs and the target property values, objective function, property constraints, and other relevant constraints are established in this step. The MINLP model for the lubricant base oil design is shown in the following equations, where bi is a binary variable indicates the selection of molecules in the database, and xi is the volume fraction of molecule i. ! X xi ln ni maxn ¼ exp (3.5) i

s.t.

X i

xi ¼ 1

(3.6)

VPPD-Lab: The Chemical Product Simulator Chapter j 3

0  xi  bi ci X bi  5 2 X

(3.7) (3.8)

i

xi ln ni  expð4:12Þ

(3.9)

i

0:001  mtot  0:9     X Tm;i 12:5 293:15 12:5 xi  1000 1000 i X 0:8  xi ri  0:9

(3.10) (3.11) (3.12)

i

ðln 493:15  2:6287Þ2 exp  0:91725

! 

X i



ln Tf;i  2:6287 xi exp  0:91725

2 !

(3.13) bi ˛f0; 1g;

0  xi  1;

ci

(3.14)

Eq. (3.5) is the objective function where the objective is to maximize the kinematic viscosity. Eq. (3.6) restricts the weight fraction of the compounds in the product. In Eq. (3.7), if molecule i is selected, the upper bound of the weight fraction xi is one; otherwise, the upper bound of the weight fraction is zero. The number of selected molecules should be between 2 and 5 as shown in Eq. (3.8). The upper and lower bounds of the target properties are shown in Eqs. (3.9)e(3.14). This optimization problem is solved using GAMS BARON solver. The results of the MINLP optimization model are shown in Table 3.3. Step 4: Model-based verification/experimental verification Input: List of promising candidates from step 3 Tools: Property toolbox and experiment toolbox Output: A set of promising candidates and property values calculated by rigorous property models and a set of experimental tests for product design verification This task (step 4) has not been performed because all the blends are ideal mixtures. In principle, the linear mixing rule gives acceptable prediction of the ideal mixtures. The experimental toolbox suggests measuring viscosity, flash point, and pour point of the optimal blend for final verification.

4.3 Design of a Jet Fuel Blend The objective of this case study is to minimize the conventional jet fuel by adding new additives that can help to improve jet fuel properties. A surrogate

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TABLE 3.3 Optimization Results of Lubricant Base Oil Design Ethyl Palmitate

1H-Dibenzo[a,i]fluorene, eicosahydro-

Groups

2 CH3, 15 CH2, 1 COO

13 CH2cyc, 8 CHcyc

xi

0.4453

0.5547

Index Chemical structure

n (cSt)

5.06739

r (g/cm )

0.89611

PP (K)

287.96

Tf (K)

493.15

Friction coefficient (mtot)

0.00138

3

conventional A1 jet fuel model is chosen to be a main ingredient (MI) (Agosta et al., 2004). The aim of this case study is to design a blend containing the selected MI and additives to obtain a tailor-made jet fuel that has properties better than the original MI. The jet fuel blend design problem is developed and solved using the blend design template from the workflow shown in Fig. 3.6. Step 1: Problem definition Input: Product type is the jet fuel Tools: Blend design template and blend design knowledge base Output: Target properties and their constraints The new formulation of jet fuel blends should have good fuel performance and meet or exceed stringent requirements for worldwide fuel handling and products standards, as listed in Table 3.4. Step 2: Problem formulation Input: List of target properties and their constraints from step 1 Tools: CAMD tools Output: Set of lubricant candidates, objective function, property constraints and equations, process/process model equations

VPPD-Lab: The Chemical Product Simulator Chapter j 3

TABLE 3.4 Product Needs and Their Target Property Constraints Need

Property

Unit

Target Value

Ability to be burned

Reid vapor pressure

kPa

RVP < 1

Flammability

Flash point

K

Tf > 311.15

Engine efficiency

Higher heating value

MJ/gal

HHV > 131.32

Density

kg/gallon

2.93 < r < 3.17

Kinematic viscosity at 20 C

cSt

V226.15 K), kinematic viscosity (>8 cSt), and elogLC50 (>4.726 mol/L). The remaining 50 additives generate 1225 alternatives at different compositions. Then, 473 of the mixtures are removed because they form immiscible blends. This miscibility test is needed to avoid phase separation in the engine. Subsequently, 8 alternatives are left, which are evaluated through mathematical programming (to find the optimal

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mixture compositions) with linear and/or nonlinear property constraints. The linear target property constraints are: HHV, V, CO2 emission, and logLC50, while the nonlinear constraints are RVP and r. Finally, the most promising ternary blends with the minimum conventional jet fuel composition are listed in Table 3.5 with target properties values. Blending MI (42% vol) with decane (26% vol) and 4-methylnonane (32% vol) helps to reduce to consumption of MI and help to improve properties (HHV and r). Furthermore, it reduces CO2 emission [3.2% compared to MI and 5.78% compared to average jet fuel (Inventory of US. Greenhouse Gas Emissions and Sinks: 1990e2005, 2007)] and toxicity (logLC50). Step 4: Model-based verification/experimental verification Input: List of promising candidates from step 3 Tools: Property toolbox and experiment toolbox Output: A set of promising candidates and property values calculated by rigorous property models and a set of experimental tests for product design verification Flash point (Tf) property model requires an iteration to obtain the flash point of the mixture; thus, it is only used for the blends from Step 3 that have been shortlisted (see Table 3.5). Therefore, Tf of all blends are higher than MI and satisfy aviation Jet A1 standards (Tf > 311.15K). Furthermore, experimental toolbox suggests experimental tests to verify V, r, RVP, distillation profiles, and jet fuel thermal oxidation tester (JFTOT) to ensure that the final blends meet the aviation fuel standards based on these properties.

4.4 Design of an Insect Repellent Lotion The objective is to design an insect repellent formulation for the European market (nontropical areas). The formulation template is developed and used under the workflow in Fig. 3.7 (Conte et al., 2011a,b). In this product design problem, the information flow in each design step is shown in VPPD-Lab layout. Step 1: Problem definition Input: Product type is insect repellent Tools: Formulation template and formulation knowledge base Output: User needs, target properties, and constraints In this step, the insect repellent is selected as a product type. The user needs for the insect repellent lotion are retrieved from the knowledge base and then translated into target properties and their constraints, as shown in Fig. 3.14. Step 2: AIs identification Input: Target properties values and constraints Tools: Knowledge base of product functions and property toolbox Output: Set of AIs and properties of AIs

ID

Composition (vol %)

RVP

HHV

r

V

CO2

logLC50

Tf

1

Main ingredient (MI)(41) 2,2-dimethyloctane(30) decane(29)

0.67

138.7

2.95

2.8

24.00

4.46

312

2

MI(42) decane(26) 4-methylnonane(32)

0.57

139.3

2.97

2.7

23.90

4.65

313.2

3

MI(42) decane(26) 5-methylnonane(32)

0.57

139.1

2.96

2.7

23.94

4.65

313.1

4

MI(41) decane(52) 2,7-dimethyloctane(6)

0.52

138.3

2.94

2.8

24.07

4.68

314.8

-

MI(100)

0.55

134.8

2.91

3.3

24.69

4.72

311.8

VPPD-Lab: The Chemical Product Simulator Chapter j 3

TABLE 3.5 Mixtures Matching the Target Properties and Their Estimated Property Values

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FIGURE 3.14 Product needs and their target property constraints of the insect repellent lotion.

An insect repellent lotion is usually constituted of the AI/AIs with the function of repelling mosquitoes. The knowledge base of product functions is used to generate a list of AI candidates with respect to the formulation product type. The list is screened based on the property constraints. In this case, the solubility parameter (HildSolPar) of AI should not less than 22.8  3 and not greater than 42.8  3 MPa0.5. Picaridin is selected because it satisfies all constraints. Furthermore, it has lowest toxicity and good material compatibility compared with others in the list (see Fig. 3.15). The properties of picaridin are retrieved from the database. The composition of AI is also suggested by the knowledge base using collected data. Step 3: Solvent mixture design Input: Target properties values, constraints, and solvent database choices Tools: Property toolbox and solvers Output: List of promising solvent mixtures Since alcohols and water can be potential solvent candidates, the databases: (1) alcoholewater soluble, (2) Alcoholewater insoluble, and (3) water are selected. The solvent mixture algorithm is then launched. The algorithm retrieves properties of solvent candidates from the property toolbox and then formulates and solves the product design problem based on the product property constraints. Results are summarized in Fig. 3.16. If the preferred performance index is the toxicity, the least toxic mixture is

VPPD-Lab: The Chemical Product Simulator Chapter j 3

FIGURE 3.15 AIs identification results.

FIGURE 3.16 Solvent mixture design results.

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water þ methanol. However, HildSolPa of methanol (29.3 MPa0.5) is greater than upper bound limit (21.1 < HildSolPa < 27.1 MPa0.5). Therefore, it has to be rejected. The most feasible mixture is water þ 2-propanol. Step 4: Additive identification Input: Target properties values and constraints Tools: Knowledge base and property toolbox Output: List of additives and qualities to be enhanced Aroma compounds can be added to give the formulation a pleasant scent. The preferred scent for the formula could be, for example, lavender. The property toolbox is used to calculate missing properties of the additive. The aroma list is screened with respect to the defined target property constraints. The additive should be alcohol soluble. Thus, the solubility of aroma compounds should be close to 2-propanol. Therefore, linalool is selected, as shown in Fig. 3.17. The composition of the selected aroma is provided by the knowledge base. Step 5: Experimental verification Input: List of the selected formulation Tools: Experiment toolbox Output: A set of experimental tests for product design verification The experimental toolbox lists the experiments that need to be performed to verify the designed formulation. The formulation template provides a summary of results together with the experimental verification list, as shown in Fig. 3.18.

FIGURE 3.17 Additive identification results.

VPPD-Lab: The Chemical Product Simulator Chapter j 3

FIGURE 3.18

Summary results and the experimental verification list.

5. CONCLUSION A computer-aided framework for design of chemical products has been developed and used as the architecture for the VPPD-Lab software. The model libraries, structured databases, and generic workflow are integrated through the product design ontology developed to represent the associated knowledge (Kalakul et al., 2015). The software is able to handle the complexity of product design and analysis problems, in terms of models, calculation algorithms, use of databases, and the various problem-specific solution strategies. The application of the product analysis template is highlighted through the stability check of solvent mixtures. The template has potential to screen feasible binary mixtures that are miscible. In addition, the application of the product design template is highlighted through case studies involving mixture/blend design of a jet fuel and a lubricant as blended liquid products and insect repellent lotion as a formulation product. The product design template is able to handle the large mixed-integer nonlinear problem formulated to design the three products. It helps to reduce the search space and provides promising chemical candidates that are competitive and environmentally feasible, making it more flexible and capable of solving a wide range of product design problems. Therefore, VPPD-Lab enhances the future development of chemical product design as huge amounts of data, models, knowledge, methodologies, and algorithms are integrated and managed in a systematic and efficient way, increasing the possibility to capture past experiences and provide better guidelines for future chemical products (Gani, 2004). However, despite the

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recent advances, with the currently available methods and tools, only a small percentage of chemical product design problems can be solved. Much work and concerted efforts are needed in the area of property modeling and their integration with data and design tools that incorporate data models in multidisciplinary solution approaches to cover a wider range of chemical-based products of significance.

REFERENCES Agosta, A., Cernansky, N.P., Miller, D.L., Faravelli, T., Ranzi, E., 2004. Reference components of jet fuels: kinetic modeling and experimental results. Experimental Thermal and Fluid Science 28, 701e708. Bardow, A., Kossack, S., Kriesten, E., Marquardt, W., 2008. MEXA goes CAMD d Computeraided molecular design for physical property model building. Computer Aided Chemical Engineering 25, 733e738. Bongaerts, J.H.H., Fourtouni, K., Stokes, J.R., 2007. Soft-tribology: lubrication in a compliant PDMS-PDMS contact. Tribology International 40, 1531e1542. Chemmangattuvalappil, N.G., Solvason, C.C., Bommareddy, S., Eden, M.R., 2010. Molecular signature descriptors for integrated flowsheet and molecular design. Computer Aided Chemical Engineering 28, 1267e1272. Cheng, Y.S., Lam, K.W., Ng, K.M., Ko, R.K.M.K., Wibowo, C., 2009. An integrative approach to product developmentda skin-care cream. Computers and Chemical Engineering 33, 1097e1113. Churi, N., Achenie, L.E.K., 1997. The optimal design of refrigerant mixtures for a two-evaporator refrigeration system. Computers and Chemical Engineering 21, 349e354. Cignitti, S., Zhang, L., Gani, R., 2015. Computer-aided framework for design of pure, mixed and blended products. Computer Aided Chemical Engineering 37, 2093e2098. Constantinou, L., Gani, R., 1994. New group contribution method for estimating properties of pure compounds. AIChE Journal 40, 1697e1710. Conte, E., Gani, R., Malik, T.I., 2011a. The virtual product-process design laboratory to manage the complexity in the verification of formulated products. Fluid Phase Equilibria 302, 294e304. Conte, E., Gani, R., Ng, K.M., 2011b. Design of formulated products: a systematic methodology. AIChE Journal 57, 2431e2449. Conte, E., Gani, R., Cheng, Y.S., Ng, K.M., 2012. Design of Formulated Products: Experimental Component. AIChE Journal 58, 173e189. Cunico, L.P., Damaceno, D.S., Falleiro, R.M.M., Sarup, B., Abildskov, J., Ceriani, R., Gani, R., 2015. Vapour liquid equilibria of monocaprylin plus palmitic acid or methyl stearate at P ¼ (1.20 and 2.50) kPa by using DSC technique. Journal of Chemical Thermodynamics 91, 108e115. Cunico, L.P., Hukkerikar, A.S., Ceriani, R., Sarup, B., Gani, R., 2013. Molecular structure-based methods of property prediction in application to lipids: a review and refinement. Fluid Phase Equilibria 357, 2e18. Fedorova, M., Sin, G., Gani, R., 2015. Computer-aided modelling template: concept and application. Computers and Chemical Engineering 83, 232e247. Folic, M., Gani, R., Jime´nez-Gonza´lez, C., Constable, D.J.C., 2008. Systematic selection of green solvents for organic reacting systems. Chinese Journal of Chemical Engineering 16 (3), 376e383.

VPPD-Lab: The Chemical Product Simulator Chapter j 3 Gani, R., 2004. Chemical product design: challenges and opportunities. Computers and Chemical Engineering 28, 2441e2457. Gani, R., Jimenez-Gonzalez, C., Constable, D.J.C., 2005. Method for selection of solvents for promotion of organic reactions. Computers and Chemical Engineering 29, 1661e1676. Gani, R., Ng, K.M., 2015. Product design e molecules, devices, functional products, and formulated products. Computers and Chemical Engineering 81, 70e79. Harper, P.M., Gani, R., 2000. A multi-step and multi-level approach for computer aided molecular design. Computers and Chemical Engineering 24, 677e683. Heitzig, M., Gregson, C., Sin, G., Gani, R., 2011. Application of computer-aided multi-scale modeling framework-Aerosol case study. Computer Aided Chemical Engineering 29, 16e20. Hill, M., Boone, K., Anwar, R., Gaumer, R.B., Camarda, K.V., 2014. The future of chemical engineering design: impact of faculty makeup and industrial needs. Computers and Chemical Engineering 34, 88e97. Hostrup, M., Harper, P.M., Gani, R., 1999. Design of environmentally benign processes: integration of solvent design and separation process synthesis. Computers and Chemical Engineering 23, 1395e1414. Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990 e 2005, 2007. EPA430-R-07-002, U.S. Environmental Protection Agency, Washington, United States of America.. Joback, K.G., Reid, R.C., 1987. Estimation of pure-component properties from group-contributions. Chemical Engineering Communication 57, 233e243. Kalakul, S., Hussain, R., Elbashir, N., Gani, R., 2015. VPPD Lab e the chemical product simulator. Computer Aided Chemical Engineering 37, 1415e1420. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2004. Optimal (solvent) mixture design through a decomposition based CAMD methodology. Computer Aided Chemical Engineering 18, 217e222. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2006. A computer-aided molecular design framework for crystallization solvent design. Chemical Engineering Science 61, 1247e1260. Mattei, M., Hill, M., Kontogeorgis, G.M., Gani, R., 2013. Design of an emulsion-based personal detergent through a model-based chemical product design methodology. Computers and Chemical Engineering 32, 817e822. Mattei, M., Kontogeorgis, G.M., Gani, R., 2014. A comprehensive framework for surfactant selection and design for emulsion based chemical product design. Fluid Phase Equilibria 362, 288e299. Mitrofanov, I., Sansonetti, S., Abildskov, J., Sin, G., Gani, R., 2012. The Solvent Selection framework: solvents for organic synthesis, separation processes and ionic liquids solvents. Computer Aided Chemical Engineering 30, 762e766. Moggridge, G.D., Cussler, E.L., 2000. An introduction to chemical product design. Chemical Engineering Research and Design 78, 5e11. Morales-Rodriguez, R., Singh, R., Cameron, I., Gani, R., 2011. Product and Process Modelling: A Case Study Approach. Elsevier, pp. 363e432. Morales-Rodriguez, R., Gani, R., 2009. Multiscale modelling framework for chemical productprocess design. Computer Aided Chemical Engineering 26, 495e500. O’Connell, J.P., Prausnitz, J.M., Poling, B.E., November 27, 2000. The Properties of Gases and Liquids, fifth ed. McGraw-Hill Education, New York, United States of America. Phoon, L.Y., Hashim, H., Mat, R., Mustaffa, A.A., 2015. Tailor-made green diesel blends design using a decomposition-based computer-aided approach. Computer Aided Chemical Engineering 37, 1085e1090.

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SECTION j I Basic Concepts and General Tools Satyanarayana, K.V., Abildskov, J., Gani, R., Tsolou, G., Mavrantzas, V.G., 2009. Multiscale modelling for computer aided polymer design. Computer Aided Chemical Engineering 27, 213e218. Sayanarayana, K.C., Abildskov, J., Gani, R., 2009. Computer-aided polymer design using group contribution plus property models. Computers and Chemical Engineering 33, 1004e1013. Teixeira, M.A., Rodriguez, O., Rogrigues, S., Martins, I., Rodrigues, A.E., 2012. A case study of product engineering: performance of microencapsulated perfumes on textile applications. AIChE Journal 58, 1939e1950. Yunus, N.A., Gernaey, K.V., Woodley, J.M., Gani, R., 2012. An integrated methodology for design of tailor-made blended products. Computer Aided Chemical Engineering 30, 752e756. Yunus, N.A., Gernaey, K.V., Woodley, J.M., Gani, R., 2014. A systematic methodology for design of tailor-made blended products. Computers and Chemical Engineering 66, 201e213. Yunus, N.A., Gernaey, K.V., Woodley, J.M., Gani, R., 2013. Design of Sustainable Blended Products using an Integrated Methodology. Computer Aided Chemical Engineering 32, 835e840. Zhang, L., Cignitti, S., Gani, R., 2015. Generic mathematical programming formulation and solution for computer-aided molecular design. Computers and Chemical Engineering 78, 79e84.

Chapter 4

Development of a Multiscale Strategy and Application to Chemical Vapor Deposition L.E.K. Achenie,*, 1 Y. Sharifix and D.G. Lee*

*Virginia Tech, Blacksburg, VA, United States; xUniversity of Connecticut, Storrs, CT, United States 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION 1.1 Background Advances in microelectronics and the demand for semiconductors is growing at a rate consistent with Moore’s famous law that the number of transistors on an integrated circuit for minimum component cost doubles every 18 months. Since the 1980s, chemical vapor deposition (CVD) has been a popular method in the mass production of semiconductors. CVD is the process of producing solid materials from volatile species in the gas phase and atomistically depositing it on a proper substrate. Chemical reaction plays an important role in a CVD system. The latter may involve several gas phase and/or surface reactions. CVD has a broad range of applications from coating ball bearings, manufacturing cutting tools, rocket engine components, and nuclear reactor components to thin film deposition in microelectronic and optoelectronic devices (i.e., lasers, detectors). A wide range of materials can be utilized in CVD such as organic, inorganic, metals, and semiconductors. CVD can operate in both batch and continuous modes with excellent control of stoichiometry. A CVD system involves a volatile precursor, reacting species, carrier gas, substrate, and the reactor body. Usually several gas phase and/or surface reactions play an important role in a CVD system, which can operate in both batch and continuous modes with excellent control of stoichiometry. Eq. (4.1) represents a very simple CVD process in which A and B are reactants in the gas phase, and C and D are products in the solid and gas phase, respectively. AðgÞ þ BðgÞ / CðsÞ þ DðgÞ Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00004-6 Copyright © 2016 Elsevier B.V. All rights reserved.

(4.1)

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For example, in the formation of zinc sulfide film on a hard substrate such as silicon (with argon as an inert carrier gas), we employ the main reactions in Eq. (4.2). ZnðgÞ þ H2 SðgÞ ! ZnSðsÞ þ H2 ðgÞ (4.2) ZnSðsÞ ! ZnSðsÞs Here, zinc reacts with the hydrogen sulfide (in the gas phase) to produce zinc sulfide and hydrogen as products; zinc sulfide is then deposited on the substrate (ZnS(s)s). The operating conditions of a CVD reactor vary depending on the application. The pressure ranges between 1 and 100 kpa (Jensen, 1994), and the temperature ranges from 250 to 500 C and even as high as 1000 C (Mahajan, 1996). In a typical CVD reactor, thermodynamic, kinetic, and mass diffusion can influence the deposition rate. The operating conditions in a CVD reactor and the reactant chemistry determine if the process is thermodynamically, kinetically, or mass diffusion controlled (Mahajan, 1996). While a broad range of materials could be processed in a CVD reactor, in our research we have considered two important materials, namely zinc sulfide (ZnS) and carbon nanotubes. Carbon nanotubes (discovered in 1991 by Iijima) have been at the center of attention because of their unique electrical, mechanical, and optical properties (Dresselhaus et al., 2001). Carbon nanotubes have a large length-to-diameter ratio (exceeds 10,000, inverse of aspect ratio) and low conductivity. The wide range of applications (Baughman et al., 2002) for carbon nanotubes include, but are not limited to nanoelectronics (Avouris, 2002; Collins et al., 1997), nanosensors (Kong et al., 2000; Chopra et al., 2003), flat panel display, water purification, and super materials. While zinc sulfide deposition may involve a simple gas phase reaction (Savage, 1991; Zhenyi and Yichao, 2002), formation of carbon nanotubes can involve up to hundreds of gas and surface reactions, which initiate from hydrogenolyses of toluene (Dresselhaus et al., 2001). However, in this chapter, we specifically concentrate on the deposition of ZnS that has a large direct band gap and can be used in many optical devices such as in laser domes (Raszewicz et al., 1993), organic light-emitting diode (OLED), self-supporting structures (Winchester et al., 1998), photonic crystals (Breen et al., 2001), nanosensors, and reflective windows (Klein et al., 1986). There is insufficient knowledge of reaction mechanisms and kinetics of many CVD processes. In addition, experimental methods are time-consuming, expensive, and difficult, and research in this field has diminished since the mid 1990s. As a result, no mechanistic chemistry models are available for many newly introduced CVD processes. The further development of computational chemistry techniques, especially for surface reactions and cluster formation, may be very important in this respect (Cavallotti et al., 2004a,b). As reported in Sharifi and Achenie (2007a) a density functional theory (DFT) study yielded two key pathways (one dominant and the other subdominant) for hydrogen

Development of a Multiscale Strategy Chapter j 4

sulfide formation and deposition on the substrate (silicon wafer). Subsequently, the authors reported particle formation due to side reactions (Sharifi and Achenie, 2009). Finally, it has been shown via a heuristic scheme of changing the substrate geometry that the deposition rate of zinc sulfide (Sharifi and Achenie, 2007b) could be tuned. In this chapter, we discuss ZnS deposition in a CVD from two points of view, namely: (1) a deterministic and multiphysics modeling approach (Section 2), and (2) an agent-based simulation approach (Section 3). The rest of Section 1 is devoted to multiscale concepts that we have employed in our deterministic modeling of the CVD process.

1.2 Multiscale Modeling Multiscale modeling of CVD is a broad research area, which includes both macroscopic and microscopic levels. Considering this, modeling of CVD reactors consists of: (1) transport phenomena models, and (2) chemistry models.

1.2.1 Transport Phenomena Models Several factors influence the performance of a CVD reactor (Mahajan, 1996; Jensen and Graves, 1983; Weu et al., 1993; Blanconnier et al., 1978). Some of these are operating conditions, mixing method, preheater, species chemistry, species concentrations, substrate inclination, and substrate position. The key issue in designing CVD reactors is to optimize their thermal and hydrodynamic behavior in such a way that the deposition rate is high and spatially uniform, and that the film has the desired physicochemical properties. This leads to various designs, depending on the process characteristics, the nature and geometry of the objects to be coated, and the required film properties. Of many modeling works previously published in the literature, only a few considered the effect of changing the substrate position or tilt direction on deposition rate. Moffat and Jensen (1988) studied the effects of thermal boundary condition and substrate inclination on the growth rate and transport phenomena using a 3-D steady state model for silane chemistry. They concluded that a tilted substrate improves uniformity in the flow direction. Ristocelli and Mahajan (1987) developed a 2-D model for epitaxial silicon deposition using the usual assumptions of neglecting buoyancy, Soret and Dufour effects, no physical property variation, and a diffusion-controlled deposition process. They computed the effect of the susceptor’s tilt angle on the deposition rate. Their results show that the flow’s acceleration in the reactor is directly proportional to the susceptor’s tilt angle. Van de Ven et al. (1986) investigated the effects of buoyancy, susceptor’s taper, and thermal boundary conditions in the reactor using a simplified 2-D formulation for Gallium arsenide (GaAs) deposition. Mahajan and Wei (1991) studied the effect of different reactor configurations on the deposition process. Based on their study, the chimney configuration with the optimum susceptor angle of

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3.5 degree provided the best uniformity and growth rate for an metalorganic chemical vapour deposition (MOCVD) reactor. The experimental work of Gao et al. (1998) showed that by slightly modifying the susceptor’s geometry, an improvement in the deposition process was achieved. Arnab et al. (2004) studied two different substrate geometries, namely convex and concave substrates, and they concluded that the convex substrate resulted in higher deposition rate.

1.2.2 Chemistry Models Chemistry models of CVD reactors may include both gas phase and surface chemistries. The temperature dependence of the forward rate constants is usually described thorough a modified Arrhenius type of expression. Reaction rate constants are computed self-consistently from thermochemistry (Kuijlaars et al., 1995). In addition, rate constants, activation energies, and thermochemical data are obtained from (1) experimental data, (2) statistical thermodynamics, and (3) ab initio calculations. Solid phase chemistry includes both gaseous molecules impinging on the surface and adsorption of molecules on the surface. These surface processes lead to the growth of the solid film. Three common approaches in modeling surface chemistry include (1) the use of single surface reactions, (2) approximating the growth rate by mass flux of the molecule towards the surface, and (3) growth due to a large number of elementary and reversible surface processes. During the last three decades, chemistry models for unraveling homogenous and heterogeneous reaction mechanism in combination with simple zero or one-dimensional reactor models have been widely investigated. Such models have been made for CVD of epitaxial silicon (Coltrin et al., 1986), B-doped silicon Lengyel and Jensen, 2000), silicon dioxide (Coltrin et al., 2000), silicon carbide, cadmium telluride (Liu et al., 1992), gallium arsenide, silicon germanium (Kim and Gill, 1994), TiS2 (Southwell and Seebauer, 1996) aluminosilicates (Nitodas and Sotirchos, 2002), tungsten (Wang and Pollard, 1994), carbon (Birakayala and Evans, 2002), and diamond (Meeks et al., 1993). To an increasing extent, theoretical and computational chemistry tools are being used to determine reaction pathways and kinetics, both in the gas phase and the surface (Cavallotti et al., 2004a). The operating conditions of a CVD reactor allow for adduct/cluster formation in the gas phase. Formation of clusters is a very important issue in CVD reactor operation. Large clusters may include hundreds of atoms that are meant to be deposited on the substrate. Clusters may settle due to gravity, leave the reactor, or deposit on the substrate. Any of these cases lowers the concentration of desired materials and results in lower performance of a CVD reactor. Hydrogen trapped in the cluster, if not properly removed, creates impurity in the deposited film, which subsequently affects the physical properties and the final product quality.

Development of a Multiscale Strategy Chapter j 4

Cluster formation for various CVD systems has been widely investigated by researchers. Cavallotti et al. (2004b) reported cluster formation of zinc selenide in MOCVD reactor at high temperature. Cini (1999) investigated formation of small zinc sulfide clusters. Matxain et al. (2001) studied small clusters (up to nine atoms) using density functional theory and reported the possible ring-like structure for small clusters and bulk-like structure for bigger clusters. Hamad et al. (2002) reported bubble-like structures for bigger clusters (up to 13 atoms). Sougata et al. (2008) considered formation of large clusters (up to 204 atoms) and reported a bubble-like stable structure for the clusters. Although the aforementioned efforts were very useful in better understanding of the CVD process, none of them considered the effect of geometry on the deposition process inside a CVD reactor. Also, the available data for new materials/processes have not been fully exploited for modeling purposes. For example, in zinc sulfide chemistry, zinc sulfide molecules can attach together and form various cluster structures. Hydrogen sulfide can also attach to these clusters and create new sites for growth. The available archival research on cluster formation of zinc sulfide is for MOCVD systems with a focus on cluster structure, stability, and formation possibility. Such systems have a source of carbon, which creates a chain reaction involving radicals. In the system considered here, there is no carbon source, and the cluster formation initiates by decomposition of hydrogen sulfide into hydrogen atom and hydrogen sulfur (Sharifi and Achenie, 2009). In the overall work, the authors employed a multiscale modeling approach that involved the use of density functional theory to investigate the gas phase hydrogenolyses of toluene (Sharifi and Achenie, 2014). Fig. 4.1 shows our multiscale modeling approach: first, we use molecular modeling, more specifically density functional theory, to study the gas phase Molecular Modeling (Density Functional Theory)

Computational Fluid Dynamics

Multi-Objective Optimization FIGURE 4.1 Multiscale approach for modeling of chemical vapor deposition reactor. The model includes both molecular modeling and computational fluid dynamics. A multiobjective optimization routine based on genetic algorithms is used to design the final substrate.

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reaction mechanism of the processes of interest and eventually calculate the reaction rate constants using transition state theory. Using the pieces of information discussed above, a computational fluid dynamics model is developed to simulate the transport phenomena in a CVD reactor. Finally, the model is used along with a multiobjective optimization method to design efficient substrate geometry for the CVD process, the main subject of this section.

2. GLOBAL OPTIMIZATION OF THE SUBSTRATE GEOMETRY IN ZINC SULFIDE DEPOSITION The aim of this section is to report the use of genetic algorithms (GAs) to do a formal optimal design of the substrate shape in order to globally optimize the zinc sulfide deposition rate on the substrate using a given performance criterion (one criterion optimization) or a set of performance criteria (multicriteria optimization). Computer-aided design tools provide a drawing of the parts in 2-D or 3-D spaces. These drawings are composed of a group of lines, arcs, and curves; the drawings are subsequently used along with a multiphysics package in order to simulate operation of the parts. In the design optimization, all the steps must be done with no human interaction at each iteration of the optimization. This approach is common in aerodynamic shape design where the shape of an object is optimized by simulating the aerodynamic forces around that object (Wang et al., 2002; Peigin and Epstein, 2004; Fuglsang and Madsen, 1999). Here, the shape of the object can be represented by parametric curves (Be´zier curves, Farin, 1996); subsequently, the shape can be smoothly modified by controlling the parameters. Here, we use a similar approach for optimal substrate shape design.

2.1 Multipoints Arbitrary Shape Design Model In our shape design model, we replace all curves in the initial geometry with Be´zier curves, which create a smooth approximation of a shape using only a few control points. Fig. 4.2 shows this process, first a line, which is defined by two points, is replaced by a five-point Be´zier curve. A Be´zier curve is formed from a convex combination of the control points, and as such, will never leave the bounding polygon of the control points (Fig. 4.2C). Only a few control points can provide smoothness and flexibility to the extent needed. A Be´zier curve B(t) is defined by Bernstein polynomials as in Eq. (4.3). BðtÞ ¼

n X

Bn;i Pi

0 xðtÞ ¼

i¼0

Bn;i ¼

Cni ti ð1

n X

Bn;i xi

i¼0

 tÞ

ni

Cni

yðtÞ ¼

n X i¼0

Bn;i yi (4.3)

n! ¼ i!ðn  iÞ!

Here, B(t) ¼ x(t) or y(t) and Pi ¼ xi or yi Thus, the coordinates of the control points are xi and yi, as in Eq. (4.3).

Development of a Multiscale Strategy Chapter j 4

(A)

(B) 2

1

Straight line represented by two points.

1

3

2

4

Straight line represented by a Bezier curve using four control points

(C)

3

4

Smooth curvature between 1 and 2 , created by using a four points Bezier curve. 1

2

FIGURE 4.2 Creating smooth arbitrary profiles by replacing geometric lines with Bezier curves.

Overall, the parameterized shape model should have the following characteristics: l

l

l

high flexibility with the ability to explore the entire search space to find potential solutions; small number of design parameters that the model shows high sensitivity with respect to parameters that are relevant to the constraints should be included.

Fig. 4.3 shows the broad outline of our parametric shape design algorithm. Once the model parameters are defined, the model is transferred to a GA that interacts continuously with an unstructured mesh generator and a computational fluid dynamics (CFD) solver in order to optimize the design of the shape

Parametric Model

Genetic Algorithm

Optimized Shape

Mesh Generator

CFD Solver FIGURE 4.3 Outline of the parametric shape design algorithm. CFD, computational fluid dynamics.

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based on the desired criteria. The GA starts from a random initial population of control points and generates new points using crossover and mutation operations and passes the fit individuals to the next generation. Due to the high cost of the iterative process of GA, it is necessary to simulate the shape optimization model in a parallel computing environment. Next, we discuss multiobjective optimization, GA, and the parallelization of our parametric model, along with the substrate design.

2.2 Genetic Algorithms John Holland (1975) invented GAs, based on the idea of survival of the fittest observed in the nature. GAs are now ubiquitous, and some of the fine attributes are their versatility and their ability to locate near global solutions, in other words, without being trapped in local optima. They are robust for large-scale optimization problems and can handle noisy functions with relative ease. They are able to explore a wider design space and can easily be implemented in a parallel computing environment. A GA can handle discontinuities introduced by constraints at the boundaries by assigning low fitness values to inferior individuals (Goldberg, 1989). This approach will eliminate the inferior individuals in the hope of finding a better solution. The GA also handles other types of constraints (such as bounds on the decision variables and general linear constraints) by mapping the search space and minimizing the number of infeasible solutions within the search space. Finally, a GA requires no gradient information (Goldberg, 1989) and is able to provide a set of solutions for multiobjective problems (Achenie and Ostrovsky, 2005; Ostrovsky et al., 2006). The shortcomings of GAs include the complexity of the fitness function identification, premature convergence, dependency on local search technique for accurate results, and the tedious parameter selection for the optimization setup. In summary, a GA, as a semistochastic method, is considerably more robust in the case of nondifferentiable, multimodal, or nonconvex functions. We refer the interested reader to a good introduction to GA by Melanie (1999).

2.2.1 Outline of a Genetic Algorithm In a nutshell, the idea of GA is to select, rank, and evolve the individuals towards the best individuals: solution of the optimization problem. The population, a group of individuals, is submitted to three genetic operators: selection, crossover, and mutation. During this process, the genetic characteristics of the fit individuals are being transferred to their offspring. The individuals can survive, reproduce, or die according to their fitness value, which is related to the value of the cost functional to be optimized. Fig. 4.4 shows the outline of a generic GA. After defining the optimization problem and initializing the parameters, the GA starts by randomly generating a population of individuals represented as bit strings. Next, the fitness value of each individual in the population is calculated based on the value of the cost

Development of a Multiscale Strategy Chapter j 4

Define the cost function, and GA parameters

Generate the initial populations

Evaluate cost for each chromosome

Selection Mating Mutation Convergence check

Done FIGURE 4.4 Flowchart of genetic algorithm; the algorithm includes such operators as selection, crossover, mutation, and termination.

function. Subsequently, the population undergoes the selection step, which randomly selects the mating pairs and retains the top 5% of the current population. This is followed by a random exchange of information between individuals via crossover; a random mutation of the individuals in each mating pair produces a fitter offspring. Finally, depending on the status of the convergence criteria, the process terminates or executes the series of steps again.

2.3 Multiobjective Optimization In practice (for example in engineering, economics, and the environment), there are many multiobjective problems in which multiple objectives have to be traded off against each other. The following representation is often employed:  gi ðxÞ  0; i ¼ 1.m2 optimize FðxÞ ¼ ff1 ðxÞ; f2 ðxÞ; .fk ðxÞg subject to : hi ðxÞ ¼ 0; i ¼ 1.m2 (4.4) Here, x is the vector of decision variables, F is the objective function, and gi(x) and hi(x) are nonlinear inequality and equality constraint functions, respectively. In a typical multiobjective problem, the objectives are in conflict with one another. As a result, a group of solutions represent optimality. These solutions are the best compromise solutions and are called nondominated solutions or Pareto optimal solutions. This means that any improvement in one objective function would deteriorate at least one of the

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other objectives. Nondominated Pareto optimality is commonly used in economics and game theory where there is an interest in multidimensional decision-making. By definition, xe is called an efficient (also called Pareto optimal, noninferior, or nondominated) solution for minimization of Eq. (4.4) if there is no x in the problem domain such that F(x)  F(xe) and F(x) s F(xe), where (x s xe). However, not all optimization algorithms can guarantee the generation of efficient solutions; instead, they can provide weakly efficient solutions. Next, by definition, xe is called a weakly efficient (also called Pareto optimal, noninferior, or nondominated) solution for minimization of Eq. (4.4), if there is no x in the problem domain such that F(x) < F(xe), where (x s xe). Since a weakly efficient condition is easier to satisfy, an efficient solution must be a weakly efficient solution; however, a weakly efficient solution is not necessarily an efficient solution. In multiobjective problems, the collection of all efficient solutions is called the efficient set. There are three different classes of methods to solve the multiobjective problems, namely the efficient solution generation method, best compromise solution based on a priori, and interactive methods influenced by decision analysis processes. In the first class of methods, a decision-maker will choose the best compromise solution from a set of desirable efficient solutions. The advantage of these methods is that the decision-maker acts after the efficient solution set is obtained. However, the drawback for this class is that it generates a large number of solutions sets, which makes it complicated for the decision-maker to determine the best compromised solution. A classic example in this class of methods is the simple weighting method where a weighted combination of the solutions generates the best compromised solution. The second class of methods requires a global preference in advance and transforms a multiobjective problem to a single objective problem, which leads to the best compromise solution of the original multiobjective problem. This conversion reduces the number of calculations, and the optimization only needs to be done once. However, the real challenge here is providing the global preference in advance, especially in the case of new optimization problems where there is little or no knowledge about the trade-offs among the objectives. The minimax method, goal attainment method, goal programming, and the preference point method are examples of this class. The third class of methods requires progressively providing the local preference by the decision-maker in an interactive optimization process. This method constructs a sequence of single-objective optimization problems, which are somehow related to the original problem, and their solution will provide the best compromised solution of the original multiobjective problem. Geoffrion’s method, the Interactive Step Trade-Off Method (ISTM) method, and the interactive gradient projection method are examples of this class (Geoffrion et al., 1972; Ko¨ksalan and Sagala, 1995).

Development of a Multiscale Strategy Chapter j 4

2.3.1 Simple Weighting Method The simple weighting method is the simplest multiobjective optimization method used in a wide range of applications. A general representation of simple weighting method is as follows: FðxÞ ¼

N X

ui fi ðxÞ

x˛U; 0  ui  1;

i¼1

N X

ui ¼ 1

(4.5)

i¼1

where ui are the weighting factors, U is the feasible region, and F(x) is the new combined objective function. The simple weighting method is typically used for two-objective optimization problems, for example, in the case of minimizing the cost while improving the efficiency in a chemical reactor, etc. Generally, a two-objective optimization problem is presented as follows:   Min f1 ðxÞ gi ðxÞ  0; i ¼ 1.m2 (4.6) Subject to : Max f2 ðxÞ hi ðxÞ ¼ 0; i ¼ 1.m2 where f1(x) and f2(x) are nonlinear objective functions, x is the solution, and gi(x) and hi(x) are nonlinear inequality and equality constraint functions, respectively. If the objective space is convex and trade-off between the two objectives is allowed, then the weighting method can be used to generate efficient solutions for the objective function in the same objective space. Min f ðxÞ ¼ u1 f1 ðxÞ þ u2 f2 ðxÞ

u1  0; u2  0;

u 2 þ u2 ¼ 1

(4.7)

Assuming u ¼ u1/u2, we have: Min f ðx; uÞ ¼ f1 ðxÞ þ uf2 ðxÞ

(4.8)

For a given u (i.e., the decision-maker’s preference), the optimal solution of this problem is an efficient solution of the original two-objective problem. Changing u will generate a new efficient solution for the two-objective optimization problem. The main advantage of this method is that the solution belongs to the effective solution set, and one objective can be controlled by comparing it to another. However, this method lacks the ability to find all the solutions and avoid illogical assignment of the weights in the optimization problem.

2.4 Multiobjective Genetic Algorithms Doing multioobjective optimization problems within the GA context is referred to as evolutionary multiobjective GA (emoGA). The latter uses two approaches in the optimization, namely non-Pareto optimization and Pareto optimization techniques. The non-Pareto optimization, which is also called vector-evaluated GA (Schaffer, 1984), aims to find multiple nondominated solutions in a single optimization run through proportional fitness assignment.

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Similar to the simple weighting method, this method selects a weighted linear combination of the objectives; then the nondominated individuals are identified as the population evolves. The non-Pareto optimization shows poor performance on problems with concave trade-off surfaces. However, the Pareto-based optimization, which guarantees equal probability of reproduction to all nondominated individuals, does not have any issue with concave tradeoff surfaces. The Pareto-based optimization method combines an artificial decision-maker with the search process in order to provide a suitable fitness assignment strategy. Here, the search process is influenced by the decisionmaker, which incorporates not only the information from the current search process, but also any environmental changes into the decision-making process. As a result, the decision-maker makes the new trade-offs and guides the GA to find a representative sampling of solutions all along the Pareto front. In ranking by front, the first layer (front one) represents the nondominated individuals of the entire population; the other fronts are ranked based on the remaining subsets of the nondominated individuals. Obviously, the worst individuals define front f (the number of fronts). Once the individuals have been ranked by front, they receive their fitness values based on the following: 8 < 1 for a minimization problem fi ¼ r (4.9) : r for a maximization problem Here, fi is the fitness of the ith front, and r is the rank of the front. However, evaluating the fitness of individuals according to multiple objectives is still a challenge for emoGA, considering the trade-offs that need to be made in order to simplify the problem. Since GAs can be used to get close to the global optimum, a conventional optimization scheme like greedy search, gradient search, or stochastic hill climbing may be used to get closer to the optimum value. These types of schemes are called hybrid GAs.

2.5 Implementation of a Genetic Algorithm in Shape Design Once the parametric shape is defined based on Be´zier curves, the GA begins by defining a chromosome or an array of variable values to be optimized. The chromosome is defined as an Nvar dimensional vector:   chromosome ¼ p1 ; p2 ; .; pNvar (4.10) where pi is a control point of the Be´zier curve and is defined as: pi ¼ pðx; yÞ Here, [x,y] represents the coordinates of the control point. The next step is to define a cost function in terms of the chromosomes defined before.     (4.11) cost ¼ f p1 ; p2 ; .; pNvar ¼ f x1 ; y1 ; x2 ; y2 ; .; xNvar ; yNvar

Development of a Multiscale Strategy Chapter j 4

To add geometric constraints, the coordinates are defined on the interval [xmin, xmax] and [ymin, ymax]. These parameters are subsequently binary encoded for the GA. The parameter values are then estimated based on: 1 0 m i 1 X xmax  xmin xi ¼ xmin þ @ (4.12) 2j a j A  2mi  1 j¼0 0 yi ¼ ymin þ @

ni 1 X

1 2j bj A 

j¼0

ymax  ymin 2n i  1

(4.13)

Here, a and mi are the value and the length of the binary string coding parameter xi, and b and ni are the value and the length of the binary string coding parameter yi. In deriving these formulas, we assumed that the minimum ymax ymin xmin accuracy of xmax 2mi 1 and 2ni 1 are desired for x and y, respectively.

2.5.1 Multiphysics Model We have considered a 2-D multiphysics model defined by momentum, energy, and mass conservation (Bird et al., 2001). For a compressible fluid, the model estimates the gas density based on the ideal gas law, assumes fully developed boundary condition in the reactor inlet, and incorporates thermal diffusion (Jensen, 1994) in the mass conservation equations. Other transport properties such as binary diffusion, viscosity, and thermal conductivity are calculated using the ChapmaneEnskog correlations (Reid et al., 1987). Continuity equation : ðV$ruÞ ¼ 0

(4.14)

Momentum Balance : V$hðVu þ ðVuÞT þ rðu$VÞu þ VP ¼ F

(4.15)

Convection and Conduction : V$ð kVT þ rcp TuÞ ¼ 0   Convection and diffusion : V$  DTi VðlnðTÞÞ þ Di Vci þ ci u ¼ Ri

(4.16)

DTi ¼

n kc2 X p jsi

r

Mi Mj Di

(4.17) (4.18)

Here, r is fluid density, u is velocity vector, h is dynamic viscosity, F is the force term including gravity, P is pressure, cp is heat capacity at constant pressure, k is thermal conductivity, ci is species concentration, DTi is thermal diffusion coefficient, Di is binary diffusion coefficient of species i in argon, and Ri is gas phase reaction rate. The distributed memory parallelization of both GA and CFD solver are employed. Calculations of the fitness of the individuals are independent and can be performed in parallel (Fig. 4.5). Since the flow solver (for fitness evaluation) spends approximately 80e90% of the computational time, we

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Genetic Algorithm parallelization

P1

P2

P3

P4

P5

P6

Evaluate the individual's cost using the parallel flow solver

Individual

Individual P1

P2

P3

P4

P5

P6

FIGURE 4.5 Parallelization strategy for the genetic algorithm and the flow solver for the case of six processors.

parallelize the flow solver using domain partitioning and a message passing interface (MPI) model. Fig. 4.5 shows the parallelization strategy for a cluster with six processors. The GA implementation utilizes all the computing nodes to perform the genetic operators (initialization, selection, crossover, and mutation). However, the cost of every two consecutive individuals is evaluated in parallel, meaning that each individual utilizes half of the computing power. The simulations show that this method provides higher computing efficiency compared to the case where the cost evaluation is performed one at a time by using all the computing power. Once the shape parameters are determined using the optimization engine, a new mesh needs to be generated before passing it to the CFD solver. The new mesh is created by moving the old mesh using the spring analogy to fit the new geometry. Since the boundary layer mesh is fine-grained, the mesh must move rigidly with the changing geometry in order to avoid any interference of the mesh elements and destruction of the boundary layer mesh. This method provides an efficient and reliable mesh for the shape design process (Farhat and Lanteri, 1994). Here, we used unstructured discretization, which makes the geometry suitable for either finite volume or finite element solver. In the parallelization of the flow solver, the underlying mesh is divided into several subdomains in which the flow solver is going to be executed simultaneously. The mesh partitions may or may not overlap with each other; while overlapping of the mesh partitions increases the accuracy, the nonoverlapping mesh models require less redundant operations and provide higher computational efficiency (Lanteri, 1996). In the next section, we first use our multipoint shape design model on an airfoil optimization case adopted from the literature in order to verify the algorithm, and then we optimize the substrate’s geometry for zinc sulfide CVD.

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2.5.2 Parameterized Substrate Geometry Model For the two-dimensional model, the substrate geometry is a thin rectangle. Fig. 4.6 shows the 2-D model for the reactor. In order to transform the 2-D rigid model to a flexible model, we need to replace the straight lines defining the boundary of the substrate with Be´zier curves. Fig. 4.7 shows the process of creating a flexible substrate from a ridged model. In this model, we only replace the vertical lines in the substrate rectangle; the other two edges of the rectangle are fixed since these have negligible effect on the overall deposition process. A characteristic of a good shape parameterization model is to create the most sensitive shapes with the least number of parameters; replacing the sides with Be´zier curves will increase the model parameters, resulting in an increased computational load with little or no improvement in the overall efficiency. Here, we use a five-point Be´zier curve to represent the substrate geometry. The smoothness and flexibility of a Be´zier curve makes it possible to create various substrate geometries with only five control points. Next, the coordinates of the control points will be used as input parameters for our GA engine. The control points for the substrate geometry are given by Pi ¼ Pi(xi,yi), i ¼ 1.5 where both x and y components are employed as optimization variables. Thus, in the GA, we define a chromosome as: chromosome ¼ fP1 ; P2 ; .; P5 g ¼ fx1 ; y1 ; x2 ; y2 ; .x5 ; y5 g

(4.19)

Here, Pi’s are the control points, and xi’s and yi’s are the coordination of these control points.

FIGURE 4.6 2-D model for a zinc sulfide chemical vapor deposition reactor.

Replacing the perpendicular lines in the substrate with Bézier curves

Creating smooth cervical substrates using five control points

FIGURE 4.7 Creating a flexible substrate geometry using Be´zier curves.

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We define the geometrical constraints as follows: l

l

l

The coordinates of each control point can vary on the interval [mini, maxi], or more specifically, [4 cm, 4 cm] and [0.8 cm, 0.8 cm] for the x and y components, respectively. The substrate thickness can vary up to 5% of its original shape; this ensures the elimination of infeasible shapes. The first and fifth control point cannot get closer to the reactor wall than their initial state; thus, we defined a constraint for their y components.

In the GA settings, we used an initial population of 40, single-point crossover probability of 80%, and mutation probability of 10%. The multiobjective function we considered is based on the deposition rate and the shear stress on various points of the substrate. The goal here is to minimize the shear stress and maximize the uniformity and the deposition rate at the same time. We define the uniformity as the difference between the samples of the deposited film collected at various points along the substrate. Since the length of the substrate varies due to its dynamic nature, we defined the sampling points in the mid-80% of the substrate arc length. We used five sample points, which were equally distributed along this part of the substrate. Thus, we define the objective function as in Eq. (4.20). Here f1(z) is the deposition rate, f2(z) is the shear stress, and z is the variable vector, including the Be´zier curves control points, operating condition, substrate location, thickness, and height. 8 > < Dxi ˛½4; 4; Dyi ˛½0:8; 0:8 Dðsubstrate thicknessÞ  5% Maxð f1 ðzÞÞ Minð f2 ðzÞÞ Subject to > : y1  0; Dy5  0 (4.20)

2.6 Results and Discussion The GA shape design was implemented on a parallel computing cluster consisting of eight quad-core (2.4 GHz) processors. The parallelization platform was in Linux (Redhat 64-bit version) environment using HelwettPackard (HP) MPI version 2.0 (64-bit). The overall optimization required almost 8600 cost function evaluations and took 184 h of the CPU time, or approximately 8 min per run. Fig. 4.8 shows the design and optimization procedure. The initial geometry was created by replacing the edges (vertical lines) of the substrate geometry by Be´zier curves, using initial values of the control points; the initial mesh was created based on the resulting geometry. The authors obtained the kinetic data (i.e., parameters) via molecular modeling and transition state theory (Sharifi and Achenie, 2007a); the parameters were used to solve a system of nonlinear

Development of a Multiscale Strategy Chapter j 4

Shape

Substrate

Operating Momentum Heat Balance Mass Balance

Kinetic data Molecular

Concentration

Velocity Shear stress GA optimizer

Deposition rate

FIGURE 4.8 Substrate design procedure to be used by genetic algorithm to maximize deposition rate and minimize the forces.

partial differential equations (momentum, mass, and energy balance) using the finite element method on an unstructured overlapping mesh. The latter was employed due to the need for high accuracy. The finite element deployment was based on Lagrange P2eP1 elements for the NaviereStokes equations and Lagrange quadratic elements for the convection/diffusion and convection/ conduction equations. Next, the deposition rate and shear stress were determined using the concentration and velocity profiles inside the reactor. These values were then passed to the GA optimizer, which generated a new set of control points based on the current value of the objective function. The new control points were used to create a new substrate geometry, new mesh, and iteratively converge the GA optimization. A spring analogy based mesh movement, along with local mesh refinement, was used in our mesh update procedure. This combination of meshing methods maximized the computational efficiency by avoiding unnecessary mesh generation during the optimization loop. Fig. 4.9 shows the sample profiles obtained from the Pareto front during the optimization run. All of these samples satisfy the Pareto optimality and can be presented as an alternative solution for a desirable deposition pattern. Our numerical models show that the deposition pattern is highly sensitive to the shape of the geometry; thus, a slight modification of the substrate changes the flow patterns, recirculation, and boundary layout around the substrate. As in all other Pareto optimality cases, it is up to the decision-maker to decide which one of the substrate geometries is optimal for the intended application. For example, the substrates A, C, and D (Fig. 4.9) give fairly uniform ZnS coverage except for the edges. Substrate B, (Fig. 4.9), on the other hand, is far from uniform coverage. One may use these shapes to force a special deposition pattern on a substrate. It is expected that not every substrate shape can be manufactured and not every shape is useful from other

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FIGURE 4.9 Samples of substrate geometry obtained from the Pareto front.

considerations not incorporated in the model; however, the design approach offers choices that may not otherwise have been imagined. We suggest that for better results, the substrate’s active materials can be used in the mid-80% of the substrate where the deposition rate is uniform. As Fig. 4.10 shows, the model has been able to successfully control the shape parameters to obtain ultimately uniform deposition along the substrate (except for edge effects). These results are consistent with the data published in the literature (Arnab et al., 2004; Moffat and Jensen, 1988; Ristocelli and Mahajan, 1987). Therefore, it is possible to achieve a more uniform deposition by changing the substrate’s configuration and ultimately controlling the deposition pattern by monitoring the underlying flow pattern. The distinction from published work in the open literature is that our systematic framework starts from a basic rectangular substrate and continuously improves the flow pattern until the desired deposition objectives are achieved. Our framework (the GA shape design) also has the advantage of utilizing global optimization techniques in order to find the globally optimum shape for uniform deposition of semiconductors.

Development of a Multiscale Strategy Chapter j 4

FIGURE 4.10 Deposition rate profile obtained from the genetic shape optimization.

2.7 Summary In this section, we have considered the multiscale modeling of one aspect of H2S deposition on a substrate. Specifically, we have developed a systematic shape optimization framework. Note that we have benchmarked on aerodynamic cases in other studies not discussed in this contribution. The framework allows multiobjective optimization in which possibly conflicting objectives are traded off against each other. Our system is able to successfully design and optimize the substrate geometry for a given chemistry in a CVD reactor. Compared to the aerodynamic shape design models, which utilize only a flow solver based on momentum conservation, our system couples a complex multiphysics system including momentum, heat, and mass conservation in order to efficiently design the substrate geometry. Our simulations show that the shape design optimization technique is also effective in the low Reynolds number flows when a chemical reaction is involved. Thus, this framework is not limited to CVD systems.

3. CHEMICAL VAPOR DEPOSITION MODELING USING AGENT-BASED SIMULATION 3.1 Modeling 3.1.1 Background Agent-based modeling (ABM) is a strategy that has evolved to be of practical use since the 2000s (Railsback et al., 2006). ABM allows interactions of independent agents (for example, molecules and other particles) while each agent behaves according to a set of rules, which may be heuristic in nature or may be governed by deterministic equations such as differential and/or

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algebraic equations. Although ABM has seen a number of uses in computer science, it has seen very limited use within molecular modeling.

3.1.2 Assumptions As stated in Eq. (4.2) (Section 1), zinc reacts with the hydrogen sulfide in the gas phase to form zinc sulfide and hydrogen as products; zinc sulfide is then deposited as a film on the substrate. The CVD model is created based on several assumptions, some of which would be relaxed in the future. To minimize computational overhead, the modeling is done in two dimensions and thus all collisions are done in a 2-D model (Fig. 4.11). The size of the molecule is proportional to the molecular mass. However, the size of hydrogen molecule in the model is adjusted because its molar mass (1 g/mol) is about one-sixty-fifth of zinc molar mass and one-ninety-seventh of a zinc sulfide (ZnS) molar mass. It is very difficult to visualize a size that is one-onehundredth smaller than the size of the desired product, ZnS. Although a hydrogen molecule is the smallest in the model, the size is adjusted so that it is visible in the simulation. Reactants flow from left to right through advection and random motion. Molecules that do not adsorb on the substrate eventually exit the reactor. Molecules collide with other molecules, the reactor walls, and the vertical substrate; each collision is currently assumed to be elastic. There are several equations to consider when modeling a molecule that bounces off from each other and the wall. Collision with a horizontal surface: the relevant equations are: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vy Vx ¼ Vx initial Vy ¼ Vy initial V ¼ V2x þ V2y q ¼ tan1 (4.21) Vx Here, Vx and Vy are the x and y components of the velocity, and q is the direction of the particle or molecule.

FIGURE 4.11 Deflection of a particle after elastic collision with another particle or wall. Reproduced from Digital Image #1, January 2016.

Development of a Multiscale Strategy Chapter j 4

Collision with a vertical surface: the relevant equations are: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vy Vx ¼ Vx initial Vy ¼ Vy initial V ¼ V2x þ V2y q ¼ tan1 Vx

(4.22)

2-D Elastic Collision Vx ¼ Vcosq

Vy ¼ Vsinq

m1 V1 þ m2 V2 mtotal V2 ¼ 2  Vcm  V1

Center of mass velocity : Vcm ¼

(4.23) V1 ¼ 2  Vcm  V2

(4.24) Time taken for the molecules to collide (Neilsen, 1997) y1 ¼ vy1 t þ y1o

y2 ¼ vy2 t þ y2o 2

x1 ¼ vx1 t þ x1o

x2 ¼ vx2 t þ x2o

2

ðy2  y1 Þ þ ðx2  x1 Þ ¼ r1 þ r2

(4.25)

where (x1, y1) and (x2, y2) are the molecules at the time of collision, t is the time until the next collision, (vx1, vx2) and (vy1, vy2) are the velocities of the molecules before the collision, and (x1o, y1o) and (x2o, y2o) are the current positions of the molecules. The expressions in Eq. (4.25) reduce to a quadratic at2 þ bt þ g ¼ 0

(4.26)

Here, a ¼ v2y1 þ v2y2 þ v2x1 þ v2x2  2vx1 vx2  2v2y1 v2y2 b ¼ 2½vy1 y1o  vy2 y2o  y1o vy2 þ vy2 y2o þ vx1 x1o  vx1 x2o  vx2 x1o þ vx2 x2o  g ¼ x21o  2x2o x1o þ x22o þ y21o  2y1o y2o þ y22o  ðr1 þ r2 Þ (4.27) Now solve for t > 0; suppress collision if t < 0 or is complex-valued. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b b2  4ag t¼ 2a Advection in x-direction Vx ¼ Vx initial þ advection constant  t Vy ¼ Vy initial Substrate covered % Covered ¼

diameter of a desired product  no:of desired product perimeter of a substrate

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Deposition rate Deposition rate ¼

Number of product deposited unit time

* unit time is used because timescale in a simulation is not in seconds, but has its own scale, ticks.

3.2 Agent-Based Modeling in NetLogo The NetLogo agentebased programming environment (Wilensky and Rand, 2015) was used to implement our model. NetLogo, which has similarities with Java, was originally developed for simulating natural and social phenomena. NetLogo is particularly well suited for modeling complex systems that evolve over time. Modelers can give instructions to hundreds or thousands of “agents,” all operating independently. This makes it possible to explore the connection between the microlevel behavior of individuals and the macrolevel patterns that emerge from their interaction (Wilensky and Rand, 2015). In a simulation environment, an agent behaves autonomously and exhibits behavior patterns that have been assigned to it; thus, conceptually, agents of different size scales can interact in a multiscale environment with respect to size. Interactions on different timescales are somewhat more complicated, but through innovative modeling, one can envision multiscale interactions on different timescales; a thrust of our research is to help solve multiscale issues at both length and timescales. There are four types of agents, namely, turtles, patches, links, and the observer. Turtles are agents that move around in the world. Within the simulation environment we employed, the “world,” object which is two dimensional and is divided up into a grid of patches. Each patch is a square piece of “ground” over which turtles can move. Links are agents that connect and somewhat constrain two turtles.

3.3 Results and Discussions Fig. 4.12 shows the chemical vapor deposition process using molecules as agents. The horizontal yellow lines define the walls of the reactor whose size can be adjusted. Different products and reactants are represented with different sizes and colors: H2S (brown) and Zn (blue) are reactants; argon (white) is an inert carrier gas; the desired product is ZnS (red), while H2 (green) is a byproduct in this reaction. Some of the desired product molecules form a film on the gray-colored vertical substrate. Molecules flow from left to right by random motion superimposed on bulk advection. Collisions among molecules are also considered in the simulation. As seen in Fig. 4.13, the number of zinc sulfide molecules in the film (red line), increases rapidly in the beginning and slowly plateaus out over time (except for random fluctuations). Our simulations indicate that in the early

Development of a Multiscale Strategy Chapter j 4

FIGURE 4.12 2-D view of chemical vapor deposition simulation.

FIGURE 4.13 Number of product molecules over time.

stages of the reaction, the desired product does not fully cover the substrate; after a certain time, the substrate is fully covered, and there are no available sites for binding to additional product molecules. We suspect that the fluctuations are artifacts of the simulation; that is, the simulation counts all the molecules present within a unit time. However, new reactant molecules are introduced and old molecules exit the reactor; thus, the total number of

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FIGURE 4.14 Deposition rate over unit time.

molecules will fluctuate. In the experimental system, it is conceivable that fluctuations arise as a result of the substrate-binding kinetics that could allow molecules to adsorb and desorb with a given probability. Fig. 4.14 is a deposition rate plot where the rate of deposition rapidly increases in the beginning and decreases over time. In the plot, it is clear that the deposition rate reaches its maximum close to the initial time. Again, fluctuations exist for the reasons given previously. Fig. 4.15 shows the percentage of product molecules in the film on the substrate over time. About 96% of desired products molecules are recovered on a substrate around the final time; this percentage is unrealistically high and assumes that the CVD process is terminated after a long time. We tried to validate the ZnS deposition results with experimental data from the literature; however, we could not find any. Instead, we considered graphite film deposition on nickel, which has been experimentally studied by Cai et al. (2009).

FIGURE 4.15 Percentage recovered over unit time.

Development of a Multiscale Strategy Chapter j 4

3.3.1 Graphite Film Deposition on Nickel From Qiangu et al. (2000), we employed the catalytic methane decomposition reaction mechanism (in a CVD) CH4 5C þ 2H2 Fig. 4.16 represents experimental results from Cai et al. (2009); this is a plot showing the mass of graphite formed on a nickel foil as a function of deposition time and temperature. The mass of graphite increases rapidly in the graphite film for the first 2 min and then decreases slowly towards an asymptote. The authors explain that the mechanism involves the decomposition of hydrocarbon gas; subsequently, the concentration gradient causes the carbon to diffuse into the nickel substrate. Fig. 4.17 is the corresponding plot of the results from the agent-based simulation where the simulation parameters have been adjusted to match the experimental results; the simulation was done at a deposition temperature of 1100 C. You will notice that this plot, which is based on graphite deposition on nickel, is very similar to the ZnS deposition (Fig. 4.13) for which we do not have experimental validation data. Thus, one hypothesis that we are studying is, is it possible to define “performanceequivalent” systems for CVD reactors?

3.4 Summary In this section, we have employed ABM to deal with the CVD of ZnS on a substrate. The results indicate that carefully constructed agent-based simulations could provide qualitative and quantitative features about film formation.

FIGURE 4.16 The mass of graphite film formed on a nickel foil as a function of deposition time at three different deposition temperatures. Reproduced from Cai, W., Piner, R.D., Zhu, Y., Li, X., Tan, Z., Floresca, H.C., Yang, C., Lu, L., Kim, M.J. Ruoff, R.S., 2009. Synthesis of isotopicallylabeled graphite films by cold-wall chemical vapor deposition and electronic properties of graphene obtained from such films. Nano Research 2, 851e856.

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FIGURE 4.17 Agent-based simulation yields the mass of graphite film formed on a nickel foil as a function of time at deposition temperature 1100 C.

Such a simulation model could be tuned on one system and used to simulate a different system with similar broad characteristics as the base system. A possible hypothesis could be developed from the question: do performanceequivalent systems exist for CVD reactors? If they do, what are the implications for design? What are the implications for reaction mechanisms?

4. CONCLUSIONS (OVERALL) In this chapter, we have looked at ZnS deposition in a CVD from two points of view. The first point of view employs a deterministic and multiphysics modeling approach that uses detailed physics and the associated modeling equations. This approach allows for mechanistic understanding of the process; it is computationally intensive and very difficult to set up. The second point of view uses agent-based simulation in which the physics is inherently captured through evolutionary random events involving molecules or particles. The approach is relatively simple to construct (albeit with a reasonable effort at programming in the multiagent environment). Here, mechanistic understanding is sacrificed. However, a different kind of mechanistic understanding is introduced in which we observe the emergence of patterns of behavior that are consistent with an expectation of what happens in a CVD reactor. The challenge is to consider the synergistic effects of marrying both types of modeling when studying systems of this nature.

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Development of a Multiscale Strategy Chapter j 4 Arnab, K.D., Muralidhar, K., Eswaran, V., Wadhawn, V.K., 2004. Modeling of transport phenomena in a low-pressure CVD reactor. 3e4, 2004. Journal of Crystal Growth 267, 598e612. Avouris, A., 2002. Molecular electronics with carbon nanotubes. Accounts of Chemical Research 35, 1026e1034. Baughman, R.H., Zakhidov, A.A., Heer, W.A., 2002. Carbon nanotubesethe route toward applications. Science 297, 787e792. Birakayala, N., Evans, E.A., 2002. A reduced reaction model for carbon CVD/CVI processes. Carbon 40, 675. Bird, R.B., Stewart, W.E., Lightfoot, E.N., 2001. Transport Phenomena. John Wiley & Sons. Blanconnier, P., Cerclet, M., Henoc, P., Jean-Louis, A.M., 1978. Growth and characterization of undoped ZnSe epitaxial layers obtained by organometallic chemical vapour deposition. Thin Solid Films 55, 375e386. Breen, M.L., Dinsmore, A.D., Pink, R.H., Qadri, Ratna, B.R., 2001. Sonochemically produced ZnS-coated polystyrene core-shell particles for use in photonic crystals. Langmuir 17, 903e907. Cai, W., Piner, R.D., Zhu, Y., Li, X., Tan, Z., Floresca, H.C., Yang, C., Lu, L., Kim, M.J., Ruoff, R.S., 2009. Synthesis of isotopically-labeled graphite films by cold-wall chemical vapor deposition and electronic properties of graphene obtained from such films. Nano Research 2, 851e856. Cavallotti, C., Lengyel, I., Nemirovskaya, M., Jensen, K.F., 2004a. A computational study of gasphase and surface reactions in deposition and etching of GaAs and AlAsin the presence of HCl. Journal of Crystal Growth 268, 76e95. Cavallotti, C., Moscatelli, D., Carra, S., 2004b. Theoretical investigation of the low- and hightemperature MOVPE of zinc selenide. Journal of Physical Chemistry A 108, 1214e1223. Chopra, S., McGuire, K., Gothard, N., Rao, A.M., 2003. Selective gas detection using a carbon nanotube sensor. Applied Physics Letters 83, 2280e2282. Cini, R., 1999. Molecular orbital study of complexes of zinc with sulfide. Journal of Biomolecular Structure and Dynamics 16, 1225e1237. Collins, P.G., Zettl, A., Bando, H., Thess, A., Smalley, R.E., 1997. Nanotube nanodevice. Science 278, 100e103. Coltrin, M.E., Kee, R.J., Miller, A., 1986. A mathematical model of silicon chemical vapor deposition. Journal of the Electrochemical Society 133, 1206e1213. Coltrin, M.E., Ho, P., Moffat, H.K., Buss, R.J., 2000. Chemical kinetics in chemical vapor deposition: growth of silicon dioxide from tetraethoxysilane (TEOS). Thin Solid Films 365, 251e263. Digital Image #1 (January 2016), http://s3.amazonaws.com/answer-board-image/4cda27d2-b1ea4912-839c-16f8dee2c1c7.gif. Dresselhaus, M.S., Dresselhaus, G., Avouris, P., 2001. Carbon Nanotubes: Synthesis, Structure, Properties, and Applications. In: Topics in Applied Physics, vol. 80. Springer, Berlin. Farhat, C., Lanteri, S., 1994. Simulation of compressible viscous flows on a variety of mpps: computational algorithms for unstructured dynamic meshes and performance results. Computer Methods in Applied Mechanics and Engineering 119, 35e60. Farin, G., 1996. Curves and Surfaces for Computer-aided Geometric Design, fourth edition. Fuglsang, P., Madsen, H.A., 1999. Optimization method for wind turbine rotors. Journal of Wind Engineering & Industrial Aerodynamics 80, 191e206. Gao, Y., Gulinoa, D.A., Higginsa, R., 1998. Effects of susceptor geometry on GaN growth on SI(111) with a new Mocvd reactor. In: Kuo, C., Pearton, S.J., Uenoyama, T., Wright, A.F. (Eds.), MRS Proceedings, 537.

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SECTION j I Basic Concepts and General Tools Geoffrion, A.M., Dyer, J.S., Feinberg, A., 1972. An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Management Science Application Series Part 1 19 (4), 357e436. Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA. Hamad, S., Cristol, S., Catlow, C.R.A., 2002. Surface structures and crystal morphology of ZnS: computational study. Journal of Physical Chemistry 106, 11002e11008. Holland, J.H., 1975. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, Michigan. Iijima, S., 1991. Helical microtubules of graphitic carbon. Nature 354, 56e58. Jensen, K.F., Graves, D.B., 1983. Modeling and analysis of low pressure CVD reactors. Journal of the Electrochemical Society 130, 1950e1957. Jensen, K.F., 1994. In: Hurle, D. (Ed.), Transport Phenomena in Epitaxy Systems, Handbook of Crystal Growth. Elsevier, Amsterdam. Kim, E.J., Gill, W.N., 1994. Modeling of CVD of silicon dioxide using TEOS and ozone in a single-wafer reactor. Journal of the Electrochemical Society 141, 3462e3472. Klein, C.A., Dibenedetto, B., Pappis, J., 1986. ZnS, ZnSe, and ZnS/ZnSe windows e their impact on FLIR system performance. Optical Engineering 25, 519e531. Ko¨ksalan, M.M., Sagala, P.N.S., 1995. Interactive approaches for discrete alternative multiple criteria decision making with monotone utility functions. Management Science 41 (7), 1158e1171. Kong, J., Franklin, N.R., Zhou, C., Chapline, M.G., Peng, S., Cho, K., Dai, H., 2000. Nanotube molecular wires as chemical sensors. Science 287 (5453), 622e625. Kuijlaars, K.J., Kleijn, C.R., van den Akker, H.E.A., 1995. Modelling of a cold wall tungsten CVD reactor: validation of PHOENICS-CVD. The PHOENICS Journal of Computational Fluid Dynamics and Its Applications 8 (4), 439e454. Lanteri, S., 1996. Parallel solutions of compressible flows using overlapping and non-overlapping mesh partitioning strategies. Parallel Computing 22, 943e968. Lengyel, I., Jensen, K.F., 2000. A chemical mechanism for in situ boron doping during silicon chemical vapor deposition. Thin Solid Films 365, 231e241. Liu, B., Hicks, R.F., Zinck, J.J., 1992. Chemistry of photo-assisted organometallic vapor-phase epitaxy of cadnium telluride. Journal of Crystal Growth 123, 500. Mahajan, R.L., Wei, C., 1991. Buoyancy, Soret, Dufour, and variable property effects in silicon epitaxy. Journal of Heat Transfer 113, 688e695. Mahajan, R.L., 1996. Transport Phenomena in Chemical Vapor-deposition Systems. In: Advances in Heat Transfer, vol. 28. Academic Press, NewYork, p. 339. Matxain, J.M., Mercero, J.M., Fowler, J.E., Ugalde, M., 2001. Small clusters of group-IIeVI. materials: ZniXi, X ¼ Se, Te, i ¼ 1e9. Phys. Rev. A 64, 053201. Meeks, E., Kee, R.J., Dandy, D.S., Coltrin, M.E., 1993. Computational simulation of diamond, chemical vapor deposition in premixed C2H2/02/H2 and CHdO2-strained. Flame 92, 144e160. Melanie, M., 1999. An Introduction to Genetic Algorithms. The MIT Press, Cambridge, MA, London, England. Moffat, H.K., Jensen, K.F., 1988. Three-dimensional flow effects in silicon CVD in horizontal reactors. Journal of the Electrochemicl Society 135, 459e471. Neilsen, E.H., 1997. Derivation of Collision Time Equations. http://home.fnal.gov/wneilsen/ publications/demon/node13.html. Nitodas, S.F., Sotirchos, S.V., 2002. Homogeneous and heterogeneous chemistry models of the codeposition of silica, alumina and aluminosilicates. Journal of the Electrochemicl Society 149 (11), 555e566.

Development of a Multiscale Strategy Chapter j 4 Ostrovsky, G., Achenie, L.E.K., Datskov, I., Volin, Y., 2006. An approach to multicriteria optimization under uncertainty. Chemical Engineering Science 61, 2379e2393. Peigin, S., Epstein, B., 2004. Robust optimization of 2D airfoils driven by full NaviereStokes computations. Computers & Fluids 33, 1175e1200. Qiangu, Y., Tinghua, W., Jitao, L., Chunrong, L., Weizeng, W., Lefu, Y., Huilin, W., 2000. Mechanism study of carbon deposition on a Ni/Al2O3 catalyst during partial oxidation of methane to syngas. Journal of Natural Gas Chemistry 9, 89e102. Railsback, S.F., Lytinen, S.L., Jackson, S.K., 2006. Agent-based simulation platforms: review and development recommendations. Simulation: Trans. Soc. Model. Simul. Int. 82, 609e623. Raszewicz, C., Pearson, G.S., Krasinski, J., 1993. Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti: sapphire self-modelocked laser. Optics Communications 102 (5e6), 464e468. Reid, R.C., Prausnitz, J.M., Poling, B.E., 1987. The Properties of Gas and Liquids. McGraw Hill, s.l, 4th. Ristocelli, J.R., Jr., Mahajan, R.L.. 1987. Silicon deposition and dopant incorporation in epitaxial processes. Hawaii: s.n., ASME/JSME 2nd Therm. Eng. Conf. Savage, J.A., 1991. New infrared window materials-from zinc sulphide through calcium lanthanum sulphide to diamond. Glass Technology 32, 35e40. Schaffer, J.D., 1984. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms (Ph.D. thesis). Vanderbilt University, Nashville, USA. Sharifi, Y., Achenie, L.E.K., 2007a. Using density functional theory to postulate a mechanism for zinc sulfide formation in a CVD reactor. Journal of Crystal Growth 307, 440e447. Sharifi, Y., Achenie, L.E.K., 2007b. Effect of substrate geometry on deposition rate in CVD. Journal of Crystal Growth 304, 520e525. Sharifi, Y., Achenie, L.E.K., 2009. Particle dynamics in a CVD reactor: a multiscale approach. Industrial & Engineering Chemistry Research 48, 5969e5974. Sharifi, Y., Achenie, L.E.K., 2014. Dft study of mechanism and kinetics of hydrogenolysis of toluene. Journal of Chemical and Process Engineering 1, 104. Sougata, P., Biplab, G., Pranab, S., 2008. Size-dependent properties of hollow ZnS nanoclusters. Journal of Physical Chemistry C 112, 6307e6312. Southwell, R.P., Seebauer, E.G., 1996. A predictive kinetic model for the chemical vapor deposition of TiSi2. Journal of the Electrochemical Society 143, 1726e1736. Van de Ven, J., Rutten, G.M.J., Raaijmakers, M.J., Giling, L.J., 1986. Gas phase depletion and flow dynamics in horizontal MOCVD reactors. Journal of Crystal Growth 76, 352e372. Wang, Y.F., Pollard, R., 1994. A method for predicting the adsorption energetics of diatomic molecules on metal surfaces. Surface Science 302, 223e234. Wang, J.F., Periaux, J., Sefrioui, M., 2002. Parallel evolutionary algorithms for optimization problems in aerospace engineering. Journal of Computational and Applied Mathematics 149, 155e169. Weu, J., Kuin, Y.S., Yokoyama, M., 1993. Effects of H2S/DMZn molar ratio on ZnS films grown by low pressure metalorganic chemical vapor deposition. Journal of Applied Physics 32, 907e910. Wilensky, U., Rand, W., 2015. An Introduction to Agent-based Modeling. MIT Press, Cambridge, MA. Winchester, K., Spaargaren, R.S.M., Dell, J.M., The use of ZnS as a sacrificial layer in the construction of PECVD SiNx self-supporting structures. Perth, WA, Australia: Proceedings Conference on, 1998. Optoelectronic and Microelectronic Materials Devices. pp. 493e496. Zhenyi, F., Yichao, C., 2002. CVD growth of bulk polycrystalline ZnS and its optical properties. Journal of Crystal Growth 237, 1707e1710.

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Chapter 5

Molecular Property Clustering Techniques F. Eljack Qatar University, Doha, Qatar E-mail: [email protected]

1. INTRODUCTION In the chemical processing industry, product design involves finding a product that exhibits certain desirable behavior or involves trying to find an additive (chemical) that, when added to another chemical or product, enhances its desirable functional properties (Achenie et al., 2003). In product design, the identity of the final product is unknown; however, the general behavior or characteristics of the product (goal) is known. This is given information. The objective is to find the most appropriate chemical or a combination/mixture of chemicals that will help accomplish this goal. Once possible solutions to the problem are generated, the next step is to test them and manufacture the product.

1.1 Molecular Design A general approach used to solve molecular design problems is empirical trialand-error methods based on experimentation. While not the most efficient method, such an approach is the only option in cases where there are no available property models that could be used to predict the properties of the desired products. However, in cases where property models exist, computeraided methods can be used where the design problem is transformed into a computer-aided molecular design (CAMD) problem. By definition, a CAMD problem is (Brignole and Cismondi, 2003): “Given a set of building blocks and a specified set of target properties, determine the molecule or molecular structure that matches these properties.” A class of CAMD software for chemical synthesis developed by Molecular Knowledge Systems Inc., focuses on three major steps in the formulation of molecules; it exemplifies the general methodology behind most CAMD methods (Joback, 2006). Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00005-8 Copyright © 2016 Elsevier B.V. All rights reserved.

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In property prediction, the component’s structural information is used in order to predict its properties; this requires committing to a list of preselected components ahead of design. The problem here is that the search space is limited, and this could lead to suboptimal solutions. CAMD is able to avoid such issues by solving the reverse of the property prediction problem. It uses available property models to formulate the design problem in terms of target values for the identifiable set of properties. The property constraints are used as input into its algorithm; then it determines candidates of molecules (or mixture of molecules) that match the specified property targets values without limiting the search space (Eden, 2003). Hence, with the problem well defined, in terms of properties, CAMD methods are able to design novel formulations that otherwise might not of have been part of the available database. A rich volume of investigative research regarding CAMD is available in literature and can be grouped into three main categories: mathematical programming, stochastic optimization, and enumeration techniques (Harper, 2000; Harper and Gani, 2000): l

l

l

Mathematical programming: solves the CAMD problem as an optimization problem where the property constraints are used as mathematical bounds and the performance requirements are defined by an objective function (Odele and Macchietto, 1993; Vaidyanathan and El-Halwagi, 1994; Duvedi and Achenie, 1996; Pistikopoulos and Stefanis, 1998). Stochastic optimization: the solution alternatives are based on the successive pseudo-random generation method. Like the previously mentioned approach, this method aims at finding the optimal value for the objective function, but the technique it uses varies. One important aspect is that stochastic optimization methods do not require any gradient information, giving it the freedom to specify discontinuous properties as design targets (Venkatasubramanian et al., 1994; Marcoulaki and Kokossis, 1998; Ourique and Silva Telles, 1998). Enumeration techniques: aims at satisfying the feasibility and property constraints by first generating molecules using a combinatorial approach and then testing against the specifications where molecules that fail to satisfy the constraints are eliminated (Gani et al., 1991; Pretel et al., 1994; Joback, 1995; Friedler et al., 1998).

Regardless of method of choice, stating the objective (predesign phase) of the CAMD problem is a prerequisite for solving any CAMD algorithm. Numerical property constraints and a selection of molecular building blocks are used as input into the CAMD algorithm; see Fig. 5.1. The design phase encompasses the generation of molecular formulation and tests their ability to satisfy the property constraints placed on the problem. Next, the postdesign phase involves using other prediction methods, database sources, engineering insight, and if possible, simulation in order to screen and rank the designed compound(s) based on suitability and capabilities (e.g., environmental impact, health and safety aspects, production cost or availability) (Eljack, 2007).

Molecular Property Clustering Techniques Chapter j 5

Molecular building blocks

PRE-DESIGN PHASE State Objectives Set goals/targets

Numerical property constraints

DESIGN PHASE Generate & Test Molecular Formulations CAMD Algorithm HIGHER LEVEL DESIGN PHASE Generate and Test Molecular Formulations

POST DESIGN PHASE Ranking of formulations and screening based on immeasurable properties

FIGURE 5.1 Formulation and solution of a computer-aided molecular design (CAMD) problem (Eljack, 2007).

1.2 Property Prediction and Group Contribution Methods Almost all CAMD algorithms rely on the ability to predict pure component and mixture properties for the analysis and design of formulations. In addition, the need for reliable and accurate property estimation methods is critical to the solution of various simulation problems where convergence is often related to failures in the reliability of predicted physical and thermodynamic properties (Constantinou and Gani, 1994). Most property estimation methods used in CAMD techniques are based on the group contribution method (GCM), where the properties of a compound are expressed in terms of function of the number of occurrences of predefined groups in the molecule (Harper, 2000). The GCM is totally predictive, meaning that as long as the structure can be fully described with the groups, the properties of the structure are immediately available. The method can be used to synthesize new structures easily, as the evaluation of the properties of a structure is straightforward, given the models and the group contributions (GCs) (d’Anterroches and Gani, 2005). GC-based design methodologies are built on the following general premise: the structure is composed of groups, and the targets are properties. The formulation of a GC-based problem is defined as looking for structures that possess target properties (e.g., molecular weight, melting temperature, etc.) while matching structural constraints (e.g., no cyclical groups, no alcohols, etc.). The

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goal is to generate the molecular structures that match the target properties within the structural constraints. The formulation of a GC-based problem is defined as looking for structures having target properties while matching constraints. For the estimation of physical and thermodynamic properties of pure compounds, GCM allows for the prediction of pure component physical properties from structural information. Any applications of GC rely on availability of groups to describe the structure, as well as tables giving the contributions of each group. The GC property data has been developed from regression using a large data bank of more than 2000 compounds collected at the Computer Aided Process and Engineering Center at Denmark Technical University. Properties that are predicted using GCM (e.g., critical properties, boiling point temperature, etc.) are referred to as primary properties, and all other properties (e.g., density, viscosity, vapor pressure, heat of vaporization, etc.) are classified as secondary properties, usually predicted as functions of primary or critical properties (Marrero and Gani, 2001).

2. PROPERTY INTEGRATION 2.1 Property Integration for Process Design In 2000, Shelley and El-Halwagi introduced the property integration framework for process synthesis to allow for property-based design instead of the conventional component-based design. This approach has proven very useful in the optimization of various industrial processes as well as product blend problems, including binary and ternary mixtures (Shelley and El-Halwagi, 2000; El-Halwagi et al., 2004; Eden, 2003; Eden et al., 2004; Eljack et al., 2005). The framework is a component-less design approach that is based on property clusters, which are conserved surrogate properties that are functions of unconserved physical properties (Shelley and El-Halwagi, 2000). The concept of a property cluster is based on functionality called a property operator (jj). The operator is a function of the original physical properties (j). Eq. (5.1) shows the property operator jjs for the property density (rs) in stream s. The operator is formulated in a manner to allow the right-hand side of Eq. (5.2) to have linear mixing rules, see Eq. (5.2). The jjM is the property operator for mixed stream M. The unique aspect of property clusters is that although the property functionalities (operators) might be highly nonlinear, the linear mixing rules simplify the formulation of the design problem and that of the process synthesis. jj ðPjs Þ ¼ jj ðPjM Þ ¼

Ns X s¼1

1 rs

xs $jj ðPjs Þ

(5.1)

(5.2)

Molecular Property Clustering Techniques Chapter j 5

In addition, property operators and property clustering framework allow for the representation of the process design problem on a visual ternary diagram (Eden et al., 2004; El-Halwagi et al., 2004).

2.2 Property Clusters and Group Contribution Methods In molecular design, the formulation and solution of the algorithm are heavily dependent on properties, as highlighted earlier, and later, the properties of the designed candidate formulations are checked to make sure that they satisfy the design requirements. Hence, it is necessary that the molecular design methods developed be based on some property platform. Eljack et al. (2007b) and Kazantzi et al. (2007) infused GCMs into the property integration framework in order to develop a systematic method capable of addressing the simultaneous process and molecular design problem whereby the process design problem is solved in terms of properties, and the molecular design problem synthesizes candidates that target the required process properties. In this paper, two methods using property clusters for molecular design are presented. A visual molecular design approach using clustering method is presented for those cases where the design problem can be described using three properties, and for all other design cases, an algebraic molecular design method using property clusters is given.

3. VISUAL MOLECULAR CLUSTERING DESIGN APPROACH The property clustering methods developed for component-less process design (Shelley and El-Halwagi, 2000) were modified to include GCM to address the molecular design problem. Here, properties of formulated molecules are estimated from structural information using GCM; see Eq. (5.3). Initially, the method was based on first-order groups that made up the molecule (Joback and Reid, 1987), but later efforts developed second-order and third-order groups to improve the accuracy of the predicted properties (Constantinou and Gani, 1994; Marrero and Gani, 2001). In Eq. (5.3), Ci is the property contribution of the first-order molecular group i, which occurs Ni times in the molecule; f(X) is a function of property X. Among the available group contribution properties are standard heat of vaporization, melting temperature, standards heat of fusion, etc. A full list of available group contribution properties can be found in the literature (Constantinou and Gani, 1994; Constantinou et al., 1995; Marrero and Gani, 2001). X f ðXÞ ¼ Ni $Ci (5.3) i

In the case of properties that do not have a GC estimation equation, termed here non-GC properties, they are usually functions of GC properties. For

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example, vapor pressure cannot be estimated using GCM; however, it is a function of boiling temperature, a property that can be estimated using GCM. See Eqs. 5.4 and 5.5.  1:7 Tbp log VP ¼ 5:58  2:7 (5.4) T   X T exp Ni $tbi (5.5) ¼ tbo i In the molecular clustering method, the GC properties are used during the synthesis, and once the formulations are identified, their non-GC properties must be back calculated using appropriate formulations to ensure that all property constraints are satisfied. The molecular design problem and the property clustering method are described as follows. Problem statement: given a set of molecular building block (first-order groups from GCM) and a set of property performance criteria Pj, each bound by a minimum and maximum property value, it is desired to synthesize and design molecular fragments that satisfy the performance criteria. The molecular property clustering methods are developed as a systematic approach to address the previously mentioned molecular design problem. The clustering method transforms the design problem into the property platform using the molecular property operator, formulated by Eljack and coworkers (Eljack, 2007; Eljack and Eden, 2008) to be similar to the original property operators formulated to describe the process design problem (Shelley and ElHalwagi, 2000; Eden, 2003). The molecular property clustering method is described by the following steps (Eljack, 2007; Eljack and Eden, 2008): Step 1: The molecular property operator of the jth property, jM j ðPj Þ, is determined as the sum of each molecular group’s property (Pjg) multiplied by the number of each group g, ng. jM j ðPj Þ ¼

Ng X

ng $jj ðPjg Þ

(5.6)

g¼1

Step 2: The molecular property operator is made dimensionless or normalized by using a reference operator, jref j ðPj Þ. The values of the reference operators are chosen by the user to make sure that the operators have similar order of magnitudes. This helps later when it comes to graphing the property clusters on a ternary diagram. UM j ¼

jM j ðPj Þ jref j ðPj Þ

(5.7)

Molecular Property Clustering Techniques Chapter j 5

Step 3: Each group g, molecular augmented property index (AUPM) is determined by summing up all normalized property operators ðUM jg Þ, where NP in Eq. (5.8) is the number of properties. AUPM g ¼

NP X

UM jg

(5.8)

j¼1

Step 4: The property cluster for group g, Cjg for property j, is determined as the fractional contribution of each group’s normalized operator ðUM jg Þ to the molecular augmented property index ðAUPM Þ. g UM jg AUPM g

Cjg ¼

(5.9)

3.1 Conservation Rules for Molecular Property Clusters Visualization of the molecular design problem is very valuable to this methodology. To ensure that the molecular clusters are conserved, they have to posses both intra- and intermolecular conservation. The intramolecular conservation rule requires that the sum of individual clusters (CjM) for each molecular formulation M must sum to unity, as shown in Eq. (5.10). This is proven by the summing all cluster values for all j properties for molecule M in Eq. (5.9) and substituting the AUP definition [see Eq. (5.11)]. NC X

CjM ¼ 1

(5.10)

j¼1 NP P NP X j¼1

CjM ¼

j¼1

UM j

AUPM

¼

AUPM ¼1 AUPM

(5.11)

The intermolecular conservation rule for adding molecular groups or fragments on the ternary diagram is derived analogous to interstream conservation. The general additive rule for molecular operators [Eq. (5.6)] is normalized by a reference value, and the definition of the dimensionless molecular operator [Eq. (5.7)] is substituted to yield the following mixing rule: UM j;mix ¼

Ng X

ng $Ujg

(5.12)

g¼1

The definition of molecular property cluster given in Eq. (5.9) applies to any cluster, including molecular fragments; therefore, the cluster of a mixture of two molecular groups or fragments is: M Cj;mix ¼

UM j;mix AUPM mix

(5.13)

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It is crucial to validate the intermolecular conservation rule. First, the mixing rule for the dimensionless property operator is inserted into Eq. (5.13). Next, the definition of a molecular fragment cluster is rearranged and substituted. This proves the intermolecular conservation rule according to Eqs. (5.14)e(5.16). Ng P M Cj;mix

¼

g¼1

Ng P

ng $UM jg ¼

AUPM mix bg ¼

g¼1

M ng $Cjg $AUPM g

AUPM mix

ng $AUPM g AUPM mix

M Cj;mix ¼

Ng X

M bg $Cjg

(5.14)

(5.15)

(5.16)

g¼1

3.2 Graphical Representation of the Molecular Design Problem The visualization of the molecular design problem is represented on a ternary diagram; see Fig. 5.2. Each vertex (C1, C2, and C3) represents a molecular property cluster. The molecular fragments, such as eCH3, eCH2e, and

FIGURE 5.2 Visual representation of the molecular design problem on a ternary property clustering diagram.

Molecular Property Clustering Techniques Chapter j 5

eCH3CO molecules, are represented as points (G1, G2, and G3) on the diagram. Given the target minimum and maximum property values, the feasible regions, referred to as a sink, is bounded by six unique points, as defined by Eden and El-Halwagi (Eden, 2003; El-Halwagi et al., 2004). The molecular design clustering visual approach, like the original clustering approach for process design, is based on using linear mixing rules that the molecular property operators possess. On the visual ternary diagram, adding or “mixing” two molecular fragments, G1 and G2, falls on a straight line. The location of the resulting mixed fragment G1eG2 on the line can be determined using lever arm analysis; see Fig. 5.3. The mixing rules developed for the molecular design are based on those developed by Eden and coworkers for the mixing of two streams in process design (Eden et al., 2004; El-Halwagi et al., 2004). The rules governing molecular design and synthesis using the visual property clustering methods are outlined in the following (Eljack, 2007; Eljack and Eden, 2008): Rule 1: Two groups, G1 and G2, are added linearly on the ternary diagram, where the visualization arm, b1, describes the location of G1eG2 molecule. b1 ¼

n1 $AUP1 n1 $AUP1 þ n2 $AUP2

(5.17)

FIGURE 5.3 Group addition visually on the ternary property clustering diagram.

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Rule 2: Molecular groups can be added to fragments as long as the free bond number (FBN) is s0; see Eq. (5.18). 2 3 2 3 Ng Ng X X FBN ¼ 4 ng $FBNg 5  4 ng  15  2$NORings (5.18) g¼1

g¼1

The FBN is the free molecular bond number of the formulation, ng is the number of occurrences of group g, FBNg is the unique FBN associated with group g, and NORings is the number of rings in the formulation. Rule 3: The location of the final molecule on the diagram does not depend on the order in which the fragments were added. The location is unique and is based on the number of each group and its GC property values. For example, consider the CH3CH2CH2CH3O molecule; it is a complete molecule with FBN equal to zero. It is composed of one eCH3, two eCH2e, and one eCH3O molecular fragment. Constructing this molecule on the ternary cluster diagram, using three chosen properties, can be done in a variety of ways. Nonetheless, the location of the final formulation (CH3OeCH2eCH2eCH3) is unique, regardless of the path. Eljack and Eden (2008) present a proof-of-concept example. Rule 4: For completeness, the designed molecule’s FBN ¼ 0. Hence, no free bonds. This is a necessary condition. Rule 5: The cluster value of the designed molecule must be inside the feasibility region (sink) on the ternary molecular cluster diagram. This is another necessary condition. Rule 6: The AUP value of the designed molecule must be within the range of the target. If the AUP value falls outside the range of the sink, the designed molecule is not a feasible solution. Rule 7: For the designed molecule to match the target properties, the AUP value of the molecule has to match the AUP value of the sink at the same cluster location. This is a sufficient condition. In the case where the design problem included non-GC properties, those properties must be back calculated for the designed molecule using the appropriate corresponding GC property, and those values have to match the target non-GC properties. Note that from the rules above, given a completed molecular formulation, three conditions must be satisfied for the designed molecule to be a valid solution to molecular design problem. Rules 4 and 5 are the necessary conditions, while Rule 7 is the sufficient condition.

3.3 Example: Solvent Design To illustrate the visual molecular property clustering approach, a solvent design case study is presented here. This problem was originally presented and solved as mixed-integer nonlinear program (MINLP) (Achenie and Sinha, 2004). The design problem is formulated and solved in the property clustering framework.

Molecular Property Clustering Techniques Chapter j 5

TABLE 5.1 Solvent Design Property Constraints and List of Molecular Building Blocks Solvent Target Property Constraints Property

Lower Limit

Upper Limit

Molecular Building Blocks

Hv (kJ/mol)

20

60

CH3 CH2

Tb (K)

350

400

COOH

Tm (K)

150

250

CH2CO

VP (mm Hg)

100

e

CH3CO CH2O

1

Rij (MPa /2 )

0

19.8

CH3O

3.3.1 Problem Statement Given the property constraints listed in Table 5.1, it is desired to synthesize candidate solvents that can have a maximum length of seven groups. The molecular formulations must be synthesized from the provided bank of molecular building blocks. In addition, the formulations can have a maximum length of seven groups. 3.3.2 Group Contribution and Property Estimation Methods Tables 5.2 and 5.3 show the estimation methods for the five properties required for the solvent design problem. Note only three of the five properties have firstorder GCM equations available: heat of vaporization (Hv), normal boiling TABLE 5.2 Molecular Property Operators for Solvent Design Problem (Group Contribution Property Estimation Equations) (Eljack and Eden, 2008)

Property Standard heat of vaporization Normal boiling temperature Normal melting temperature

Molecular Property Operator PNg jM j ðPj Þ ¼ g¼1 ng $jj ðPjg Þ

Reference Values

DHv  hvo ¼

20

PNg

g¼1 ng $hv

(5.19)

  PNg T ng $tb (5.20) ¼ g¼1 exp tbo   PNg T exp ng $tm (5.21) ¼ g¼1 tmo

7 7

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TABLE 5.3 Non-GC Property Estimation Equations (Eljack and Eden, 2008) Property Vapor pressure Solvent solubility Hansen solubility parameters Molar volume

Property Estimation Method  1:7 Tbp log VP ðmm HgÞ ¼ 5:58  2:7 (5.22) T qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j j j R ij ðMPa1=2 Þ ¼ 4ðdid  dd Þ2 þ ðdip  dp Þ2 þ ðdih  dh Þ2 P dd ¼

Fdi

Vm

Vm  d ¼

pP ffiffiffiffiffiffiffiffiffiffi2ffi ;

dp ¼

P i

gi $v1i

F pi

Vm

(5.23)

rP ffiffiffiffiffiffiffiffiffiffi ;

dh ¼

Ehi

Vm

(5.24)

(5.25)

temperature (Tb), and normal melting temperature (Tm). The vapor pressure (VP) is a non-GC property; however, it is a function of boiling temperature, which is a GCM property. The solvent solubility (Rij) is estimated based on the interaction of the solvent with the solute it is intended to dissolve. The Rij is estimated using Hansen parameters (Barton, 1985), which are group-based; however, there is not a GCM equation available. The three properties estimated using GCM will be used for visualization of the molecular design problem, and the other non-GCM properties will be used as screening properties; see molecular property clustering Rule 7 mentioned previously. Table 5.2 provides a summary of the property operator formulations for each of the GC properties, along with their reference values. Notice that the right-hand side of the molecular property operator equations is formulated to allow for the addition of groups using linearly as per Rule 1.

3.3.3 Visualization of the Solvent Design Problem The first step to synthesizing molecular formulations is to transform the property constraints of the problem as a feasibility region on the ternary molecular clustering diagram. The given lower and upper limit property constraints in Table 5.1 for the GC properties (standard heat of vaporization, normal boiling point, and normal melting temperature) are translated into property operators using Eqs. (5.19)e(5.21). Next, their cluster values are determined following Steps 1e4 [Eqs. (5.6)e(5.9)], as described in Section 3. The cluster values for the minimum and maximum values of the three properties are used to visualize the feasibility region as six unique points, as defined by Eden (2003):  min min max   min max max   min max min  U1 ; U2 ; U3 U1 ; U2 ; U3 U1 ; U2 ; U3  max max min   max min min   max min max  U1 ; U2 ; U3 U1 ; U2 ; U3 U1 ; U2 ; U3

Molecular Property Clustering Techniques Chapter j 5

The AUP values of the six points that define the feasibility region are used to define the AUP range of sink. Here, the AUP range is 2.29e5.09. Later, this AUP range of sink will be used as a screening tool for the synthesized molecular candidates, in order to see if they satisfy the necessary feasibility condition (Rule 7). The molecular building blocks given in the problem statement are represented as points on the ternary diagram following Steps 1e4 [Eqs. (5.6)e(5.9)]. Fig. 5.4 shows the feasibility region as well as the molecular groups that will be used in the synthesis. It should be emphasized here that the molecular synthesis process is simplified when using the molecular property clustering tool because groups are added on the diagram using linear additive rules.

3.3.4 Molecular Synthesis The candidate molecules are restricted to a maximum of seven groups length as per the problem statement. The synthesis of the molecules is conducted following Rules 1e4. Candidate molecules were generated visually on the ternary diagram; see Fig. 5.5. Note that the 11 generated candidates (M1eM11) are located inside the feasibility region. Hence, they satisfy the necessary condition as per Rule 5.

FIGURE 5.4 Visual representation of the molecular clustering solvent design problem on ternary diagram (Eljack et al., 2008).

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SECTION j I Basic Concepts and General Tools

FIGURE 5.5 Candidate solvents for molecular design problem represented on the ternary molecular clustering diagram (Eljack et al., 2008).

Table 5.4 lists the candidate molecules, their corresponding property values, and AUP. The vapor pressure and solubility properties for the candidate molecules were estimated postsynthesis using Eqs. (5.22)e(5.25). l

l

Applying Rule 6 to the generated molecules, it can be seen that the AUP value of candidates M9, M10, and M11 falls outside the previously defined sink’s AUP range of 2.29e5.09. Hence, these formulations fail to satisfy this necessary condition. The remaining M1eM8 formulations satisfy the constraints of the nonGCM properties, the vapor pressure, and solubility. The vapor pressure values for all candidates are >100 mm Hg; and their solubility 1 1 (6.6) i2 i2 ; i1 ; i2 ˛ G1 ; j1 ; j2 ˛ ID

(6.9)

cj1 > j2 ; i1 ˛ G1 ; j1 ; j2 ˛ ID

(6.10)

ð1Þ ðni Þ

of groups i to Additional constraints may be placed on the number keep it within lower and upper bounds, nLi and nU , respectively. i ð1Þ

nLi  ni

 nU i

ci ˛ G1

(6.11)

Also, a constraint on the total number of groups making up a molecule may be imposed. X ð1Þ nmin  ni  nmax (6.12) i ˛ G1

A collection of equations from Eqs. (6.6)e(6.12) with or without those introduced by Zhang et al. (2015) represents the structural constraints [Eq. (6.2)] in the mathematical problem definition given previously.

2.2 Property Constraints Selection of the generated molecules depends on the values of their target properties. The set of target properties vary with the chemical product. Gani (2004) classifies these properties into four types: l

l

l

l

Primary properties: these are single value properties of pure compounds and are dependent only on molecular structures. Secondary properties: these properties of pure compounds depend on other properties. Functional properties: these properties of pure compounds depend on temperature and/or pressure. Mixture properties: there are two types of mixture properties: l Bulk properties: these are average properties of mixtures of a specified phase, where composition, temperature, and/or pressure are also specified. l Phase equilibrium properties: these are phase equilibriumerelated properties of compounds present in mixtures in equilibrium, where phase composition, temperature, and/or pressure are specified.

Examples of the four classes of properties are given in Table 6.1. The property constraints [see Eq. (6.3)] could be represented by Eq. (6.13), where, PN is the set of all target properties of the molecule and, all

159

160

Functional (Unless Specified Otherwise, as Function of Temperature)

Mixture: Bulk (T, P, x)

Mixture: Phase Equilibrium (T, P, x)

Primary

Secondary

Normal boiling point

Enthalpy of vaporization at boiling point (Tb)

Liquid density

Density

Activity coefficient

Critical temperature

Entropy of Vaporization Tb

Vapor pressure

Saturation pressure

Fugacity coefficient

Critical pressure

Acentric factor

Thermal conductivity

Saturation temperature

Saturation composition

Critical volume

Surface tension

Liquid viscosity

Viscosity

Compound solubility

Normal melting point

Refractive index

Diffusion coefficient

Surface tension

Enthalpy of formation at 298K

Entropy of formation

Compressibility factor*

Enthalpy of fusion at 298K

Hildebrand solubility parameter

Liquid specific heat

Enthalpy of vaporization 298K

Liquid density

Vapor specific heat

Gibbs free energy of formation at 298K

Liquid viscosity

Heat of vaporization

Hildebrand solubility parameter at 298K

Molar liquid volume*

Auto ignition temperature Dipole moment Note: *, as function of temperature and pressure; T, temperature; P, pressure; x, vector of compositions.

SECTION j II Molecular Design

TABLE 6.1 List of Examples According to Property Types

Computer-Aided Molecular Design and Property Prediction Chapter j 6

the feasible molecules must be within the specified bounds of the target properties ½pLk ; pU k . pLk  pk  pU k

ck ˛ P

(6.13)

If the target property is a primary property, pk is obtained directly from the molecular structural variables. The model equations for these primary properties in terms of functional groups can be found in Constantinou and Gani (1994), in Marrero and Gani (2001), who extended the list of groups and provided reestimated group parameters, and in Hukkerikar et al. (2012a,b), who further extended and improved the group parameter tables together with the addition of new properties. A total of 27 primary properties have been modeled by Hukkerikar et al. (2012a). All the primary models are of the additive type that is, the property pk or a function of it [the left-hand side of Eq. (6.14)], is a linear combination of the contributions of the groups representing the molecule for the corresponding property. X ð1Þ ð1Þ X ð2Þ ð2Þ pk ¼ ni pk þ nj pk þ . ck ˛ P (6.14) i ˛ G1

j ˛ G2

For secondary, functional, mixture, and phase equilibriumerelated properties, the equations differ from Eq. (6.14), and therefore, the molecular structural parameters implicitly affect the corresponding properties. Therefore, their inclusion in the molecular design problem makes the problem nonlinear and/or requires a decomposition-based solution approach. For some problems, however, as Zhang et al. (2015) has shown, the direct solution of the MILP or MINLP is also possible. Since the functional groups are the molecular structural variables and also explicitly (primary properties) or implicitly (all other properties) influence the target properties, a brief overview of the functional groupsebased property prediction is discussed as follows.

2.2.1 Group ContributioneBased Methods As mentioned above, group contribution (GC)ebased methods for primary properties only require the molecular structural information. The general formula for GC methods is as follows (Hukkerikar et al., 2012a): X X X f ðXÞ ¼ Ni Ci þ w Mj Dj þ z O k Ek (6.15) i

j

k

where X is a property of the function f(X), N, and M are the number first- and second-order groups, respectively, and C and D are the contributions to the first- and second-order groups, respectively. The first-order approximation utilizes representation of simple molecular groups and functional groups, such as CH3 and OH. The second-order approximations use the combination of first-order groups to increase the model accuracy by taking into account

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SECTION j II Molecular Design

adjacent first-order groups, such as (CH3)2CH group. Similarly, O and E refer to the third-order approximation by its number of groups and its contribution, respectively. Second-order groups provide an improved description of polyfunctional components and can differentiate between some isomers. Third-order groups allow prediction of complex heterocyclic and larger polyfunctional acyclic components (Hukkerikar et al., 2012b). w and z are binary variables that determine if a certain order of approximation is to be included. Early GC methods for prediction of thermophysical and transport properties for molecules include the work by Klincewicz and Reid (1984) and Lydersen (1955) for the prediction of critical properties using first-order groups (w and z are zero). Lydersen (1955) obtained the GC of the molecular groups by studying the change in properties similar types of molecules, whereas Klinceweics and Reid (1984) used a least square regression method. Newer GC methods also utilized a least square regression method. These include the methods by Joback and Reid (1987) and Constantinou and Gani (1994). In Constantinou and Gani (1994), the first- and second-order approximations are only used (z in Eq. (6.15) is set to zero). These two newer GC-based methods used larger sets of functional groups and enabled the prediction of many other primary properties, such as normal boiling point, normal melting point, acentric factor and standard enthalpy of formation, standard entropy of formation, and density at room temperature. Further enhancement of the Constantinou and Gani method has been reported by Marrero and Gani (2001), who extended the number of primary properties, the application range through the introduction of third-order groups, as well as the accuracy of prediction. Further refinement of the models have been reported by (Kolska´ et al., 2005), where the GC concept is employed to accurately model the enthalpy and entropy of vaporization at room temperature and at normal boiling points of compounds. Also, Modarresi et al. (2008) reported the development of GC-based models for prediction of Hansen solubility parameters, while Conte et al. (2009) reported the development of GC-based models for prediction of liquid viscosity and surface tension, using the MarreroeGani groups as the basis. Tabernero et al. (2012) developed a new GC-based method for enthalpy of fusion for prediction of molecules that include polycyclic aromatics/aliphatic hydrocarbons. This method only utilizes first-order GCs. In 2013, Ceriani et al. (2013) developed GC-based functional property models for properties such as vapor pressure and enthalpy of vaporization. Also, the perturbed-chain statistical associating fluid (PC-SAFT) equation of state (Gross and Sadowski, 2001) has been converted into its GC form (Privat et al., 2010) for prediction of density, vapor pressure, heat of vaporization, and volume. Also, the GC version of the PC-SAFT equation of state has been successfully employed to predict bulk properties (density, saturated temperature, and/or pressure) of mixtures. Because of the model complexity and computationally intensive nature of these calculations, the PC-SAFT equation of state is mainly used in the “generate-and-test” and/or hybrid (decomposition-based) solution strategies (see Section 3).

Computer-Aided Molecular Design and Property Prediction Chapter j 6

For phase equilibrium properties, the well-known GC-based method is the UNIQUAC functional-group activity coefficients (UNIFAC) method and its various versions; the original UNIFAC (Fredenslund et al., 1975) and secondorder UNIFAC, called the KT-UNIFAC (an extended UNIFAC model with first-order and second-order mixture property estimations permitted) (Kang et al., 2002), are two examples. Details of various other versions of the UNIFAC method can be found in Kontogeorgis and Gani (2004). Table 6.2 gives a comprehensive list of all primary properties that can be predicted with the Marrero and Gani (2001) method using the latest extended group parameter tables of Hukkerikar et al. (2012a,b). The model equations are also given for each property in Table 6.2. For secondary, functional, and TABLE 6.2 Primary Properties and Example Calculation With Marrero and Gani and GCþ Method (Hukkerikar et al., 2012a,b; Marrero and Gani, 2001) Primary Property

Calculation as left-hand side of Eq. (6.15)

Normal boiling point (K)

exp(Tb/Tbo)

Critical temperature (K) Tc

exp(Tc/Tco)

Critical pressure (bar) Pc

(Pc/Pc1)0.5  Pc2

Critical volume (cm3/mol)

(Vc  Vco)

Melting point (K)

exp(Tm/Tmo)

Gibbs free energy (kJ/mol)

(DGf0  Gfo)

Enthalpy of formation (kJ/mol)

(DHf0  Hfo)

Enthalpy of fusion (kJ/mol)

(DHfus  Hfuso)

Octanol/water partition coefficient

log(Kow)  log(Kow0)

Flash point (K)

(Fp  Fpo)

Hansen SP (solubility parameter) (MPa1/2) D

(dD)

Hansen SP (solubility parameter) (MPa1/2) P 1/2

Hansen SP (solubility parameter) (MPa

) H2

(dp) (dH)

Enthalpy of vaporization 298 (kJ/mol)

(DHv0eHvo)

Enthalpy of vaporization Tb (kJ/mol)

(DHv  Hvbo)

Entropy of vaporization Tb (J/mol.K)

(DSv  Svbo)

1/2

)

Hildebrand SP (MPa

(d  d0)

Auto ignition temp (K)

TAiT

Acentric factor (u)

exp(u/ua) ub  uc 3

Liquid molar vol (cm /kmol)

(Vm  Vmo) Continued

163

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SECTION j II Molecular Design

TABLE 6.2 Primary Properties and Example Calculation With Marrero and Gani and GCþ Method (Hukkerikar et al., 2012a,b; Marrero and Gani, 2001)dcont’d Primary Property

Calculation as left-hand side of Eq. (6.15)

Liquid viscosity (mPa s)

log(m)

Liquid surface tension (mN/m)

S

Thermal conductivity at 298K (mW/mK)

K

Lethal concentration, fathead minnow

log(LC50FM)

Lethal concentration, Daphnia magna

log(LC50DM)

Water solubility coefficient

log(Ws)

Lethal dose oral, rat

log(LD50)

Bioconcentration factor

log(BCF)

Permissible exposure limit Occupational Safety and Health Administration - Time Weighted Average (OSHA-TWA)

log(PEL)

Photochemical oxidation potential

log(PCO)

Global warming potential

log(GWP)

Ozone depletion potential

log(ODP)

Acidification potential

log(AP)

Emission to urban air (carcinogenic)

log(EUAC)

Emission to urban air (noncarcinogenic)

log(EUANonC)

Emission to rural air (carcinogenic)

log(ERAC)

Emission to rural air (noncarcinogenic)

log(ERANonC)

Emission to freshwater (carcinogenic)

log(EFWC)

Emission to freshwater (noncarcinogenic)

log(EFWNonC)

Emission to seawater (carcinogenic)

log(ESWC)

Emission to seawater (noncarcinogenic)

log(ESWNonC)

Emission to natural soil (carcinogenic)

log(ENSC)

Emission to natural soil (noncarcinogenic)

log(ENSNonC)

Emission to agricultural soil (carcinogenic)

log(EASC)

Emission to agricultural soil (noncarcinogenic)

log(EASNonC)

Computer-Aided Molecular Design and Property Prediction Chapter j 6

TABLE 6.3 Secondary Properties and Example Calculation (Constantinou and Gani, 1994; Gani, 2004; Marrero and Gani, 2001) Secondary Properties

Functional Form

Enthalpy of vaporization Tb

f(Hv,Tb)

Critical compressibility

f(Tc,Pc,Vc)

Acentric factor (u)

f(Tb,Tc,Pc)

Liquid molar volume at Tb

f(Vc,Tb)

Liquid molar volume at 298K

f(Tc,u,Pc)

Surface tension

f(SolPar,Vm)

Refractive Index (RI)

f(SolPar)

Molar refraction

f(RI,Vm)

Entropy of fusion

f(Hfus,Tm)

Entropy of formation at 298K

f(Hf,Gf)

Closed flash temperature

f(Tb)

Open flash temperature

f(Tb)

Dipolar moment (DM)

f(SolPar,Vm)

Dielectric constant

f(SolPar,RI,DM)

Henry constant

f(Pvap,Ws,Mw)

Mw, molecular weight.

mixture properties, the functional forms in terms of the variables involved are given in Tables 6.3e6.5, respectively. A comprehensive list of models and model parameters can be found in Kontogeorgis and Gani (2004). 2.2.1.1 Example of Property Models Examples of primary, secondary, functional, and phase equilibrium properties are given below: l

primary property: molar volume at 298K (Vm298) and heat of vaporization at 298K (Hv298) X X X Vm298 ¼ vm298 þ NI CVm298 ;I þ MJ DVm298 ;J þ OK EVm298 ;k (6.16) I

Hv298 ¼ hv298 þ

J

X I

NI CHv298 ;I þ

X J

K

MJ DHv298 ;J þ

X

OK EHv298 ;k

(6.17)

K

The parameters for Eqs. (6.16) and (6.17) are explained after Eq. (6.15).

165

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SECTION j II Molecular Design

TABLE 6.4 Functional Properties and Example Calculation (Gani, 2004; Marrero and Gani, 2001; O’Connell et al., 2000; Smith et al., 2005)

l

Functional Properties

Function Form

Diffusion coefficient at infinite dilution in water

f(VmTb,T)

Liquid density

f(Tc,Pc,u,T)

Thermal conductivity

f(Tb,Tc,Mw,T)

Vapor pressure

f(Tc,Pc,T)

Enthalpy of vaporization

f(Tc,u,T)

Solubility parameter

f(Hv,Vm,T)

Liquid viscosity

f(Mw,structure,T)

Liquid heat capacity

f(Tc,u,Cpig,T)

Compressibility factor (Z)

f(Tc,Pc,u,T,P)

Enthalpy

f(Tc,Pc,u,T,P,Z,Cpig)

Entropy

f(Tc,Pc,u,T,P,Z,Cpig)

Fugacity coefficient

f(Tc,Pc,u,T,P,Z,Cpig)

secondary property: Hildebrand solubility parameter (SolPar) as a function of Hv298 and Vm298 SolPar ¼ ½ð1000  Hv298  8:314  298:15Þ=Vm298 0:5

l

functional property: vapor pressure (Pvp) as a function of temperature (T) Log10 ðPvp Þ ¼ A  B=ðT þ CÞ

TABLE 6.5 Mixture Properties and Example Calculation (O’Connell et al., 2000) Mixture Properties

Example Calculation

Activity coefficient (g)

f(T,x)

Fugacity coefficient

f(T,P,x)

Density (liquid)

f(T,P,x)

Saturation pressure

f(P,V,T)

Saturation temperature

f(P,V,T)

Solubility (liquid)

f(g,x,T,P)

Solubility (vapor)

f(g,x,T,P)

(6.18)

Computer-Aided Molecular Design and Property Prediction Chapter j 6

where, A, B, and C are fitted coefficients. The vapor pressure model of Eq. (6.18) can be converted into its GC form by making the coefficients a function of the functional groups (Ceriani et al., 2013) B lnðPvp Þ ¼ A þ þ C1k $lnðTÞ T P A ¼ Nk $ðA1k þ M$A2k Þ þ ðso þ Ncs $s1 Þ þ a$ðfo þ Nc $f1 Þ k



P

Nk $ðB1k þ M$B2k Þ þ b$ðfo þ Nc $f1 Þ

(6.19)

k



P

Nk $ðC1k þ M$C2k Þ

k l

mixture (bulk) property: the saturated temperature T or composition (solubility, x1) of a pure solid in a liquid solution is obtained from the following: ln g1 x1 ¼ 

l

    DCp Tm  T DCp Tm DHfus T ln  þ 1 Tm T RT R R T

(6.20)

where DHfus is the enthalpy of fusion, Tm is the melting temperature, x1 is the molar fraction of compound 1, g1 is the activity coefficient of component 1 for the pure compound standard state, R is the gas constant, and T is the system temperature. phase equilibrium property: activity coefficient (g1) of compound 1 in the liquid phase is obtained through the UNIFAC model as a linear combination of combinatorial and residual terms, both of which are nonlinear functions of GCs. More details of the UNIFAC model equations can be found in Kontogeorgis and Gani (2004). ln gi ¼ ln gCi þ ln gRi

(6.21)

2.3 Process Model and Other Constraints Eq. (6.4) of the mathematical problem definition represents the process model equations (usually the mass and/or energy balance equations) and other constraints, such as specifications on product purity and upperelower bounds on process operational variables.

3. MOLECULAR DESIGN: SOLUTION METHODS There are various ways to solve the product design problems as formulated by Eqs. (6.1)e(6.4). The developed solution approaches are grouped in terms of (1) heuristic or rule-based generate-and-test techniques, (2) mathematical programming techniques, and (3) hybrid techniques.

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3.1 Heuristic or Rule-Based Techniques Here, the product design problems are solved indirectly by generating alternatives and testing them for feasibility, that is, a systematic reduction of the number of alternatives through heuristics (Hill, 2004). A set of rules is derived from a combination of experience, insights, and available knowledge. A major difficulty with the rule-based methods is that the rules are sometimes contradictory and therefore difficult to apply, and they are valid within a narrow product context, and a comprehensive methodology for incorporating heuristics across many product domains has yet to be established (Hill, 2009). The advantage, on the other hand, is that these methods are easy to apply, and when the search space is not very large, the best solution can be determined. Rule-based “generate-and-test” synthesisedesign methods have been developed by Gani and Brignole (1983) and then Joback and Stephanopoulos (1989) for computer-aided molecular design (CAMD), which were based on rules to generate molecular structures by combining functional groups and use of the same functional groups for test of the molecular structures with GC-based property estimation techniques. Harper and Gani (2000) proposed a multistep and multilevel version of the “generate-and-test” method for CAMD, while heuristic design methods for cosmetic products like creams and pastes were proposed by Wibowo and Ng (2001). Fung et al. (2006) proposed rules to select chemicals for specific product applications in the form of a database search and then test them through a combination of models and experiments. Gani et al. (2008) extended the multistep and multilevel CAMD method for selection and design of solvents for organic synthesis, which was further extended by Satyanarayana et al. (2009) for design of polymer repeat unitebased products, such as bottle stops, synthetic fabric, or a heat-resistant film. Solvason et al. (2009) developed a systematic method for CAMD through a graphical approach. Here, the solution method is composed of three steps: (1) determination of the feasible property target region, (2) identification of candidate additives and ingredients, and (3) product validation. The graphical representation is based on the property cluster method (Shelley and El-Halwagi, 2000).

3.2 Mathematical Programming Techniques Here, the product design problems are solved directly through an appropriate numerical solver. A wide range of numerical methods have been developed and applied to solve the various design problems. A selection of them is highlighted as follows. A major difficulty for mathematical programming techniques is the size and complexity of the mathematical programming model. The scope and significance of the problems solved depends on the availability and application range of the models used, especially the propertyeprocess models. Odele and Macchietto (1993) used mathematical

Computer-Aided Molecular Design and Property Prediction Chapter j 6

programming in chemical product design for the optimal solvent selection problem. Venkatasubramanian et al. (1994) applied genetic algorithms to solve CAMD problems. Later, the application of mathematical programming methodology was expanded to polymer design (Vaidyanathan and El-Halwagi, 1994) and refrigerants design with the inclusion of environmental impacts as constraints (Duvedi and Achenie, 1996). Maranas (1997) employed MINLP models for molecular design with uncertainty in the functional group parameters employed for property prediction. Raman and Maranas (1998) and then Camarda and Maranas (1999) proposed the use of a lower scale for representation of the molecular structures (connectivity indices) and employed MILP models for chemical product design. Sahinidis et al. (2003) also used an MINLP model, but for a refrigerant design problem. Sinha et al. (2003) extended the MINLP models to the design of solvent blends and employed interval analysis to obtain the optimal blend. However, this type of methods can be computationally expensive for large problems. This issued was addressed by Karunanithi et al. (2005, 2006), The method utilizes an MINLP decomposition approach to design pure and mixture-based solvents. Here, the MINLP is divided into smaller subprograms of mixed integer programming (MIP), LP, and NLP that ensure all feasible candidates are searched. Solvents are not only used for extraction of solutes, but also for phase splitting to enhance the separation. Solvents are also widely used in reactions. Folic et al. (2008) presented an optimization-based method for designing solvents for optimal reaction rates. The method is divided into three steps: first, for a given model, solvents effects are modeled; second, an MINLP problem is formulated and solved; and third, the designed solvent is verified by experiments or rigorous simulation models. Kinetic data is gathered from experiments, while thermodynamic properties are estimated through developed GC-based methods. Introduction of quantum mechanical calculations for reaction rate estimation into the CAMD framework has been proposed by Struebing et al. (2013). In 2013, Samudra and Sahinidis (2013) proposed a three-stage framework consisting of composition design, structure determination, and extended design to solve the CAMD problem. The novelty of this solution approach is the structure determination stage, which enables the possibility of identifying unique molecular structures, such as isomers.

3.3 Hybrid Techniques Here, rule-based methods, the generate-and-test techniques, and the mathematical programmingebased methods are integrated for various efficient solutions. The objective here is to use different methods in the region where they perform best. The computer-aided product design framework presented in the following section employs hybrid techniques for various product design problems.

169

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SECTION j II Molecular Design

4. COMPUTER AIDED PRODUCT DESIGN: FRAMEWORK In this section, the computer-aided framework (Cignitti et al., 2015) for chemical product design is presented. The framework is composed of four sequential steps that enable the formulation and solution of various types of CAMD problems based on selection of appropriate solution strategies. The four steps with their associated methods, tools, and information flow are shown in Fig. 6.3. Each step is briefly described, together with its required databases, model libraries, and tools in the following text.

4.1 Step 1: Problem Definition In this step, the chemical product needs are defined. These are translated into target properties and target specifications and the target property values are set. Step 1.1 The problem definition includes the needs, chemical product type, and the process and/or application of the chemical product. It is important to specify this as clearly and concisely as possible. The needs include target properties, cost, and environmental impact of the chemical product. The chemical product type includes a combination of the four types of properties, depending on the molecular design problem. A database is used to help identifying the needs for specific products. The database used here is part of VPPD-Lab (Kalakul et al., 2016). Step 1.2 The needs are translated into target properties. For this, specific property types and respective models are to be selected based on the needs. For example, if the need is to generate a solvent that is a higher boiling component than the mixture, the normal boiling point is the target property. Similarly, if a refrigerant is to be designed that has a high efficiency in a vaporecompression cycle. the enthalpy of vaporization can be the target property (see Table 6.4). Step 1.3 Target property values are set in terms of lower and upper bounds or as fixed values. These are derived from the needs and specifications on the product. Here, it is useful to utilize a database to see what target values can be set for the given needs. For example, if it is needed that the solubility of the generated chemical product should be similar to that of water (47.8 MPa0.5), then the target solubility can be between 45 and 50 MPa0.5. If a working fluid should be designed to operate in the subcritical region of a cycle with maximum pressure of 40 bars, critical pressures lower than 40 bars are the target value. Similarly, if an ingredient in a blend is to be designed to be within the toxicity limits for humans, an LC50 value above three can be selected as the target value.

Methods and Tools

Work Flow

InformaƟon Flow

START

Product needs



• • • •

(1) Define the problem (2) Translate needs into target properƟes (3) Set the target property values

Databases

• •

Target property values Economic/Sustainability/ Environment models

• • • •

Set of candidate groups ObjecƟve funcƟon Upper and lower bound of target properƟes Process/Product model equaƟons



MI(N)LP model

• •

List of candidates Report generaƟon

Step 2: CAMD constraint selecƟon

Knowledge base Model libraries Model generaƟon Grand Product Design model

(1) Structure model, groups & backbone (2) Property Thermodynamic model (3) Process model selecƟon (5) ObjecƟve funcƟon selecƟon

Step 3: CAMD formulaƟon • • •

Generate&Test (ProCAMD, SolventPro, CAPEC-Database) OpƟmizaƟon soŌware (Solvers: CPLEX, BARON, ...) Simultaneous or decomposed approach

Step 4: SoluƟon strategy (1) SelecƟon of soluƟon algorithm (2) SelecƟon of MI(N)LP solver (3) SoluƟon of MI(N)LP

SoluƟon found? N END

FIGURE 6.3 Computer-aided framework for chemical product design.

Computer-Aided Molecular Design and Property Prediction Chapter j 6

• Step 1: Problem DefiniƟon

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SECTION j II Molecular Design

4.2 Step 2: Computer-Aided Molecular Design Constraint Selection In this step, the CAMD constraints are selected based on the problem definition. The constraints needed include objective function and structure, property, thermodynamic, and process models (See Section 2). Step 2.1 The structural model is selected here, including the desired groups and, if needed, backbone structure is used. Structural models include models for how groups can be connected to form feasible molecules. The adjacency matrix can be used as a model here if differentiation between isomers and higher property prediction accuracy of primary properties is needed. The target molecular groups are based on a selection of the 220 Marrero and Gani groups and the occurrence of molecular and functional groups (a list of the 220 first order groups are given in Appendix A). In the backbone structure, a fixed part of the molecule can be defined, such as a benzene ring, and the molecules generated will be built on the benzene structure. In addition, for the generation of polymer monomer units, two free-bonding sites should be left free. If a pure molecule in a mixture is to be designed, it also needs to be defined. This is necessary when calculating mixture properties where the application process of the designed solvents needs to be evaluated. Step 2.2 Thermodynamic model selection is necessary when a phase equilibrium model or equation of state is to be utilized for the prediction of mixture miscibility, azeotropic composition, phase behavior, and other problem-specific properties. These types of models are readily available; for example, solvent design problems require the estimation of liquid phase activity coefficients for use in phase equilibrium (vaporeliquid, liquideliquid, or solideliquid systems). Examples of models of this type are UNIFAC (Fredenslund et al., 1975) for liquid phase activity coefficients and/or the Soave-Redlich-Kwong (SRK) equation of state (Soave, 1972) for vapor phase fugacity coefficients. Property models must be selected based on the identified target properties for a specific product design problem. Depending on the type of property (primary, secondary, functional, and mixture), relevant models are stored in the model library of the framework, which has been implemented in the VPPD-Lab (product design simulator). For example, if it is necessary to estimate the critical temperature of the generated molecules, the appropriate model plus group parameters are retrieved from the model library of the framework. The framework has a large collection of property models (Kalakul et al., 2016). Step 2.3 The process model, if applicable, is introduced in this step and depends on whether the process issues are included or not in the product design problem. In the case of a refrigerant design, availability of a process operation models helps to simultaneously design the molecule and optimize the application

Computer-Aided Molecular Design and Property Prediction Chapter j 6

process operation. Also in the case of solvent design, the application process performance model may be included. The process variables that affect the design problem objective function need to be clearly identified, and the process model equations are usually introduced as equality constraints, while process specifications are given as inequality constraints. The process variables should ideally be variables that also affect the chemical product properties; for example, the temperature of operation defines the process operation feasibility as well as the functional properties of the chemical product. For example, in a refrigerant design problem, a set of target properties, together with an objective function that is dependent on process variables affecting the operation of a thermodynamic cycle, may be specified. Step 2.4 The objective function is defined here. Depending on the specific design problem, the selected objective function will be optimized subject to the process operation, the chemical product properties, with or without other specifications (cost, environmental impact, etc.). It is also possible not to define (select) any objective function, in which case, a set of unranked feasible solutions will be obtained.

4.3 Step 3: Computer-Aided Molecular Design Formulation In step 3, the constraint equations are collected to define the generic CAMD problem formulation as a mathematical programming problem. The general form of the MINLP is given by Eqs. (6.1)e(6.4). The type of mathematical program MILP or MINLP formulated depends on the constraints selected in step 2. The CAMD problem includes integer variables, which come from the selection of molecular groups. The form of the CAMD problem (linear or nonlinear) depends on the choice of the property model and process model equations. Note that depending on how the property constraints are defined, many of the property constraints can be represented as linear equations. For example, if the boiling point target is given as the property function (left-hand side of primary property models), then the property constraints introduced are linear functions, as can be seen from Eq. (6.22).   X Tb Ni Ci ¼ exp (6.22) T bo i

4.4 Step 4: Solution Strategy In this step, the solution strategy is chosen to solve the corresponding mathematical programming problem. Note that all three types of solution techniques are available through the framework, and in principle, any solution strategy can be applied to solve a problem. For example, a simple database search may be applied if experimentally measured data based solution is

173

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desired (ignoring, for example, the objective function), or, for a given set of functional groups, all structures satisfying the set of structural constraints are first generated and then tested for the target properties and then the process constraints. For the final feasible set of molecules, the objective function is calculated to identify the optimal, or all the constraints and the objective function may be solved together for the same set of functional groups through an appropriate numerical solver. Step 4.1 The solution strategies implemented in the framework and available in the VPPD-Lab product design simulator are shown in Fig. 6.4. Database approach: This solution strategy is used when an objective function is either not defined or used and only pure component property targets are specified. In many cases, it is useful to solve a partial problem with only selected property constraints to get a good initial idea of the design problem search space. ProCAMD approach: Here, the generate-and-test algorithm of Harper and Gani (2000) is employed to solve a wide range of single molecular product design problems. Any number of property constraints may be added as long as they are available in the property model library. Also, some implicit process constraints are possible to include. This approach generates (enumerates) all the feasible solutions within the defined search space. Finding the optimal in this case requires the calculation and ordering of the objective function values for the feasible molecules. Mathematical programming approach: For this approach, two solutions options are available: direct solution and decomposed solution of MINLP problem. Both of these solution strategies are highlighted in Fig. 6.5.

Soluon Approach

No obj. fucnon

Obj. funcon

Database search

ProCAMD or Mathemacal Programming (Cigni et al., 2015)

ProCAMD (Harper and Gani, 2000) or Mathemacal programming (unranked feasible soluons)

FIGURE 6.4 Solution strategies.

Computer-Aided Molecular Design and Property Prediction Chapter j 6

FIGURE 6.5 The workflow for mathematical programming approach (direct and decomposed). MINLP, Mixed-integer nonlinear programming.

175

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SECTION j II Molecular Design

In the direct solution of the MINLP problem, all constraints are solved simultaneously with the objective function. Thus, the chemical product is designed together with the process design issues. This is an advantage when feasible, as both the chemical product and process design problems sometimes contain a common set of variables. However, the MINLP problem, depending on the type of problem, may become very large due to the number of equations and variables. It is therefore recommended to utilize the direct solution approach when the MINLP problem is reduced to an MILP problem or when the numerical solver is able to handle the nonlinearity of the equations. When the problem cannot be solved directly, use of a decomposed solution strategy is an option. Here, the constraints and objective function are separated into smaller subsets according to a hierarchical order (Karunanithi et al., 2005). Each subproblem (except the final) requires only the solution of a subset of the constraints from the original set. The final subproblem contains the objective function and the remaining constraints. In this way, the solution of the decomposed set of subproblems is equivalent to that of the original MINLP problem. The advantage is a more flexible solution approach together with relatively easy to solve subproblems and a solvable “final” MINLP subproblem. As each subproblem is being solved, a large portion of the infeasible part of the search space is deleted, thereby leading to a final subproblem that is a significantly smaller MINLP or NLP problem, which can be solved more easily. As all the subproblems except the final subproblem are constraint satisfaction problems, global optimality can be guaranteed if a global optimization algorithm is used to solve the final subproblem. For example: l l l l

Step I: structural constraints form an MILP subset. Step II: pure component constraints form an LP subset. Step III: mixture property constraints form an MILP or MINLP subset. Step IV: the objective function and process design constraints as a final subset of smaller NLP problems; note that an NLP problem is solved for each candidate chemical product in this step.

Step 4.2 Here, the MINLP solver is chosen. The framework provides links to the GAMS optimization environment (GAMS, 2011) if it is selected as the solver. If utilizing a decomposed approach, an MILP, MINLP, LP, and NLP are employed according to the specific problem type. Step 4.3 Here, the MINLP program is solved with the chosen solution strategies (direct or decomposed) and with the chosen optimization solver. If a solution is not found with the direct approach, the decomposed approach is tried. Good initial estimates may be obtained through database search and/or generate and test (ProCAMD).

Computer-Aided Molecular Design and Property Prediction Chapter j 6

5. CASE STUDIES The application of the framework is highlighted here through two case studies involving the design of refrigerant and a surfactant.

5.1 Refrigerant Design A refrigerant for a refrigeration cycle is to be designed. This is a replacement problem for a vaporecompression cycle using R-134a refrigerant. Due to recent regulations, R-134a and other commonly used refrigerants are being phased out (Mota-Babiloni et al., 2015). A study suggests R-1234yf to be a promising replacement for R-134a (Navarro-Esbrı´ et al., 2013). Step 1: Problem definition In this case study, promising candidates to replace R-134a are to be found. The refrigeration cycle is shown in Fig. 6.6. The refrigerant to be designed is sought to have the same or better performing target properties. In addition, it should be able to function under similar operating conditions as typical systems that use R-134a. Therefore, the new refrigerant should have similar or better environmental properties, similar or improved thermodynamic properties, and should be able to operate under similar conditions. Analysis of thermodynamic properties requires the consideration of both the molecular thermodynamic properties and the performance of the refrigerant in the application process (the refrigeration cycle). Analysis of similar process performance requires the analysis of thermodynamics of the

Compressor

P1, T1

P2, T2

Evaporator

Condenser

P4, T4

P3, T3 Expansion Vavle

FIGURE 6.6 Vapor compression cycle.

177

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SECTION j II Molecular Design

refrigeration cycle. An indication of similar process and thermodynamic behavior is initially obtained through analysis of pressureevolumee temperature energy diagrams. Such diagrams for R134a and R1234yf are found in handbooks (ASHRAE, 2009). Comparison of the energy diagrams point to a clear similarity between the diagrams of R134a and R1234yf, while values of normal boiling point temperature, critical temperature, pressure, and the range of pressures with their respective enthalpy values all appear to be also similar. Step 2: CAMD constraint selection The CAMD problem is formulated based on the collected properties of R134a (see Table 6.6). Based on the data of Table 6.6, the target properties are selected (see Table 6.7). From Navarro-Esbrı´ et al. (2013), the ranges for condensation and evaporation temperatures are obtained (see Table 6.8). The following molecular groups are included in the search: CH3, CH2, CH, C, CF3, CF2, CF, CH2F, CHF, CHF2, CCl2F, HCClF, CClF2, CHCl, CCl, CHCl2, CCl2, and CCl3. As the objective function, the cycle efficiency (that is, coefficient of performance, COP) is selected. The COP is the ratio of enthalpy difference in the evaporator and the compressor. The evaluation of the objective function therefore needs models for enthalpy at different states. Note that for calculation of enthalpy at state 2 (superheated vapor), the entropy must also be calculated for the isentropic compression. Fugacity coefficients are needed to TABLE 6.6 R-134a Properties Property of R134a

Value

Molecular weight

102.03 mol/g

Normal boiling point

247.15K

Critical temperature

374.15K

Critical pressure

40.59 bar

Acentric factor

0.33

Enthalpy of Vaporization at Tb

215.9 kJ/kg

ODP

0

GWP

1370

Atmospheric lifetime

13.4 years

Thermal conductivity (liquid, Tb)

0.103 W/m K

Thermal conductivity (vapor, Tb)

0.009 W/m K

Computer-Aided Molecular Design and Property Prediction Chapter j 6

TABLE 6.7 Target Product Properties Target Product Property

Lower Bound

Molecular mass

Upper Bound 110 g/mol

a

250K

Normal boiling point a

Critical temperature a

Critical pressure

Enthalpy of Vaporization at

Tba

Thermal conductivity (liquid, Tb)

350K

400K

30 bar

50 bar

200 kJ/kg a

0.08 W/m K

a

0

ODP

a

1400

GWP

b

14 years

Atmospheric lifetime Number of groups

1

10

Number of functional groups

0

2

a

Properties calculated with Marrero and Gani (2001) and (Hukkerikar et al., 2012a,b) method. Property must be looked up in literature.

b

check that in state 3, a saturated liquid is obtained, and in state 1, a saturated vapor is obtained. Enthalpy, entropy, and fugacity coefficients are calculated as a function compressibility factor and temperature by the model of Rao (1997) derived from SoaveeRedlicheKwon (Soave, 1972) equation of state. For the molecular design, constraints for the generation of feasible acyclic molecules and constraints for the number of groups and functional groups are obtained from Cignitti et al. (2015). Since cubic equation of state has three roots (for the compressibility factor, Z) at the two-phase region and one root in the liquid and vapor regions, the search for the roots needs special attention. The three roots in the two-phase region include a lower liquid root, midroot that is not to be used, and a higher vapor root. For the solution of the cubic equation of state, it is recommended to use as initial estimate, Zv ¼ 1 and Zl ¼ B (Lawal, 1987). Kamath et al. (2010) proposed a set of constraints for inclusion in the TABLE 6.8 Process Specifications Process Specifications

Lower Bound

Upper Bound

Condensation temperature

313.15K

333.15

Evaporation temperature

265.65K

280.15

179

180

SECTION j II Molecular Design

mathematical problem formulation to ensure that the correct root is always found by the solver. These constraints are applied for vapor and liquid compressibilities at states 1, 2, and 3. Step 3: CAMD problem formulation The CAMD problem is now formulated in terms of the given the target properties, process constraints by retrieving the corresponding models from the model library of the framework as Tables 6.7 and 6.8 shows. The CAMD problem formulation is given in Appendix B. The obtained mathematical formulation is an MINLP model. It is worth pointing out here that multiobjective optimization can also be used for the CAMD problem formulation if multiple criteria decision-making is considered. In this case study, the efficiency and environmental impact can be two objective functions if these two factors are considered at the same time. Step 4: Solution strategy Three options [database search, ProCAMD as well as MINLP (direct and decomposed)] are used to solve the problem. For the mathematical programming approach, the BARON optimizer (Sahinidis, 1996) is employed with direct optimization. There are 92 equations, 49 continuous variables, and 19 discrete variables in this MINLP optimization problem. The properties of five promising molecules found by the solver are given in Table 6.9. It can be noted that R134a is also found by the solver. The second molecule is a known chemical also called 1,1-difluoroethane or R-152a. The third and fourth molecules are triple-bonded and double-bonded refrigerants, respectively. As they may suffer self-polymerization, they are not considered further. The fifth molecule is 2,2-difluorobutane, which probably has not been reported before as a refrigerant. R-152a has very similar properties to R134a, but performs better in terms of environmental properties. To further refine the solution, all three refrigerants (without the third and fourth) are now used for the NLP subprogram (step IV) to find the optimal operating conditions. Two NLP problems, one for each candidate, are now solved to establish the best refrigerant. The KNITRO optimizer in GAMS (Byrd et al., 2006) is used. KNITRO utilizes an interior point optimization method. The last row of Table 6.9 gives the optimal COP values for each refrigerant. It can be seen from the results that R152a obtains a higher COP value than R134a in addition to having better environmental properties. The solution strategies using ProCAMD and database search are also employed to highlight alternative solution approaches available through the framework. The problem has to be simplified by removing the process constraints and objective function equations. A database search with constraints for Mw, Tb, Tc, Pc, and u found the following six molecules. These are propylene, propane, methylsilane, 1,1-difluoroethane, chlorodifluoromethane, and 1,1,1,2-tetrafluoroethane. 1,1-Difluoroethane is the R-152a found through the mathematical programming also.

Property

R134a

R152a

3,3,3-Trifluoropropyne

3,3-Difluorobutene

2,2-Difluorobutane

Mw

102 g/mol

66 g/mol

94 g/mol

92 g/mol

94.1 g/mol

Tb

236K

230K

242K

246K

252K

Tc

374K

366K

369K

392K

389K

Pc

37.32 bar

46.75 bar

38.13 bar

39.27 bar

37.8 bar

U

0.33

0.27

0.28

0.14

0.18

k

0.082 W/m K

0.097 W/m K

0.086 W/m K

0.093 W/m K

0.092 W/m K

DHv at Tb

26523 J/mol

28562 J/mol

18635 J/mol

21312 J/mol

26991 J/mol

ODP

0

0

0

0

0

GWP

1370 (ASHRAE, 2009)

133 (ASHRAE, 2005)

134.6

2.4

0.9

Atmospheric lifetime

13.4 years (ASHRAE, 2009)

1.5 years (ASHRAE, 2005)

e

e

e

COP

10.1

12.8

9.5

11

11.1

Computer-Aided Molecular Design and Property Prediction Chapter j 6

TABLE 6.9 Molecular Design Results

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FIGURE 6.7 ProCAMD screenshot (Harper and Gani, 2000).

Applying also ProCAMD, 11 molecules were found, including the ones listed in Table 6.9. A screenshot from ProCAMD highlighting the solution statistics is given in Fig. 6.7.

5.2 Surfactant Design as Emulsifier for Emulsified Ultraviolet Sunscreen The aim of this case study is the design of a UV sunscreen in the emulsified form with a high sun protection factor. In this case study, second-order groups are considered in the group contribution model for more accurate property estimation, and the structural constraints including the adjacency matrix added to the mathematical programming problem so that large complex molecules can be obtained. Step 1: Problem definition A UV sunscreen is a product that absorbs or reflects some of the UV radiations, and it is applied on the human skin to help protect from sunburns when exposed to sunlight. From the available knowledge base, the consumer needs found for this type of products are listed in Table 6.10.

Computer-Aided Molecular Design and Property Prediction Chapter j 6

TABLE 6.10 Distinction Between Main and Secondary Consumer Needs for UV Sunscreen Consumer Needs

Main Consumer Needs

Protection from sunburns

O

Protection from the risk of skin cancer

O

Secondary Consumer Needs

Prevention of skin aging

O

Waterproofness

O

Pleasant odor

O

Pleasant color

O

Pleasant skin feeling

O

Good stability

O

Low toxicity

O

High safety

O

Sprayability

O

Based on information in the knowledge base, the consumer needs are separated into main consumer needs and secondary consumer needs (see Table 6.10). Those ingredients satisfying the main needs are classified as AI, while those ingredients satisfying the secondary needs are defined as additives. In this case study, only the design of the AI is considered. Therefore, some secondary consumer needs are not considered (these needs can be satisfied through adding additives to the product). The main consumer needs are translated into target properties to formulate the UV sunscreen design problem. The upper and lower bounds for the target properties are set (see Table 6.11) based on the consumer needs (Mattei et al., 2014). The most important consumer needs for a UV sunscreen is protection from sunburns, but there is no specific molecular property that could be attributed to this need, so after molecules that satisfy all other target properties are found, UV sunscreen protection can be verified by experiment. From the analysis of all sunscreens available on the market, it is seen that all molecules contain a benzene ring (Shaath, 2005). Thus, benzene ring is fixed as backbone structure in the design of surfactants for this product. Step 2: CAMD constraint selection In the CAMD formulation step, candidate groups for the formulation of the molecule is selected based on the known UV sunscreen product. The basic set

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TABLE 6.11 Target Properties and Their Values for a UV Sunscreen in the Emulsified Form Consumer Needs

Target Properties

Boundaries of Acceptance

Unit of Measure

Protection from sunburns

e

e

e

Protection from the risk of skin cancer

e

e

e

Waterproofness

Solubility parameter (dT)

dT < 25

MPa1/2

Good stability

Cloud point (Tcp)

Tcp > 70



Low toxicity

Toxicity parameter (LC50)

LC50 > 3.16

log(mol/L)

High safety

Flash point (Tf)

Tf > 70



Other needs

Molar volume (Vm)

0.1 < Vm < 0.3

cc/mol

Molecular type I

Number of identical molecular groups

0 < ni1 < 5

e

Molecular type II

Functional molecular groups

10 < ni < 15

e

C

C

of groups is selected from the 220 groups of Marrero and Gani (2001) to include: CH3, CH2, CH, C, aCH, aCeOH, CH2COO, CH3O, CH2O, aCeO, and OCH2CH2OH. eOeC6H4eOH is fixed as backbone structure for the function of protection from sunburns. The target property values are listed in Table 6.11. Predictive property models are needed here to estimate the properties from the molecular structure information. Group contribution methods are extensively considered here since they only need the molecular structure of the pure component and they exhibit a good accuracy together with a wide range of applicability. Marrero and Gani group contribution model (Marrero and Gani, 2001) is used to estimate dT, LC50, Tf, and Vm, employing two levels. One of the surfactantrelated pure compound properties considered necessary for the development of a model-based methodology for surfactant design is the cloud point (Tcp), sometimes called the cloud temperature. In this case study, a group contribution model developed by Mattei et al. (2014) for the estimation of cloud point is used. Step 3: CAMD formulation In the MINLP formulation step, a mathematical programming model consisting of objective function, structural constraints (including adjacency,

Computer-Aided Molecular Design and Property Prediction Chapter j 6

property constraints (of target property values), and other relevant constraints are established in this step. The full set of constraint equations are given in Zhang et al. (2015). Step 4: Solution strategy The established MINLP model from step 3 is solved. In this case study, the optimization model is solved directly using the GAMS software CPLEX solver. There are 1,324,764 equations, 1,286,278 continuous variables, and 1,286,266 discrete variables in this MILP optimization model. The optimization results are given in Table 6.12.

5.3 Other Application Examples The CAMD framework and its associated tools are applied to solve a very large range of problems, for example, solvent design for various applications, lubricant design, and many more. Interested readers can obtain detailed problem formations and solutions of these problems by contacting the corresponding author of this chapter.

TABLE 6.12 Optimization Results of UV Sunscreen Design Problem Molecular structure

HO

O

O O

O

OH

n1

1 CH3, 5 CH2, 1 CH, 4 aCH, 1 aCeOH, 1 CH2COO, 1 aCeO and 1 OCH2CH2OH

n2

O HO

Property

Unit of measure

Value

LC50

log(mol/L)

4.124

1/2

dT

MPa

24.732

Tcp

K

300.016

Tf

K

552.383

Vm

cc/mol

0.281

185

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SECTION j II Molecular Design

6. FUTURE CHALLENGES AND CONCLUDING REMARKS A computer-aided framework for chemical product design has been presented, and its application has been shown through two chemical product design case studies. The first case study involves the design of a molecular product (refrigerant) where the application process has been included in the mathematical programming problem and simultaneously optimized with the molecular design problem. Promising refrigerants have been found as the replacement of R-134a. In the second case study, a surfactant has designed for a UV sunscreen blend. Here, how molecular design is important in the design of other chemical products is highlighted. The designed surfactant meets the specified needs as well as the environmental constraints. These case studies also illustrate the general nature of the chemical product design framework, which has been implemented into the VPPD-Lab, the chemical product design simulator (Kalakul et al., 2016). Finally, although not highlighted in this chapter, the framework can also be applied to multiple molecule-based products, such as lubricant blends and solvent mixtures. This confirms the generic nature of the computer-aided product design framework, which can play a major role in the future development of innovative new chemical-based products. However, even though it has been shown that a wide selection of chemical products can be designed, there are still challenges and many unsolved problems. To design novel molecules and novel chemical products, a wide range of property models and data are necessary. Some models needed today are simply not available or too inaccurate to be reliable. The lack of data drives the need for more predictive property methods. Methods, tools, and solution strategies also need to be carefully selected, and new versions may need to be developed, depending on the nature of the chemical product design problems.

APPENDICES Appendix A: List of Marrero and Gani (2001) First-Order Groups Groups CH3 CH2 CH C CH2]CH CH]CH CH2]C CH]C C]C

Groups CN, except as above CH2NCO CHNCO CNCO aCeNCO CH2NO2 CHNO2 CNO2 aCeNO2

Groups CH3S CH2S CHS CS aCeSe SO SO2 SO3 (sulfite) SO3 (sulfonate)

Computer-Aided Molecular Design and Property Prediction Chapter j 6

Groups CH2]C]CH CH2]C]C C]C]C CH^C C^C aCH aC fused with aromatic ring aC fused with nonaromatic ring aC, except as above aN in aromatic ring aCeCH3 aCeCH2 aCeCH aCeC aCeCH]CH2 aCeCH]CH aCeC]CH2 aCeC^CH aCeC^C OH aCeOH COOH aCeCOOH CH3CO CH2CO CHCO CCO aCeCO CHO aCeCHO CH3COO CH2COO CHCOO CCOO HCOO aCeCOO aCeOOCH aCeOOC COO, except as above CH3O CH2O CHeO CeO aCeO CH2NH2 CHNH2 CNH2

Groups NO2, except as above ONO ONO2 HCON(CH2)2 HCONHCH2 CONH2 CONHCH3

Groups SO4 (sulfate) aCeSO aCeSO2 PH (phosphine) P (phosphine) PO3 (phosphite) PHO3 (phosponate)

CONHCH2

PO3 (phosponate)

CON(CH3)2 CONCH3CH2 CON(CH2)2 CONHCO CONCO aCeCONH2 aCeNH(CO)H aCeN(CO)H aCeCONH aCeNHCO aCe(N)CO NHCONH NH2CONH NH2CON NHCON NCON aCeNHCONH2 aCeNHCONH NHCO, except as above CH2Cl CHCl CCl CHCl2 CCl2 CCl3 CH2F CHF CF CHF2 CF2 CF3 CCl2F HCClF CClF2 aCeCl aCeF aCeI aCeBr eI, except as above

PHO4 (phosphate) PO4 (phosphate) aCePO4 aCeP CO3 (carbonate) C2H3O C2H2O C2HO CH2 (cyclic) CH (cyclic) C (cyclic) CH]CH (cyclic) CH]C (cyclic) C]C (cyclic) CH2]C (cyclic) NH (cyclic) N (cyclic) CH]N (cyclic) C]N (cyclic) O (cyclic) CO (cyclic) S (cyclic) SO2 (cyclic) >NH eOe eSe >CO PO2 CHeN SiHO SiO SiH2 SiH Si (CH3)3N N]N Ccyclic]Ne Ccyclic]CHe Ccyclic]NH

187

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SECTION j II Molecular Design

Groups CH3NH CH2NH CHNH CH3N CH2N aCeNH2 aCeNH aCeN NH2, except as above CH]N C]N CH2CN CHCN CCN aCeCN

Groups eBr, except as above eF, except as above eCl, except as above CHNOH CNOH aCeCHNOH OCH2CH2OH OCHCH2OH OCH2CHOH eOeOH CH2SH CHSH CSH aCeSH eSH, except as above

Groups N]O Ccyclic]C P]O N]N C]NH >C]S aCeCON aC]O aNe eNa eK HCONH CHOCH C 2O SiH3 SiH2O CH]C]CH CH]C]C OP(]S)O R CF2cyclic CFcyclic

Appendix B: Refrigerant Design Computer-Aided Molecular Design Formulation Objective function

max Obj ¼

s.t. Molecular constraints Octet rule

X

H1  H3 H2  H1

ni ð2  vi Þ ¼ 2

i

Total number of groups

Number of functional groups

1

X

ni  10

i

0

X

ni  ni ðCH3 Þ  ni ðCH2 Þ

i

 ni ðCHÞ  ni ðCÞ  5

Computer-Aided Molecular Design and Property Prediction Chapter j 6

Property constraints Critical temperature

X

Tc ¼ Tc0 log

! ni Tci

i

Critical pressure

12

0 B Pc ¼ @P i

1 ni Pci þ Pc02

Acentric factor u ¼ uA log

X

C A þ Pc01

! uB ni ui þ uC

i

Thermal conductivity Global warming potential Ozone depletion potential Compressibility factor (Rao, 1997)



X

n i ki

i

GWP ¼ log

X

! ni GWPi

i

ODP ¼ log

X

! ni ODPi

i

 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Tc2 P1  1 þ k 1  T1 =Tc T12 Pc   !  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 T 3P 2 Tc P1 Tc P1 2 U  U  UJR c3 12 1 þ k 1  T1 =Tc Pc T1 Pc T1 T1 Pc

0 ¼ ZV3 1  ZV2 1 þ ZV 1 JR

 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Tc2 P2  1 þ k 1  T2 =Tc T22 Pc   !  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 T 3P 2 Tc P2 Tc P2 2 U  U  UJR c3 22 1 þ k 1  T2 =Tc Pc T2 Pc T2 T2 Pc

0 ¼ ZV3 2  ZV2 2 þ ZV 2 JR

 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Tc2 P3  1 þ k 1  T3 =Tc T32 Pc   !  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 T 3P 2 Tc P3 Tc P3 2 U  U  UJR c3 32 1 þ k 1  T3 =Tc Pc T3 Pc T3 T3 Pc

0 ¼ ZV3 3  ZV2 3 þ ZV 3 JR

 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Tc2 P1  1 þ k 1  T1 =Tc T12 Pc   !  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 T 3P 2 Tc P1 Tc P1 2 U  U  UJR c3 12 1 þ k 1  T1 =Tc Pc T1 Pc T1 T1 Pc

3 2 0 ¼ ZL1  ZL1 þ ZL1 JR

 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Tc2 P3  1 þ k 1  T3 =Tc 2 T3 Pc  !   pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 T 3P 2 Tc P3 Tc P3 2 U  U  UJR c3 32 1 þ k 1  T3 =Tc Pc T3 Pc T3 T3 Pc

3 2 0 ¼ ZL3  ZL3 þ ZL3 JR

189

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SECTION j II Molecular Design

For correct root identification (Kamath et al., 2010)

Entropy

f ðZV 1 Þ ¼ 0 f 0 ðZV 1 Þ  0 f 00 ðZV 1 Þ  0 f ðZV 2 Þ ¼ 0 f 0 ðZV 2 Þ  0 f 00 ðZV 2 Þ  0 f ðZL3 Þ ¼ 0 f 0 ðZL3 Þ  0 f 00 ðZL3 Þ  0 X

SV 1 ¼ S0 þ

! ni CpAi  CpA0

þ

i

þ

X

X

! ni CpBi þ CpB0 T1

i

! ni CpCi  CpC0 T12 þ

i

X

! ni CpDi þ CpD0 T13

i

    P1 Tc P1  R ln þ R ln ZV 1  U P0 Pc T1 1 0   Tc P1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi ZV 1 þ U C Tc k B RJ 1 þ k 1  T1 =Tcn Pc T1 C B pffiffiffiffiffi lnB  C A @ U ZV 1 T1

X

SV 2 ¼ S0 þ

! ni CpAi  CpA0

þ

i

þ

X i

X

! ni CpBi þ CpB0 T2

i

! ni CpCi  CpC0 T22 þ

X

! ni CpDi þ CpD0 T23

i

    P2 Tc P2 þ R ln ZV 2  U  R ln P0 Pc T2 1 0   Tc P2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi Tc k B Z V 2 þ U P T C RJ 1 þ k 1  T2 =Tcn c 2C pffiffiffiffiffi  lnB A @ U ZV 2 T2

Computer-Aided Molecular Design and Property Prediction Chapter j 6

Enthalpy

X

HV 1 ¼ H0 þ

! þ

ni CpAi  CpA0

X

i

þ

X

! ni CpBi þ CpB0 T1 þ

X

i

! ni CpCi  CpC0 T12

i

! ni CpDi þ CpD0 T13 þ RT1 ðZV 1

i

 pffiffiffiffiffiffiffiffiffiffiffiffiffi  JR   1Þ  1 þ k 1  T1 =Tc U

0 1 Tc P1 ZV 1 þ U C pffiffiffiffiffiffiffiffiffiffiffi   pffiffiffiffiffiffiffiffiffiffiffiffiffi   B Pc T1 C B  T1 Tc k þ 1 þ k 1  T1 =Tc Tc lnB C @ A ZV 1

X

HV 2 ¼ H0 þ

! þ

ni CpAi  CpA0

X

i

þ

X

! ni CpBi þ CpB0 T2 þ

X

i

! ni CpCi  CpC 0 T22

i

! ni CpDi þ CpD0 T23 þ RT2 ðZV 2  1Þ 

i

 pffiffiffiffiffiffiffiffiffiffiffiffiffi  JR  1 þ k 1  T2 =Tc U

0 1 Tc P2 pffiffiffiffiffiffiffiffiffiffi   pffiffiffiffiffiffiffiffiffiffiffiffiffi   BZV 2 þ U P T C c 2C B  T2 Tc k þ 1 þ k 1  T2 =Tc Tc ln@ A ZV 2 X

HV 3 ¼ H0 þ

! ni CpAi  CpA0

þ

X

i

þ

X

! ni CpBi þ CpB0 T3 þ

X

i

! ni CpCi  CpC 0 T32

i

! ni CpDi þ CpD0 T33 þ RT3 ðZV 3  1Þ 

i

 pffiffiffiffiffiffiffiffiffiffiffiffiffi  JR  1 þ k 1  T3 =Tc U

0 1 Tc P3   pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi   BZV 3 þ U Pc T C 3 C  T3 Tc k þ 1 þ k 1  T3 =Tc Tc lnB @ A ZV 3 X

HL1 ¼ H0 þ

! þ

ni CpAi  CpA0

i

þ

X

X

! ni CpBi þ CpB0 T1 þ

i

X

! ni CpCi  CpC 0 T12

i

! ni CpDi þ CpD0 T13 þ RT1 ðZL1

i

 pffiffiffiffiffiffiffiffiffiffiffiffiffi  JR  1 þ k 1  T1 =Tc  1Þ  U

1 0 Tc P1 pffiffiffiffiffiffiffiffiffiffi   pffiffiffiffiffiffiffiffiffiffiffiffiffi   BZL1 þ U P T C c 1 C  T1 Tc k þ 1 þ k 1  T1 =Tc Tc lnB A @ ZL1 X

HL3 ¼ H0 þ

! ni CpAi  CpA0

i

þ

X i

þ

X

! ni CpBi þ CpB0 T3 þ

i

! ni CpDi þ CpD0 T33 þ RT3 ðZL3

X

! ni CpCi  CpC 0 T32

i

 pffiffiffiffiffiffiffiffiffiffiffiffiffi  JR   1Þ  1 þ k 1  T3 =Tc U

0 1 Tc P3 pffiffiffiffiffiffiffiffiffiffi   pffiffiffiffiffiffiffiffiffiffiffiffiffi   BZL3 þ U P T C c 3C  T3 Tc k þ 1 þ k 1  T3 =Tc Tc lnB @ A ZL3

191

192

SECTION j II Molecular Design

Fugacity coefficient

0

  B Tc P1 4V 1 ¼ expB @ZV 1  1  ln ZV 1  U Pc T1 11 0 Tc P1  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 BZV 1 þ U P T CC JR Tc  c 1 CC 1 þ k 1  T1 =Tc lnB  AA @ U T1 ZV 1 0

  B Tc P1 4L1 ¼ expB @ZL1  1  ln ZL1  U Pc T1 11 0 Tc P1  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 BZL1 þ U P T CC JR Tc  c 1 CC 1 þ k 1  T1 =Tc lnB  AA @ U T1 ZL1 0

  B Tc P2 4V 2 ¼ expB @ZV 2  1  ln ZV 1  U Pc T2 11 0 Tc P2  pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 BZV 2 þ U P T CC JR Tc  c 2 CC 1 þ k 1  T2 =Tc lnB  AA @ U T2 ZV 2 0

  B Tc P2 4L2 ¼ expB @ ZL2  1  ln ZL1  U Pc T2 11 0 Tc P2 Z þ U    L2 ffiffiffiffiffiffiffiffiffiffiffiffi ffi p 2 C B JR Tc Pc T2 C CC 1 þ k 1  T2 =Tc lnB  AA @ U T2 ZL2

Process constraints Isentropic constraint for compressor Iso-fugacity constraint for vapor pressure calculation Equality and inequality constraints

SV2  SV1 ¼ 0 0 ¼ 4L1  4V1 0 ¼ 4L2  4V2

P1 ¼ P4 P2 ¼ P3 T1 ¼ T4 P2  Pc T2  Tc P1 ¼ 1 bar

Computer-Aided Molecular Design and Property Prediction Chapter j 6

REFERENCES ASHRAE, 2009. ASHRAE Handbook: Fundamentals. American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc., Atlanta, USA. Byrd, R.H., Nocedal, J., Waltz, R.A., 2006. Knitro : an integrated package for nonlinear optimization. Energy 83, 1e25. Camarda, K.V., Maranas, C.D., 1999. Optimization in polymer design using connectivity indices. Industrial and Engineering Chemistry Research 38, 1884e1892. Ceriani, R., Gani, R., Liu, Y.A., 2013. Prediction of vapor pressure and heats of vaporization of organic compounds by group contribution. Fluid Phase Equilibria 337, 53e59. Churi, N., Achenie, L.E.K., 1996. Novel mathematical programming model for computer aided molecular design. Industrial and Engineering Chemistry Research 35, 3788e3794. Cignitti, S., Zhang, L., Gani, R., 2015. Computer-aided framework for design of pure, mixed and blended products. Computer Aided Chemical Engineering 37, 2093e2098. Constantinou, L., Gani, R., 1994. New group contribution method for estimating properties of pure compounds. AIChE Journal 40, 1697e1710. Conte, E., Morales-Rodriguez, R., Gani, R., 2009. The virtual product-process design laboratory for design and analysis of formulations. Computer Aided Chemical Engineering 27, 825e830. Cussler, E.L., Wei, J., 2003. Chemical product engineering. AIChE Journal 49, 1072e1075. Duvedi, A.P., Achenie, L.E.K., 1996. Designing environmentally safe refrigerants using mathematical programming. Chemical Engineering Science 51, 3727e3739. Folic, M., Adjiman, C.S., Pistikopoulos, E.N., 2008. Computer-aided solvent design for reactions: maximizing product formation. Industrial and Engineering Chemistry Research 47, 5190e5202. Fredenslund, A., Jones, R.L.R., Prausnitz, J.M.J., 1975. Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE Journal 21, 1086e1099. Fung, H.K., Wibowo, C., Ng, K.M., 2006. Product-centered process synthesis and development: 669 Detergents. Computer Aided Chemical Engineering 23, 239e274. GAMS Development Corporation, 2011. General Algebraic Modeling System (GAMS) Release 703 23.7.3. Washington, DC, USA. Gani, R., 2004. Chemical product design: challenges and opportunities. Computers and Chemical Engineering 28, 2441e2457. Gani, R., Brignole, E.A., 1983. Molecular design of solvents for liquid extraction based on UNIFAC. Fluid Phase Equilibria 13, 331e340. Gani, R., Go´mez, P.A., Folic, M., Jime´nez-Gonza´lez, C., Constable, D.J.C., 2008. Solvents in organic synthesis: replacement and multi-step reaction systems. Computers and Chemical Engineering 32, 2420e2444. Gani, R., Ng, K.M., 2015. Product design e molecules, devices, functional products, and formulated products. Computers and Chemical Engineering 1e10. Gani, R., Nielsen, B., Fredenslund, A., 1991. A group contribution approach to computer-aided molecular design. AIChE Journal 37, 1318e1332. Gasteiger, J., Engel, T., 2003. Chemoinformatics: A Textbook, Computational. Gross, J., Sadowski, G., 2001. Industrial Engineering and Chemistry Research 40, 1244e1260. Harper, P.M., Gani, R., 2000. A multi-step and multi-level approach for computer aided molecular design. Computers and Chemical Engineering 24, 677e683. Hill, M., 2004. Product and process design for structured products. AIChE Journal 50, 1656e1661. Hill, M., 2009. Chemical product engineering-the third paradigm. Computers and Chemical Engineering 33, 947e953.

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SECTION j II Molecular Design Hukkerikar, A.S., Kalakul, S., Sarup, B., Young, D.M., Sin, G., Gani, R., 2012a. Estimation of environment-related properties of chemicals for design of sustainable processes: development of group-contributionþ (GCþ) models and uncertainty analysis. Journal of Chemical Information and Modeling 52 (11), 2823e2839. Hukkerikar, A.S., Sarup, B., Ten Kate, A., Abildskov, J., Sin, G., Gani, R., 2012b. Groupcontributionþ (GCþ) based estimation of properties of pure components: improved property estimation and uncertainty analysis. Fluid Phase Equilibria 321, 25e43. Joback, K.G., Reid, R.C., 1987. Estimation of pure-component properties from group-contributions. Chemical Engineering Communications 57, 233e243. Joback, K.G., Stephanopoulos, G., 1989. Designing molecules possessing desired physical property values. Proceedings FOCAPD, CACHE Corporation, Austin, Texas 11, 631e636. Kalakul, S., Zhang, L., Gani, R., 2016. VPPD-Lab: the chemical product simulator. In: Martin, M., Eden, R. (Eds.), Tools for Chemical Product Design. Computer Aided Chemical Engineering, 39, Elsevier Science. Kamath, R.S., Biegler, L.T., Grossmann, I.E., 2010. An equation-oriented approach for handling thermodynamics based on cubic equation of state in process optimization. Computers and Chemical Engineering 34, 2085e2096. Kang, J.W., Abildskov, J., Gani, R., Cobas, J., 2002. Estimation of mixture properties from firstand second-order group contributions with the UNIFAC model. Industrial and Engineering Chemistry Research 41, 3260e3273. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2005. New decomposition-based computer-aided molecular/mixture design methodology for the design of optimal solvents and solvent mixtures. Industrial and Engineering Chemistry Research 44, 4785e4797. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2006. A computer-aided molecular design framework for crystallization solvent design. Chemical Engineering Science 61, 1247e1260. Klincewicz, K.M., Reid, R.C., 1984. Estimation of critical properties with group contribution methods. AIChE Journal 30, 137e142. Kolska´, Z., Růzicka, V., Gani, R., 2005. Estimation of the enthalpy of vaporization and the entropy of vaporization for pure organic compounds at 298.15 K and at normal boiling temperature by a group contribution method. Industrial and Engineering Chemistry Research 44, 8436e8454. Kontogeorgis, G.M., Gani, R., 2004. Computer-Aided Property Estimation for Process and Product Design. CACE 19. Elsevier Science B.V, The Netherlands, pp. 1e425. Lawal, A.S., 1987. A consistent rule for selecting roots in cubic equations of state. Industrial and Engineering Chemistry Research 26, 857e859. Lydersen, A.L., 1955. Estimation of Critical Properties of Organic Compounds. University of Wisconsin. Maranas, C.D., 1997. Optimization accounting for property prediction uncertainty in polymer design. Computers and Chemical Engineering 21, S1019eS1024. Maranas, C.D., Floudas, C.A., 1994. A deterministic global optimization approach for molecular structure determination. Journal of Chemical Physics 100, 1247. Marrero, J., Gani, R., 2001. Group-contribution based estimation of pure component properties. Fluid Phase Equilibria 183e184, 183e208. Mattei, M., Kontogeorgis, G.M., Gani, R., 2014. A comprehensive framework for surfactant selection and design for emulsion based chemical product design. Fluid Phase Equilibria 362, 288e299. Modarresi, H., Conte, E., Abildskov, J., Gani, R., Crafts, P., 2008. Model-based calculation of solid solubility for solvent selection e a review. Industrial and Engineering Chemistry Research 47, 5234e5242.

Computer-Aided Molecular Design and Property Prediction Chapter j 6 ´ ., Mole´s, F., Peris, B., 2015. Analysis Mota-Babiloni, A., Navarro-Esbrı´, J., Barraga´n-Cervera, A based on EU Regulation No 517/2014 of new HFC/HFO mixtures as alternatives of high GWP refrigerants in refrigeration and HVAC systems. International Journal of Refrigeration 52, 21e31. Navarro-Esbrı´, J., Mendoza-Miranda, J.M., Mota-Babiloni, A., Barraga´n-Cervera, A., BelmanFlores, J.M., 2013. Experimental analysis of R1234yf as a drop-in replacement for R134a in a vapor compression system. International Journal of Refrigeration 36, 870e880. O’Connell, J.P., Prausnitz, J.M., Poling, B.E., November 27, 2000. The Properties of Gases and Liquids, fifth edition. McGraw-Hill Education. Odele, O., Macchietto, S., 1993. Computer aided molecular design: a novel method for optimal solvent selection. Fluid Phase Equilibria 82, 47e54. Privat, R., Gani, R., Jaubert, J.-N., 2010. Fluid Phase Equilibria 295 (1), 76e92. Raman, V.S., Maranas, C.D., 1998. Optimization in product design with properties correlated with topological indices. Computers and Chemical Engineering 22, 747e763. Rao, Y., 1997. Chemical Engineering Thermodynamics. Universities Press. Sahinidis, N.V., 1996. BARON: a general purpose global optimization software package. Journal of Global Optimization 8, 201e205. Sahinidis, N.V., Tawarmalani, M., Yu, M., 2003. Design of alternative refrigerants via global optimization. AIChE Journal 49, 1761e1775. Samudra, A.P., Sahinidis, N.V., 2013. Optimization-based framework for computer-aided molecular design. AIChE Journal 59, 3686e3701. Satyanarayana, K.C., Abildskov, J., Gani, R., 2009. Computer-aided polymer design using group contribution plus property models. Computers and Chemical Engineering 33, 1004e1013. Shelley, M.D., El-Halwagi, M.M., 2000. Component-less design of recovery and allocation systems: a functionality-based clustering approach. Computers and Chemical Engineering 24, 2081e2091. Shaath, N., 2005. The chemistry of sunscreens. In: Sunscreens: Development, Evaluation and Regulatory Aspects, third ed. CRC Press, pp. 211e233. Sinha, M., Achenie, L.E.K., Gani, R., 2003. Blanket wash solvent blend design using interval analysis. Industrial and Engineering Chemistry Research 42, 516e527. Smith, J.M., Van Ness, H.C., Abbott, M.M., 2005. Introduction to Chemical Engineering Thermodynamics. Chemical Engineering. Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science 27, 1197e1203. Solvason, C.C., Chemmangattuvalappil, N.G., Eden, M.R., 2009. A systematic method for integrating product attributes within molecular synthesis. Computers and Chemical Engineering 33, 977e991. Struebing, H., Ganase, Z., Karamertzanis, P.G., Siougkrou, E., Haycock, P., Piccione, P.M., Armstrong, A., Galindo, A., Adjiman, C.S., 2013. Computer-aided molecular design of solvents for accelerated reaction kinetics. Nature Chemistry 5, 952e957. Tabernero, A., del Valle, E.M.M., Galan, M.A., 2012. Estimation of sublimation enthalpies of solids constituted by aromatic and/or polycyclic aliphatic rings by using a group contribution method. AIChE Journal 58, 2875e2884. Vaidyanathan, R., El-Halwagi, M., 1994. Computer-aided design of high performance polymers. Journal of Elastomers and Plastics 26, 277e293. Venkatasubramanian, V., Chan, K., Caruthers, J.M., 1994. Computer-aided molecular design using genetic algorithms. Computers and Chemical Engineering 18, 833e844.

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Chapter 7

The Incorporation of Safety and Health Aspects as Design Criteria in a Novel Chemical Product Design Framework J.Y. Ten,* M.H. Hassim,x D.K.S. Ng* and N.G. Chemmangattuvalappil*, 1

*The University of Nottingham Malaysia Campus, Semenyih, Selangor, Malaysia; xUniversiti Teknologi Malaysia, Johor, Malaysia 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION When it comes to the decision-making stage in a process and product design problem, the two principal criteria taken into account are often the engineering aspects and economic performance. Some aspects of sustainability such as environment, health, and safety have received much recognition in process plant design (Rathnayaka et al., 2014). This is mainly due to the impacts of a chemical plant has on the community and environment, which have brought about great concern, especially to the public and regulatory agencies. These concerns are primarily linked to the increased amount of industrial accidents that occurred in the chemical process industries. For instance, the industrial catastrophe that took place in Bhopal has resulted in a death toll of more than 3800 people immediately after the leakage of more than 40 tons of methyl isocyanate gas from the pesticide plant (Broughton, 2005). In 2015, a warehouse located in Tianjin has erupted in an explosive blaze, which resulted in the death of 165 people and injured over 700. Most of these accidents are resulted by the mishandling of hazardous materials, combustible dusts, and reactive chemicals. This has resulted in negative public perceptions of the chemical processing industries (Chen et al., 2015). Following these tragedies, process safety has received much attention to serve as a paramount decision-making criterion, especially in the chemical and petrochemical industries (Ee et al., 2015). Globally, the incorporation of process safety in plant design has led to the development and application of Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00007-1 Copyright © 2016 Elsevier B.V. All rights reserved.

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SECTION j II Molecular Design

hazard identification and analysis techniques, risk assessment and evaluation, and safety measures (Khan et al., 2015). Techniques like failure modes and effect analysis, quantitative risk assessment, and the hazard and operability analysis are implemented to help minimize the likelihood of potential accidents and reduce the magnitude of impacts. The installation of protective devices, such as controllers, alarms, and emergency response systems, to the operating plant are some of the conventional safety measures to control the hazards. However, these add-on devices are only able to minimize the overall safety impacts of the plant, and it does not completely help in eliminating the intrinsic hazards present in the plant. Thus, the safety level of the plant is highly dependent on the reliability of protective equipment, and accidents can still occur in the event of device malfunction or human errors. An alternate concept known as inherent safety design has been recognized as a reliable and better approach to synthesize a safer, sustainable, and economically viable process plant. The concept was first introduced by Trevor Kletz (1978), which was prompted by the fatal Flixborough blast in 1974. The application of inherent safety in process design strives to eliminate or minimize hazards that are present in the plant. Rather than controlling the hazards through the conventional technique of installing add-on safety measures, the alteration on process operation and operating conditions along with the properties of materials used can contribute to risk minimization or elimination (Khan et al., 2015). The hazards present can be eliminated or reduced by operating the processes with milder conditions and substituting hazardous substances with less hazardous materials. When inherently safer materials are used in the process, any unintentional leakage of these substances will not bring much adverse impacts to the community and environment. Thus, any hazard scenarios that are associated to the presence of hazardous chemicals can be prevented. Besides process safety, the aspect of occupational health has also received increasing attention in plant design. As defined by the World Health Organization (WHO), occupational health strives to enhance the working conditions and other elements related to environment hygiene. Besides, WHO also helps in identifying the controlling the health risks that have arisen from physical, chemical, and other workplace-related hazards. Generally, safety impacts result in acute effects, whereas health impacts often deal with chronic diseases, also known as noncommunicable diseases (NCDs). Some of the common NCDs include cardiovascular disease, diabetes, cancer, and chronic obstructive pulmonary disease. These diseases are regarded as the main health problems in most countries (Cahalin et al., 2015). The International Labour Organization has reported that more than two million people die annually due to workrelated diseases, while over 300,000 people die yearly from fatal occupational accidents. Thus, occupational health impacts should be managed as equally significant as the aspect of process safety in process plants. This gives rise to the establishment of inherent occupational health (Hassim and Edwards,

The Incorporation of Safety and Health Aspects as Design Chapter j 7

2006), which strives to minimize the occupational health risks caused by the chemical processes to the workers. When it comes to selecting the appropriate chemicals used in a process route, both inherent safety and occupational health promote in reducing the amount of hazardous chemicals used. For instance, a highly flammable chemical can be replaced with a less or nonflammable chemical. However, the substitution of chemicals with improved safety and health characteristics must also exhibit similar or higher functionality performance as compared to the replaced chemicals. The traditional product design approach for the search of promising chemical candidates involves laboratory synthesis and test methodology. However, this method is often very costly and time-consuming, which cannot be appropriately employed in the demanding global business environment (Gebreslassie and Diwekar, 2015). An alternate approach known as the chemical product design technique, a type of top-down reverse engineering approach, has received increasing attention. It begins with the identification of customers’ needs, followed by the synthesis of molecule that exhibits the desired properties to satisfy the product needs (Ng et al., 2015). Existing databases consisting of molecular building blocks can be applied to explore a vast number of conventional or novel molecular structures complying with the product needs of interest (Papadopoulos et al., 2010). This systematic search can be attained by coupling it with computer-aided molecular design (CAMD) technique, which is highly recognized as a powerful tool to determine molecules with desirable set of physicochemical properties (Valdez-Patrinos et al., 2015). In this work, the concept of inherent safety and occupational health will be integrated into a CAMD framework to help synthesizing a molecule with high product functionality performance and favorable intrinsic safety and health attributes.

2. COMPUTER-AIDED MOLECULAR DESIGN A property prediction method is a technique to estimate the physicochemical properties of a molecule depending on its molecular structure. Meanwhile, CAMD helps to determine the identity of molecule or molecular structure synthesized from the given set of chemical building blocks and a specified set of target properties (Gani, 2004). In other words, CAMD is actually a methodology of controlling the properties and behaviors of compounds through the alteration of their molecular structures (Zhou et al., 2015). In the early problem formulation phase, a set of relevant target properties that can achieve the product needs are defined, along with their respective target range. The appropriate molecular building blocks used to construct the molecule are also identified. In the next stage, a molecule has to be validated, whether it complies with the property target specification. Thus, property prediction methods, such as group contribution method (GCM) and empirical correlation, can be coupled with CAMD to estimate the physical and chemical properties of the

199

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SECTION j II Molecular Design

molecule. In GCM, the contributions for all molecular building groups present in the compound of interest are summed up to determine the property value (Achenie et al., 2003). Marrero and Gani (2001) have proposed a general form of GCM, as shown in Eq. (7.1): X X X f ðPÞ ¼ Ni Ci þ w Mj D j þ z O k Ek (7.1) i

j

k

where Ci is the contribution of the first-order group of type-i that occurs Ni times, Dj is the contribution of the second-order group of type-j that appears Mj times, and Ek is the contribution of the third-order group of type-k that has Ok occurrences in a chemical compound. The left-hand side of Eq. (7.1) is a simple function f(P) of the target property P. The first-order groups are made up of a large set of simple and basic molecular groups that cover a wide range of organic compounds. Some of the examples include CH3, CH2, OH, CHO, CHNH, etc. Meanwhile, the second- and third-order groups are applied for more comprehensive molecular structural information on the molecular building blocks, as they are able to assist in differentiating some distinct isomeric molecular structures. The constants w and z are binary values where a user can choose whether to incorporate higher-order groups in their GCM. Once a list of molecules satisfying the target properties are synthesized, they will be evaluated in a subsequent performance analysis stage. In this stage, molecules with undesirable attributes are removed with the assistance of the solving algorithm (Heintz et al., 2014). An optimization approach with iterations is employed to systematically generate and assess the molecules until the optimal candidates have been identified (Papadopoulos et al., 2010). CAMD approach has been widely employed in many chemical industries, such as the design of chemical-based products, solvents, active ingredients, polymers, refrigerants, lubricants, extractants, catalysts, and more (Karunanithi et al., 2006; Zhang et al., 2015). In most conventional CAMD problems, the design objective is to develop molecules that can achieve the desirable target properties, which are specified by their physical and thermodynamic properties. The aspects of safety and occupational health are often not selected as the molecular design criteria, but they are only employed as evaluation tools in a later phase to examine the safety and health performance of the generated molecules. However, there is a lack of systematic evaluation methodology to integrate both aspects into a CAMD problem. Since the concept of sustainability has been widely promoted in the chemical industries, both safety and health aspects should be considered equally significant to the target properties when it comes to decision-making in a molecular design problem. Hence, in this novel CAMD framework, the concept of inherent safety and occupational health will be incorporated as design criteria in a molecular design problem to ensure that the generated molecules exhibit a low intrinsic hazard level.

The Incorporation of Safety and Health Aspects as Design Chapter j 7

3. INTEGRATION OF INHERENT SAFETY AND HEALTH IN A COMPUTER-AIDED MOLECULAR DESIGN FRAMEWORK In this section, the methodology applied to incorporate the aspects of safety and occupational health into the CAMD problem is demonstrated. The overall methodology can be divided into five stages, namely, problem formulation, inherent safety and occupational health indexes selection, model development, molecular design, and optimization model.

3.1 Problem Formulation The stage begins with the identification of chemical product needs specified by the customers. These needs can then be defined by the desired product specifications. These product specifications can be represented in terms of target properties, which will have effects on the functionality and physical behavior of a product. All selected target properties must be expressed in terms of property range, where each property must fall within their respective predefined range to ensure that the product attains its desired functionality. This range can be represented with two inequality expressions bounded by lower bound ðvpL Þ and upper bound ðvU p Þ of the range, as shown in Eq. (7.2), where p represents the target property, while Vp represents the target property value. vpL  Vp  vU p

cp ˛P

(7.2)

3.2 Inherent Safety and Occupational Health Indexes Selection Both inherent safety and inherent occupational health are initially introduced to measure the intrinsic hazard level of different process routes during earlier plant design stage. In order to quantify and compare the inherent safety and occupational health of each route, one of the frequently used techniques is the index-based approach, where each process route will be assessed based on its safety and health factors. Each factor is given an index value to depict the potential hazard level. This approach offers quick and reliable results that can assist the user in deciding the process route with better safety and health attributes. Furthermore, its simplicity and convenience enable easy comprehension by any user with different technical background (Gnoni and Bragatto, 2013). The pioneer of inherent safety index (ISI) approach was the Prototype Index for Inherent Safety (PIIS) introduced by Edwards and Lawrence (1993). It was developed to rank the inherent safety of different process routes through the allocation of index values. A process route with lower total index value is considered to be inherently safer and vice versa. Edwards and Lawrence (1993) have first identified a list of 16 safety parameters for possible

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integration in PIIS. They then shortlisted the list to seven parameters based on their data availability in the literature during conceptual design stage. The seven parameters were divided into two groups, namely, chemical score and process score. Chemical score includes inventory, flammability, explosiveness, and toxicity, while process score contains temperature, pressure, and yield. The total index value of a process route can be calculated through the summation of index scores for all seven parameters of each reaction step in the route. Another well-developed safety index was established by Heikkila¨ (1999), named the ISI. A wider scope of safety parameters are considered in which their data must be readily available during the preliminary process design phase. The parameters in ISI can be divided into two groups, namely the Chemical ISI and the Process ISI. The former category covers subindexes of chemical reactivity, flammability, explosiveness, toxicity, and corrosiveness of chemical species present in the process. Chemical reactivity can be further assessed by the subindexes for heat of main reaction, heat of side reactions, and chemical interaction. On the other hand, the Process ISI contains subindexes of inventory, process temperature, process pressure, equipment safety, and safe process structure. For inherent occupational health, the concept was first brought up by Johnson (2001) in the Occupational Health Hazard Index (OHHI). OHHI is applied for the evaluation of hazard associated with occupation health in the plant design stage. Meanwhile, Hassim and Edwards (2006) proposed to enhance the shortcomings of OHHI by establishing the Process Route Healthiness Index (PRHI). PRHI can be employed to examine the potential occupational hazards of new plants by taking into account numerous parameters that may bring about adverse impact on human health in the workplace during early process design stage. Another important occupational health index is the Inherent Occupational Health Index (IOHI), which was developed by Hassim and Hurme (2010) to evaluate the potential health-related hazards of different process routes in the research and development stage. In IOHI, the consequence of health hazard is influenced by the potential for harm and the potential for exposure. The potential of harm is directly affected by the types and amounts of chemicals present in the plant, the duration and frequency of exposure, and the conditions in the workplace. Meanwhile, the potential of exposure is associated with the physical properties of chemicals present, the process operating conditions, and operational activities. There are two principal indexes in the IOHI, namely, Index for Physical and Process Hazards (IPPH) and Index for Health Hazards (IHH). The former index covers health parameters such as mode of process, material phase, volatility, pressure, corrosiveness, and temperature, while the latter index contains health parameters like exposure limit and R-phrase. The total IOHI value of a process route is the summation of IPPH and IHH.

The Incorporation of Safety and Health Aspects as Design Chapter j 7

TABLE 7.1 Parameters Evaluated in the Inherent Safety Indexes Parameters

Prototype Index for Inherent Safety

Inherent Safety Index

Heat of reaction

U

Heat of side reaction

U

Chemical interaction

U

Flammability

U

U

Explosiveness

U

U

Toxicity

U

U U

Corrosiveness Inventory

U

U

Yield

U

Temperature

U

U

Pressure

U

U

Type of equipment

U

Process structure

U

In summary, all the mentioned inherent safety and occupational health indexes are developed to assess the intrinsic hazard level of different process routes. Table 7.1 shows a summary of the safety parameters considered in PIIS and ISI, while Table 7.2 shows a summary of the occupational health parameters considered in PRHI and IOHI. Based on Tables 7.1 and 7.2, the safety and occupational health parameters can be distinctly categorized into process-related parameters and chemicalrelated parameters. Only the chemical-related parameters are useful in evaluating the safety and health characteristics of the molecules. The safety parameters associated to the chemical properties are heat of reaction, heat of side reaction, chemical interaction, flammability, explosiveness, toxicity, and corrosiveness. The selection of safety parameters must depend on whether a particular parameter can be directly linked to molecular properties that can be estimated through property prediction models. For instance, the flammability of a molecule can be measured by its flash point. The property prediction model for flash point can be found in the literature. Flammability can thus be chosen as one of the safety parameters. However, not all safety parameters can be directly linked to the properties. For instance, the corrosiveness parameter from ISI is based on the basis of the required construction material, such as

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TABLE 7.2 Parameters Evaluated in the Inherent Occupational Health Indexes Parameters

Process Route Healthiness Index

Inherent Occupational Health Index

Mode of process

U

U

Material phase

U

U U

Volatility Pressure

U

U

Corrosiveness

U

U

Temperature

U

U

Viscosity

U

Ability to precipitate

U

Density difference

U

Volume changes

U

Solubility

U

Exposure limit

U

R-phrase

U

Transport

U

Venting or flaring

U

Maintenance works

U

carbon steel, stainless steel, and special materials. These construction materials have no relations to the molecular properties. Hence, corrosiveness will not be included in the CAMD problem. Two parameters are chosen from the safety indexes, namely flammability (IFL) and explosiveness (IEX). Flammability is evaluated by the flash point and boiling point, while explosiveness is measured by the upper and lower explosion limits (UELs and LELs, respectively). The index values for explosiveness subindex are taken from ISI, while the scores for flammability subindex are taken from National Fire Protection Association (NFPA) flammability rating (National Fire Protection Association, 2007). The penalty scores for the two selected safety subindexes are shown in Tables 7.3 and 7.4. Meanwhile, the selected health parameters include viscosity (Ih) from the PRHI, as well as material phase (IMS), volatility (IV), and exposure limit (IEL) from the IOHI. These health parameters are evaluated at 25 C and 1 atm, as

The Incorporation of Safety and Health Aspects as Design Chapter j 7

TABLE 7.3 Flammability (IFL) Subindex (National Fire Protection Association) Factor

Score Information

Penalty

Flammability, IFL

Nonflammable

0



1



2

Fp  93.4 C Fp < 93.4 C 

Fp < 37.8 C 

3 

Fp < 22.8 C and Tb < 37.8 C

4

TABLE 7.4 Explosiveness (IEX) Subindex Factor

Score Information

Penalty

Explosiveness, IEX

Nonexplosive

0

S ¼ (UEL  LEL) vol%

0  S < 20

1

20  S < 45

2

45  S < 70

3

70  S  100

4

Modified from Inherent Safety Index.

the on-site workers would typically handle the materials at these conditions. The material phase of a molecule is dependent on its boiling point and melting point, while the volatility is examined based on its boiling point. Molecules with lower boiling point are considered to be more volatile. The assessment for exposure limit of a material employs the basis of 8 h daily exposure time. It is a chronic-typed toxicity that is represented in the form of PEL (Hassim and Hurme, 2010). Since the chronic-typed toxicity has been covered in the work, another acute toxicity is equally as significant and should also be taken into account in this work. This acute-typed toxicity is presented by acute health hazard (IAH) in which the index values for this subindex are based on the NFPA health hazard rating (National Fire Protection Association, 2007). The subindex of acute health hazard will be measured by LD50 for acute oral toxicity. The penalty scores for the five selected health subindexes are shown in Tables 7.5e7.9. The total index score of a molecule (ISHI) is simply the summation of all the subindex values allocated to it, which is shown in Eq. (7.3). One of the

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TABLE 7.5 Viscosity (Ih) Subindex Factor

Score Information

Penalty

Viscosity, Ih

Low (0.1 cP  h < 1 cP)

1

Medium (1 cP  h < 10 cP)

2

High (10 cP  h  100 cP)

3

Modified from Process Route Healthiness Index.

TABLE 7.6 Material Phase (IMS) Subindex Factor

Score Information

Penalty

Material phase, IMS

Gas

1

Liquid

2

Modified from Inherent Occupational Health Index.

TABLE 7.7 Volatility (IV) Subindex Factor

Score Information

Volatility, IV

Liquid and gas

Penalty

Very low volatility (Tb > 150 C) 



0

Low (150 C  Tb > 50 C)

1



2



Medium (50 C  Tb > 0 C) 

High (Tb  0 C)

3

Modified from Inherent Occupational Health Index.

design objectives is to generate molecules with lower index score, as it indicates that the molecules are inherently safer and “healthier.” ISHI ¼ IFL þ IEX þ Ih þ IMS þ IV þ IEL þ IAH

(7.3)

3.3 Model Development In this stage, all properties that are either linked to the target properties or safety and health parameters have to be estimated through the property prediction models. One of the most notable approaches used is GCM, which is

The Incorporation of Safety and Health Aspects as Design Chapter j 7

TABLE 7.8 Exposure Limit (IEL) Subindex Factor

Score Information

Exposure limit, IEL

Vapor (ppm)

Penalty

Permissible exposure limit (PEL) > 1000

0

PEL  1000

1

PEL  100

2

PEL  10

3

PEL  1

4

Modified from Inherent Occupational Health Index.

TABLE 7.9 Acute Health Hazard (IAH) Subindex (National Fire Protection Association) Factor

Score Information

Acute health hazard, IAH

Oral rat LD50 (mg/kg)

Penalty

LD50 > 2000

0

500 < LD50  2000

1

50 < LD50  500

2

5 < LD50  50

3

LD50  5

4

able to estimate the physicochemical properties of a molecule based on its molecular structure (Marrero and Gani, 2001). The general form of GCM is shown in Eq. (7.1). PEL and LD50 for acute oral toxicity can be estimated using GCM models developed by Hukkerikar et al. (2012a). Physical properties like flash point (Fp), normal boiling point (Tb), and melting point (Tm) are estimated using GCM models developed by Hukkerikar et al. (2012b). Conte et al. (2008) have established a GCM model to calculate viscosity (h). In this work, only first-order groups and second-order groups are considered. Properties with no GCM available can be estimated using correlations or empirical relationships. Both UEL and LEL can be estimated using correlations developed by Ma et al. (2013).

3.3.1 Disjunctive Programming on Allocation of Index Value After a molecule that meets the design objectives is identified, subindex scores will be simultaneously assigned to the molecule, depending on its properties.

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FIGURE 7.1 The graphical illustration of viscosity subindex (Ih).

Based on Tables 7.3e7.9, all seven subindexes are made up of several property intervals, with each interval representing a distinct subindex value. For instance, for the viscosity subindex (Ih) as shown in Fig. 7.1, if the viscosity of a molecule falls in the interval of 0.1 cP to 1 cP, an Ih of one will be allocated to it. In the event where the viscosity falls between 1 cP and 10 cP, then an Ih of two will be assigned and so on. Hence, when the viscosity moves across 1 cP, the scoring changes abruptly from one to two. The viscosity intervals have resulted in a disjunction for the constraint. A modeling method known as disjunctive programming incorporates discontinuous functions to describe abrupt changes over a certain decision variable (El-Halwagi, 2012). Since different viscosity intervals have distinct subindex value, disjunctive programming can be applied in this scenario. The molecular properties are estimated through property prediction models, while disjunctive programming inputs these properties into the safety and health subindexes to translate them into subindex scores. In this way, the target functionality of the product and its safety and health criteria can be simultaneously taken into consideration during design stage. The working algorithm applied to model the disjunctive function can be referred to El-Halwagi (2012).

3.4 Molecular Design In this stage, the possible first-order molecular groups serving as the potential building blocks to synthesize the molecule are selected. For instance, if the desired end molecule is an alcohol, then the hydroxyl (OH) must be chosen as one of the molecular groups. Then, the possible second-order molecular groups will be chosen based on the selection of first-order groups. The application of second-order groups can enhance the accuracy of the estimated properties and help to differentiate distinct isomeric structures. Once all the relevant groups are selected, the structural constraints are introduced to eliminate combination of infeasible solution. This is to ensure that only structurally feasible molecules are generated. For a molecule to contain no free

The Incorporation of Safety and Health Aspects as Design Chapter j 7

bonds, the octet rule of structural feasibility is applied (Odele and Macchietto, 1993): GT X

Ni ð2  vi Þ ¼ 2g

(7.4)

i¼1

where Ni is the number of occurrences of first-order group i, GT is the total number of first-order groups chosen to synthesize the molecules, vi is the valence of first-order group i, and g is 1, 0, 1, or 2 for acyclic, monocyclic, bicyclic, and tricyclic compounds, respectively. The mathematical constraints developed by Churi and Achenie (1996) are utilized to ensure that only single molecular structure is formed.

3.5 Multiple-Objective Optimization In this final stage, all the target properties will either be selected as the objective function to be optimized or be chosen as the property constraints to fulfill. For instance, if the design goal of a particular CAMD problem is to develop a molecule with low volatility, then the objective function would be to maximize the boiling point of the molecule. However, in most cases, multiple target properties are often selected as the objective functions. Some of these target properties may possibly be conflicting to one another; hence, decision-making has to be made on the trade-off between these properties. An optimization approach known as fuzzy optimization algorithm can be implemented to ensure that all objective functions are simultaneously optimized. A degree of satisfaction, lp, is first introduced to each objective function. Fig. 7.2 shows the degree of satisfaction curve for objective function to be maximized or minimized. lp is a continuous variable ranging from zero to one. Based on Fig. 7.2A, the objective is to maximize the target property, Vp. The objective is considered fully satisfied when Vp is above the upper boundary vU p; thus, the objective has a lp value of one. On the contrary, the objective is considered not satisfied when Vp is below the lower boundary vpL ; thus the objective is assigned a lp value of zero. In between vpL and vU p , the lp value is

FIGURE 7.2 The degree of satisfaction, lp curve for objective function to be maximized (A) or minimized (B).

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represented by a linear function, where lp increases linearly from zero at vpL to one at vU p . The reverse mechanism is illustrated in Fig. 7.2B where the objective is to minimize Vp. The value of lp in Fig. 7.2A and B can be represented by the linear membership functions given by Eqs. (7.5) and (7.6), respectively. Eq. (7.5) is employed for maximizing the target property, while Eq. (7.6) is applied to minimize the target property. 8 0 Vp  vLp > > > > > < V p  vL p L U lp ¼ cp ˛P (7.5) U L v p  Vp  v p > v  v > p p > > > : 1 Vp  v U p 8 0 > > > > > < v U  Vp p lp ¼ U L > v > p  vp > > > : 1

Vp  vU p vLp  Vp  vU p

cp ˛P

(7.6)

Vp  vLp

Maxemin operator method by Zimmermann (1978) will then be employed to maximize the target property with the least satisfied degree of satisfaction, l, by using Eq. (7.7). Through this method, the remaining target properties will be satisfied partially to at least the degree of l. The overall objective now is to maximize the value of l. lp  l

cp˛P

(7.7)

Once the value of l is maximized, a molecular structure with the optimal result will be generated. In order to generate another molecule with the next optimal result, integer cuts can be applied by introducing an additional constraint, which prevents the formation of an optimal solution that has already been identified.

4. CASE STUDY: SOLVENT DESIGN FOR GAS SWEETENING PROCESS The proposed methodology for the integration of inherent safety and occupational health into a CAMD problem will be conducted in an industrial case study. The aim of this case study is to develop a solvent for application in the gas sweetening process. Over the years, huge amounts of carbon dioxide (CO2) are being emitted into the atmosphere due to many human anthropogenic activities, such as deforestation and the burning of fossil fuels (oil, gas, and coal). In May 2015, the US science agency National Oceanic and Atmospheric Administration has reported that the global atmospheric CO2 concentrations

The Incorporation of Safety and Health Aspects as Design Chapter j 7

have reached a new milestone of 400 ppm, an increase of 40% over the past 150 years (Sabine and Feely, 2015). The accumulation of greenhouse gas in the atmosphere has brought about adverse impact to the environment, i.e., global warming. According to the International Energy Agency, the world is on course for a long-term global average temperature increase of 3.6 C. The goal now is to reduce the emission of CO2 for maintaining a maximum of 2 C warming. The Intergovernmental Panel on Climate Change has warned that the amount of permissible CO2 emission must be kept below 1000 gigatons of CO2. One way to help minimizing the emissions is through the application of carbon capture and storage (CCS), which could contribute in 19% of the global emission reductions by 2050 (Seigo et al., 2014). CCS assists in capturing CO2 from power stations and industrial processes before it is released into the atmosphere. Captured CO2 will then be compressed into fluid and transported through pipeline, truck, rail, or ship to an appropriate storage site. The capture CO2 is then pumped and stored safety away from the atmosphere in the underground. The three main CO2 capture technologies include precombustion, postcombustion, and oxyfuel combustion. In this case study, the postcombustion CO2 capture is studied. The commonly used technology for the removal of CO2 is the chemical absorptions by using alkanolamines as solvents (Muhammad and GadelHak, 2015). The combustion exhaust sour gas will be in contact with the amine solution in an absorber, where CO2 is removed by the weak CO2eamine bonding (Shakerian et al., 2015). The rich CO2eamine solution is then regenerated by heating the solvent to strip off the CO2 at low pressure. This technology has been applied extensively in the food and beverage industry.

4.1 Case Study: Problem Formulation One of the most established technologies utilized in the gas industry for the removal of acid gas from sour gas stream is the application of alkanolamines. This is due to their low solvent cost and high reactivity in terms of CO2 removal. Aqueous monoethanolamine (MEA) solution is deemed as the commonly applied solvent in gas sweetening process, as it offers high reaction rate, low solvent production cost, reasonable thermal stability, and high absorbing capacity (Kumar et al., 2014). However, MEA has a high vapor pressure that results in high vaporization losses. Thus, the aim of this case study is to develop an amine-based solvent, which can minimize the amount of solvent loss in an acid gas removal unit. Besides achieving the design objective, the synthesized solvent must be safe and does not bring much adverse health impact to humans. The three target properties selected as the objective functions of this case study are shown as follows: 1. Vapor pressure (VP) of the solvent should be low to prevent high vaporization losses.

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2. Soil sorption coefficient (log Koc) of the solvent should be low to prevent the accumulation of the escaping solvent in one place (Chemmangattuvalappil and Eden, 2013; Ng et al., 2014). 3. Total index score of the solvent should be low for an inherently safer and healthier molecule. Meanwhile, the target properties selected as properties constraints include heat of vaporization (Hv), liquid molar volume (Vm), viscosity (h), molecular weight (Mw), boiling point (Tb), and melting point (Tm). These constraints can help to ensure that the generated molecule possesses similar characteristics as the conventional amine solvents. Table 7.10 shows the target property ranges of the solvent at standard condition (298K and 1 atm). The lower and upper bound values for Hv, VP, Mw, h, Tb, and Tm are taken from Kumar et al. (2014), while the lower and upper bound values for Vm are taken from Chemmangattuvalappil and Eden (2013). The molecules will be evaluated by the selected inherent safety and occupation health subindexes, as shown in Tables 7.3e7.9. The total index score (ISHI) that a molecule is assigned with can be calculated using Eq. (7.3). GCM models developed by Hukkerikar et al. (2012b) can be applied to estimate Hv, Vm, Tb, and Tm. Meanwhile, h can be estimated using GCM by Conte et al. (2008). VP cannot be predicted by GCM, but it can be calculated from Tb using an empirical relationship. Meanwhile, log Koc can be calculated through a correlation given in terms of octanolewater partition coefficient (log Kow). log Kow can be calculated using GCM by Hukkerikar et al. (2012b). The selected first-order molecular groups include CH3, CH2, CH, OH, CH2O, CH2NH2, CH2NH, CHNH, CH3N, and CH2N, which are derived from the

TABLE 7.10 Property Targets for Molecular Design Property

Lower Bound

Upper Bound

Hv (kJ/mol)

50

528

VP (mm Hg)

e

11

Vm (cm /mol)

40

224

Mw (g/mol)

60

250

h (cP)

3

e

460



111

350



Tm ( C)

65

25

log Koc

e

e

ISHI

e

e

Tb ( C)

The Incorporation of Safety and Health Aspects as Design Chapter j 7

conventional absorbents that are utilized in gas sweetening process. Some of these commonly used solvents include MEA, diethanolamine, triethanolamine, methyldiethanolamine, diglycolamine, diisopropanolamine (Kumar et al., 2014), and diisopropylamine (Chemmangattuvalappil and Eden, 2013). From the selected first-order groups, the second-order groups that are considered in this problem are (CH3)2CH, CH(CH3)CH(CH3), CHOH, CHm(OH)CHn(OH), and CHm(OH)CHn(NHp), where m, n, and p can be 0, 1, or 2.

4.2 Case Study: Fuzzy Optimization The target properties listed in Table 7.10 are then converted into their respective property operator, Up as shown in Table 7.11. The property operator is given by the simple function f(p) for each target property p, which is exactly the left-hand side of Eq. (7.1). For instance, the property operator of h is given by the function of ln h (Conte et al., 2008). By substituting the lower and upper bounds of h from Table 7.10 into ln h, the lower and upper property operator bounds of h are shown in Table 7.11. The property operator range for the three properties serving as the objective functions (VP, log Koc, and ISHI) can be determined by optimizing each of these three properties one at a time to identify their respective upper and lower property operator bounds, which are listed in Table 7.12. All objectives are then expressed by linear membership functions, as shown in Eqs. (7.8)e(7.10): UVP  5:2373 ¼ lVP 9:6504  5:2373

(7.8)

TABLE 7.11 Property Operator Targets for Molecular Design Property p

Up

Lower Bound

Upper Bound

Hv

Hv  Hv0

40.3873

518.3873

VP

exp(Tb/Tb0)

5.2289

e

Vm

Vm  Vm0

0.024

0.208

Mw

Mw

60

250

h

ln h

e

6.1312

Tb

exp(Tb /Tb0)

4.8117

12.7879

Tm

exp(Tm /Tm0)

4.2623

7.9779

log Koc

log Kow  Kow0

e

e

ISHI

ISHI

e

e

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TABLE 7.12 Property Operators and Targets (Objective Functions) Property p

Up

Lower Bound

Upper Bound

VP

exp(Tb/Tb0)

5.2373

9.6504

log Koc

log Kow  Kow

2.6284

3.5933

ISHI

ISHI

10

13

3:5933  Ulog Koc ¼ llog Koc 3:5933 þ 2:6284

(7.9)

13  UISHI ¼ lISHI 13  10

(7.10)

The overall objective is to maximize the value of l, subjected to the following constraints: lVP  l

(7.11)

llog Koc  l

(7.12)

lISHI  l

(7.13)

4.2.1 Case Study: Results Six solvents with the six highest l values are generated. Their molecular structures are shown in Fig. 7.3. Tables 7.13 and 7.14 show the properties of the six generated solvents. From the generated results, solvent A1 has the lowest VP value, while solvent A5 has the lowest log Koc value. Since MEA is by far the most utilized solvent in gas sweetening process, a comparison between MEA and the six generated solvents will be studied. The properties of MEA are shown in Table 7.16. The values of Tb, Tm, Fp, S, and LD50 are taken from material safety data sheet (MSDS), provided by SigmaeAldrich. The values of log Kow and h are extracted from the US National Library of Medicine. Meanwhile, VP and PEL of MEA can be found in the Occupational Safety and Health Administration Occupational Chemical Database. Since the value of log Koc for MEA is not available, it can be predicted via a simple correlation by Seth et al. (1999), which returns a value of 1.96. All the safety and health subindex scores for MEA are shown in Table 7.17. From Tables 7.13 and 7.14, all six solvents have a relatively lower VP compared to MEA, which indicates that they will have lower vaporization losses than MEA. However, their log Koc values are still larger than that of

The Incorporation of Safety and Health Aspects as Design Chapter j 7

FIGURE 7.3 The six generated solvents with their molecular structures.

MEA. For the aspects of inherent safety and occupational health, all six solvents obtained a similar ISHI value of 11, as shown in Table 7.15. The two subindexes with the highest penalty score are viscosity and exposure limit. Nevertheless, the solvents still exhibit low flammability, low explosiveness, very low volatility, and low acute health hazard. The six solvents also have a lower ISHI value as compared to that of MEA, as shown in Table 7.17. This is due to the fact that MEA exhibits a higher flammability. Thus, the results show that the methodology proposed by this work is able to generate solvents with lower hazard level.

TABLE 7.13 The Six Generated Solvents With Their Properties Solvent

l

ISHI

log Koc

VP (mm Hg)

Hv (kJ/mol)

Vm (cm3/mol)

Mw (g/mol)

A1

0.614

11

0.931

0.0832

84.22

133.6

133.2

A2

0.612

11

1.051

0.0841

84.45

132.7

133.2

A3

0.559

11

0.339

0.1223

74.01

147.2

131.2

A4

0.558

11

0.460

0.1237

74.24

146.3

131.2

A5

0.545

11

1.308

0.1360

81.92

116.5

119.2

A6

0.533

11

0.511

0.1473

72.65

144.8

131.2

215

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SECTION j II Molecular Design

TABLE 7.14 The Six Generated Solvents With Their Properties (Continued) Solvent

h (cP)

Tb ( C)

Tm ( C)

Fp ( C)

S (vol %)

PEL (ppm)

LD50 (mg/kg)

A1

78.52

233.69

22.46

119.23

7.553

1.057

898

A2

77.42

233.47

21.68

119.05

7.553

1.006

836

A3

25.24

226.16

23.74

100.67

6.265

2.437

1022

A4

24.88

225.93

22.97

100.49

6.265

2.320

952

A5

71.63

224.06

20.26

113.94

8.930

1.113

858

A6

33.15

222.49

22.67

97.79

6.265

2.578

887

TABLE 7.15 The Six Generated Solvents With Their Subindex Values Solvent

IFL

IEX

Ih

IMS

IV

IEL

IAH

ISHI

A1

1

1

3

2

0

3

1

11

A2

1

1

3

2

0

3

1

11

A3

1

1

3

2

0

3

1

11

A4

1

1

3

2

0

3

1

11

A5

1

1

3

2

0

3

1

11

A6

1

1

3

2

0

3

1

11

The application of inherent safety and occupational health indexes in a CAMD problem is definitely a great initiative for the integration of safety and health aspects as design criteria in product design and development. This is on course for the growing interest in promoting the concept of sustainable development in chemical industries. By employing the methodology proposed in this work, all the design criteria are now simultaneously optimized, as the generated molecules exhibit optimal product functionality and favorable safety and health characteristics.

5. CONCLUSIONS A novel chemical product design framework has been developed to design a molecule with a set of desired properties while possessing low safety and health hazards levels. The evaluation of safety and health aspects has been conducted through the integration of inherent safety and occupational health

The Incorporation of Safety and Health Aspects as Design Chapter j 7

TABLE 7.16 Properties of Monoethanolamine Property

Property Value

log Kow

1.31

log Koc

1.96

VP (mm Hg)

0.4

h (cP)

18.95



Tb ( C)

170



Tm ( C)

10



Fp ( C)

86

S (vol%)

14.5

PEL (ppm)

3

LD50 (mg/kg)

1720

TABLE 7.17 The Subindex Scores of Monoethanolamine IFL

IEX

Ih

IMS

IV

IEL

IAH

ISHI

2

1

3

2

0

3

1

12

indexes into a CAMD problem. Each subindex is assessed by molecular physicochemical property using disjunctive programming to translate the properties into their respective subindex values. The total index score allocated to a molecule is useful in quantifying its inherent hazard. Fuzzy optimization is then applied to simultaneously optimize multiple design objectives: product functionality and safety and health performance. A case study on the solvent design for CO2 removal process is considered, and the primary objective is to synthesize a solvent that can help minimize the amount of solvent loss in the gas sweetening process. The performance of the generated solvents is compared to that of MEA, and the results show that the solvents have lower volatility and flammability than those of MEA. Thus, the synthesized solvents are able to offer better product functionality and preferable safety and health performance. The future work in this field will quantify the uncertainty involved in property prediction models and their effect in final decisionmaking. More work must be conducted in developing systematic strategies for prioritizing various target performance indexes in chemical product design.

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REFERENCES Achenie, L.E.K., Gani, R., Venkatasubramaniam, V., 2003. Computer Aided Molecular Design: Theory and Practice. Elsevier, Amsterdam. Broughton, E., 2005. The Bhopal disaster and its aftermath: a review. Environmental Health 4. Cahalin, L.P., Kaminsky, L., Lavie, C.J., Briggs, P., Cahalin, B.L., Myers, J., Forman, D.E., Patel, M.J., Pinkstaff, S.O., Arena, R., 2015. Development and implementation of worksite health and wellness programs: a focus on non-communicable disease. Progress in Cardiovascular Diseases 58, 94e101. Chemmangattuvalappil, N.G., Eden, M.R., 2013. A novel methodology for property-based molecular design using multiple topological indices. Industrial and Engineering Chemistry Research 52, 7090e7103. Chen, H., Pittman, W.C., Hatanaka, L.C., Harding, B.Z., Boussouf, A., Moore, D.A., Milke, J.A., Mannan, M.S., 2015. Integration of process safety engineering and fire protection engineering for better safety performance. Journal of Loss Prevention in the Process Industries 37, 74e81. Churi, N., Achenie, L.E., 1996. Novel mathematical programming model for computer aided molecular design. Industrial and Engineering Chemistry Research 35, 3788e3794. Conte, E., Martinho, A., Matos, H.A., Gani, R., 2008. Combined group-contribution and atom connectivity index-based methods for estimation of surface tension and viscosity. Industrial and Engineering Chemistry Research 47, 7940e7954. Edwards, D.W., Lawrence, D., 1993. Assessing the inherent safety of chemical process routes: is there a relation between plant costs and inherent safety. Chemical Engineering Research and Design 71, 252e258. Ee, A.W.L., Shaik, S.M., Khoo, H.H., 2015. Development and application of a combined approach for inherent safety and environmental (CAISEN) assessment. Process Safety and Environmental Protection 96, 138e148. El-Halwagi, M.M., 2012. Sustainable Design Through Process Integration: Fundamentals and Applications to Industrial Pollution Prevention, Resource Conservation, and Profitability Enhancement. Elsevier, Oxford. Gani, R., 2004. Chemical product design: challenges and opportunities. Computers and Chemical Engineering 28, 2441e2457. Gebreslassie, B.G., Diwekar, U.M., 2015. Efficient ant colony optimization for computer aided molecular design: case study solvent selection problem. Computers and Chemical Engineering 78, 1e9. Gnoni, M.G., Bragatto, P.A., 2013. Integrating major accidents hazard into occupational risk assessment: an index approach. Journal of Loss Prevention in the Process Industries 26, 751e758. Hassim, M.H., Edwards, D.W., 2006. Development of a methodology for assessing inherent occupational health hazards. Process Safety and Environmental Protection 84, 378e390. Hassim, M.H., Hurme, M., 2010. Inherent occupational health assessment during process research and development stage. Journal of Loss Prevention in the Process Industries 23, 127e138. Heikkila¨, A.-M., 1999. Inherent Safety in Process Plant Design. An Index Based Approach. Doctoral Thesis. VTT Publications 384. Technical Research Centre of Finland, Espoo. Heintz, J., Belaud, J.-P., Pandya, N., Teles Dos Santos, M., Gerbaud, V., 2014. Computer aided product design tool for sustainable product development. Computers and Chemical Engineering 71, 362e376. Hukkerikar, A.S., Kalakul, S., Sarup, B., Young, D.M., Sin, G., Gani, R., 2012a. Estimation of environment-related properties of chemicals for design of sustainable processes: development of group-contributionþ (GCþ) property models and uncertainty analysis. Journal of Chemical Information and Modeling 52, 2823e2839.

The Incorporation of Safety and Health Aspects as Design Chapter j 7 Hukkerikar, A.S., Sarup, B., Kate, A.T., Abildkov, J., Sin, G., Gani, R., 2012b. Groupcontributionþ (GCþ) based estimation of properties of pure components: improved property estimation and uncertainty analysis. Fluid Phase Equilibria 321, 25e43. Johnson, V.S., 2001. Occupational Health Hazard Index for Proposed Chemical. Master thesis. Loughborough University, Loughborough. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2006. A computer-aided molecular design framework for crystallization solvent design,. Chemical Engineering Science 61, 1247e1260. Khan, F., Rathnayaka, S., Amyotte, P., 2015. Methods and models in process safety and risk management: past, present and future. Process Safety and Environmental Protection 98, 116e147. Kletz, T.A., 1978. What you don’t have, can’t leak. Chemistry and Industry (London) 278e292. Kumar, S., Cho, J.H., Moon, I., 2014. Ionic liquid-amine blends and CO2BOLs: prospective solvents for natural gas sweetening and CO2 capture technologyda review. International Journal of Greenhouse Gas Control 20, 87e116. Ma, T., Wang, Q., Larran˜aga, M.D., 2013. Correlations for estimating flammability limits of pure fuels and fuel-inert mixtures. Fire Safety Journal 56, 9e19. Marrero, J., Gani, R., 2001. Group-contribution based estimation of pure component properties. Fluid Phase Equilibria 183e184, 183e208. Muhammad, A., GadelHak, Y., 2015. Simulation based improvement techniques for acid gases sweetening by chemical absorption: a review. International Journal of Greenhouse Gas Control 37, 481e491. National Fire Protection Association, 2007. NFPA 704: Standard System for the Identification of the Hazards of Materials for Emergency Response. National Fire Protection Association, Quincy. Ng, L.Y., Chemmangattuvalappil, N.G., Ng, D.K.S., 2014. A multiobjective optimization-based approach for optimal chemical product design. Industrial and Engineering Chemistry Research 53, 17429e17444. Ng, L.Y., Chong, F.K., Chemmangattuvalappil, N.G., 2015. Challenges and opportunities in computer-aided molecular design. Computers and Chemical Engineering 81, 115e129. Odele, O., Macchietto, S., 1993. Computer aided molecular design: a novel method for optimal solvent selection. Fluid Phase Equilibria 82, 47e54. Papadopoulos, A.I., Stijepovic, M., Linke, P., 2010. On the systematic design and selection of optimal working fluids for Organic Rankine Cycles. Applied Thermal Engineering 30, 760e769. Rathnayaka, S., Khan, F., Amyotte, P., 2014. Risk-based process plant design considering inherent safety. Safety Science 70, 438e464. Sabine, C.L., Feely, R.A., 2015. Climate and Climate Change: Carbon Dioxide In: Reference Module in Earth Systems and Environmental Sciences, From Encyclopedia of Atmospheric Sciences, second ed., vol. 2, pp. 10e17 Seigo, S.L., Dohle, S., Siegrist, M., 2014. Public perception of carbon capture and storage (CCS): a review. Renewable and Sustainable Energy Reviews 38, 848e863. Seth, R., Mackay, D., Muncke, J., 1999. Estimating the organic carbon partition coefficient and its variability for hydrophobic chemicals. Environmental Science and Technology 33, 2390e2394. Shakerian, F., Kim, K.-H., Szulejko, J.E., Park, J.-W., 2015. A comparative review between amines and ammonia as sorptive media for post-combustion CO2 capture. Applied Energy 148, 10e22.

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Chapter 8

Molecular Design in the Pharmaceutical Industries K. Boone,* F. Abedin,x M.R. Anwar* and K.V. Camarda*, 1

*The University of Kansas, Lawrence, KS, United States; xCalifornia State Polytechnic University, Pomona, CA, United States 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION The concept of a computer-aided molecular design (CAMD) methodology fits in very well with the search for novel therapeutic agents since the key step is the discovery of a novel active agent, along with a set of additive molecules that moderate the properties of the overall formulation. Pharmaceutical agents were the focus of many of the initial CAMD studies, especially with regard to improvement of solubility for small-molecule drugs. The enormous cost and effort associated with the development of a novel pharmaceutical product also motivates the use of CAMD within this field. The design of a pharmaceutical product is very lengthy and involves several stages. The beginning stage is the drug discovery phase. During this phase, the active pharmaceutical ingredient (API) is determined. Once the API is known, the formulation of the pharmaceutical product must be determined. Other chemical compounds, called excipients, are added to the formulation to help stabilize the API and increase its efficacy. The final delivery method of the pharmaceutical product is determined, with oral methods such as tableting or encapsulation the most common choices. Successive phases handle design of the manufacturing process, from pilot plant to scale-up (Siddhaye et al., 2004). Finally, the product can be approved and marketed. Product design principles can be applied to many of the stages in the pharmaceutical development process. In practice, many new pharmaceutical products are discovered and developed using exhaustive trial-and-error approaches (Roughton et al., 2012a). Rational product design using CAMD aims to limit trial-and-error expenses through optimization and property estimation of the target molecule. Property prediction can identify excipients, which would most improve the API’s stability and efficacy. The final delivery of the Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00008-3 Copyright © 2016 Elsevier B.V. All rights reserved.

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drug in vivo can also be improved by designing molecules that have properties allowing the drug to be delivered at the desired conditions. Several concepts are vital to product design for pharmaceuticals. From a process systems engineering standpoint, the most important are the target product profile (TPP), design specifications, critical quality parameters, and health, safety, and environmental (HS&E) considerations (McAllister et al., 2008). The TPP sets the design space for the pharmaceutical product, while the other considerations place constraints on the design space. For the final design of the pharmaceutical product to be successful, the design should match the TPP as closely as possible.

2. GENERAL CONCEPTS IN PHARMACEUTICAL PRODUCT DESIGN The concepts of TPP, design specification, critical quality parameters, and HS&E considerations hold for all aspects of pharmaceutical product design. The TPP will determine which API and excipients are considered (Roughton et al., 2012a; McAllister et al., 2008; Camarda and Sunderesan, 2005; Jonasson et al., 2002; Lin et al., 2005). The ultimate delivery method will also be influenced by the TPP. While designing any of the components of the pharmaceutical product, design specifications and quality parameters will constrain the possible targets considered. The specifications will also be used to identify the optimal molecule for the considered product component. The TPP is a template that is maintained by a pharmaceutical industry to store information about new drug products. It is established based upon a determined consumer health need. TPP provides all key attributes of the product, which represent the ideal product properties. During designing pharmaceutical products, it is important that the design meets the TPP. Some key attributes of pharmaceutical products are listed below (McAllister et al., 2008): l l l l

therapeutic effect efficacy dosage safety or tolerability

The design specifications are a list of user-defined specifications that the final product must meet. Such specifications could include solubility, particle size, and pH (for liquid products) (McAllister et al., 2008). Quality parameters are added as well. Such parameters include cosmetic concerns such as the color and overall appearance of the pharmaceutical product. Taste is important in products that are delivered orally. Other quality parameters include desired shelf-life and consistency of the product from batch to batch (Siddhaye et al., 2004). Health assessment of the pharmaceutical product is very important. Toxicity must be evaluated during the product development

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process for both the API and the final product. Often, established excipients are chosen for the formulation due to time constraints. Similarity to previously approved excipients is often cited as leading to similar toxicological effects, avoiding additional regulatory approval (McAllister et al., 2008). Environmental concerns play a part, as use of environmentally benign excipients is encouraged. For example, much work has been done to determine alternates to the chlorofluorocarbons used in metered-dose aerosols (McAllister et al., 2008).

3. DESIGN AND DEVELOPMENT OF THE ACTIVE PHARMACEUTICAL INGREDIENT 3.1 Overview Since the API is the essential component, or collection of components, that actuate the intended effect of a pharmaceutical drug, its design and design concepts are critical for understanding the design methodology for the rest of the formulation in support of it and to build an effective quality system for the robust manufacture and administration of the drug (Siddhaye et al., 2004; Roughton et al., 2012a). The intended effects of the API are to inhibit or to activate metabolic pathways in the patient’s cells. The goal is to design a molecule to accomplish the intended effects without having unintended effects. Pharmaceutical drug design has traditionally relied on discovery through scientific observation yielding unexpected results, such as the discovery of penicillin. More rational drug design has been developed using combinatorial chemistry, which can create large numbers of candidate molecules to be screened (McAllister et al., 2008; Camarda and Sunderesan, 2005; Jonasson et al., 2002). These methods require high-throughput methods to scan libraries of molecules in an effort to find molecules meeting desired target properties. Adding direction to combinatorial chemistry by screening compounds in silico or refining the methods by which candidate molecules are generated results in CAMD (Lin et al., 2005; Roughton et al., 2012b). CAMD can use varied physical and chemical property predictions for screening. Connectivity indices of the topology of generated molecules as well as structure-based properties of a method of further increasing the rationality of drug design (Siddhaye et al., 2004; Lin et al., 2005; Zanuy et al., 2013; Camarda and Maranas, 1999; Prado-Prado et al., 2008; Siddhaye et al., 2000). The following schematic shows the approach taken by CAMD to discover drugs or design of formulations. Here, quantitative structure property relationships (QSPRs) represent mathematical correlations between the properties of interest and structure of the molecules (Fig. 8.1). Traditional small molecule drug design tools are finding new applications in the design of new biological molecules as APIs (Roughton et al., 2012a; Szabo et al., 2010). The design of peptides holds enormous promise because

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FIGURE 8.1 Schematic showing CAMD approach in drug discovery or design of new formulations. QSPR, Quantitative structure property relationships.

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many proteins bind specifically a single target or a collection of targets in a way that peptides may be suitable to mimic. Additionally, the topology of canonical peptides is a 1-D chain of amino acids, which is simple compared to some small molecule drugs. Sequenceeactivity relationships are being investigated very actively (Currin et al., 2015; He et al., 2014; Sevy et al., 2015) to realize the promise of peptides. Understanding the relations of structure and function, as well as allosteric effects, are also key challenges to the design of peptides (Wang et al., 2014; Kovacs et al., 2013; Nussinov and Tsai, 2015; Motlagh et al., 2014). Peptides also hold promise for expanding the role of pharmaceutical drugs into inorganic-to-biological interfaces (Yazici et al., 2013; Yucesoy et al., 2015).

3.2 Ligand Screening The drug molecule component that binds to an intended target is defined as a ligand. The target of a drug molecule is defined as a receptor. The method for ligand design varies among drug design approaches. While high-throughput methods collect information about a large library of molecules, a directed search using a computational screening method can result in a dramatic reduction in the number of molecules experimentally evaluated to find suitable solutions. A directed screening process can reduce the cost and time resources in pharmaceutical drug development while providing more information about how the drug molecule is performing its intended function. In order to realize these benefits, computational tools are often used to direct the screening process. One basic approach is to start with information about an intended target and to design a ligand to bind to it. This is the ligand-based approach (Geppert et al., 2010). A second approach to designing ligandereceptor interactions is to transfer structural characteristics or other properties from a known ligand to a candidate ligand. This is known as the receptor-based approach (Moon and Howe, 1991).

3.3 Structure-Based Drug Design A range of drug candidate types can be used with either the ligand-based approach or the receptor-based approach: small molecules, polymers, or other biological molecules. The 3-D structures of these candidates must be studied to estimate the likelihood of a good fit with the intended receptor target. Computational prediction of structure, which is itself a nested optimization problem, is used to screen the fitness of drug candidates (Melero et al., 2014; Tsai et al., 2015; Joo et al., 2014). The inverse problem, which seeks to discover a drug candidate given a receptor structure, is of particular interest for drug design. Approaches for small-molecule drugs (Lin et al., 2005; Siddhaye et al., 2000) as well as for protein-based ligands (Gront et al., 2011; Leaver-Fay et al., 2011; King et al., 2012; Koga et al., 2012; Meiler and Baker, 2006) have been developed.

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Once the structures of the candidates are created, the next step in the CAMD methodology is to determine the relationship between activity of the candidate and its structure, through development of quantitative structure activity relationships (QSARs). Normally, experimental data on a specific set of structurally similar molecules are regressed against structural descriptors to create QSARs. These descriptors can be as simple as the molecular weight of a functional group, or as complex as a measure of the 3-D sphericity of a portion of the molecule. Once appropriate structural descriptors have been selected (which can involve an optimization step), then a functional form and a set of coefficients for those descriptors are found via regression. Many methods are used for solving this optimization problem, including deterministic methods (McAllister et al., 2008; Floudas, 2013; Roberts et al., 2015) and stochastic approaches (Siddhaye et al., 2004; Roughton et al., 2012a; Lin et al., 2005; Eslick et al., 2009; Spencer et al., 2010; Thompson et al., 2006; Wang, 2015; Mernik et al., 2015; Karaboga and Gorkemli, 2014). Although these optimization problems tend to have large search spaces, the candidates produced from them are generally near optimal when compared to the hard lower bound of a perfect match between desired properties of the pharmaceutical agent and predicted property values for the candidate molecule.

3.4 Receptor-Based Approaches Molecular simulation is used in receptor-based design to model the 3-D structure of a binding site on a target. Once identified, the binding site is categorized based upon hydrogen bonding or electrostatic or hydrophobic interactions. The interaction sites can be used to limit the number of possible ligand structures that are considered. With the binding site finalized, a docking tool can then be used to computationally model ligandereceptor interactions. Two basic methods are employed in modeling ligand docking with the binding sites. Lock and key approaches assume that the binding structure is rigid (Roughton et al., 2012b). Flexible ligand molecules are then docked with the fixed structure. Induced fit docking approaches allow for flexibility in both the ligand and the receptor structure and are therefore much more computationally intensive. To reduce computational costs, the protein backbone is often assumed to be rigid, while the side chains are allowed to be flexible. Docking algorithms use scoring functions, usually based on free energy, to evaluate the interactions between drug candidates and identified docking sites (Roughton et al., 2012b). A docking that minimizes the scoring function being utilized identifies successful ligand candidates. The following shows the steps employed in a receptor-based design approach (Fig. 8.2).

3.5 Ligand-Based Approaches When the 3-D structure of the receptor is not precisely known, ligand-based approaches can be successfully employed. A ligand-based strategy is based

Molecular Design in the Pharmaceutical Industries Chapter j 8

FIGURE 8.2 Schematic showing steps in a receptor-based design approach.

on the known structure or topology of one or more ligands. From this known ligand, a pharmacophore can be established. The pharmacophore acts as a pseudo receptor, which can be used to screen for binding sites that are structurally similar on a biological target. Then ligand-docking models can be used, as seen in structure-based design. To develop the pharmacophore model, the set of known ligands must be evaluated using one of two common approaches. The first approach is to develop a target quantitative structureeactivity relationship that must exist between the ligands and a pharmacophore. Other molecules can then be screened to determine how well they match the QSAR specifications. The second approach computes molecular descriptors and similarity indices for the ligand set. Other molecules can then be screened for a match to the similarity index for a specific pharmacophore. All molecules that match on a similarity index are considered fits for the pharmacophore for which the index was developed. Various computational approaches can be used for receptor-based and ligand-based drug design. The approaches vary in the fundamental building blocks, the basic algorithm employed, and the scoring function used. The computational approaches may only work for one approach or may apply to either design strategy. The fundamental building blocks are either atoms or commonly used fragments composed of several atoms. The main algorithms used in receptor-ligand approaches are: depth first search, breadth first search,

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random, Monte Carlo/simulated annealing, and evolutionary algorithms (Roughton et al., 2012b) The scoring functions are diverse. Some of the most common include force field, empirical scoring, and pharmacophore constraints. All scoring approaches are an attempt to approximate binding energies. Once key binding fragments, or ligands, have been identified through computational screening, further lead optimization can be used to generate the final drug molecule. The ligand alone may not successfully match the specified TPP of the pharmaceutical product (McAllister et al., 2008). Of specific concern are the absorption, distribution, metabolic, and excretion properties (referred to as the ADME properties). The ligand identified through receptor-ligand design serves as a scaffold to which functional groups can be added to improve the properties of the drug molecule that will become the API (Lin et al., 2005). A growth procedure can be used to add fragments to the docked scaffold. Fragments can be selected from a database of molecular segments that are often found in drug-like molecules. When scanning molecular libraries, traditional QSAR methods are often used. New adaptive functional group reordering techniques use random sampling of the molecular fragments to measure targeted properties (Lin et al., 2005). Estimation over the entire library can then result in discovery of fragments or molecules with desirable property values. When multiple functional groups can be added to the ligand scaffold, the number of combinations can be very large. Using iterative rounds of adaptive functional group reordering, an optimal drug molecule can be more quickly found than when direct scanning methods are used.

4. PHARMACEUTICAL FORMULATION DESIGN 4.1 Overview Once a drug molecule has been chosen, a formulation for the final pharmaceutical product must be selected. The physical and chemical characteristics affect the choices available during the formulation design. Pharmaceutical research and development has been primarily concerned with the design and development of the API, with formulation design as a secondary concern (McAllister et al., 2008) Contemporarily, the pharmaceutical industry has experienced diminished productivity and fewer drug approvals. A possible reason for this trend is that the criteria for drug design are not sufficient. API design often focuses on the potency and selectivity of the chosen drug molecule, as represented by ligandereceptor binding. However, other criteria are important for success of a pharmaceutical product. The final product must have an acceptable safety profile, as indicated by the TPP (McAllister et al., 2008). The drug must have the correct pharmacokinetic profile as measured by appropriate values of the ADME properties. Finally, the drug must lend

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itself to successful scale-up and production (Siddhaye et al., 2004; Zanuy et al., 2013). The correct formulation can improve the API’s performance and ensure that the final pharmaceutical product meets all criteria. By considering formulation concerns throughout the drug discovery and development process, the final product will more likely match the desired TPP and have an increased chance of regulatory and commercial success. Traditionally, the selections of excipient molecules for the formulation have been made from a preapproved list. The rationale is that using excipients that are generally regarded as safe or have been included in previous Food and Drug Administration (FDA)eapproved submissions reduces regulatory concerns and therefore overall time to market (McAllister et al., 2008). Similarity to previously approved excipients is often cited as leading to similar toxicological effects, avoiding additional regulatory approval. However, new progress made in biologics and the development of novel drug delivery systems has led to increased importance of innovation in formulation design. By looking at new combinations of excipients or design of new excipients, formulation design can contribute significantly to the success of a pharmaceutical product. The selection and design of an API focuses on optimizing the therapeutic or biological effect of the pharmaceutical product. However, for the product to be successful, the formulation must contain excipients that will lend the right physical properties to the final product. Such physical properties include solubility, density, viscosity, and particle size. The combination of known excipients can be optimized to best match the target physical properties. The desired physical properties can be used to place restrictions on the types of excipients used and the amount used in the formulation. Experimental design can use the valid ranges of excipient amounts to rationally determine what excipient mixtures should be tested (Prado-Prado et al., 2008). The experiments on excipient mixtures then determine the properties of each mixture. The mixture that most closely matches the desired target properties can be identified and used in the final pharmaceutical product. Visualization techniques can be used to easily compare the experimental results (Siddhaye et al., 2000). The excipient mixture that best matches the target can be identified visually very quickly and the pharmaceutical product development can proceed.

4.2 CAMD Approaches to Formulation Design Statistical experimental design and optimization techniques are employed for pharmaceutical formulation design. Selection of existing excipients during pharmaceutical formulation usually involves mixture experiments to determine optimal compositions, which will impart desired properties to the product (Campisi et al., 1998). In a mixture experiment, the percentage of API and excipients are studied in relation to the properties of the product, which form the responses (Campisi et al., 1998; Zelaya et al., 2007). Response

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surface methodology has been used at least since the late 1950s for pharmaceutical formulation design (Box et al., 1959; Campisi et al., 1998; Nestorovska-Gjosevska et al., 2005). This method limits the extent of experiments, and hence makes the design process cost-effective (Nestorovska-Gjosevska et al., 2005). This technique involves rational experimental design, obtaining relation between responses and process variables such as composition of a mixture by regression, and finally using optimization technique on the problem to evaluate optimal solutions for the process variables (Nestorovska-Gjosevska et al., 2005). For example, Campisi et al. (1998) determined a region of high solubility of theophylline in a four-component system, which were polyethylene glycol, water, propylene glycol, and ethanol. Here, the constraints were imposed on the components’ proportions (Campisi et al., 1998). In another study, the impact of formulation variables on the properties of orally disintegrating tablet was evaluated (Nestorovska-Gjosevska et al., 2005). Instead of optimizing the proportion of excipients as discussed above, it is possible to optimize the molecular structure of the excipients to meet the stringent requirements for optimal performance of the pharmaceutical product. CAMD can be used as a tool to develop novel excipients. It is an efficient method to identify molecules that yield properties closest to the desired values. There is a possibility that it can yield existing excipient molecules as the solution of the design problem or it can also give novel molecular structures as the solution. CAMD requires that the target properties possess some relation with the structure of the molecule. CAMD involves two sets of problems: forward and inverse problems. While formulating a pharmaceutical product, certain characteristics of the product need to be achieved, which have been discussed above. These can form the target properties for the design. Then existing excipients possessing the desired characteristics can be chosen to form the model building set. The properties of interests can be obtained for the selected excipients, either experimentally or from the literature. Using descriptors, which describe the molecular structures of the excipients mathematically, QSPRs can be obtained. The success of CAMD depends significantly on the accuracy of the QSPRs. These steps form the forward problem of CAMD. In the inverse problem, QSPRs and constraints on molecular structure, variables or target property values, are employed to formulate an optimization problem. The objective of the problem will be to minimize the difference between the properties of the novel molecules and target set values for the properties. This problem can be solved by an optimization algorithm to obtain novel molecular structures for excipients with properties close to the target set values. This is an efficient and inexpensive technique. Siddhaye et al. (2000) demonstrated how CAMD could be used in designing excipient molecules for pharmaceutical product development. Here, the authors showed an example problem by designing an alcohol for the target property, octanol/water partition coefficient (Siddhaye et al., 2000). Topological indices (connectivity indices) were used to develop correlation between them and the octanol/water partition coefficient

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(QSPR), and the molecules within the model building set were decomposed into basic groups, which were connected in various combinations to design the novel molecule (Siddhaye et al., 2000). The connectivity indices of the new molecule were evaluated and used in the QSPR to predict its property (Siddhaye et al., 2000). This actually forms a combinatorial problem. Polymers are extensively used in drug formulations as binders, matrix, stabilizers, viscosity enhancers, bioadhesives, emulsifiers, microparticles, implants, targeted drug delivery, drug release modifier, thickeners, injectables, and coatings (Beneke et al., 2009). Previous studies have already demonstrated polymer design by CAMD, which can be adapted for pharmaceutical formulation development (Camarda and Maranas, 1999; Eslick et al., 2009; Whitmore et al., 2013; Venkatasubramanian et al., 1994). Whitmore et al. (2013) designed cellulose ether based polymer as delivery vehicle for an HIV microbicide by CAMD. The target properties in this case were shear-thinning index and power-law consistency, which define the flow behavior. The other property of interest was antichlamydial activity. Eslick et al. (2009) demonstrated a CAMD framework for cross-linked polymers. The properties of interests were tensile strength, modulus, glass transition temperature, and initial polymerization rate. The optimization problem in CAMD can be solved by deterministic or stochastic methods. Stochastic methods such as Tabu Search and genetic algorithms have been employed in the past to design polymers by CAMD (Camarda and Maranas, 1999; Eslick et al., 2009; Venkatasubramanian et al., 1994). Previous studies using CAMD have demonstrated it to be an effective technique for designing various materials such as polymers, catalysts, solvents, and refrigerants, and so the method can be adapted for excipient design as long as appropriate target properties are used. Regulatory complications for novel excipients can be reduced by designing molecules, which are structurally similar to the existing excipients. Moreover, correlations for properties relevant to excipient design such as boiling point, octanol/water partition coefficient, and solubility already exist in the literature, which can be used to quickly design novel excipients by CAMD. Novel excipients can have a considerable positive impact on the overall performance of a pharmaceutical product.

4.3 Formulation Design to Minimize the Aggregation of Protein Drugs Proteins offer promising therapeutic candidates in the pharmaceutical industry (Manning et al., 2010). Protein stability is vital for its proper function, and many diseases are caused by the inactivity or improper activity of proteins. A destabilized protein drug can become completely ineffective. Therefore, an essential step in protein therapeutics development is the design of a formulation, which is stable during processing, shipping, and storage (Manning et al., 2010; Agrawal et al., 2011; Carpenter et al., 1997). A major concern in

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protein-based drug formulations is the stability of the product due the existence of many degradation routes: aggregation, precipitation, deamidation, and oxidation, to name a few (Manning et al., 2010; Cleland and Langer, 1994). Degradation can also result in regulatory disapproval since FDA requires pharmaceutical product degradation to be less than 10% of the final product weight (Cleland and Langer, 1994). Protein drugs are often delivered in liquid form. However, proteins that are unstable in aqueous conditions can be stored in lyophilized state. The lyophilized state is created by removal of water via sublimation which is performed in two steps: (1) freezing, and (2) primary and secondary drying (Cleland and Langer, 1994). The lyophilized protein is again reconstituted by the addition of solvent before it is used. Fraction of the proteins can undergo irreversible aggregation in the lyophilized state (Cleland and Langer, 1994; Wang, 2005; Wang et al., 2010). Physical interaction of the exposed protein surfaces or chemical reactions between amino acids can initiate aggregation (Manning et al., 2010; Wang, 2005). Aggregation can result is loss of therapeutic efficacy and illicit immune response (Rosenberg, 2006). Excipients are added in the lyophilized formulation to stabilize the formulation by minimizing aggregation (Roughton et al., 2012a; Li et al., 2008).

4.3.1 Prediction of Protein Drug Aggregation The methods for estimating the aggregation propensity can be classified into two main types: heuristic-based methods and simulation-based methods (Roughton et al., 2013). Heuristic-based approaches use experimental aggregation data to develop predictors for aggregation propensity. The aim is to relate the protein properties to the experimental data on aggregation. Predictive models are developed in these approaches to relate aggregation propensity to protein structure. Several qualitative predictive algorithms such as AGGRESCAN (Conchillo-Sole´ et al., 2007), PASTA (Trovato et al., 2007), and Zyggregrator (Tartaglia and Vendruscolo, 2008) have been reported in literature. The protein primary structures have been used in these methods to return one or more parameters that are suggestive of aggregation propensity. For example, AGGRESCAN provides the number of aggregation hotspots (regions which are prone to aggregation), which is an indicator of propensity to aggregate. However, these qualitative aggregation predictors must be interpreted. A quantitative predictive approach has been reported by Roughton et al. (2013), which correlates the different aggregation predictors with the experimental measures of aggregation. Simulation-based methods use energetics of proteineprotein interactions, or dynamics of single protein molecule to investigate whether aggregation is likely to occur (Irba¨ck and Mohanty, 2006; Ma & Nussinov, 2006). Although simulation-based techniques are quantitative, and first principle-based in nature, they are, in general, computationally expensive and require case studies for every system of interest.

Molecular Design in the Pharmaceutical Industries Chapter j 8

Hybrid approaches have also been reported which combines molecular simulation results with heuristic prediction models (Lauer et al., 2012).

4.3.2 Design of Carbohydrate Excipients for Minimizing Protein Aggregation via CAMD Roughton et al. (2012a) demonstrated a CAMD framework for carbohydrate excipient design to minimize aggregation of lyophilized protein drug. Carbohydrates have been known to stabilize the protein structure. Vitrification is a means to stabilize protein in which the excipient becomes glassy during lyophilization (Roughton et al., 2012a). In this study based on the vitrification hypothesis, the target properties were selected to be glass transition temperature of the maximally concentrated solute, melting point of ice, and glass transition temperature of the anhydrous solute (Roughton et al., 2012a). It is necessary to keep the first two properties sufficiently high so that they are feasible during the lyophilization process and the last property need to be high as well to ensure that the carbohydrate excipient maintains its glassy state during storage of the product (Roughton et al., 2012a). Therefore, by careful selection of target properties, which are related to protein aggregation, it is possible to design novel excipient molecules to stabilize protein drugs. Here, the descriptors used for developing the QSPRs were connectivity indices, but many other descriptors are available in the literature, which can be employed for designing excipient specifically to prevent protein aggregation. This was a complex problem because the chirality of the excipient molecules was taken into account, and the use of higher-order indices made the problem nonlinear (Roughton et al., 2012a). Integer variables and higher-order indices in this problem resulted in a mixed-integer nonlinear program (Roughton et al., 2012a). Such problems possess multiple local minima rather than a global minima. These types of problems are combinatorial in nature. For example, if 42 molecular subgroups are available and a maximum of 6 subgroups are allowed to build a solution, then there will be approximately 5489 million possible solutions, considering the order in which the subgroups are connected and repeated groups within a solution. Solutions to such a problem leads to a combinatorial explosion, which emphasizes the implementation of optimization techniques to solve such complex problems. The optimization formulation for the excipient design discussed previously is given as follows (Roughton et al., 2012a):  P 1   min s ¼ P  Ptarget m scale m M Pm Pm ¼ fm ðyÞ y ¼ gðaijk ; wi Þ hc ðaijk ; wi Þ  0

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Where Pm is the predicted value of mth property, Pm is the target value of the mth property, Pscale is the scaling factor for the property, fm is the QSPR of m the mth property, which is a function of the molecular descriptors y, g is the function employed to calculate the molecular descriptors y by using adjacency matrix aijk and vector wi of molecular subgroup i, aijk and wi are binary variables, which indicate whether there is a bond between the groups i and j, k is the type of bond, and hc represents structural constraints. Roughton et al. (2012a) proposed three candidate carbohydrate excipient molecules with glass transition temperature of the anhydrous solute such that the lyophilized product could be stored at room temperature. This increases the storage compliance of the product, which is very important since many lyophilized products do not possess the flexibility to be stored at room temperature (Roughton et al., 2012a). This CAMD framework can be extended to other types of excipients for protein stabilization. CAMD can be a convenient and an efficient tool, which can be used for the formulation of protein drugs to improve its quality and reduce storage/transportation complications and hence cost. The novel molecular structures obtained by CAMD can be validated via molecular simulation. Among the several candidate molecules given by CAMD, the candidate that generates maximum interaction with the protein’s hotspot can be identified using docking algorithm. CAMD can also be employed for the design of excipient mixture capable of interacting with various types of protein hotspots.

5. CONCLUSIONS The examples provided in this chapter show a variety of methods by which CAMD methods are being introduced in the pharmaceutical industry. The ever-increasing power of computing technology, along with great improvements in property prediction techniques and optimization algorithms, is moving from a purely academic realm into industrial practice. This trend is being aided by the availability of docking software and techniques, which avoid the need for full molecular simulation but still provide essential information about properties of both APIs and crucial excipients for practical drug formulations. Industrial pharmaceutical concerns often have vast databases of experimentally determined property values for a wide range of compounds, which they can use not only for the traditional screening, but also to produce high-accuracy QSARs, which can be applied to CAMD approaches. Product design has now joined process design as being a truly computeraided activity. This means significant savings to drug designers, since many fewer compounds will be synthesized that turn out not to possess acceptable values of important properties, particularly solubility. Hopefully, this will allow more effort to be expended on finding receptor targets, and understanding the fundamentals behind disease states, and significantly shorten the drug development process.

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REFERENCES Agrawal, N.J., Kumar, S., Wang, X., Helk, B., Singh, S.K., Trout, B.L., 2011. Aggregation in protein-based biotherapeutics: computational studies and tools to identify aggregation-prone regions. Journal of Pharmaceutical Sciences 100 (12), 5081e5095. Beneke, C.E., Viljoen, A.M., Hamman, J.H., 2009. Polymeric plant-derived excipients in drug delivery. Molecules 14 (7), 2602e2620. Box, G.E., Draper, N.R., 1959. A basis for the selection of a response surface design. Journal of the American Statistical Association 54 (287), 622e654. Camarda, K.V., Maranas, C.D., 1999. Optimization in polymer design using connectivity indices. Industrial and Engineering Chemistry Research 38 (5), 1884e1892. Camarda, K.V., Sunderesan, P., 2005. An optimization approach to the design of value-added soybean oil products. Industrial and Engineering Chemistry Research 44 (12), 4361e4367. Campisi, B., Chicco, D., Vojnovic, D., Phan-Tan-Luu, R., 1998. Experimental design for a pharmaceutical formulation: optimisation and robustness. Journal of Pharmaceutical and Biomedical Analysis 18 (1e2), 57e65. Carpenter, J.F., Pikal, M.J., Chang, B.S., Randolph, T.W., 1997. Rational design of stable lyophilized protein formulations: some practical advice. Pharmaceutical Research 14 (8), 969e975. Cleland, J.L., Langer, R.S., 1994. Formulation and Delivery of Proteins and Peptides. USA, American Chemical Society Washington, DC. Conchillo-Sole´, O., de Groot, N.S., Avile´s, F.X., Vendrell, J., Daura, X., Ventura, S., 2007. AGGRESCAN: a server for the prediction and evaluation of. BMC Bioinformatics 8 (1), 65. Currin, A., Swainston, N., Day, P.J., Kell, D.B., 2015. Synthetic biology for the directed evolution of protein biocatalysts: navigating sequence space intelligently. Chemical Society Reviews 44 (5), 1172e1239. Eslick, J.C., Ye, Q., Park, J., Topp, E.M., Spencer, P., Camarda, K.V., 2009. A computational molecular design framework for crosslinked polymer networks. Computers and Chemical Engineering 33 (5), 954e963. Floudas, C.A., 2013. Deterministic Global Optimization: Theory, Methods and Applications. Springer Science & Business Media. Geppert, H., Vogt, M., Bajorath Jr., 2010. Current trends in ligand-based virtual screening: molecular representations, data mining methods, new application areas, and performance evaluation. Journal of Chemical Information and Modeling 50 (2), 205e216. Gront, D., Kulp, D.W., Vernon, R.M., Strauss, C.E., Baker, D., 2011. Generalized fragment picking in Rosetta: design, protocols and applications. PLoS One 6 (8), e23294. He, J., Krauson, A.J., Wimley, W.C., 2014. Toward the de novo design of antimicrobial peptides: lack of correlation between peptide permeabilization of lipid vesicles and antimicrobial, cytolytic, or cytotoxic activity in living cells. Biopolymers 102 (1), 1e6. Irba¨ck, A., Mohanty, S., 2006. PROFASI: a Monte Carlo simulation package for protein folding and aggregation. Journal of Computational Chemistry 27 (13), 1548e1555. Jonasson, P., Liljeqvist, S., Nygren, P.-A., Sta˚hl, S., 2002. Genetic design for facilitated production and recovery of recombinant proteins in Escherichia coli. Biotechnology and Applied Biochemistry 35 (2), 91e105. Joo, K., Lee, J., Sim, S., Lee, S.Y., Lee, K., Heo, S., et al., 2014. Protein structure modeling for CASP10 by multiple layers of global optimization. Proteins: Structure, Function, and Bioinformatics 82, 188e195. Karaboga, D., Gorkemli, B., 2014. A quick artificial bee colony (qABC) algorithm and its performance on optimization problems. Applied Soft Computing 23, 227e238.

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SECTION j II Molecular Design King, N.P., Sheffler, W., Sawaya, M.R., Vollmar, B.S., Sumida, J.P., Andre´, I., et al., 2012. Computational design of self-assembling protein nanomaterials with atomic level accuracy. Science 336 (6085), 1171e1174. Koga, N., Tatsumi-Koga, R., Liu, G., Xiao, R., Acton, T.B., Montelione, G.T., et al., 2012. Principles for designing ideal protein structures. Nature 491 (7423), 222e227. Kovacs, D., Szabo, B., Pancsa, R., Tompa, P., 2013. Intrinsically disordered proteins undergo and assist folding transitions in the proteome. Archives of Biochemistry and Biophysics 531 (1e2), 80e89. Lauer, T.M., Agrawal, N.J., Chennamsetty, N., Egodage, K., Helk, B., Trout, B.L., 2012. Developability index: a rapid in silico tool for the screening of antibody aggregation propensity. Journal of Pharmaceutical Sciences 101 (1), 102e115. Leaver-Fay, A., Tyka, M., Lewis, S.M., Lange, O.F., Thompson, J., Jacak, R., et al., 2011. Rosetta3: an object-oriented software suite for the simulation and design of macromolecules. Methods in Enzymology 487, 545e574. Li, Y., Williams, T.D., Topp, E.M., 2008. Effects of excipients on protein conformation in lyophilized solids by hydrogen/deuterium exchange mass spectrometry. Pharmaceutical Research 25 (2), 259e267. Lin, B., Chavali, S., Camarda, K., Miller, D.C., 2005. Computer-aided molecular design using Tabu search. Computers and Chemical Engineering 29 (2), 337e347. Ma, B., Nussinov, R., 2006. Simulations as analytical tools to understand protein aggregation and predict amyloid conformation. Current Opinion in Chemical Biology 10 (5), 445e452. Manning, M.C., Chou, D.K., Murphy, B.M., Payne, R.W., Katayama, D.S., 2010. Stability of protein pharmaceuticals: an update. Pharmaceutical Research 27 (4), 544e575. McAllister, S.R., Feng, X.-J., DiMaggio Jr., P.A., Floudas, C.A., Rabinowitz, J.D., Rabitz, H., 2008. Descriptor-free molecular discovery in large libraries by adaptive substituent reordering. Bioorganic and Medicinal Chemistry Letters 18 (22), 5967e5970. Meiler, J., Baker, D., 2006. ROSETTALIGAND: proteinesmall molecule docking with full sidechain flexibility. Proteins: Structure, Function, and Bioinformatics 65 (3), 538e548. Melero, C., Ollikainen, N., Harwood, I., Karpiak, J., Kortemme, T., 2014. Quantification of the transferability of a designed protein specificity switch reveals extensive epistasis in molecular recognition. Proceedings of the National Academy of Sciences of the United States of America 111 (43), 15426e15431.  Mernik, M., Liu, S.-H., Karaboga, D., Crepin sek, M., 2015. On clarifying misconceptions when comparing variants of the Artificial Bee Colony Algorithm by offering a new implementation. Information Sciences 291, 115e127. Moon, J.B., Howe, W.J., 1991. Computer design of bioactive molecules: a method for receptor-based de novo ligand design. Proteins: Structure, Function, and Bioinformatics 11 (4), 314e328. Motlagh, H.N., Wrabl, J.O., Li, J., Hilser, V.J., 2014. The ensemble nature of allostery. Nature 508 (7496), 331e339. Nestorovska-Gjosevska, B., Glavas-Dodov, M., Goracinova, K., 2005. Orally Disintegrating Tablet: Formulation Design and Optimisation Using Response Surface Methodology. Instabilities of Proteins: Theoretical Aspects, Degradation Products and Methods for Their Detection, p. 15. Nussinov, R., Tsai, C.J., 2015. Allostery without a conformational change? Revisiting the paradigm. Current Opinion in Structural Biology 30, 17e24. Prado-Prado, F.J., Gonzalez-Diaz, H., de la Vega, O.M., Ubeira, F.M., Chou, K.C., 2008. Unified QSAR approach to antimicrobials. Part 3: first multi-tasking QSAR model for input-coded

Molecular Design in the Pharmaceutical Industries Chapter j 8 prediction, structural back-projection, and complex networks clustering of antiprotozoal compounds. Bioorganic and Medicinal Chemistry 16 (11), 5871e5880. Roberts, K.E., Gainza, P., Hallen, M.A., Donald, B.R., 2015. Fast gap-free enumeration of conformations and sequences for protein design. Proteins: Structure, Function, and Bioinformatics 83 (10), 1859e1877. Rosenberg, A.S., 2006. Effects of protein aggregates: an immunologic perspective. AAPS Journal 8 (3), E501eE507. Roughton, B.C., Topp, E.M., Camarda, K.V., 2012a. Use of glass transitions in carbohydrate excipient design for lyophilized protein formulations. Computers and Chemical Engineering 36, 208e216. Roughton, B.C., Christian, B., White, J., Camarda, K.V., Gani, R., 2012b. Simultaneous design of ionic liquid entrainers and energy efficient azeotropic separation processes. Computers and Chemical Engineering 42, 248e262. Roughton, B.C., Iyer, L.K., Bertelsen, E., Topp, E.M., Camarda, K.V., 2013. Protein aggregation and lyophilization: protein structural descriptors as predictors of aggregation propensity. Computers and chemical engineering 58, 369e377. Sevy, A.M., Jacobs, T.M., Crowe Jr., J.E., Meiler, J., 2015. Design of protein multi-specificity using an independent sequence search reduces the barrier to low energy sequences. PLoS Computational Biology 11 (7), e1004300. Siddhaye, S., Camarda, K.V., Topp, E., Southard, M., 2000. Design of novel pharmaceutical products via combinatorial optimization. Computers and Chemical Engineering 24 (2e7), 701e704. Siddhaye, S., Camarda, K., Southard, M., Topp, E., 2004. Pharmaceutical product design using combinatorial optimization. Computers and Chemical Engineering 28 (3), 425e434. Spencer, P., Ye, Q., Park, J., Topp, E.M., Misra, A., Marangos, O., et al., 2010. Adhesive/dentin interface: the weak link in the composite restoration. Ann Biomed Eng 38 (6), 1989e2003. Szabo, D., Ostorhazi, E., Binas, A., Rozgonyi, F., Kocsis, B., Cassone, M., et al., 2010. The designer proline-rich antibacterial peptide A3-APO is effective against systemic Escherichia coli infections in different mouse models. International Journal of Antimicrobial Agents 35 (4), 357e361. Tartaglia, G.G., Vendruscolo, M., 2008. The Zyggregator method for predicting protein aggregation propensities. Chemical Society Reviews 37 (7), 1395e1401. Thompson, S.M., Sinha, S., Topp, E.M., Camarda, K.V., 2006. A molecular design approach to peptide drug stabilization. Molecular Simulation 32 (3e4), 291e295. Trovato, A., Seno, F., Tosatto, S.C., 2007. The PASTA server for protein aggregation prediction. Protein Engineering Design and Selection 20 (10), 521e523. Tsai, M.Y., Zheng, W., Balamurugan, D., Schafer, N.P., Kim, B.L., Cheung, M.S., et al., 2015. Electrostatics, structure prediction and the energy landscapes for protein folding and binding. Protein Science 25. Venkatasubramanian, V., Chan, K., Caruthers, J.M., 1994. Computer-aided molecular design using genetic algorithms. Computers and Chemical Engineering 18 (9), 833e844. Wang, W., 2005. Protein aggregation and its inhibition in biopharmaceutics. International Journal of Pharmaceutics 289 (1), 1e30. Wang, B., 2015. A novel artificial bee colony algorithm based on modified search strategy and generalized opposition-based learning. Journal of Intelligent and Fuzzy Systems 28 (3), 1023e1037. Wang, W., Nema, S., Teagarden, D., 2010. Protein aggregationdpathways and influencing factors. International Journal of Pharmaceutics 390 (2), 89e99. Wang, Q., Liang, G., Zhang, M., Zhao, J., Patel, K., Yu, X., et al., 2014. De novo design of selfassembled hexapeptides as beta-amyloid (Abeta) peptide inhibitors. ACS Chemical Neuroscience 5 (10), 972e981.

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SECTION j II Molecular Design Whitmore, T.W., Osaka, I., Hefty, P.S., Camarda, K.V., Kieweg, S.L., 2013. Rational Design of Polymeric Delivery Vehicles for Anti-HIV and Anti-Chlamydial Microbicides. AIChE Annual Meeting; November 3e8; San Francisco, California, USA. Yazici, H., Fong, H., Wilson, B., Oren, E.E., Amos, F.A., Zhang, H., et al., 2013. Biological response on a titanium implant-grade surface functionalized with modular peptides. Acta Biomaterialia 9 (2), 5341e5352. Yucesoy, D., Hnilova, M., Boone, K., Arnold, P., Snead, M., Tamerler, C., 2015. Chimeric peptides as implant functionalization agents for titanium alloy implants with antimicrobial properties. JOM 67 (4), 754e766. Zanuy, D., Sayago, F.J., Revilla-Lo´pez, G., Ballano, G., Agemy, L., Kotamraju, V.R., et al., 2013. Engineering strategy to improve peptide analogs: from structure-based computational design to tumor homing. Journal of Computer-Aided Molecular Design 27 (1), 31e43. Zelaya, M.I., Cho, B.R., Shin, S., Choi, Y. (Eds.), 2007. Experimental Design Aspects for Pharmaceutical Formulations. IIE Annual Conference Proceedings. Institute of Industrial Engineers-Publisher.

Chapter 9

Ionic Liquid Product Design A.T. Karunanithi1 and R. Farahipour University of Colorado Denver, Denver, CO, United States 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION 1.1 Ionic Liquids Ionic liquids are organic molten salts that possess melting points at or below 100 C and exist as liquids at relatively low temperatures. These liquid salts are entirely composed of ions and are characterized by weak interactions between the cation and anion through hydrogen bonds and van der Waals forces. Ionic liquids consist of a large organic cation and a charge-delocalized inorganic or organic anion (shown in Fig. 9.1). The most attractive feature of ionic liquids is the countless possibilities that exist to fine-tune their structures to impart specific functionalities in view of the broad range of potential cation and anion combinations. Ionic liquids can be formed through any combination of cations and anions. Further, in ionic liquids, cations, and occasionally anions, are composed of several alkyl side chain groups (CH2, CH3, etc.), which can be accompanied with one or more functional groups (OH, NH2, COOH, etc.). A vast number of ionic liquids (estimated to be about 1014) (Armand et al., 2009)

Cation side chain

Cation core

Anion

FIGURE 9.1 Structure of 1-n-butyl-3-methylimidazolium (cation) AuCl4 (anion). Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00009-5 Copyright © 2016 Elsevier B.V. All rights reserved.

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can be potentially synthesized through distinct combinations of different cation cores (cation head groups), anions, alkyl side chain groups attached to cation, and functional groups (attached to cation core or sometimes anion). Most of these structural variations are feasible from a chemical synthesis point of view due to the easy nature of preparation of their components (Armand et al., 2009). Even though in theory, several thousand ionic liquids are possible, to date, only a few hundreds have been actually synthetized and used. Due to the extraordinarily large number of ionic liquids that are theoretically possible, we need methods to customize and intelligently design them before we start to explore development of synthesis routes to target their use in specific applications. Current strategies to design novel ionic liquids tend to focus on tailoring their structures, through experimental synthesis, with an objective to impart specific functionalities (e.g., high CO2 solubility for carbon capture applications). However, this approach entirely relies on existing data and knowledge base, and can potentially miss crucial game-changing ionic liquid candidates. In this context, screening and design methods that employ fully predictive physical property as well as thermodynamic models are important, as they may add significant value by reducing the time and cost associated with identification and selection through trial and error experiments. The nonvolatile nature of ionic liquids greatly limits their direct impact on air quality by reducing their emissions to the environment. For this reason, ionic liquids are often considered as inherently green solvents with the potential to replace traditional volatile organic solvents. However, in recent years, several studies have countered this view by reporting that many ionic liquids possess relatively high toxicity towards freshwater organisms. While both arguments are valid, a realistic picture can only emerge through analysis of the life cycle impacts that also considers the upstream impacts associated with the production of these compounds (Mehrkesh and Karunanithi, 2013; Farahipour and Karunanithi, 2014; Mehrkesh and Karunanithi, 2016a). This needs a holistic consideration of ionic liquid environmental impacts during the design stage. In addition, ionic liquids have high viscosities in comparison to their molecular counterparts, thereby greatly limiting their utility in several industrial applications, especially processes that require pumping. However, there are ionic liquids that possess moderate viscosities that can be considered for these applications. This leads to another need of identifying low to moderately viscous ionic liquids for many of the industrial applications (Mehrkesh and Karunanithi, 2016c). Potential Applications of Ionic Liquids l electrolytes (redox flow and lithium batteries) l biomass pretreatment for biofuels (cellulose) l thermal storage media (solar trough collectors) l solvent media for lipase catalyzed biodiesel l CO2 capture and sequestration l energetic materials (fuels, propellants) l separations (aliphatic/aromatic, olefin/paraffin)

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1.2 Computer-Aided Molecular Design Computer-aided molecular design (CAMD) is a technique that has been widely employed towards design and development of molecular chemical products, such as pharmaceutical drugs, solvents, and other functional products. Gani and Brignole (1983) first conceptualized CAMD as an efficient method for computerized synthesize of molecular structures, with specific solvent properties, on the basis of Universal quasichemical Functional group Activity Coefficients (UNIFAC) group contribution (GC) approach (Fredenslund et al., 1975). The main goal of molecular product design is to identify optimal products that possess desired properties to perform specific functions. To achieve this, CAMD integrates structurebased property prediction models [e.g., GC methods, quantitative structure-property relationships (QSPR), connectivity index (CI) methods, molecular descriptors] with optimization algorithms to design optimal molecular structures with desired physical and/or thermodynamic properties. Achenie et al. (2003) define CAMD as “given a set of building blocks and a specified set of target properties, determine the molecule or molecular structure that matches these properties.” In this technique, the reverse problem of property estimation is tackled; that is, for a specified set of properties (target properties), chemicals that satisfy the property requirements are determined (Constantinou et al., 1996). In the 1990s and 2000s, several research groups utilized the CAMD approach towards the design of molecular compounds for different applications, such as polymer design (Vaidyanathan and El-Halwagi, 1996; Maranas, 1997; Camarda and Maranas, 1999), solvents for separation (Macchietto et al., 1990; Gani et al., 1991; Naser and Fournier, 1991; Klein et al., 1992; Gani and Fredenslund, 1993; Odele and Macchietto, 1993; Pretel et al., 1994; Wang and Achenie, 2002; Eden et al., 2004; Karunanithi et al., 2006; Karunanithi and Achenie, 2007; Folic et al., 2004; Chemmangattuvalappil et al., 2010; Samudra and Sahinidis, 2013), solvents for environmental impact minimization (Sinha et al., 1999; Buxton et al., 1999), refrigerant design (Duvedi and Achenie, 1996, 1997; Churi and Achenie, 1997), and pharmaceutical product design (Siddhaye et al., 2000).

1.3 Computer-Aided Ionic Liquid Design More recently, the CAMD approach has been extended to the design of ionic liquids (McLeese et al., 2010; Roughton et al., 2012; Karunanithi and Mehrkesh, 2013; Chong et al., 2014; Hada et al., 2015). A comprehensive framework for computer-aided ionic liquid design (CAILD) was recently published by our group (Karunanithi and Mehrkesh, 2013). Key to the successful development and use of CAILD methods is the availability of predictive models for the properties of interest. Previous studies have

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employed the CAMD approach towards limited search and design of ionic liquids. McLeese et al. (2010) solved an ionic liquid refrigerant design problem in which one cation was considered while the structure of the anion was allowed to vary. Chavez-Islaz et al. (2011) used the CAMD method towards design of ionic liquids for ethanol/water separation. Their model considered five cations and five anions, resulting in consideration of only 25 ionic liquid combinations. Hada et al. (2015) employed a combination of characterization-based method and chemometric techniques towards physical property optimization, employing three cation cores, seven anions, and two alkyl groups. Mai and Koo (2016) combined artificial neural network (ANN)ebased QSPR property prediction with optimization method to reverse design ionic liquids for cellulose dissolution. Mehrkesh and Karunanithi (2016b) considered five cation cores, nine anions, two alkyl groups, and three other functional groups within a CAMD framework to design ionic liquids as a thermal storage medium. The above publications have shown that adaptation of CAMD methods for ionic liquid design problems are both desirable and feasible, and have contributed significantly towards methodological advancements in this area. However, the common theme in all of the above papers is the limited types and numbers of ionic liquids that are considered, primarily due to the limited availability of GC parameters and/or the physical and thermodynamic data needed to fit these parameters. It is clear that consideration of a structurally diverse set of building blocks is necessary to design new and novel structural variants of ionic liquids tailored specifically for different applications.

2. CAMD FORMULATION OF THE IONIC LIQUID DESIGN PROBLEM The generic optimization formulation of the CAILD model is presented as follows [Eqs.(9.1)e(9.11)]. For more specific details and in depth discussion, the readers are referred to Karunanithi and Mehrkesh (2013). This generic CAILD mathematical formulation takes the form of a mixed-integer nonlinear programming (MINLP) model. fobj ¼ max f ðc; a; y; ng; xÞ

(9.1)

h1 ðc; a; y; ngÞ ¼ 0

(9.2)

h2 ðc; a; y; ngÞ  0

(9.3)

g2 ðc; a; y; ngÞ  0

(9.4)

d1 ðc; a; y; ng; xÞ ¼ 0

(9.5)

Ionic Liquid Product Design Chapter j 9

d2 ðc; a; y; ng; xÞ  0

(9.6)

c ˛Rm

(9.7)

a ˛Rn

(9.8)

y ˛Ru

(9.9)

ng ˛Rq

(9.10)

x ˛Rr

(9.11)

where h1 represents equality constraints related to feasibility of ionic liquid structures, their sizes, and complexity; h2 represents inequality constraints related to feasibility of ionic liquid structures, their sizes, and complexity; g2 represents inequality constraints that relate to ionic liquid pure component physical property (e.g., density, viscosity, heat capacity, melting point, etc.) requirement for the given design problem; d1 represents equality design constraints; d2 represents inequality design constraints related to solution (mixture) property (e.g., solubility) requirements for the design problem; c is an m-dimensional vector of binary variables denoting cation cores (e.g., imidazolium, sulfonium etc.); a is an n-dimensional vector of binary variables denoting different anions; y is a u-dimensional vector of binary variables denoting the cation side chain groups; ng is a q-dimensional vector of integer variables representing number of groups in the cation side chains; and x is an r-dimensional vector of continuous variables representing compositions, flow rates, etc.

2.1 Generation of Feasible Ionic Liquid Structures The multitude of ionic liquids generated in the reverse problem need to satisfy certain molecular rules in order to ensure structural feasibility. They include chemical feasibility rules such as the octet rule and chemical bonding rules. In addition to molecular feasibility, control of the size, shape, and functionalities of the generated ionic liquids can be achieved through the incorporation of molecular complexity rules. Taken together, the mathematical representation and implementation of these requirements are referred to as structural constraints. Similar rules have been previously developed for molecular compounds (Sheldon et al., 2006). Eqs. (9.12)e(9.24) represent a comprehensive set of constraints that were developed to ensure design of ionic liquid candidates that are chemically feasible (Karunanithi and Mehrkesh, 2013). X ci ¼ 1 (9.12) i˛c

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SECTION j II Molecular Design

X

aj ¼ 1

(9.13)

j˛a 6 X

yl ¼

ð2  yci Þci þ

i˛c

ci yci

(9.14)

i˛c

l¼1

X

X

6 X X ð2  yGkl Þyl ngkl ¼ 2

(9.15)

l¼1 k˛G

X

yl ngkl ð2  yGkl Þ ¼ yl

(9.16)

k˛G 6 X X

yl ngkl  nU G

(9.17)

l¼1 k˛G

X

yl ngkl  nU Gl

(9.18)

k˛G

X

yl ngkl  t1

(9.19)

yl ngkl  t2

(9.20)

yl ngkl ¼ t3

(9.21)

k˛G

X

k˛G

X k˛G

6 X X

yl ngkl  t4

(9.22)

yl ngkl  t5

(9.23)

yl ngkl ¼ t6

(9.24)

l¼1 k˛G 6 X X l¼1 k˛G 6 X X l¼1 k˛G

In these equations, vectors c; a; and G represent the building blocks available to construct the ionic liquid molecules. Specifically, c is the set of cation cores or head groups (see Fig. 9.1) considered for the design, and a is the set of anions (see Fig. 9.1) available for selection. G represents the set of groups (including alkyl groups such as CH2, CH3, etc., and functional groups such as COOH, OH, benzyl, phenyl, etc.) available for inclusion in the different side chains of the cation. ci is a vector of binary variables representing different cation cores (i.e., cation head groups such as imidazolium,

Ionic Liquid Product Design Chapter j 9

pyridinium, ammonium, etc.), and ai is a vector of binary variables representing different anions. yl is a vector of binary variables representing the cation side chains l. ngkl is a vector of integer variables representing the number of groups of type k in the cation side chain l. yci , yGkl are vectors of group valencies of the cation cores and cation side chain groups, respectively. Eqs. (9.12) and (9.13) impose the selection of a maximum of one cation core and one anion, respectively, for each generated ionic liquid candidate. Eq. (9.14) helps us fix the number of cation side chains available to a given cation core based on the free valence of the cation core (e.g., a dialkylimidazolium cation core can only have two side chains attached to the two nitrogen atoms in the ring). Modified octet rule: The implementation of the modified octet rule for ionic liquids [Eq. (9.15)] ensures that the generated cations are structurally feasible, and the valence of all structural groups present in the cation is satisfied with a covalent bond. Note that this formulation has already internalized the positive charge associated with the cation (i.e., its ionic bond with anion). In addition, we also require Eq. (9.16) to ensure that the octet rule holds good for each side chain l present in the cation, making sure the valences in the individual cation side chains are satisfied with a covalent bond. Cation size: The size of the cation can be controlled by introducing an upper bound on maximum number of side chain groups ðnU G Þ that are allowed in the cation [Eq. (9.17)]. Cation side chain size: The size of the cation side chains are controlled by introducing an upper bound on the maximum number of groups nU Gl that are allowed in each cation side chain [Eq. (9.18)]. Further, Eqs. (9.19)e(9.21) (optional constraints) can be utilized to put in place restrictions related to number of occurrences (t1, t2, and t3) of a certain group, G , in each side chain l. In other words, Eq. (9.19) can be used to make sure that a certain functional group, such as methoxy group, is not present more than a fixed number of times in each side chain of the cation. Eq. (9.20) can be applied when we want a certain side chain group to be present at least t2 times. Eq. (9.21) can be used when an exact number of occurrence of a certain side chain group is desired, for example, when we want to have exactly one methoxy group in a certain side chain of the cation. Eqs. (9.22)e(9.24) can be utilized to place restrictions on number of occurrences (t4, t5, and t6) of a certain group G in the cation, which can be calculated as summation of number of occurrences of the particular group in all the side chains of the cation. The purpose of Eqs. (9.22)e(9.24) is exactly similar to that of Eqs. (9.19)e(9.21), with the difference being placement of limits on the number of occurrences of a particular group in the whole cation (summation of all of the side chains) versus only one side chain. Note that Eqs. (9.19)e(9.24) are all optional constraints and not mandatory in nature.

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SECTION j II Molecular Design

3. IONIC LIQUID PROPERTY PREDICTION Structure property models provide insights into the relationship between molecular structures and their properties. Examples include QSPR, CI models, molecular signature models (MS), and GC models. In QSPRs, a set of relevant molecular descriptors, such as conformational, electronic, quantum mechanical, and topological, are used. These descriptors are then linked to molecular properties through methods such as ANN models. CI and MS models are a subclass of QSPRs that are based only on topological information. In GC models, the molecular structure is represented as a combination of functional groups. Generalized QSPRs are not suited for CAMD, as molecular descriptors based on ab initio quantum chemical calculations do not readily lend themselves to the solution of reverse problem. CI and MS models have been used in CAMD problems for physical properties, but have rarely been developed for solution properties (activity coefficients) of molecular systems. GC models have been used to predict both pure component and solution properties of ionic liquids.

3.1 Thermodynamic Modeling of Ionic Liquids for CAILD Predictive thermodynamic models of activity coefficient that are not based on the concept of functional groups, such as the non-random two-liquid (NRTL) model, are not suited for CAMD, as these models require molecular parameters rather than group parameters. Models based on solution of groups’ concept, such as UNIFAC, are necessary for this purpose. Solution of groups concept: In 1962, Wilson and Deal from Shell Development Co. first presented the solution of groups concept to calculate activity coefficients on the basis of solute and solvent structures. The authors further expanded this approach in 1968 to develop the “analytical solutions of groups” model (Derr and Deal, 1969). In 1975, Fredenslund et al. adopted the functional groups approach to come up with the well-known UNIFAC GC model. Previously, ionic liquid groups have been included in the modified UNIFAC (Dortmund) model (Nebig and Gmehling, 2010). It only includes three cation cores and three anions. However, in comparison to original UNIFAC, the modified UNIFAC method needs relatively large number of experimental vaporeliquid equilibrium data since the fitted interaction parameters are temperature dependent. This presents a significant barrier towards inclusion of additional ionic liquid groups. In its current form, the original UNIFAC model is designed specifically for molecular mixtures and is not fully reliable for systems involving ionic species. This is because unlike molecular systems, ionic systems are governed by strong electrostatic interactions. The UNIFAC model only accounts for the short-range energetic interactions and does not account for long-range electrostatic interactions. Therefore, treating the positively charged cation skeleton and negatively charged anion as separate groups

Ionic Liquid Product Design Chapter j 9

FIGURE 9.2 s profile of four common industrial solvents. MEA, monoethanolamine; DEA, Diethanolamine; MDEA, Methyl Diethanolamine.

30 25 20 15

Series1

10

Series2

5 0 -0.04

-0.02

-5

0

0.02

0.04

FIGURE 9.3 s profile of an ionic liquid calculated by group contribution [red (gray in print versions)] and DFT [blue (dark gray in print versions)].

might lead to unreliable predictions. In order to use the UNIFAC model in its current form, Wang et al. (2008) and Lei et al. (2009) treated ionic liquids as a single nondissociate neutral entity. For example, the ionic liquid [BMIM]þ [BF4], was decomposed into two CH3 groups, three CH2 groups, and one [IM] [BF4] group. Using the above representation, Lei et al. (2009) have added 12 new ionic groups (e.g., [IM][PF6]) to the existing UNIFAC table. These groups include only two base cation cores with few anions. However, if we want to extend this approach to include a broad spectrum of ionic species, the number of groups needed increases by several fold. However, with the original UNIFAC representation, we would need a much smaller set of ionic groups to cover these structures. Roughton et al. (2012) took such an approach and were the first to incorporate solution properties through the integration of UNIFAC model for ionic liquid design problems. They were able to fit UNIFAC interaction parameters for three cation cores, several anions, and several side chain groups.

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However, limited experimental data prevented estimation of many binary group interaction parameters, thereby limiting the search space when the reverse problem (CAMD) was solved. Karunanithi and Mehrkesh (2013) employed the CAMD approach to solve problems related to extractant and solvent design. However, these problems also considered only limited number of ionic liquid combinations due to nonavailability of UNIFAC group interaction parameters. Chong et al. (2014) employed CAMD towards the design of ionic liquids for CO2 capture, where they considered two cation core groups, three anions, and two alkyl groups to generate ionic liquid combinations. In general, the practical utility of the CAILD approach for the design of solvents for separation processes, such as CO2 absorption and aliphaticearomatic separations, is greatly hindered by the limited availability of UNIFAC interaction parameters that cover a wide range of ionic liquid building blocks (i.e., cation cores, anions, and side chain groups) as well as other molecular groups (e.g., CO2). This limitation has proven to be the Achilles heel to the adoption of the CAILD approach towards meaningful solution of ionic liquid design problems.

3.2 A New Group Contribution Approach for the Prediction of Activity Coefficients in Systems Involving Ionic Liquids Conductor-like screening model for realistic solvents (COSMO-RS) (Klamt and Eckert, 2000) and conductor-like screening model- segment activity coefficient (COSMO-SAC) (Lin and Sandler, 2002) methods provide a fully predictive approach for activity coefficients that rely on surface charge density obtained from quantum chemical calculations. The advantage of these methods is that it does not require any fitted parameters (similar to UNIFAC or NRTL models) and consequently no experimental data is needed. However, these methods are not directly compatible with CAMD or CAILD approach, as electronic structure calculations are possible only through ab initio quantum chemical programs such as Gaussian or Turbomole, and these electronic structures are specific for each ionic liquid as a whole. Further, these calculations are extremely time-consuming and sometimes can take several hours for a single compound. Therefore, in this work, our objective was to develop GC predictions of ionic liquid surface charge density (s profile) and cavity volumes that can be subsequently integrated with the COSMO-SAC method to enable prediction of activity coefficients from ionic liquid structural information alone (without requiring any fitted parameters based on experimental data). In this method, we express the s profile and COSMO volume (which are identities of a whole molecule, in our case, an ionic liquid) of a given ionic liquid as a summation of contribution of the constituent groups (fragments: cation core, cation side chain groups, and anion) forming the ionic liquid structure with an aim to estimate the s profile through a GC approach. This method will save significant time in estimating the electronic structure (s

Ionic Liquid Product Design Chapter j 9

profile) and COSMO volume, which are required for the estimation of activity coefficient through the COSMO-SAC model. Fairly similar work has been carried out for regular molecules, but the application of that model for ionic liquids is not possible due to the fact that the charge on anions and cations dramatically change the electronic structure of the ionic liquids. Once we have the s profile contribution of every group in an ionic liquid structure, we can add these contributions to obtain the total sigma profile of the ionic liquid while skipping the tedious and time-consuming quantum chemical calculations. The whole process is just a simple algebraic operation, although there are some preliminary assumptions in the calculation of group sigma profiles. The definition of the fragments (cation core, cation side chain groups, anions) were made consistent with the structural representation proposed in Karunanithi and Mehrkesh (2013) where the cation was split into core groups (e.g., imidazolium, pyrrolidinium, pyridinium, sulfonium, etc.) and cation side chain groups. Most of the other groups were defined based on Nannoolal et al.’s (2004) work except some, which we defined in a particular way to make the predictions more precise as well as to be consistent with group definitions of other models and properties. Another assumption was that only the conformer with the least energy was used for each cation or anion in the group s profile calculations, which we believe is accurate enough for molecular design purposes. By using the quantum mechanical calculation of surface charge density distribution and cavity volume of the ionic liquids, we were able to calculate the corresponding s profile by introducing an ensemble averaging procedure, as shown in Eq. (9.25) P m

  2 r2 r2 dmv sm r2mþrav2 exp  r2 þr 2

sv ¼ P m

m

2 rm2 rav 2 rm2 þrav

av



exp 

m

2 dmv 2 rm2 þrav

av



(9.25)

where dmv represents the distance between two segments m and v, rm is the mean radius of segment m calculated from the area of this segment, and rav is an adjustable parameter. Fig. 9.2 shows the s profile of four common industrial solvents, while Fig. 9.3 shows the s profile of an ionic liquid derived from density functional theory (DFT) calculations and our GC method. As you can see from Fig. 9.3, s profiles predicted by the proposed GC method look very satisfactory. The same holds for the COSMO volume, and on an average, our GC method can predict within a 2% error.

4. COMPUTER-AIDED IONIC LIQUID DESIGN SOLUTION Several other chapters in this book provide detailed description about optimization and other solution methods used to solve the reverse problem. Therefore, in this chapter, we do not focus much on the solution algorithms, but only provide

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a brief description of methods used to solve the presented case studies. Essentially, we used two methods, one based on genetic algorithm (GA) and another based on branch and bound/outer approximation (OA) approach. GA is a stochastic method that can be used to solve both constrained and unconstrained optimization problems. This method is based on the process of natural selection, which is designed to mimic biological evolution. The basic idea in this approach is fairly straightforward: the algorithm first generates a random set of initial population candidates; this population is constantly updated at each iteration by selecting a subset of highfitness individuals from the current population and use them as parents to produce offsprings for the next generation, using operators such as crossover and mutation. The population “evolves” towards an optimal solution with improvements in the fitness of generated solutions. The second solution approach uses Bonmin, an open-source deterministic MINLP solver with implementation of nonlinear programmingebased branch and bound (NLP-BB), outer approximation (OA) and two different LP/ NLP-BB algorithms with different default parameters. Source code of Bonmin is available from COINeOR (http://www.coin-or.org) under the Common Public License as well as the Matlab implementation of the code within the OPTI Toolbox (http://www.i2c2.aut.ac.nz/Wiki/OPTI/index.php). The reader is referred to Bonami and Lejeune (2009) for a detailed description of these algorithms and their implementation.

5. CASE STUDY 1: DESIGN OF IONIC LIQUIDS FOR POLYMER DISSOLUTION A major research area in solution thermodynamics relates to understanding polymeresolvent systems, as it is relevant for several applications in packaging, adhesive, membrane separation, and pharmaceutical (drug development) industries. In this context, modeling solventepolymer interactions as well as optimal solvent selection for polymer dissolution is important since providing a suitable medium for polymerization reactions and enhancing polymer processability is critical. Ionic liquids, due to their high solvency power, have been considered as potential game changers as polymer solvents (e.g., to dissolve cellulosic biomass). They have also shown catalytic effect for certain polymerization reactions (Vygodskii et al., 2001). In this section, we present a case study that relates to the design of an optimal ionic liquid for dissolution of polyvinyl acetate, an important industrial polymer. A crucial requirement for solvent design and selection for polymer processing relates to the prediction of polymer solubility in the solvent (in this case, ionic liquids). For calculating the mole fraction xli of the dissolved solid component i in a saturated solution at equilibrium with the solid, we use the following equation derived by Prausnitz et al. (1998):    Dhm;i T 1 xli ¼ exp 1 (9.26) RT Tm gli

Ionic Liquid Product Design Chapter j 9

According to Eq. (9.26), at a given temperature and for a specific system (solventesolute), the exponential term is dependent only on the pure component properties of the solute (polymer), namely heat of fusion and melting point, and would be a constant term. Therefore, the reciprocal of activity coefficient ðgli Þ is a representation of solubility of the solute in a given ionic liquid solvent ðxli Þ. The activity coefficient can be split into two distinct terms: first, the nonideality caused by energetic (enthalpic) interactions of the mixture, also known as residual contribution, and the second representing the influence of size and shape of different molecules on the mixing entropy (entropic) effects, also known as combinatorial contribution. The total activity coefficient can be represented as a product of these two contributions: res comb gtot i ¼ gi  gi

(9.27)

To model polymer dissolution, approaches based on activity coefficient models or equation of state methods and their extensions for polymer systems can be used. However these models, in most cases, are highly parameterized, requiring large number of system-specific parameters (fitted) to produce reasonable results and lead to poor predictions beyond the core region of their parametrization. In contrast, as stated before, COSMO-RS offers an efficient and very general alternative route with minimal fitted parameters that are not system-specific, making the approach fully predictive in nature. However, it is a significant challenge (and at first it might seem impossible) to perform DFT calculations, and subsequently COSMO calculations, on extremely large polymer molecules with practically indefinite number of atoms. Having said that, there is still a reliable way to overcome this problem by choosing a representative part of the polymer chain that is small enough to make it feasible to perform quantum chemical calculations but large enough to capture the characteristic features of the molecule. This approach usually results in a very accurate estimation of the enthalpic part of the overall Gibbs free energy that is necessary to calculate the residual part of the activity coefficient. Because of the different shapes of polymer molecules, calculation of the combinatorial term is not as straightforward as that of regular molecules. There are different approaches that have been proposed to calculate the combinatorial term for systems that involve polymers. For example, Goss (2011) ignored the combinatorial term in COSMO-RS results and showed that the residual part correlates with experimental data with a mean squared correlation coefficient of R2 ¼ 0.84. Another study by Kuo et al. (2013) used evaluation of free volume effects for polymer solutions with the COSMO-RS reimplementation, COSMO-SAC, showing an overall improvement when free volume effects were taken into account. Loschen and Klamt (2014) used a free volume model proposed by Elbro et al. (1990) and were able to obtain satisfactory results for vaporliquid and gaseliquid systems as well as partition coefficients on systems containing polymers. In many cases, consideration of free volume effect seems to improve results as opposed to the omission of the combinatorial term.

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SECTION j II Molecular Design

For this cases study, we picked polyvinyl acetate as the polymer with Mn;polymer ¼ 84300 g=mol and Munit ¼ 86:09 g=mol, and the objective was to design the optimal solvent (ionic liquid) structure that has the highest solubility for this polymer. We used COSMO-RS reimplementation, COSMO-SAC, and as proposed by Yang et al. (2010), we used the default combinatorial term in COSMO-RS and COSMO-SAC formulation, known as StavermaneGuggenheim equation, with the following COSMO VCOSMO polymer ¼ Nunit  Vunit

(9.28)

COSMO ACOSMO polymer ¼ Nunit  Vunit

(9.29)

where Nunit ¼

Mpolymer Munit

(9.30)

Another important consideration during treatment of ionic liquids with COSMO-RS is the “sum of ions” view where the calculations involve a ternary mixture of the cation, the anion, and the solute, with the boundary condition approximation of molar equivalency of anion and cation in the mixture. On the other hand, the experimental determination of ionic liquid thermodynamic properties in the “one substance” view is based on the assumption of a binary system consisting of the ionic liquid (as a single neutral compound) and the solute.

5.1 Computer-Aided Ionic Liquid Design Problem Formulation and Solution The objective of this case study was to design a task specific ionic liquid that has the highest solubility for the polymer polyvinyl acetate at 300K. As discussed earlier, the CAILD methodology requires that any feasible ionic liquid should first satisfy the below constraints: X ci ¼ 1 (9.31) i˛c

X

aj ¼ 1

(9.32)

j˛a

where c is a set of all cation core groups considered (for this problem: diR-imidazolium, tri-R-imidazolium, pyridinium, piperidinium, ammonium, and pyrrolidinium), and a is a set of all anions considered (for this problem: Cl, BF4, PF6, and Tf2N). The next set of feasibility constraints take care of valence satisfaction of cations, which enable us to add feasible side chains to the open valence positions in the cation core. According to our representation, anions are considered as a single group and therefore do not require constraints

Ionic Liquid Product Design Chapter j 9

related to valence satisfaction. In other words, the three equations shown below, taken together, guarantee that octet rule for the cation as a whole as well as for each side chain (branch) is not violated. n X

yl ¼

X

ci yci

n X X X ð2  yci Þci þ ð2  yGkl Þyl ngkl ¼ 2 i˛C

(9.33)

i˛c

l¼1

(9.34)

l¼1 k˛G

X

yl ngkl ð2  yGkl Þ ¼ yl

(9.35)

k˛G

For this design problem, we fixed n* ¼ 6 and yci , which represents the vector consisting of valence of the cation core groups, were 2, 3, 1, 2, 4, and 2 for di-R-imidazolium, tri-R-imidazolium, pyridinium, pyrrolidinium, ammonium, and piperidinium, respectively. The selection of the cation cores for this design problem was based on the fact that all of the selected cation types within their categories have similar sigma profiles. More specific details and definitions related to the categorization of the groups can be found in Karunanithi and Mehrkesh (2013). Other than the above-mentioned feasibility constraints, we also implemented constraints related to the restriction of the size of the whole cation and the cation side chains (i.e., limits on the number of groups). These constraints can simply be imposed within the solver structure (GA in our case). In this proof of concept case study, for simplification and clarity purposes, we limited ourselves to the consideration of the two alkyl groups: eCH2- and eCH3 as the only groups that can be added to the cation side chain. A complete list of the ionic liquid building blocks (cation core, anion, side chain groups) considered for this design problem is presented in Table 9.1. A useful step in solvent screening is the consideration of activity coefficient of the solute at infinite dilution ðgN i Þ, which can be used as a qualitative measure to establish the dissolution power of the solvent. Calculation of infinite dilution activity coefficient can be performed by either considering just the residual part (to identify more impactful groups) or by taking into account both the residual and the combinatorial parts (more precise). The complete CAILD optimization model formulation for the polymer dissolution problem is shown as follows:    Dhm;i T 1 l max x1 ¼ exp 1 (9.36) RT Tm gl1 X ci ¼ 1 (9.37) i˛c

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TABLE 9.1 Subgroups Considered to Design Ionic Liquids for Polyvinyl Acetate Dissolution Cation Cores

Valence

Di-R-imidazolium

2

Tri-R-imidazolium

3

Pyrrolidinium

2

Pyridinium

1

Ammonium

4

Side Chain Groups Methylene

2

Methyl

1

Anions [Cl]

Structure

Ionic Liquid Product Design Chapter j 9

TABLE 9.1 Subgroups Considered to Design Ionic Liquids for Polyvinyl Acetate Dissolutiondcont’d Cation Cores [BF4]

Valence

Structure



[PF6]

[Tf2N]

X

aj ¼ 1

(9.38)

j˛a n X l¼1

yl ¼

X

ci yci

n X X X ð2  yci Þci þ ð2  yGkl Þyl ngkl ¼ 2 i˛C

(9.39)

i˛c

(9.40)

l¼1 k˛G

X

yl ngkl ð2  yGkl Þ ¼ yl

(9.41)

k˛G

gN i < 1    Dhm;i T 1 l x1  exp 1 ¼0 RT Tm gl1 X xi ¼ 1

(9.42) (9.43) (9.44)

The CAILD implementation algorithm and the corresponding MATLAB code consist of three blocks. The first one is the main block, which includes the solver specification (GA) and solver setup (parameters). The second is the constraint block that includes feasibility constraints and other structural constraints as well as any other required property constraints that the ionic liquid

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should possess. For example, we might be required to design a solvent that has a maximum melting point of 350K or maximum viscosity of 100 cp at 300K. This is where we specify all of these requirements as property constraints. The third block is the fitness function (objective function) that calculates the key desired property, which we usually refer to as functional property (for this problem, the solvency power to dissolve the polymer). The output of this block is the value of the defined objective function that needs to be maximized or minimized. For the polyvinyl acetate case study, our algorithm was implemented as follows: first, by considering just the residual part for the infinite dilution activity coefficient, we invoked the property constraint ðgN i < 1Þ for each feasible ionic liquid structure that satisfies the structural constraints while the candidates that satisfy this property constraint would be considered further and the fitness function would be evaluated. The fitness function (objective function) is the solubility of polyvinyl acetate in ionic liquid candidates and is calculated through Eq. (9.36) and COSMO-SAC thermodynamic model.

5.2 Results The optimal ionic liquid structure for this design problem is shown in Fig. 9.4. This structure consists of an ammonium [N4]þ cation and bis(trifluoromethylsulfonyl)imide [Tf2N] anion. The model resulted in a solution that has 10 CH2 and 1 CH3 terminal group attached to each alkyl side chain of the ammonium cation (valence for ammonium is 4). Note that the maximum allowed CH2 per side chain for this problem was 10. Subsequently, the melting point of the optimal ionic liquid was estimated at 195.4K, confirming that the designed optimal ionic liquid is a room temperature ionic liquid and meets the

FIGURE 9.4 Optimal ionic liquid structure for polymer dissolution: cation core- ammonium, [N 10, 10, 10, 10]þ; anion: bis(trifluoromethylsulfonyl) imide, [Tf2N].

Ionic Liquid Product Design Chapter j 9

requirement of being liquid at the temperature at which the dissolution is to be performed (i.e., at 300K).

6. CASE STUDY 2: IONIC LIQUID DESIGN FOR HEAT TRANSFER APPLICATIONS Thermal conductivity is a material property that represents the degree to which it can conduct heat. Knowledge on thermal conductivity of ionic liquids is crucial to tailor them for applications related to their use as heat transfer fluids. Ionic liquids have great potential to be a good substitute for traditional heat transfer fluids, which are usually synthetic organic and silicone-based compounds. For other thermal applications, such as thermal energy storage (e.g., solar thermal energy storage), thermal conductivity is one of the key physical properties that needs to be considered along with other fluid properties, such as density, viscosity, heat capacity, and melting point. Ionic liquids also usually possess better thermal stability (i.e., higher decomposition temperature) than their molecular counterparts, making them appropriate for processes that operate at high temperatures. The most important requirement of a heat transfer fluid is that it should possess high thermal conductivity. Compared to other thermophysical properties of ionic liquids, very limited data and information is available on thermal conductivities, as experimental measurements are difficult and relatively expensive. In this case study, we focus on designing optimal ionic liquids, utilizing the presented CAILD optimization methodology, for use as heat transfer fluids in thermal applications. In the following sections, we present the structureeproperty models that will be utilized to predict ionic liquid physical and thermal properties, the CAILD optimization problem formulation of the heat transfer fluid problem, and design results and analysis. The two ionic liquid thermophysical properties considered in this case study are thermal conductivity and melting point. The melting point is an important consideration since not all ionic liquids exist in liquid state at room temperature. In the following, we present details about the existing GC models from literature, which were used to estimate these two properties.

6.1 Thermal Conductivity There are few GC models that have been previously developed for predicting thermal conductivity of ionic liquids. Gardas and Coutinho (2009) proposed a linear model [Eq. (9.45)] to estimate thermal conductivity as a function of temperature. l ¼ Al  Bl T

(9.45)

In this model, Al and Bl are fitted parameters that can be obtained from GC approach, and T represents the temperature of interest.

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Wu et al. (2013) developed a GC-based method to estimate the thermal conductivity of ionic liquids via contributions of cation, anion, and groups. This GC model is shown in Eq. (9.46). 0 1i 2 k h i X X 2 l¼ ai @ nj Dl0; j A 1 þ k0 ð1  Tr Þ3 (9.46) i¼0

j¼1

The different required parameters to estimate l using Eq. (9.46) and the estimating procedure are shown in the following [Eqs. (9.47)e(9.50)]: Tr ¼ Tc ¼

T Tc

(9.47)

Tb

" AþB

Pk j¼1

nj DTc 

Tb ¼ 198:2 þ

k X

Pk j¼1

nj DTb

!2 #!

(9.48)

nj DTc

(9.49)

j¼1

where, Tr is reduced temperature, A ¼ 0.5703, B ¼ 1.0121, k0 is a temperature-independent constant, and nj is the number of occurrence of group j in the molecule. DTb ; DTc ; and Dl are the contributions to the boiling point temperature Tb , critical point temperature Tc , and thermal conductivity l, and l0 can be obtained from the following equation. 0 1i 2 k X X l0 ¼ ai @ DTb A (9.50) j¼i

j¼i

The authors regressed the contributions using 286 data points covering 36 different ionic liquids consisting of imidazolium, phosphonium, and ammonium cations with octyl sulfate (OcSO4), ethyl sulfate (EtSO4), bis(trifluoromethanesulfonyl) amide (NTf2), hexafluorophosphate (PF6), tetrafluoroborate (BF4), chloride (Cl), trifluoromethanesulfonate (TfO), dicyanamide (DCA), tris(pentafluoroethyl)trifluorophosphate (FAP), acetate (CH3COO), tricyanomethanide (C(CN)3), serinate (Ser), taurinate (Tau), lysinate (Lys), threonate (Thr), prolinate (Pro), and valinate (Val) anions. These ionic liquids (both cations and anions) were broken down into 25 molecular groups, and the experimental data were fitted to regress the GC parameters for these 25 simple groups. The structural information and the thermal conductivity data of these ionic liquids were used to obtain the values of the coefficients ai and k0 and the group parameters Dl0;j . More details about this model can be found in Wu et al. (2013).

Ionic Liquid Product Design Chapter j 9

6.2 Melting Point Since we are interested in room temperature ionic liquids, the melting point of the designed compound should be adjusted to meet this need. An ionic liquid with a low melting point is desirable since it is mandatory that, at all times, the operating temperature needs to be kept above the melting point of the heat transfer fluid in order to avoid solid formation in the system. When the melting point is too high, a high process temperature is necessary, which will lower the system efficiency by reducing the rate of heat transfer (sensible heat). For this case study, we wanted to design room temperature ionic liquids, and hence, we place a requirement that the heat transfer fluid should possess a melting point below 25  C. To calculate the melting point of ionic liquids, the GC method proposed by Lazzu´s (2012) was used. In this approach, two different sets of melting point contributions were used: (1) the contribution of the cation head group (cation core) as well as the alkyl groups/functional groups attached to the side chains of the cation core, and (2) the contribution of groups present in the anion. Cation head groups (i.e., core) are consolidated as whole (e.g., imidazolium or pyridinium), but side chain groups and anions are split into smaller structural fragments. The melting point of any given ionic liquid can then be estimated as a summation of contribution of cation, anion, and the cation side chain groups as following: X X Tm ðkÞ ¼ 288:7 þ ni Dtci þ nj Dtaj (9.51) where ni is the number of occurrence of group i, Dtci is the contribution of cation groups to the melting point, and Dtaj is the contribution of anion groups to the melting point of the given ionic liquid. More details about this model can be found in Lazzus (2012).

6.3 Computer-Aided Ionic Liquid Design Problem Formulation and Solution In this section, we present a CAILD model to find (design) optimal ionic liquid structures with high thermal conductivity. The presented framework allows consideration of variety of building blocks, which include cation cores, cation side chain groups, and anions to construct the ionic liquid structures. In this approach, thermal conductivity of ionic liquids were estimated using the GC model proposed by Wu et al. (2013) and discussed in the previous section, and the optimal ionic liquid structures were generated by solving an optimization formulation of the design problem. Melting point requirement was posed as a constraint and was estimated using the GC model proposed by Lazzus (2013). The CAILD framework proposed by Karunanithi and Mehrkesh (2013), and discussed earlier, was utilized to formulate the heat transfer fluid design problem as an optimization model. Structural constraints [Eqs. (9.54)e(9.58)] were included to design feasible ionic liquid

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structures. These constraints are a subset of the comprehensive set of structural constraints presented in Karunanithi and Mehrkesh (2013). The full CAILD optimization model for the design of ionic liquid heat transfer fluids with high thermal conductivity is shown in the following.

Objective Function 0 f obj ¼ max@l ¼

2 X

0 ai @

k X

i¼0

1i

h

i 2

1

nj Dl0;j A 1 þ k0 ð1  Tr Þ3 A

(9.52)

j¼1

Constraints Tm ðkÞ ¼ 288:7 þ

X

ni Dtci þ

X

nj Dtaj < 298K ðAdjustment for RTILÞ (9.53)

Equations to take care of feasibility of ionic liquids X ci ¼ 1

(9.54)

i˛C

X

ai ¼ 1

(9.55)

j˛A n X

yl ¼

X

ci yci

(9.56)

i˛c

l¼1

X

gkl ¼ yl

(9.57)

gkl ð2  yGkl Þ ¼ yl

(9.58)

k˛G

X k˛G

Tr ¼

T Tc

(9.59)

Tb

Tc ¼ " AþB

Pk j¼1

nj DTc 

Tb ¼ 198:2 þ

k X j¼1

Pk j¼1

nj DTb

!2 #

(9.60)

nj DTc

(9.61)

Ionic Liquid Product Design Chapter j 9

A ¼ 0:5703; B ¼ 1:0121

(9.62)

where C and A are binary vectors representing the cation cores and anions considered as building blocks, yl is binary vector representing alkyl chains, and gk represents alkyl side chain groups considered. yci and yGkl are vectors of cation core and alkyl side chain group valences. The basis set (i.e., set of ionic liquid building blocks) used for this design problem is show in Table 9.2. The building blocks include five different cation core groups, three alkyl side chain groups, and three different anions. We utilized a deterministic algorithm BONMIN based on branch and bound/OA method to solve the resulting MINLP model.

6.4 Results and Analysis Fig. 9.5 shows the optimal ionic liquid structure for the heat transfer fluid problem. The designed ionic liquid consists of a tetrafluoroborate [BF4] anion and a pyridinium cation (valence 6) with six methyl groups attached to each of the side chains. The objective function value (i.e., maximum thermal conductivity) of the optimal ionic liquid was 0.2113 W/m K, and the melting point was 298K. Next, we compare the properties of the optimal ionic liquid with that of a commercial heat transfer oil VP-1. The thermal conductivity of the designed ionic liquid (0.2113 W/m K) is higher than the thermal conductivity of VP-1TM oil (0.12 W/m K). The melting point of the designed ionic liquid is 298K, suggesting that it should be in liquid state at the operating temperatures. Overall, the design results suggest that the optimal ionic liquid has better heat transfer characteristics than an existing commercial heat transfer fluid. We performed further analysis using available experimental thermal conductivity data from literature to study more in depth the relationship between ionic liquid structures and thermal conductivity values as well as to qualitatively validate the design results. In this study, we considered three different types of anions: [Tf2N], [PF6], and [BF4]. First, in order to study which of these anions usually lead to higher thermal conductivity values, based on available experimental data, we considered two cation structures, namely 1-butyl-3-methyl imidazolium [BMIM]þ and 1-hexyl-3-methyl imidazolium [HMIM]þ (since these were the two cations for which thermal conductivity data were available for all three anions). For the case of [BMIM]þ cation, the corresponding experimental thermal conductivity values were 0.127, 0.145, and 0.169 W/m K for [Tf2N], [PF6], and [BF4] anions, respectively. For the case of [HMIM]þ cation, the corresponding experimental thermal conductivity values were 0.124, 0.142, and 0.156 W/m K for [Tf2N], [PF6], and [BF4] anions, respectively. From these two cases, it is clear that [BF4] anion consistently leads to higher thermal conductivity values than either [Tf2N], or [PF6] anions. This analysis is consistent with our design result, as the optimal ionic liquid picked by our model has a [BF4] anion. Next,

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TABLE 9.2 Ionic Liquid Subgroups Considered for Ionic Liquid Design for Thermal Conductivity Cation Core Group

Cation Side Chain Groups

Anion

Imidazolium (valence 1)

CH3 (valence 1)

Tetrafluoroborate [BF4]

Pyridinium (valence 2)

CH2 (valence 2)

bis(trifluoromethylsulfonyl) imide [Tf2N]

Pyridinium (valence 6)

CH (valence 3)

Hexafluorophosphate [PF6]

Ammonium (valence 4)

Piperedinium (valence 6)

FIGURE 9.5 Optimal ionic liquid structure for heat transfer fluid: cation core- pyridinium; anion: tetrafluoroborate, [BF4].

Ionic Liquid Product Design Chapter j 9

we fixed the anion as [Tf2N] and looked at the experimental thermal conductivity data of different cations having the following cation cores: imidazolium, ammonium, and pyridinium (unfortunately, we could not find any experimental data on piperidinium ionic liquids). When the anion was fixed as [Tf2N], we observe the following thermal conductivities for different cations: (1) imidazolium cores: 1-ethyl-3-methylimidazolium [C2MIM]; k ¼ 0.129 W/m K; 1-butyl3-methylimidazolium [C4MIM], k ¼ 0.127 W/m K; 1-hexyl3-methylimidazolium [C6MIM], k ¼ 0.124 W/m K; 1-octyl-3-octylimidazolium [C8MIM], k ¼ 0.128 W/m K; 1,3-dibutylimidazolium [BBIM], k ¼ 0.118 W/ m K; (2) ammonium cores: trioctylmethylammonium [N8,8,8,1], k ¼ 0.127 W/ m K; trimethylbutylammonium, [N4,1,1,1], k ¼ 0.123 W/m K; and (3) 1-butyl-4(dimethylamino) pyridinium [hDMApy], k ¼ 0.13 W/m K 1–hexyl-4-(dimethylamino)pyridinium [HmDMApy], k ¼ 0.13 W/m K. From these data, it clear that in general, the ionic liquids with pyridinium cation cores seem to have higher thermal conductivity than imidazolium and ammonium cation cores. This is consistent with our design results, as the optimal ionic liquid picked by our model has a pyridinium cation core (valence 6). Also, based on fixing the anion as [Tf2N] and the first series of numbers related to imidazolium cation cores that are presented previously, one can see that in general (except for one case of 1-octyl3-methylimidazolium), when the number of alkyl groups in the side chain increases, the thermal conductivity decreases (i.e., thermal conductivity (k) of 1-ethyl-3-methylimidazolium [C2MIM] > 1-butyl-3-methylimidazolium [C4MIM] > 1-hexyl-3-methylimidazolium [C6MIM]). Therefore, there is reason to believe that the lower the number of alkyl groups in the cation side chain, the higher the thermal conductivity. This is consistent with our design results, as the optimal ionic liquid has only one methyl group in each of the cation side chains (total of 6). Note that our model did not add any CH2 groups to the side chains, since such an addition can potentially reduce the thermal conductivity. Also note that since the optimal cation core, pyridinium (valence 6), has six open positions, there needs to be at least one alkyl group minimum that has to be added to each open position (total of six) to make the cation, as a whole, a feasible structure. Another observation is that for a fixed cation, when we vary the anion, the thermal conductivity changes significantly, while for a fixed anion and varying cations, the thermal conductivity does not change much. Therefore, it is also clear that anion contributes significantly more towards thermal conductivity than cation, and, hence, consideration of a wide variety of anions in the future can significantly improve the design results.

7. SUMMARY AND CONCLUSIONS This chapter reviews and presents state-of-the art knowledge related to the extension and application of CAMD methods towards the design of novel ionic liquids. The proposed framework, referred to as CAILD, and the mathematical formulations have been discussed extensively, and two case studies related to

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the optimal design and selection of ionic liquids for use as solvents for polymer dissolution and for use as heat transfer fluids are presented. Initially, we discussed the evolution of CAMD approach over the years and subsequently extended the discussion to recent developments in applying this technique towards ionic liquid design (for problems related to both pure component physical properties and solution properties). Next, we presented a general mathematical framework that can be used for formulating the CAILD problem with a particular emphasis on ionic liquid structure generation and constraint modeling based on information from our previous publication (Karunanithi and Mehrkesh, 2013). Subsequently, we discuss a new methodology to predict activity coefficients of ionic liquid systems based on our research groups’ recent work (Farahipour and Karunanithi, 2016). As for the two case studies, the design goals included tuning ionic liquid structures to attain optimal targets for polyvinyl acetate (polymer) dissolution and maximizing thermal conductivity, respectively. With an objective to design ionic liquids, a structurally diverse set of building blocks that included different cation core groups and different anions was considered. The two design problems were formulated as MINLP models with an objective to maximize polyvinyl acetate solubility (for solvent design for polymer) and thermal conductivity (for heat transfer fluid design). Structural constraints were invoked to consider only feasible ionic liquid candidates, restrict the size of the cations, and limit group occurrences, while property constraints were used to set target ranges for infinite dilution activity coefficients (for solvent design for polymer) and melting point (heat transfer fluid). For the polymer dissolution case study, the activity coefficients that were needed to perform solid liquid equilibrium calculations as well as for estimation of composition of the polymer in a saturated solution (i.e., solubility) was calculated using a novel methodology developed by our group that links quantum chemical calculations of electronic charge densities of ionic liquids, GC approach for sigma profile predictions, and the COSMO-SACebased thermodynamic model for activity coefficients. The same approach was utilized to predict infinite dilution activity coefficients. For the heat transfer fluid case study, existing GC models for ionic liquid thermal conductivity and melting point predictions were utilized. The solution of the reverse problem, i.e., the CAILD optimization model, was achieved through a GA methodology for polymer dissolution case study and through a deterministic branch and bound/OA algorithm for the heat transfer fluid case study. Further detailed analysis related to the comparison of the designed ionic liquid with other commercial products, analysis for each category based on available experimental data, and model prediction validations based on selected experimental data were also presented for the heat transfer fluid case study. The results from this work show the potential of CAILD approach to systematically design and select optimal ionic liquids for any given application. The results also indicate the ability of this approach to computationally identify new candidates that can be further evaluated

Ionic Liquid Product Design Chapter j 9

experimentally. We identify two critical areas for future research: (1) improvement in the predictive capability of different physical and thermodynamic properties of more diverse ionic liquid structures, which will enable consideration of other cation core groups, anions, and functional groups; and (2) devise synthesis routes for the designed ionic liquids and experimentally test and evaluate the properties.

REFERENCES Achenie, L.E.K., Gani, R., Venkatasubramanian, V., 2003. Computer Aided Molecular Design: Theory and Practice. Elsevier Science. Armand, M., Endres, F., MacFarlane, D.R., Ohno, H., Scrosati, B., 2009. Ionic-liquid materials for the electrochemical challenges of the future. Nature Materials 8 (8), 621. Buxton, A., Livingston, A.G., Pistikopoulos, E.N., 1999. Optimal design of solvent blends for environmental impact minimization. AIChE Journal 45 (4), 817e843. Bonami, P., Lejeune, M.A., 2009. An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Operations Research 57 (3), 650e670. Camarda, K.V., Maranas, C.D., 1999. Optimization in polymer design using connectivity indices. Industrial and Engineering Chemistry Research 38, 1884e1892. Chavez-Islas, L.M., Vasquez-Medrano, R., Flores-Tlacuahuac, A., 2011. Optimal molecular design of ionic liquids for high-purity bioethanol production. Industrial and Engineering Chemistry Research 50 (9), 5175e5190. Chemmangattuvalappil, N.G., Solvason, C.C., Bommareddy, S., Eden, M.R., 2010. Reverse problem formulation approach to molecular design using property operators based on signature descriptors. Computers and Chemical Engineering 34 (12), 2062e2071. Chong, F.K., Eljack, F.T., Atilhan, M., Foo, D.C., Chemmangattuvalappil, N.G., 2014. Ionic liquid design for enhanced carbon dioxide capture e a computer aided molecular design approach. Chemical Engineering Transactions 39. Churi, N., Achenie, L.E.K., 1997. The optimal design of refrigerant mixtures for a two-evaporator refrigeration system. Computers and Chemical Engineering 21, S349eS354. Constantinou, L., Bagherpour, K., Gani, R., Klein, J.A., Wu, D.T., 1996. Computer aided product design: problem formulations, methodology and applications. Computers and Chemical Engineering 20, 685e702. Derr, E.L., Deal, C.H., 1969. Analytical solution of groups: correlation of activity coefficients through structural group parameters. Institution of Chemical Engineers Symposium Series 32, 44. Duvedi, A.P., Achenie, L.E.K., 1996. Designing environmentally safe refrigerants using mathematical programming. Chemical Engineering Science 51 (15), 3727e3739. Duvedi, A.P., Achenie, L.E.K., 1997. On the design of environmentally benign refrigerant mixtures: a mathematical programming approach. Computers and Chemical Engineering 21 (8), 915e923. Eden, M.R., Jørgensen, S.B., Gani, R., El-Halwagi, M.M., 2004. A novel framework for simultaneous separation process and product design. Chemical Engineering and Processing 43, 595e608. Elbro, H.S., Fredenslund, A., Rasmussen, P., 1990. A new simple equation for the prediction of solvent activities in polymer solutions. Macromolecules 23 (21).

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SECTION j II Molecular Design Farahipour, R., Karunanithi, A.T., 2014. Life cycle environmental implications of CO2 capture and sequestration with ionic liquid 1-butyl-3-methylimidazolium acetate. ACS Sustainable Chemistry and Engineering 2 (11), 2495e2500. Farahipour, R., Karunanithi, A.T., 2016. A new group contribution approach to estimate electronic structures of ionic liquids. Under review. Fluid Phase Equilibria. Fredenslund, A., Jones, R.L., Prausnitz, J.M., 1975. Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE Journal. 21 (6), 1086e1099. Folic, M., Adjiman, C.S., Pistikopoulos, E.N., 2004. The design of solvents for optimal reaction rates. Proceedings of European Symposium of Computer Aided Process Engineering 14, 175e180. Gani, R., Brignole, E.A., 1983. Molecular design of solvents for liquid extraction based on UNIFAC. Fluid Phase Equilibria 13, 331. Gani, R., Neilsen, B., Fredenslund, 1991. A. Group contribution approach to computer aided molecular design. AIChE Journal 37, 1318. Gani, R., Fredunslund, A., 1993. Computer aided molecular and mixture design with specified property constraints. Fluid Phase Equilibria 82, 39. Gardas, R.L., Coutinho, J.A., 2009. Group contribution methods for the prediction of thermophysical and transport properties of ionic liquids. AIChE Journal 55 (5), 1274e1290. Goss, K., 2011. Predicting equilibrium sorption of neutral organic chemicals into various polymeric sorbents with COSMO-RS. Analytical Chemistry 83 (13), 5304e5308. Hada, S., Herring III, R.H., Davis, S.E., Eden, M.R., 2015. Multivariate characterization, modeling, and design of ionic liquid molecules. Computers and Chemical Engineering 81, 310e322. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2006. A computer-aided molecular design framework for crystallization solvent design. Chemical Engineering Science 61, 1247e1260. Karunanithi, A.T., Achenie, L.E., 2007. Chemical Product Design: Toward a Perspective Through Case Studies. Elsevier, Philadelphia. Karunanithi, A.T., Mehrkesh, A., 2013. Computer-aided design of tailor-made ionic liquids. AIChE Journal 59 (12), 4627e4640. Klamt, A., Eckert, F., 2000. COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids. Fluid Phase Equilibria 172 (1), 43e72. http://www. sciencedirect.com/science/journal/03783812. Klein, J.A., Wu, D.T., Gani, R., 1992. Computer aided mixture design with specified property constraints. Computers and Chemical Engineering 16, S229. Kuo, Y., Hsu, C., Lin, S., 2013. Prediction of phase behaviors of polymeresolvent mixtures from the COSMO-SAC activity coefficient model. Industrial and Engineering Chemistry Research 52 (37), 13505e13515. Lazzu´s, J.A., 2012. A group contribution method to predict the melting point of ionic liquids. Fluid Phase Equilibria 313, 1e6. Lei, Z., Zhang, J., Li, Q., Chen, B., 2009. UNIFAC model for ionic liquids. Industrial and Engineering Chemistry Research 48 (5), 2697e2704. Lin, S.T., Sandler, S.I., 2002. A Priori Phase Equilibrium Prediction from a Segment Contribution Solvation Model. Ind. Eng. Chem. Res. 41, 899. http://dx.doi.org/10.1021/ie001047w. Loschen, C., Klamt, A., 2014. Prediction of solubilities and partition coefficients in polymers using COSMO-RS. Industrial and Engineering Chemistry Research 53 (28), 11478e11487. Macchietto, S., Odele, O., Omatsone, O., 1990. Design of optimal solvents for liquid-liquid extraction and gas absorption processes. Transactions of the Institution of Chemical Engineers 68 (A), 429e433.

Ionic Liquid Product Design Chapter j 9 Mai, N.L., Koo, Y., 2016. Computer-aided design of ionic liquids for high cellulose dissolution. ACS Sustainable Chemistry and Engineering 4 (2), 541e547. Maranas, C.D., 1997. Optimal molecular design under property prediction uncertainty. AIChE Journal 43 (5), 1250e1264. Mehrkesh, A., Karunanithi, A.T., 2013. Energetic ionic materials: how green are they? A comparative life cycle assessment study. ACS Sustainable Chemistry and Engineering 1 (4), 448e455. Mehrkesh, A., Karunanithi, A.T., 2016a. Life cycle perspectives on aquatic ecotoxicity of common ionic liquids. Environmental Science and Technology 50 (13), 6814e6821. Mehrkesh, A., Karunanithi, A.T., 2016b. Optimal design of ionic liquids for solar energy storage. Computers and Chemical Engineering 93, 402e412. Mehrkesh, A., Karunanithi, A.T., 2016c. New quantum chemistry-based descriptors for better prediction of melting point and viscosity of ionic liquids. Fluid Phase Equilibria 427, 498e503. McLeese, S.E., Eslick, J.C., Hoffmann, N.J., Scurto, A.M., Camarda, K.V., 2010. Design of ionic liquids via computational molecular design. Computers and Chemical Engineering 34, 1476e1480. Nannoolal, Y., Rarey, J., Ramjugernath, D., Cordes, W., 2004. Estimation of pure component properties: part 1. Estimation of the normal boiling point of non-electrolyte organic compounds via group contributions and group interactions. Fluid Phase Equilibria 226, 45e63. Naser, S.F., Fournier, R.L., 1991. A system for the design of an optimum liquid-liquid extractant molecule. Computers and Chemical Engineering 15 (6), 397e414. Nebig, S., Gmehling, J., 2010. Measurements of different thermodynamic properties of systems containing ionic liquids and correlation of these properties using modified UNIFAC (dortmund). Fluid Phase Equilibria 294 (1e2), 206e212. Odele, O., Machietto, S., 1993. Computer aided molecular design: a novel method for optimal solvent selection. Fluid Phase Equilibria 82, 47e54. Praunnitz, J.M., Lichtenthaler, R.N., Azevedo, E.G., 1998. Molecular Thermodynamics of FluidPhase Equilibria. Pearson Education, New York. Pretel, E.J., Lopez, P.A., Bottini, S.B., Brignole, E.A., 1994. Computer-aided molecular design of solvents for separation processes. AIChE Journal 40, 1349e1360. Roughton, B.C., Christian, B., White, J., Gani, R., 2012. Simultaneous design of ionic liquid entrainers and energy efficient azeotropic separation processes. Computers and Chemical Engineering 42, 248e262. Samudra, A.P., Sahinidis, N.V., 2013. Optimization-based framework for computer-aided molecular design. AIChE Journal 59 (10), 3686e3701. Sheldon, T.J., Folic, M., Adjiman, C.S., 2006. Solvent design using a quantum mechanical continuum solvation model. Industrial and Engineering Chemistry Research 45, 1128e1140. Sinha, M., Achenie, L.E.K., Ostrovsky, G.M., 1999. Environmentally benign solvent design by global optimization. Computers and Chemical Engineering 23 (10), 1381e1394. Siddhaye, S., Camarda, K.V., Topp, E., Southard, M., 2000. Design of novel pharmaceutical product via combinatorial optimization. Computers and Chemical Engineering 24, 701e704. Vaidyanathan, R., El-Halwagi, M., 1996. Computer aided synthesis of polymers and blends with target properties. Industrial and Engineering Chemistry Research 35 (2), 627e634. Vygodskii, Y.S., Lozinskaya, E.I., Shaplov, A.S., 2001. Ionic liquids as novel promising reaction media for organic and polymer syntheses. Polymer Science Series 43 (2), 236e251. Wang, Y., Achenie, L.E.K., 2002. A hybrid global optimization approach for solvent design. Computers and Chemical Engineering 26, 1415e1425.

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Chapter 10

Integrated Multiobjective Molecular and Process Design: Operational and Computational Frontiers A.I. Papadopoulos,*, 1 P. Linkex and P. Seferlis{

*Centre for Research and Technology Hellas (CERTH), Thessaloniki, Greece; xTexas A&M University at Qatar, Doha, Qatar; {Aristotle University of Thessaloniki, Thessaloniki, Greece 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION Certain materials are selected for particular applications because they possess specific chemical, physical, economic, functional, environmental, or other characteristics that make them the most suitable options. For example, the chemical industry employs solvents or heat exchange fluids as intermediate materials to enhance the driving forces and increase the efficiency of chemical or physical separations and heat exchange operations. Computer-aided molecular design (CAMD) is a technological approach, which supports the systematic identification of the most appropriate material for a particular application using as selection criteria the characteristics of the material that make it a suitable candidate. In this context, CAMD approaches have been proposed for several different types of materials. An overview of different published works is provided in Tables 10.1 and 10.2. Review papers analyzing different CAMD-based approaches, including additional publications, have been presented by Ng et al. (2015) and Gani and Ng (2015). Characteristics used as criteria in CAMD methods are usually properties of pure compounds or mixtures, which are calculated using group contribution (GC) models. Such models are based on the idea that a particular molecular property may be calculated based on the functional groups that comprise the molecule. The contribution of each functional group to the calculation of such a property remains the same, regardless of the molecular structure in which it is used. This is very convenient because it allows the exhaustive evaluation of Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00010-1 Copyright © 2016 Elsevier B.V. All rights reserved.

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TABLE 10.1 Overview of Approaches for Integrated or Simultaneous Solvent and Process Design Literature Sources

Key Features

Solvent and Process Design Approaches Marcoulaki and Kokossis (2000a) and Linke and Kokossis (2002)

Separation and reactive separation systems, superstructure-based process synthesis

Papadopoulos and Linke (2005, 2006a,b, 2009a,b)

Multiobjective optimization, superstructure-based process synthesis, data mining, grid computing separation, and reactive separation systems

Pistikopoulos and Stefanis (1998), Buxton et al. (1999), and Giovanoglou et al. (2003)

Environmental constraints, blends and batch separation processes

Hostrup et al. (1999) and Harper and Gani (2000)

Multiple separation process tasks, superstructure-based approach, insightful analysis of solventeprocess interactions

Wang and Achenie (2002) and Cheng and Wang (2007, 2008, 2010)

Advanced optimization approaches, separation and reactive separation systems

Kim and Diwekar (2002) and Xu and Diwekar (2007)

Systematic uncertainty quantification methods, multiobjective optimization, batch separation processes

Hamad and El-Halwagi (1998)

Synthesis of solvents and mass exchange networks

Eden et al. (2004), Chemmangattuvalappil et al. (2010), Bommareddy et al. (2010), and Chemmangattuvalappil and Eden (2013)

Property clustering approach, advanced molecular representations, and property prediction models.

Kazantzi et al. (2007), Eljack et al. (2007), and Kheireddine et al. (2013)

Visualization tools for solvent and process design, property clustering approach

Pereira et al. (2011) and Burger et al. (2015)

Use of SAFT-VR or SAFT-g-Mie equations of state, physical CO2 capture solvents and processes

Bardow et al. (2010), Oyarzun et al. (2011), Stavrou et al. (2014), Qadir et al. (2014), and Lampe et al. (2015)

Use of PCP-SAFT or group contribution PC-SAFT equations of state, physical CO2 capture solvents, and processes

Mac Dowel et al. (2010) and Papadokonstantakis et al. (2015)

Use of SAFT-VR or SAFT-g-SW equations of state, chemical CO2 capture solvents and processes

Integrated Multiobjective Molecular and Process Design Chapter j 10

TABLE 10.1 Overview of Approaches for Integrated or Simultaneous Solvent and Process Designdcont’d Literature Sources

Key Features

Salazar et al. (2013)

Use of eNRTL and UNIFAC, chemical CO2 capture solvents and processes

Siougkrou et al. (2014)

Solvent and process design for gasexpanded systems

Zhou et al. (2015)

Solvent and process design for optimum reaction rates

TABLE 10.2 Overview of Computer-Aided Molecular Design Applications in the Design of Different Materials Literature Sources

Key Features

Refrigerants Sahinidis et al. (2003) and Samudra and Sahinidis (2013)

Deterministic global optimization, problem decomposition, graph-based representation of molecules

Duvedi and Achenie (1996, 1997)

Deterministic optimization, environmental performance constraints, blends

Marcoulaki and Kokossis (2000a,b)

Stochastic optimization, systematic molecular representation, pure refrigerants

Roskosch and Atakan (2015)

Molecular properties used as continuous variables in optimization, application to heat pumps

Working Fluids for Organic Rankine Cycles Papadopoulos et al. (2010a,b, 2012, 2013a,b), Mavrou et al. (2015), and Linke at el. (2015)

Multiobjective optimization, design of mixtures, nonlinear sensitivity analysis, integrated fluid and process design

Lampe et al. (2012, 2014, 2015)

Simultaneous fluid and process design, use of PC-SAFT and group-contribution PC-SAFT equations of state, continuous molecular targeting (COMT)ecomputeraided molecular design (CAMD) approach Continued

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TABLE 10.2 Overview of Computer-Aided Molecular Design Applications in the Design of Different Materialsdcont’d Literature Sources

Key Features

Palma-Flores et al. (2014) and MolinaThierry and Flores-Tlacuahuac (2015)

Simultaneous fluid and process design, design of mixtures

Polymers Venkatasubramanian et al. (1994)

Stochastic optimization

Vaidyanathan and El-Halwagi (1996)

Deterministic optimization, design of polymers and blends

Maranas (1997) and Camadra and Maranas (1999)

Deterministic optimization, design under uncertainty, advanced molecular representation

Satyanarayana et al. (2007, 2009, 2010)

Advanced group contribution models, multscale models for property predictions

Pavurala and Achenie (2014)

Polymers for oral drug delivery

Biofuel Additives or Bioderived Chemicals Hada et al. (2014)

Biofuel additives, property clustering and chemometric techniques

Yunus et al. (2011, 2012)

Decomposition-based approach for design of blended products, bioderived chemicals for gasoline blends

Ionic Liquids Chong et al. (2015)

CO2 capture solvents for physical absorption

Hada et al. (2013)

Property clustering and decomposition techniques, latent variable property models

Cha´vez-Islas et al. (2011)

Solvents for separation of bioethanol water mixtures

Karunanithi and Mehrkesh (2013)

Prediction models for pure component and equilibrium models, comparison of generate and test, and genetic algorithms

McLeese et al. (2010) and Roughton et al. (2012)

Quantitative structureeproperty relationships, refrigerants and solvents, deterministic and stochastic optimization approaches

Integrated Multiobjective Molecular and Process Design Chapter j 10

molecular structures for a particular application; molecular properties indicate the performance of the molecule in the desired application; hence, the one with the highest performance may be selected. This is greatly facilitated when CAMD approaches combine GC methods with optimization algorithms. An optimum molecule with desired properties is automatically identified based on the computational emulation of a molecular synthesis process (i.e., the iterative transformation and evolution of an initial structure using different combinations of functional groups). An optimization algorithm guides the synthesis towards optimum structures, using properties as performance measures that reflect desired molecular behavior in the corresponding application. From a computational perspective, optimization-based CAMD is very efficient when the molecular properties of pure components that reflect on physical or chemical characteristics are used as design and selection criteria. However, the physical and chemical characteristics of the molecule are also linked tightly with the operating characteristics of the application in which they are used. In the case where molecules are used as intermediate materials in chemical processes, operating characteristics translate to processing conditions as well as design features required to meet such conditions in the most economically and environmentally efficient manner (e.g., equipment types and sizes, ways of connecting different equipment to form a flow sheet structure, etc.). Clearly, the CAMD-based design and selection of molecules should also account for process design decisions, since there are direct links between the two, demanding that the process should also be specifically tailored to the intermediate material that is used to enhance its efficiency. This may be approached through a “simultaneous” or an “integrated” molecular and process design rationale. The meaning of “simultaneous” is that decisions regarding the molecular structure, composition, or concentration (in case that the intermediate material is a mixture of components) are taken within the same optimization algorithm also used to identify the optimum process operating and/or design characteristics. The advantage of a simultaneous approach is that the molecular and process interactions are explicitly accounted for and drive the optimization search to identify an optimum solution using economic criteria. However, the computations may become very demanding due to (1) combinatorial complexity (i.e., the need to consider a very extensive pool of molecular and process design options in order to obtain optimum solutions), and (2) the highly nonlinear algebraic or differential algebraic models required to capture with high accuracy the interactions of the intermediate materials with other molecules used in the process, the material and heat flows, their temporal evolution, and so forth. Considering such an extensive set of details and decision options would result in an intractable optimization problem. This is avoided in most existing implementations of simultaneous approaches by employing process representations, which account, in the most advanced cases, for equilibrium (EQ) process models used to determine the optimum

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materials using process economic design criteria under steady-state conditions. Indicative examples of simultaneous approaches include, among others, work by Hamad and El-Halwagi (1998), Eden et al. (2004), Kazantzi et al. (2007), Eljack et al. (2007), Kheireddine et al. (2013), Bommaredy et al. (2010), Chemmangattuvalappil and Eden (2013), Chemmangattuvalappil et al. (2010), Marcoulaki and Kokossis (2000a,b), Wang and Achenie (2002), Cheng and Wang (2007, 2008, 2010), Siougkrou et al. (2014), Pistikopoulos and Stefanis (1998), Buxton et al. (1999), Linke and Kokossis (2002), Giovanoglou et al. (2003), Pereira et al. (2011), Mac Dowel et al. (2010), Bardow et al. (2010), and Stavrou et al. (2014). In contrast to “simultaneous” approaches, “integrated” molecular and process design approaches decompose the design problem into several decision-making stages by often employing appropriate information analysis and extraction methods, which ensure that useful design insights are systematically identified and exchanged between adjacent stages. For example, in the work of Papadopoulos et al. (2010a,b) on the design of working fluids for Organic Rankine Cycles (ORCs), working fluids are first designed using fluid properties as objective functions using a multiobjective approach, and the obtained Pareto optimum fluids are then introduced in a full ORC model optimization. This decomposition supports the consideration of an extensive design space in both the molecular and process design stages. Both stages may also use more detailed process models than possible in a simultaneous approach without suffering from high computational effort. It has already been demonstrated in published literature that simultaneous approaches may become part of the problem decomposition rationale employed in integrated approaches. Burger et al. (2015) presented an approach where a process model of reduced detail is considered simultaneously with CAMD in a multiobjective optimization formulation. The obtained solvent options are then introduced into optimization-based process design using a more detailed process model. This is reasonable because, at some point, optimum molecular and process characteristics obtained from the simultaneous design stage will need to be transferred to a subsequent, independent design stage to perform optimizations, either using more detailed and realistic process models or exploring a much wider process design space. Additional indicative examples of decomposition-based approaches include other works by Papadopoulos and Linke (2005, 2006a,b, 2009a), Hostrup et al. (1999), Harper and Gani (2000), Kim and Diwekar (2002), Xu and Diwekar (2007), and Karunanithi et al. (2005, 2006). Papadopoulos and Linke (2005, 2006a,b) showed that a multiobjective formulation of the CAMD optimization problem could be an efficient approach to support the decomposition of the molecular and process design problem while considering molecular and process design decisions in an integrated manner. Major advantages of the approach include the ability to consider multiple different performance indices simultaneously, to identify

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their trade-offs, and to include Pareto optimum molecular options (obtained without the use of a process model), which already contain all the solutions that are identified when a process model is used in the course of CAMD. Multiobjective optimization has also been proposed by Kim and Diwekar (2002) for the simultaneous integration of environmentally benign solvent selection and in-process solvent recycling. Furthermore, Ng et al. (2014) proposed the combination of a fuzzy optimization approach with CAMD within a multiobjective product design framework, whereas Burger et al. (2015) proposed a decomposition-based solvent and process approach using multiobjective optimization as noted previously. Clearly, multiobjective optimization could be used as the backbone for the development of new decomposition-based approaches, which can efficiently handle an even larger space of optimization options or models that capture more details than currently demonstrated. This goal may be achieved while maintaining a manageable computational effort at each decision-making stage so that the obtained molecular and process design solutions become industrially more relevant and realistic. Within such a context, this chapter presents the evolution of the work by Papadopoulos and Linke (2005, 2006a,b, 2009a) toward two frontiers that signify potentially new research directions in the area of integrated molecular and process design: 1. Regarding the first frontier, we describe a new framework supporting the integration of molecular and process design with process operability decisions (i.e., the ability of the process to operate under conditions other than the nominal design settings). The aim of this framework is to support molecular and process design and selection decisions under the influence of variability in process operation. This work is motivated by the fact that (1) the molecules identified as optimum when operating variability is considered will be different to those identified under nominal operation, hence significantly affecting the economic system performance, and (2) that a systematic method is required in order to be able to identify such molecules. 2. Regarding the second frontier, we illustrate the exploitation of advanced computing environments (e.g., grid or cloud computing) in the context of the above framework to improve the efficiency of the necessary computations and to support automated decision-making through user interfaces and workflows that allow the interoperation of heterogeneous design tools. This part of the work is motivated by the fact that the integrated solvent and process design problem involves increased combinatorial complexity and detailed molecular and process models in order to identify solutions that are both optimum and realistic. These goals may be best reached through the coordinated and systematic use of tools that support the efficient identification and analysis of optimum results within advanced computing infrastructures.

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2. DECOMPOSITION-BASED APPROACH FOR THE INTEGRATED MOLECULAR AND PROCESS DESIGN 2.1 Approach Overview The approach for integrated molecular and process design outlined in Fig. 10.1 has been previously proposed by Papadopoulos and Linke (2006a). This section provides a brief overview of each step. The proposed approach builds upon multiple objective optimization (MOO) technology employed at the CAMD stage in order to identify a set of Pareto optimum molecules, which may then be used as intermediate materials into a process design optimization stage. The objectives considered at the CAMD stage may include pure component properties calculated directly by GC models, mixture EQ properties calculated using equations of state, and/or activity coefficient models and process models at different levels of abstraction. In this respect, the MOO-based CAMD results in a comprehensive set of materials with a broad range of structural, physical, chemical, economic, and sustainability characteristics. The design information included in the obtained Pareto optimal set can then be systematically exploited in a process design stage, which may employ models of even lower abstraction than before or models that are able to capture a very wide range of potential design options (e.g., superstructurebased synthesis models). The introduction of the optimal set of molecules into the process design stage capitalizes on the available design information

FIGURE 10.1 Main decision-making stages of a decomposition-based approach for integrated materials and process design. CAMD, computer-aided molecular design.

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through the formation of molecular clusters, thus partitioning the molecular set into smaller compact groups of similar molecules. A representative molecule from each cluster is introduced into the process design stage as a discrete option. This is based on the reasonable assumption that molecules of similar structure and/or properties will exhibit a similar behavior in the process where they are utilized. As a result, only a limited number of molecules is selected from the Pareto front and introduced into process design until a cluster is identified, which contains very few molecules of higher process performance than all the other available options. This design philosophy breaks down the design procedure into several steps, whereby rich intermediate design insights can be extracted, interpreted, and analyzed by the users prior to transferring meaningful conclusions as inputs to subsequent design activities. This engages the users in the design process and promotes the import of valuable engineering knowledge. All the underlying trends and trade-offs among the properties of the candidate optimal molecules, as well as the structureeproperty relations, may be analyzed and unveiled. The computational requirements at each stage are determined by the degree of detail or range of decision options considered in the employed molecular or process models. However, they are considerably lower than an approach that would attempt to fit and solve both highly detailed and decisioninclusive models simultaneously. The use of both MOO and molecular clustering supports the extraction and transfer the necessary design information between adjacent decision-making stages without premature exclusion of potentially useful design options and within a computationally efficient context.

2.2 Computer-Aided Molecular Design and Multiobjective Formulation The design of molecules using CAMD is based on the systematic combination of molecular (functional) groups with the aim to synthesize a molecule of particular chemical structure and physicochemical properties. Such properties are calculated using GC methods, which are based on databases containing a preregistered contribution of each molecular group in the molecular structure containing this group. The desired properties take the form of design targets in the context of an optimization problem formulation, allowing the systematic consideration and combination of the available molecular groups for the design of an optimum molecular structure. The basic algorithmic steps of the employed CAMD approach are outlined in Fig. 10.2. The CAMD approach of Fig. 10.2 was first proposed by Marcoulaki and Kokossis (2000a,b) and extended to account for MOO in Papadopoulos and Linke (2006a). Molecules are described as a set of functional groups allowed to link together, while groups are characterized by their free bonds and functionality and classified as either aromatic or nonaromatic, depending on

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FIGURE 10.2 Main algorithmic operations of the optimization-based computeraided molecular design (CAMD) approach of Papadopoulos and Linke (2006a).

the availability of free bonds. Valence of the group is the overall amount of nonaromatic free bonds, and functionality relates to the atoms within the group and the way in which they are bonded. This establishes the contribution of each of the available groups to the overall behavior of the molecule. Molecules are represented by a molecular row vector M, composed by the group row vector m and the composition matrix A. The molecular vector M is therefore defined as follows: M ¼ m$A

(10.1)

where the group vector m details the groups included in the molecule, and the composition matrix A contains information on the number of occurrences of each group. Group vectors are generated based on a set of connectivity constraints ensuring feasible molecules. The molecules represented through the M vector are optimized against a desired performance measure using an optimization algorithm, such as simulated annealing (SA). In the context of MOO, the employed performance measure involves a set of indices representing design targets (i.e., objective functions), which are aggregated into a single index to perform the necessary algorithmic operations. In mathematical terms, the MOO CAMD problem can be written as follows: optimize F1 ðX; DÞ; .; FNof ðX; DÞ

(10.2)

hðX; DÞ ¼ 0

(10.3)

gðX; DÞ  0

(10.4)

D

Subject to

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XL  X  XU

(10.5)

DL  D  DU

(10.6)

where X and D are the vectors of the state and the design variables, respectively. Vector D may contain vector m and column Ai, (i.e., the selected molecule i for the process) in addition to other design options (e.g., related to process characteristics if a process model is included in the course of CAMD). Vector F(X,D) represents the considered set of Nof objective functions, while h(X,D) and g(X,D) are vectors of equality and inequality constraints representing the employed models and the operating or design constraints. The indices L and U represent upper and lower bounds utilized for all the variables. Following formulation Eqs. (10.2)e(10.6), a feasible molecule Dopt hMopt is called a Pareto optimum or nondominated solution if there exists no other point D satisfying the following condition (Papadopoulos et al., 2013a,b): FðD Þ  FðDÞ ^ dj ˛ f1; . Nof g : Fj ðD Þ < Fj ðDÞ

(10.7)

To enable the simultaneous assessment of the desired set of objective functions through the algorithmic operations of SA, the objective function that is actually optimized takes the form of an aggregate objective function as follows: f ðX; DÞ ¼

Nof X j¼1

wi Fi ðX; DÞ þ

Nin X

Penk gk ðX; DÞ þ

k¼1

Neq X

Pene he ðX; DÞ

(10.8)

e¼1

where wi is a set of weights imposed in each objective function Fi, either based on its considered significance or randomly to enable a search of all the potential combinations (Papadopoulos and Linke, 2006a). Penk and Pene represent penalty weights that might be imposed to inequality or equality constraints, while Nin and Neq represent the total considered inequality and equality constraints, respectively. The continuous assessment of Eq. (10.8) through the SA algorithmic operations results in the iterative generation of new solutions until algorithmic termination criteria are satisfied.

2.3 Classification Using Data Mining As noted previously, prior to the introduction of the Pareto optimal set of molecules into the process design stage, the Pareto optimum set is partitioned into smaller compact groups of similar molecules (Papadopoulos and Linke, 2006b). A representative molecule from each cluster is introduced into process design as a discrete option. By implementing this procedure of solvent selection iteratively, the optimization problem takes the form of a tree-like representation (Fig. 10.3).

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FIGURE 10.3 Parallel clustering approach proposed in Papadopoulos and Linke (2006b).

Starting from the Pareto optimal set, each branch leads to the emergence of new clusters at each iteration, which contain fewer molecules. The decision regarding which clusters will be formed next is based on several criteria, which include the following: l l l l

l

the number of the generated clusters in each iteration; the number of molecules included in each cluster; the distances among the molecules within a cluster; the distances among the molecules that lie in the cluster centers (i.e., between the clusters); and the cost of the optimal process designed for the representative molecule selected from each cluster (i.e., the molecule in the cluster center).

The within- and between-cluster distances are calculated based on the properties used as design criteria in the MOO CAMD stage. All the clustering decision criteria are combined under a single index through a probability function, namely the clustering heuristic probability. The obtained process cost for the representative molecule selected from each cluster is linked to the contents of the cluster (i.e., the properties of the molecules in the cluster) through a probability distribution function that allows the stochastic comparison of molecular and process performance (e.g., process cost for each molecule tested) in various clusters without requiring process performance data for all the molecules. This is because the clustering heuristic probability combines process performance with statistical information that accounts for cluster within homogeneity (i.e., similarity of molecules within each cluster) and between heterogeneity (i.e., clusters which are statistically distinct and far apart, containing very similar molecules). We therefore identify the molecules that benefit the process where they are utilized only by optimizing the process for a few, statistically significant molecules.

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2.4 Process Design The use of process design generally serves to provide process and equipment configurations which are: 1. optimum with respect to a number of performance criteria (e.g., economic, sustainability, etc.); and 2. rigorously validated with respect to realistic operating requirements so that they can be immediately implemented in practice. The first goal requires the consideration of numerous structural and operating parameters as decision options in optimization. The second goal requires the consideration of often highly nonideal material and process interactions (e.g., thermodynamic, transport characteristics, and so forth) through the utilization of detailed process models. Both these characteristics may have a detrimental effect on the efficiency of the calculations; hence, the employed models need to be sufficiently compact in both the decision range and phenomena depth they are able to capture in order to balance the need for highly performing designs and modeling rigor with computational efficiency.

2.4.1 Systematic Flow Sheet Design Methods The proposed framework for integrated and process design can account for systematic process synthesis and modeling methods. Papadopoulos and Linke (2005, 2009a) demonstrated the use of the framework in the design of solvents considering synthesis approaches, which account for reaction, separation, and reactive separation options. Such approaches combine generic representations of process layouts, called superstructures, with optimization algorithms to systematically investigate an enormously wide range of options (Linke and Kokossis, 2003a,b; 2007) for diverse applications, such as liquideliquid extraction processes (Papadopoulos and Linke, 2004), carbon dioxide separations (Darmatzis et al., 2014, 2016), processes with heterogeneously catalyzed gas phase reactions (Montolio-Rodriguez et al., 2010, 2012), wastewater treatment (Rigopoulos and Linke, 2002), seawater desalination (Alnouri and Linke, 2012, 2013, 2014), or membrane-based separations (Uppaluri et al., 2004, 2006). Fig. 10.4 illustrates a superstructure for an absorberestripper loop to remove carbon dioxide from a gas stream. Superstructures consist of cells representing process tasks (reactions, separations, and reactive separations) and of connecting streams representing material flows. Each cell can be assigned with a process model representing a particular task (e.g., reaction kinetics, different types of chemical and physical equilibria or other ways of mass transfer, heat transfer, and so forth), the type of equipment utilized (e.g., ideal and real reactor models, multiphase reaction, mass exchangers, and so forth), and operating conditions. Many different tasks may be connected in the same flow sheet using an inclusive set of streams to account for recycle and bypass options to generate flow sheet superstructures. This enables the

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FIGURE 10.4 Solvent-based CO2 capture process superstructure (Damartzis et al., 2014, 2016).

representation and facilitates the investigation of an enormous and exhaustive set of options that may lead to optimum performance.

2.4.2 Rigorous Equipment Models The assignment of highly detailed (low abstraction) process models in each superstructure cell is very important to enable the identification of both optimum and practically applicable designs. Damartzis et al. (2014, 2016) demonstrated the use of rigorous reduced order process models in a system where the solvent and process behaviors are highly nonideal, namely in the design of CO2 capture absorption/desorption systems considering different solvents. In this case, the model reduction technique of the orthogonal collocation on finite elements (OCFE) was combined with a superstructure representation (Fig. 10.4). The approach has proved very useful in the effort to keep the model size at a compact and computationally manageable level. Transition from the full order model to its reduced equivalent can be achieved in one or more steps depending on the desired size and accuracy of the resulting model. The employed model needs to be both compact and versatile enough in order to be used in multiparametric design optimization studies. It is therefore evident that the minimum model size is sought, but at the same time, the applied reduction formulation must be such that it does not compromise its main characteristics and predictive capabilities of the full-order model.

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The basic building block considered for column design in Fig. 10.4 is the column section. Each section is subdivided into finite elements (FE) of variable size, while within each FE, a given number of collocation points (CP) are defined as the roots of the discrete Hahn family orthogonal polynomials. This offers the advantage that in the limiting case, when the number of CP equals the number of actual stages in the column, the CP are automatically placed at the exact location of the stage, thus reproducing the full-order model. The OCFE approximating technique provides a significant reduction in terms of total number of modeling equations without compromising the resolution of the model details. The twofold objective is achieved through the satisfaction of the material and energy balances of an EQ model at a smaller number of spatial locations, namely the CP. The OCFE formulation approximates temperature and composition profiles in the column domain with continuous polynomials of appropriate degree, thus transforming them into continuous functions of position. Moreover, the transformation of the model key variables behavior into continuous functions of position in the column eliminates the need for the use of integer variables for the representation of stages, hence facilitating the optimization problem greatly.

3. INTEGRATION OF MOLECULAR AND PROCESS DESIGN WITH PROCESS OPERABILITY DECISIONS 3.1 Motivation A number of research efforts have been reported in published literature that propose the design of materials as part of the process design of the broader flow sheet, motivated by the reasons analyzed in the previous section. Existing design methods focus on optimizing process design characteristics, such as process structure and size, topology of recycle streams, and solvent feed flow rates, to name a few. The performed optimization is combined with a CAMD-based method for the generation of material alternatives; hence, the effects of various material options in the economic design of the particular process addressed are investigated. However, processes are essentially dynamic environments susceptible to variations of a number of operating parameters. For example, a solvent process scheme designed for optimality under the assumption of certain purity levels in the process feed streams or constant process pressure will not necessarily be optimal if any of those parameters vary during the process operation, as is often the case in industrial practice. Available approaches aiming to design solvent process schemes of optimum performance often overlook the effects of such variations. While a number of methods have been developed to address process design optimality under operating parameter variations, the effects of using alternative material options in process design under operating variability have yet to be addressed systematically.

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3.2 Proposed Framework In our current work, we describe the main stages of a systematic method, which explicitly considers the impacts of material and process design/operating decisions on process operability (i.e., the ability of the process system and the employed intermediate material to operate efficiently under conditions other than its nominal design settings). Fig. 10.5 provides a conceptual illustration of some basic points of the proposed approach. Materials and process characteristics of optimum performance obtained from the integrated material and process design for nominal operation (i.e., framework outlined in Fig. 10.1) are now evaluated through a systematic sensitivity analysis procedure. The goal is to identify materials and process operating/design characteristics that optimize the overall performance under nominal operation while simultaneously minimizing the system sensitivity under variability. The proposed method supports: 1. the identification of parameters with high influence on the overall processe material performance; 2. the quantification of the overall system sensitivity with respect to these parameters; and 3. the incorporation of sensitivity metrics to the quest for optimum material and process design options. The proposed method is presented within a formal mathematical analysis framework, which avoids arbitrary assumptions regarding the effects of the selected design and operating parameters and subjective interpretations of the obtained results. It is further based on steady-state process simulations, avoiding the need to develop and use dynamic models. It also remains generic

FIGURE 10.5 Main stages of the approach proposed for the consideration of operation under variability in the course of integrated solvent and process design.

Integrated Multiobjective Molecular and Process Design Chapter j 10

and independent of the proposed application. Formally, the steps of the proposed method include the following: 1. Let a vector Snom incorporating a total of Nε nominal values for the design and operating parameters of an existing process system, which will be subjected to variability, a vector M of materials used as intermediates in this system, a vector X of state variables of a process model, and a vector OF of totally NF system performance indices. For every material i in M, implement steps 1e7 as follows: 2. External or internal variability is emulated by imposing a vector of infinitesimal variations dS on each element of vector Snom, hence resulting in vector S ¼ Snom þ dS, which represents variations. The values of the performance indices in OF are then calculated by simulating the process model for each element of S. 3. The design and operating parameters, which are the most sensitive with respect to the performance indices in OF, are identified by generating a local sensitivity matrix P around Snom. Note that the elements in P represent the scaled derivatives of the performance index values in OF with respect to the system parameters that change under the influence of variability represented by S. 2 3 vln OF1 vln OF1 / 6 vln s vln sNε 7 1 6 7 6 7 6 7 « 1 « P¼6 (10.9) 7 6 7 4 vln OFNF vln OFNF 5 / vln s1 vln sNε Mi The subscript Mi in the above equation indicates that the matrix is expanded to cover all materials included in M. 4. The major directions of variability are derived by calculating the eigenstructure of matrix PTP followed by the rank ordering of the resulting ε eigenvectors fQl gNl¼1 , based on the magnitude of the corresponding eigenvalues (Seferlis and Grievink, 2001). 5. The dominant direction of the system variability is identified as the eigenvector Q1 directions associated with the largest in magnitude eigenvalue of PTP. The dominant direction of variability represents the combinations of the design and operating parameters in S that cause the largest change in the performance indices in OF in a least squares sense. 6. A sensitivity metric U(z,M) is calculated accounting for the aggregate performance indices variability within a wide variation range, explored

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through a parameter variation magnitude coordinate z along the dominant direction Q1 as follows: X Calculate Uðz; Mi Þ ¼ wU ðzÞ jðOFj ðX; Mi ; SðzÞÞ Mi ;z

 OFj ðX; Mi ; Snom ÞÞ=OFj ðX; Mi ; Snom Þj hðX; Mi ; SðzÞÞ ¼ 0

s:t:

gðX; Mi ; SðzÞÞ  0 ððSðzÞ  Snom Þ=Snom Þ  Q1 $z ¼ 0 XL  X  XU ;

z ˛ ½ zlim ; zlim  (10.10)

U

where w (z) is a weighting factor accounting for the significance of each variation segment within the parametric sensitivity space, and matrices h and g represent the model equality and inequality constraints. 7. U(z0 ,Mi) is calculated at a desired point z0 and an augmented vector OF0 is developed, which contains both the performance indices under nominal operation and U(z0 ,Mi). 8. The elements of OF0 are used in a multiobjective optimization problem formulation considering the materials in M as the decision parameters in order to select the ones that simultaneously minimize all performance indices in OF as well as the sensitivity index (or indices) in U by generating a Pareto front (Papadopoulos et al., 2013a,b). The condition of Eq. (10.7) applies again in this case for the performance criteria in OF and U. STEPS 1e3: The proposed approach is based on the development of a sensitivity matrix, which incorporates the derivatives of multiple process performance measures with respect to multiple operating parameters and materials. The sensitivity matrix constitutes a measure of the process operating variation under the influence of infinitesimal changes imposed on the selected parameters. STEPS 4e5: The sensitivity matrix is decomposed into major directions of variability to identify the largest in magnitude eigenvector. This represents the dominant direction of variability for the system, causing the largest change in the performance measures. The entries in the dominant eigenvector determine the major direction of variability in the multiparametric space and indicate the impact of each parameter in this direction. Having identified this direction, it is not necessary to explore all directions of variability (i.e., combinations of parameters) arbitrarily, hence reducing the dimensionality of the sensitivity analysis problem. STEP 6: The dominant eigenvector is then exploited in a sensitivity index, which accounts for all performance indices simultaneously within a wide variation range. This range is explored through an appropriate coordinate z

Integrated Multiobjective Molecular and Process Design Chapter j 10

FIGURE 10.6 Conceptual representation of (A) the sensitivity index against the parameter variation magnitude coordinate, (B) the Pareto front of sensitivity against (economic) process performance at nominal operating settings.

that accounts for the magnitude of variability of all the selected process operating and design parameters. Fig. 10.6A presents a conceptual illustration of the sensitivity index for several different materials (lines of different inclination and color). The desirable materials with are the ones with a flatter profile than others because they are less sensitive to variability. A higher sensitivity index value indicates increased changes in the performance measures under variability. Different inclinations toward opposite directions indicate different sensitivity when the variability conditions change. STEPS 7e8: The sensitivity index is used as an additional objective function in a multicriteria assessment problem, together with all performance indices calculated under nominal operation. Fig. 10.6B illustrates the resulting Pareto front. Assuming that desired performance indices represent economic performance in the form of process cost, different materials (dots in Fig. 10.6B) exhibit different sensitivity characteristics. Materials with very low sensitivity may exhibit a high cost, whereas materials of very low cost may exhibit a higher sensitivity. The multicriteria assessment approach allows the identification of such trade-offs.

3.3 Application to Organic Rankine Cycles 3.3.1 Organic Rankine Cycle Description and Variability Issues ORCs have received increased attention in the last 20 years, spanning a wide range of applications, including power generation from industrial waste heat recovery, geothermal energy, and solar irradiation, to name but a few. Their operation is based on the extraction of heat, which is used to evaporate an appropriate organic working fluid subsequently expanded in a turbine to produce work. The type of employed working fluids is clearly very important for the overall system efficiency. ORCs utilizing pure working fluids have been

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widely investigated (Wang et al., 2013), due to their simpler thermodynamic and operating characteristics compared to mixed working fluids. An important limitation of pure working fluids is their constant temperature profile during phase change (Papadopoulos et al., 2013a,b). The pinch point encountered at the evaporator and the condenser gives rise to large temperature differences at one end of the heat exchanger, leading to high irreversibility. The use of mixtures as working fluids may considerably improve system efficiency, as the emergence of the pinch can be avoided. The latter is possible due to the variable temperature profile of mixtures during phase change, avoiding pinches and resulting in lower irreversibility and higher cycle exergy efficiency. Fewer reported works have addressed the use of mixtures in ORCs (e.g., Papadopoulos et al., 2013a,b; Mavrou et al., 2014; Linke et al., 2015). ORC process flow sheets involve various complex options, including multiple pressure loops, expansion stages, etc., to increase the energetic and exergetic efficiencies (Stijepovic et al., 2014; Linke et al., 2015). Their use with intermittent heat sources implies that ORCs are often required to operate under variable heat input conditions, while as in every other process system, internal variability is always important due to leaks, malfunctions, fouling, and so forth. Unless variability is accounted for, it will have detrimental effects on the ORC ability to perform satisfactorily under conditions different from the nominal design settings, namely on the ORC operability. This is because potential unexpected changes in the system operation may result in significant deviations from the performance for which the system was initially designed. To ensure efficient operability, ORCs need to be designed so that they are sufficiently flexible to handle operating variations. Working fluids are inherent to ORC operation; hence, their impact on operability should also be accounted for, together with ORC design decisions for a wide range of operating conditions. Whereas some working fluids or ORC system design and operating characteristics may be less sensitive to such changes, others may significantly deviate from their expected performance, eventually failing to meet the desired operating specifications. Published research generally considers such issues as an afterthought to the selection of working fluids and determination of optimum ORC features under nominal operating conditions (Linke et al., 2015; Lecompte et al., 2015). The employed methods are often heuristic, as design or operating system parameters are selected within an arbitrarily defined range and with very limited consideration of their combined effects into the system performance. Such approaches fail to provide assurances regarding the validity of the resulting insights or that they will not be affected by the consideration of additional parameters or more extensive design and operating ranges. It is only in the last five years that a number of published works are concerned with the study of off-design (i.e., other than nominal) (Quoilin et al., 2011) or dynamic (i.e., transient) (Pierobon et al., 2014; Wang et al., 2014) ORC performance. However, the consideration of different working fluids as a means to address variability has yet to be addressed.

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FIGURE 10.7

Layout of solar Organic Rankine Cycle (ORC) system.

3.3.2 Implementation Details The system employed in this work is a solar ORC layout, presented in Fig. 10.7,together with major parameters, which affect its performance and consist of three subsystems: the solar collector, the storage tank, and the ORC. A review of publications on solar ORC systems can be found in Mavrou et al. (2015). The solar collector heats water, which is stored in the tank. If the temperature at the collector outlet TSC,out is greater than the temperature inside the tank Ts then the three-way valve allows the water to flow to the tank. Otherwise, it is directed back to the collector for further heating. The temperature inside the tank is monitored, and at all times must be lower than a predefined Ts,max in order to avoid phase change. If the temperature inside the tank becomes greater than a predefined Tmin,ORC, then the ORC is activated. Circulators are added to the system in order to impose the desired mass flow rates. The proposed method is illustrated considering four mixtures several different concentrations shown in Table 10.3. The selected mixtures were previously shown (Mavrou et al., 2015) to exhibit favorable trade-offs between power generation and overall system operating performance under nominal operation. These mixtures were synthesized by Papadopoulos et al. (2013) for optimality using a CAMD approach. The parameters used in vector OF as system performance indices are shown in Table 10.4. The parameters in vector S that were varied in the solar ORC system are shown in Table 10.5. Parameter m_ FPC;sub represents the number of installed collector loops. As it increases, the heat transferred to the storage tank increases accordingly. Parameters Tmin,ORC and m_ hc impact directly on power generation. All these parameters refer to the solar ORC system operation. Additional important parameters refer to the capacity (i.e.,

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TABLE 10.3 Investigated Working Fluid Mixtures ID

M1

M2

M3

M4

Component 1

1,1,1-Trifluoropropane

1,1,1-Trifluoropropane

Neopentane

Neopentane

Component 2

2-Fluoromethoxypropane

1-Fluoromethoxypropane

1,1,1-Trifluoro2-trifluoromethyl-butane

2-Fluoromethoxy2-methylpropane

Concentration of Component 1 in Component 2

30e40%/60e70%

30e40%/60e70%

60%

60e70%

TABLE 10.4 Performance Criteria Considered in the Investigation of the Solar Organic Rankine Cycle System Organic Rankine Cycle (ORC) Performance Indices

Use in Multicriteria Assessment

hORC : ORC Thermal efficiency

Maximization

W_

: ORC net work output

Maximization

V : Volume ration across turbine

Minimization

m_

Minimization

net

Tr

wf

: Mass flow rate of working fluids

DTglEv :

Temperature glide across evaporator

Minimization

top : Operating cycle duration

Maximization

Ir : Cycle irreversibility

Minimization

TABLE 10.5 Parameters Varied in the Investigation of the Solar Organic Rankine Cycle System Operation Parameters Varied

Elaboration

m_ FPC

Mass flow rate for the collectors installed in series

m_ FPC ;sub

Total mass flow rate of the solar collector subsystem

Tmin,ORC

Minimum temperature in the storage tank that would result in Organic Rankine Cycle (ORC) activation/ deactivation

m_ hc

Heat carrier mass flow rate in the evaporator

Acoll

Total collector area connected in line

V

Volume of the heat storage tank

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size) of some solar ORC components; hence, they are considered as design parameters. Parameters such as Acoll and V may also change during operation. For example, a malfunction in part of the collector will reduce the nominal capacity of the system, whereas a leak in the tank may also reduce the amount of stored water. As a result, the influence of this type of variability in the ORC performance is also worth investigating. In particular, Acoll impacts on TFPC,out. Finally, V is considered due to the fact that it represents the ORC heat source capacity. The above elaboration highlights the nonlinear associations among the system components and thus the importance of the employed nonlinear sensitivity analysis.

3.3.3 Results and Discussion Fig. 10.8 illustrates for selected mixtures the sensitivity index U(z), which represents the combined effect of all parameters of vector S on the change of all investigated performance criteria of vector OF for magnitudes defined by coordinate z. The following observations derived from Fig. 10.8 can assist in the assessment of the sensitivity features of the mixtures: 1. Mixtures with a profile of steep increase exhibit sensitivity to variability, as they present significantly different performance for operation at points other than the nominal. These mixtures are likely to have detrimental effects in the ORC performance, especially along unfavorable variation; hence, they should be avoided. 2. Mixtures with a flatter profile (e.g., 60% M2 and M1) are preferable, as they can handle variability much more efficiently.

FIGURE 10.8 Sensitivity index U(z) against parameter variation magnitude coordinate z.

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3. Different mixtures may exhibit different ORC performance profiles at different directions of z. For example, although mixtures 60% and 70% M2 perform similarly toward the positive direction, 70% M2 exhibits a steeper profile in the negative direction. 4. The profiles of some mixtures (e.g., 60% M3) are discontinued earlier than others. This indicates violation of process constraints; hence, the diagram of Fig. 10.8 determines the operating feasibility region. 5. Mixtures such as 60% M3 (in the negative direction) exhibit a change in the slope of their profile after a particular z value. This indicates that variability does not affect the system performance significantly after this value. The performance of the working fluid mixtures at nominal operating settings with respect to the sensitivity index is illustrated in the Pareto fronts of Fig. 10.9AeD for selected criteria. The dashed values indicate dominated (suboptimal) mixture options. The results are reported for z0 values of 0.03,

FIGURE 10.9 Pareto fronts of the sensitivity index against (A) average Organic Rankine Cycle (ORC) thermal efficiency, (B) average turbine volume ration, (C) average evaporator temperature glide, (D) operating duration. All data are reported for a year of operation using a prespecified weather profile derived based on historical solar irradiation for northern Greece. ORC, Organic Rankine Cycle.

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TABLE 10.6 Performance of Selected Mixtures in All Organic Rankine Cycle Criteria, Including the Sensitivity Index Compared to 70% M4. Blue Bars (Gray in Print Versions) Pointing Right Indicate Better Performance Than 70% M4. Red Bars (Dark Gray in Print Versions) Pointing Left Indicate Worse Performance Than 70% M4

based on steps 7 and 8 of the proposed approach. However, the selection of the mixture, which exhibits the best trade-offs among the ORC performance criteria and the sensitivity index (Table 10.6), is also based on the evaluation of z0 ¼ 0.03 as well as z0 ¼ 0.06. This is necessary because, as explained previously, different slopes in Fig. 10.8 indicate different sensitivity characteristics for each mixture; hence, they need to be considered during performance evaluation. Fig. 10.9A indicates that despite the high thermal efficiency of mixture 70% M4, it also exhibits higher sensitivity compared to 60% M1. 70% M2 is a mixture that provides a good balance between sensitivity and thermal efficiency. In Fig. 10.9B, it is worth noting that 70% M4 is not in the Pareto front, which consists only of 60% M1. Mavrou et al. (2015) found at nominal operating settings, 70% M4 is an optimum choice, although in this case, it is clearly outperformed. This mixture also lies at the extremes of the Pareto fronts of Fig. 10.9A,C, and D, indicating in all cases that it presents higher performance than the other mixtures, but at the expense of increased sensitivity under variability. This means that 70% M4 might require a more difficult to implement operating strategy in order to maintain high overall ORC efficiency under variability. As noted previously, variability may appear in any potential direction; hence, the selected mixture needs to appear in the Pareto fronts and to exhibit favorable trade-offs in all potential directions for the different z0 values that are investigated. Mixture 70% M2 is one such case; hence, it is selected, and its performance compared to 70% M4 is illustrated in Table 10.6, together with some other mixtures that exhibit useful trade-offs. Clearly, 70% M2 is not the best option in all the performance criteria; however, it simultaneously combines low sensitivity with higher performance than other options in the considered ORC criteria.

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4. UTILIZATION OF ADVANCED GRID AND CLOUD COMPUTING RESOURCES 4.1 Motivation The framework described in the previous sections is based on the combined use of several decision-making tools, which exchange molecular and process design information between adjacent implementation steps. In the most general case, there will be a need to combine an extensive design space with detailed molecular or process models. The employed tools can be greatly benefited from advanced computing infrastructures to expedite execution; however, this will require the development of automated workflows, which integrate the use of the heterogeneous tools within an algorithmic approach based on the steps prescribed in the proposed framework. In this work, we describe workflows, which support the coordinated use of the tools described in the previous sections in computational grids. The proposed workflows are necessary ingredients to provide the complex underlying software tools as services to future computational clouds. Computational grids were originally developed to serve the needs of scientific communities for high-performance computations (Armbrust et al., 2010). They are based on the use of protocols to offer shared computation on thousands of available computing elements and vast storage capacity over long distances. Their operation is based on an operating system called middleware, which coordinates software execution on geographically dispersed and technically heterogeneous computing resources that cannot be accessed physically by the users. In recent years, the underlying rationale of computational grids has evolved to a technology known as computational cloud, which provides software applications delivered as services to the wider public over the Internet, using extensive data centers and advanced middleware (Armbrust et al., 2010). The services provided by current clouds include mainly software applications, which are considerably simpler than the more complex tools required by scientific communities for high-performance computations. In this respect, the protocols and software available in computational grids have yet to lead to a service-oriented environment that can grow beyond scientific communities. Developments in the computer-aided process engineering (CAPE) community, which can be considered as useful steps for utilization of CAPE tools in computational grids or clouds, focus mainly on the organization of knowledge in the form of ontologies. Knowledge organization through appropriate formal standards is important in the development of complex workflows that combine multiple and heterogeneous decision-making tools. Important efforts also include the use of multiagent systems, which can act as independent decision-making entities operating at distributed computing environments, such as grids or clouds. Table 10.7 provides an overview of such approaches.

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TABLE 10.7 Overview of Ontologies and Agent-Based Approaches in Computer-Aided Process Engineering Literature Sources

Key Features

Ontologies Bradt et al. (2008), Morbach et al. (2009), and Wiesner et al. (2011)

General computer-aided chemical engineering software applications

Mun˜oz et al. (2010, 2011, 2013)

Process scheduling and control, batch process management, and enterprisewide decision-making

Singh et al. (2010)

Selection of process monitoring and analysis tools

Natarajan et al. (2012)

Distributed process supervision in largescale plants

Sesen et al. (2010), Suresh et al. (2010a,b), and Hailemariam and Venkatasubramanian (2010a,b)

Pharmaceutical product development and engineering

Labrador-Darder et al. (2009)

Knowledge-based process optimization of reactor networks

Raafat et al. (2013)

Identification of process technologies, which can be used in industrial symbiosis

Agent-Based and Parallel Computing Yang et al. (2008) and Antonopoulos et al. (2005)

Multiagent systems for identification of appropriate process models in design activities

Gao et al. (2009, 2010)

Agent-based intelligent systems for decision-making in process monitoring and performance prediction in chemical processes

Du et al. (2007) and Kokossis et al. (2011)

Optimization algorithms, which can be parallelized in extensively distributed computing resources of grid environments

Satyanarayana et al. (2007, 2009)

Software technology, which supports the parallelization of computations in a grid environment to regress group contribution models for polymer properties

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4.2 Existing Infrastructures and Challenges in the Deployment of Computer-Aided Process Engineering Tools Although the reviewed developments represent important steps toward the utilization of CAPE tools in massively distributed and unattended computing environments, additional work is required for their further utilization in grid infrastructures to serve the scientific community and their future wider proliferation as services in computational clouds. Existing grid infrastructures employ general purpose middleware, which consists of (1) the core middleware that offers services such as remote management, access to remote job execution nodes and storage systems, security services, and so forth; and (2) the user middleware that offers access to computational tools, development of applications (e.g., compilers for the development of programs), and so forth. All the services provided by the core and user-level middleware can be summarized under four main categories, namely security, job submission and resource allocation, job management, as well as data transfer and storage (Baker et al., 2002). Security services are implemented through an authentication system, which includes passphrases, cryptography, and digital certificates, to name but a few. Job submission is implemented through resource querying and allocation services based on the availability and suitability of the computational resources for different kinds of applications. For the automated monitoring of different jobs, management services register data regarding the state, position, and progress of submitted jobs, updating the corresponding systems and users. Finally, data transfer is implemented through secure services, which allow the use of the corresponding data by computational resources and users. Globus (www.globus.org) is one of the most widely used middlewares that provide such services. Clearly, existing grids involve increased complexity, supported to a certain extent by the user middleware, which provides all the underlying services in the form of Linux shell commands. In this context, the use of such infrastructures still requires extensive programming skills, whereas there are very few user-friendly interfaces to reduce the corresponding effort. Furthermore, scientific problems often require the use of multiple different tools, which go beyond the simple submission and execution of a job; they are not directly supported by existing user-level middleware and programming environments, while they require the iterative use and combination of multiple different commands with programming techniques, such as parallel programming, shell scripting, etc. Despite the usefulness of existing user-level middleware, the supported tools maintain a generic targeting, which is independent of particular applications with the aim to serve different disciplines. In this respect, they have the functionality of a programming language and not of a computing environment that targets specific scientific problems of increased complexity.

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These challenges also apply to the particular tools pertaining to integrated molecular and process design, discussed in the previous sections. The employed tools cannot be supported directly by the services of the available user-level middleware. The submission and execution of jobs using the proposed tools for integrated molecular and process design comprises a sequence of independent calculations, which are tightly connected through an algorithmic framework that describes the collection, processing, and exploitation of design information among adjacent decision-making activities. Such characteristics require the development of appropriate services, which are able to automate and monitor the execution of all the corresponding tools in a grid environment by exploiting the existing middleware functionalities.

4.3 Proposed Software-as-a-Service Architecture The use of the available CAMD and process design tools in grid or a cloud computing environment serves two main purposes: (1) the integrated and automated use of all the tools within a unified and widely available framework, and (2) the support of the computationally demanding design activities through the use of distributed computing resources, either on the grid or on the web. In this context, we propose a computing environment, which provides the available software tools as a service through appropriate interfaces to facilitate their submission, execution, and monitoring on the grid. The overall architecture is shown in Fig. 10.10. This architecture was first proposed in Papadopoulos and Linke (2009b) and is now updated with the tools discussed in the previous section for the evaluation for molecular and process design options under variability. The tools for integrated molecular and process design are provided as reusable software in the end user through a web portal, which accounts for usability and functionality. The web portal supports the simultaneous exploitation of distributed computing and storage resources available on the grid and on external web databases and repositories. The underlying service layer provides a set of integrated services, which transform the user selections into appropriate workflows and interface the technical specifications of the grid middleware with the specific requirements of the decision-making tools to facilitate the submission of the selected workflows. The services layers required to support the submission, execution, and monitoring of the proposed tools in a grid environment are detailed in Fig. 10.11. They include a workflow generator, a query service, a deployment service, a data manager, a job manager, and a resource allocator (Papadopoulos and Linke, 2009b). The first three services operate directly at the problem solving level under the decision-making tools for integrated molecular and process design. The remaining three services transform the workflows based on the specifications of the grid middleware and support the dynamic probing of the grid resources during execution of the workflows.

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FIGURE 10.10 Software-as-a-service (SaaS) architecture for the exploitation of grid or cloud computing infrastructures in the integrated materials and process design. CAMD, Computer-aided molecular design. The computer cluster images are obtained under license Creative Commons BY 2.0 and BY-SA 3.0 (Wikipedia). The world map image is obtained under GNU Free Documentation License (Wikipedia). The “database” and “end user” images are obtained from pixabay.com under CC0 license. In all cases, no change has been applied. All the other parts of this figure are original images.

4.4 Workflows for Integrated Molecular and Process Design The efficient utilization of the previously proposed architecture requires the development of workflows that provide usable combinations of the available software. In this respect, numerous workflows can be implemented for the solution of the integrated CAMD and process design problem using grid computing. Fig. 10.12 proposes a simplified flow diagram of such potential workflows based on various user requirements. To perform materials design, the user selects the CAMD software component, which must be combined with an optimization algorithm as well as the process-related properties of the material, which will take the form of the objective function in the performed optimization. Single-objective optimization (SOO) or multiobjective

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FIGURE 10.11 Components of the services layer of the proposed software-as-a-service (SaaS) of Fig. 10.10.

optimization (MOO) options are available for selection. Whereas SOO will result in a single optimum material or in a list of rank-ordered materials, MOO will result in a set of Pareto optimum materials containing several options. To make use of the distributed processing capabilities of the grid infrastructure, the CAMD optimization is deployed in parallel processors in order to facilitate the required computations. The results obtained from the parallel runs are stored in repositories available in the distributed computing resources. Queries may also be deployed in web databases to identify existing molecules among the ones designed. If the SOO option was previously selected at the solvent design stage, the design molecules are introduced directly into the process design stage. On the other hand, solvents designed through the MOO option require the use of data mining methods in order to further reduce the required computations when they are entered into the process synthesis stage, based on the previously described framework. The incorporation of the obtained

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FIGURE 10.12 Workflows proposed for integrated solvent and process design considering operating variability. Gray blocks indicate the solvent synthesis, process design, and operability evaluation parts. Workflows without operability evaluation part originally proposed by Papadopoulos and Linke (2009b). CAMD, Computer-aided molecular design; MOO; SOO, singleobjective optimization.

materials design results into the process design stage requires selection of the appropriate process models, the optimization methods that will be used, as well as definition of the objective functions. The available in-house process models support separation and reactive separation process models that come in different levels of detail, as well as ORC models suitable for thermodynamic analysis. Optimization methods further include SA, genetic algorithms, and ant colony optimization. Materials and process design optimization runs may be launched in distributed processors to facilitate computations. Selected material and process options may be further introduced into the sensitivity analysis stage of the proposed framework where different performance indices and parameters that need to be varied may be selected. This stage implements the sensitivity analysis approach described previously in this chapter. The calculations of the sensitivity metric may be performed by deploying process simulations for each tested material in parallel processors. The obtained results are stored in processematerial repositories, and external databases can be queried to evaluate their applicability in practical applications.

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4.5 Implementation of Workflows 4.5.1 Parameterization of Tools For the implementation of the proposed approach in a typical case of design of solvents for liquideliquid extraction processes with a subsequent optimization of each one of the design solvents in the process itself, there is a need to select a workflow that consists of the following tools: l

l

l

l

an optimization algorithm, namely SA in this case, which will be used for both process and solvent design; an optimization-based CAMD model with appropriate objective functions for the design of solvents for liquideliquid extraction; a process model of liquideliquid extraction, which will use specific objective functions and constraints suitable for this process; and a K-means clustering algorithm to interface the solvent and process design stages based on the available workflows.

The entire computational approach was developed and implemented combining Fortran algorithms with Bourne Again Shell scripting and PHP in the South Eastern European (SEE) Grid infrastructure provided through the SEE virtual organization (http://www.see-grid-sci.eu/). The parameters that need to be used in order to launch the selected workflow are described in the following tables. The selection of these particular parameters is described in Papadopoulos and Linke (2004, 2006a,b). Fig. 10.13 shows how the parameters shown in Tables 10.8e10.11 are utilized to combine a stochastic search algorithm with the CAMD and process simulators. The two simulators are fitted within the same optimization algorithm; hence, the user can swap between models and objective functions without having to change the anything in the algorithmic operations. The numbers in brackets indicate the corresponding table number where each one of the parameters can be found. The circles indicate the parameters, which are transferred between adjacent algorithmic operations, depending on whether the target is to run a process design, an SOO, or an MOO CAMD case. The frames to the left indicate the parameters that need to filled by the users in order to perform the simulation. The vectors and matrices for all the parameters are initiated, and then the results from the simulation are transferred to the calculation of the objective function(s). The objective function(s) are evaluated based on the criteria of the employed algorithm. The values of the design variables are then changed by appropriate algorithmic operations and transferred to the simulator to close the loop. This is repeated until the algorithmic termination criteria are satisfied. Apparently, different parameters are exchanged as inputs and outputs at different stages of the optimization. In this respect, the services developed in this work are used to monitor and manage the flow of design information. A parallelized version of Fig. 10.13 implemented here involves the simultaneous allocation of different simulations on multiple processors. Fig. 10.13 applies in both the CAMD and process design blocks of the workflow.

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FIGURE 10.13 Algorithmic workflow and parameters used for materials or process design.

TABLE 10.8 Input Parameters Required in Simulated Annealing Algorithm Parameter

Description

NMCL

Number of continuous iterationsefunction evaluations in every annealing temperature level

Tmax

Maximum number of allowed temperature evaluations

Tstart

Initial annealing temperature

Nmove_vars

Number of utilized design variables

Vi

Vector of initial values for design variables (i ¼ 1,Nmove_vars)

Li,j

Matrix containing the upper (j ¼ 1) and lower (j ¼ 2) bounds for the employed design variables

Pi

Vector containing the probability of change of each design variable value i (i ¼ 1,Nmove_vars) in every algorithmic iteration

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TABLE 10.9 Input Parameters Required in Computer-Aided Molecular Design Parameter

Description

mk,i

Vector containing the functional groups comprising each molecule (i ¼ 1-solute, 2-separation solvent, 3-solvent, which already contains the solute)

Ak,i

Matrix indicating the frequency of appearance of each group in the molecule

Kmax

Maximum number of allowed functional groups in the molecule

S TBP ;j

Upper and lower boiling point limits in for the design solvent (K)

DTmin

Minimum temperature difference

A TBP

Boiling point of solute (K)

Ss,min

Minimum selectivity limit of solvent (wt/wt)

Sl,max

Maximum allowed solvent losses (wt%)

Mmin

Minimum allowed distribution coefficient (wt/wt)

MW

Solvent molecular weight (gr/gmole)

TABLE 10.10 Input Parameters Required in the Design of LiquideLiquid Extraction Processes Parameter

Description

Nst

Number of theoretical extraction column

Sfl

Solvent flow rate (kg/hr)

mk,i

Vector containing the functional groups comprising each molecule (i ¼ 1-solute, 2-separation solvent, 3-solvent, which already contains the solute)

Ak,i

Matrix indicating the frequency of appearance of each group in the molecule

Fjtot

Total flow rate of input process stream in phase j (j ¼ 1-extract phase, 2-raffinate phase)

Xj;i

Mass fraction of component i in phase j

Cst

Annualized cost of theoretical stage in liquideliquid extraction column ($/yr)

Csol

Cost per kilogram of utilized solvent ($/kg)

OF

Objective function containing Cst and Csol terms

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TABLE 10.11 Parameters Required in the Clustering Tool Input Parameters

Description

cl Nmax

Maximum number of clusters to be generated

cl Nmin

Minimum number of clusters to be generated

cl ND

Total number of dimensions of data introduced into the algorithm (e.g., number of properties characterizing the solvents)

Npcl

Total number of data included in each dimension

Acl (i,j )

Vector containing the data that will be clustered cl ) (i ¼ 1, Npcl ,j ¼ ND

Output Parameters

Description

cl Nkms

Total number of generated clusters

Bcl (i)

The cluster, which contains each one of the original data

BCcl (k)

The number of data points (e.g., solvents) contained cl ) in each cluster (k ¼ 1, Nkms

Fig. 10.14 illustrates one of the workflows available in Fig. 10.12, which is based on the proposed framework for integrated materials and process design. It shows the flow of information and the corresponding parameters in cases of MOO- and SOO-based CAMD, where the designed materials are either introduced into a clustering step prior to process design (MOO case) or directly into a the process design step (SOO case). Each material can be introduced into process design in parallel by sending each process optimization run simultaneously into different processors.

4.5.2 Results and Discussion The proposed workflows and services were used for the design of solvents required for the separation of a butanolewater mixture using liquideliquid extraction. Overall, 120 jobs were submitted for the integrated solvent and process design workflow (SOO case) utilized in two job batches. Each job started from a different initial state for the solvent and process design cases in order to evaluate the quality of the optimized solutions obtained from SA. The developed services managed simultaneously up to 70 jobs running in parallel in the available distributed computing resources, while the remaining jobs involved in the second batch were submitted automatically and were also managed simultaneously by the services. Fig. 10.15 depicts the number of jobs that terminated and provided retrievable results as a percentage of the

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FIGURE 10.14 Algorithmic workflow and parameters used in the implementation of the framework for integrated materials and process design. MOO; SOO, single-objective optimization.

FIGURE 10.15 Computational performance of integrated solvent and process runs on the grid.

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submitted jobs with respect to the total job processing time. It appears that up to 85e90% of the results for both the process and the solvent design stages of the integrated workflow were obtained within an hour from their submission. These results are typical in grid computing where the total time for processing a job from submission to retrieval is different for each job, regardless of their simultaneous submission. This is mainly due to the simultaneous utilization of the resources by multiple users that adds system processing time requirements to the net cpu time required for execution of each job. The use of the proposed system for the submission and execution of the selected workflows reduced the required time by 83% with respect to the time that would be required if the 120 jobs were submitted sequentially in a single computer. Furthermore, the submission, monitoring, and overall management of the jobs was done automatically and without physical access of the user to the computers where the runs were held. The user simply provided the necessary input parameter values for the workflow, requested its submission, and retrieved the results.

5. CONCLUSIONS The presented work has addressed the utilization of a multiobjective optimization approach for the integration of CAMD with process design in view of two new research frontiers: the impact of materials selection decisions on process operation under variability and the utilization of advanced computing infrastructures, such as grids and clouds, to help expedite the underlying computations through workflows that combine diverse design and analysis tools. The first approach supports the evaluation of the sensitivity of different materials by imposing variations in multiple parameters of interest of a steadystate process model. The variations are investigated as part of a systematic nonlinear sensitivity analysis method with the aim to identify their impact on desired process performance indices. The analysis of such interactions enables the identification of materials, which will have a detrimental effect on process performance even under small magnitude variations, whereas it further determines the ranges of the operating conditions where such effects will be observed. In this respect, it is possible to identify materials, which are able to sustain large magnitude variability from multiple parameter sources while maintaining process performance close to the desired settings. The method is implemented in a solar ORC system for transformation of heat into power. The results show that materials, which were originally selected for optimum performance under nominal design settings (i.e., steady-state operation), are not efficient under variability. As a result, operation under variability needs to be always considered in the selection of appropriate materials. The proposed framework is then incorporated into a general framework for integrated molecular and process design, which is able to efficiently exploit grid and future cloud computing resources. The framework consists of several

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workflows, which combine design and analysis tools of diverse technical requirements in order to support their automated execution in the demanding and challenging environment of grids and clouds. In this context, the underlying idea is to be able to provide the available decision-making software tools as a service within architectures that go beyond the conventional parallelization of optimization algorithms. The proposed architectures are included into several different services, which are able to generate, submit, monitor, and manage the complex workflows selected by users. Complex workflows have been submitted to an actual grid, and the results showed that the proposed services can monitor and manage a large number of parallel jobs.

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Integrated Multiobjective Molecular and Process Design Chapter j 10 Hamad, A.A., El-Halwagi, M.M., 1998. Simultaneous synthesis of mass separating agents and interception networks. Transactions of the Institution of Chemical Engineers 76, 376e388. Harper, P.M., Gani, R., 2000. A multi-step and multi-level approach for computer aided molecular design. Computers and Chemical Engineering 24, 677e683. Hostrup, M., Harper, P.M., Gani, R., 1999. Design of environmentally benign processes: integration of solvent design and separation process synthesis. Computers and Chemical Engineering 23, 1395. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2005. A new decomposition based computer-aided molecular/mixture design methodology for the design of optimal solvents and solvent mixtures. Industrial and Engineering Chemistry Research 44, 4785. Karunanithi, A.T., Achenie, L.E.K., Gani, R., 2006. A computer-aided molecular design framework for crystallization solvent design. Chemical Engineering Science 61, 1247e1260. Karunanithi, A.T., Mehrkesh, A., 2013. Computer-aided design of tailor-made ionic liquids. AIChE Journal 59, 4627e4640. Kazantzi, V., Qin, X., El-Halwagi, M., Elijack, F.T., Eden, M., 2007. Simultaneous process and molecular design through property clustering techniques: a visualization tool. Industrial and Engineering Chemistry Research 46 (10), 3400. Kheireddine, H.A., El-Halwagi, M.M., Elbashir, N.O., 2013. A property-integration approach to solvent screening and conceptual design of solvent-extraction systems for recycling used lubricating oils. Clean Technologies and Environmental Policy 15 (1), 35e44. Kim, K.J., Diwekar, U.M., 2002. Integrated solvent selection and recycling for continuous processes. Industrial and Engineering Chemistry Research 41 (18), 4479. Kokossis, A.C., Linke, P., Yang, S., 2011. The Cascade Optimisation Algorithm e a new distributed stochastic optimisation approach for engineering applications. Industrial and Engineering Chemistry Research 50 (9), 5266e5278. Labrador-Darder, C., Cecelja, F., Kokossis, A.C., Linke, P., 2009. Integration of superstructurebased optimization and semantic models for the synthesis of reactor networks. Computer Aided Chemical Engineering 26, 865e870. Lampe, M., Groß, J., Bardow, A., 2012. Simultaneous process and working fluid optimization for organic Rankine cycles (ORC) using PC-SAFT. Computer Aided Chemical Engineering 30, 572e576. Lampe, M., Stavrou, M., Bu¨cker, M., Gross, J., Bardow, A., 2014. Simultaneous optimization of working fluid and process for organic Rankine cycles (ORCs) using PC-SAFT. Industrial and Engineering Chemistry Research 53, 8821e8830. Lampe, M., Stavrou, M., Schilling, J., Sauer, E., Gross, J., Bardow, A., 2015. Computer-aided molecular design in the continuous-molecular targeting framework using group-contribution PC-SAFT. Computers and Chemical Engineering 81, 278e287. Lecompte, S., Huisseune, H., van den Broek, M., Vanslambrouck, B., De Paepe, M., 2015. Review of organic Rankine cycle (ORC) architectures for waste heat recovery. Renewable and Sustainable Energy Reviews 47, 448e461. Ng, L.Y., Chemmangattuvalappil, N.G., Ng, D.K.S., 2014. A Multiobjective Optimization-Based Approach for Optimal Chemical Product Design Industrial and Engineering Chemistry Research 53 (44), 17429e17444. Linke, P., Kokossis, A.C., 2002. Simultaneous synthesis and design of novel chemicals and process flowsheets. In: Grievink, J., van Schijndel, K. (Eds.), Proceedings of the 12th European Symposium on Computer Aided Process Engineering. Elsevier, pp. 115e120. Linke, P., Kokossis, A.C., 2003a. Attainable reaction and separation processes from a superstructure-based method. AIChE Journal 49 (6), 1451e1470.

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SECTION j II Molecular Design Linke, P., Kokossis, A.C., 2003b. On the robust application of stochastic optimisation technology for the synthesis of reaction/separation systems. Computers and Chemical Engineering 27 (5), 733e758. Linke, P., Kokossis, A.C., 2007. A multi-level methodology for conceptual reaction-separation process design. Chemical Product and Process Modeling 2 (3). Linke, P., Papadopoulos, A.I., Seferlis, P., 2015. Systematic methods for working fluid selection and the design, integration and control of organic Rankine cyclesdA Review. Energies 8, 4755e4801. Mac Dowell, N., Llovell, F., Adjiman, C.S., Jackson, G., Galindo, A., 2010. Modelling the fluid phase behavior of carbon dioxide in aqueous solutions of monoethanolamine using transferable parameters with the SAFT-VR approach. Industrial and Engineering Chemistry Research 49, 1883e1899. Maranas, C.D., 1997. Optimal molecular design under property prediction uncertainty. AIChE Journal 43 (5), 1250e1264. Marcoulaki, E.C., Kokossis, A.C., 2000a. On the development of novel chemicals using a systematic optimization approach. Part II. Solvent design. Chemical Engineering Science 55 (13), 2547. Marcoulaki, E.C., Kokossis, A.C., 2000b. On the development of novel chemicals using a systematic synthesis approach. Part I. Optimisation framework. Chemical Engineering Science 55, 2529e2546. Mavrou, P., Papadopoulos, A.I., Stijepovic, M., Linke, P., Seferlis, P., Voutetakis, S., 2014. Assessment of working fluid mixtures for solar Rankine cycles. Chemical Engineering Transactions 39, 283e288. Mavrou, P., Papadopoulos, A.I., Stijepovic, M., Seferlis, P., Linke, P., Voutetakis, S., 2015. Novel and conventional working fluid mixtures for solar Rankine cycles: performance assessment and multi-criteria selection. Applied Thermal Engineering 75, 384e396. McLeese, S.E., Eslick, J.C., Hoffmann, N.J., Scurto, A.M., Camarda, K.V., 2010. Design of ionic liquids via computational molecular design. Computers and Chemical Engineering 34 (9), 1476e1480. Molina-Thierry, D.P., Flores-Tlacuahuac, A., 2015. Simultaneous optimal design of organic mixtures and Rankine cycles for low-temperature energy recovery. Industrial and Engineering Chemistry Research 54, 3367e3383. Montolio-Rodriguez, D., Linke, P., Linke, D., 2012. Multi-level reactor optimisation in the conceptual design of processes with heterogeneous catalytic reactors. Chemical Product and Process Modeling 7(1) (6), 1e35. Montolio-Rodriguez, D., Linke, P., Linke, D., Stijepovic, M.Z., 2010. Optimal conceptual design of processes with heterogeneous catalytic reactors. Chemical Engineering Journal 163 (3), 438e449. Morbach, J., Wiesner, A., Marquardt, W., 2009. OntoCAPEdA (re)usable ontology for computeraided process engineering. Computers and Chemical Engineering 33 (10), 1546e1556. Mun˜oz, E., Capo´n-Garcı´a, E., Laı´nez, J.M., Espun˜a, A., Puigjaner, L., 2013. Integration of enterprise levels based on an ontological framework. Chemical Engineering Research and Design 91 (8), 1542e1556. Mun˜oz, E., Capo´n-Garcı´a, E., Moreno-Benito, M., Espun˜a, A., Puigjaner, L., 2011. Scheduling and control decision-making under an integrated information environment. Computers and Chemical Engineering 35 (5), 774e786. Mun˜oz, E., Espun˜a, A., Puigjaner, L., 2010. Towards an ontological infrastructure for chemical batch process management. Computers and Chemical Engineering 34 (5), 668e682.

Integrated Multiobjective Molecular and Process Design Chapter j 10 Natarajan, S., Ghosh, K., Srinivasan, R., 2012. An ontology for distributed process supervision of large-scale chemical plants. Computers and Chemical Engineering 46, 124e140. Ng, L.Y., Chong, F.K., Chemmangattuvalappil, N.G., 2015. Challenges and opportunities in computer-aided molecular design. Computers and Chemical Engineering 81, 115e129. Oyarzu´n, B., Bardow, A., Gross, J., 2011. Integration of process and solvent design towards a novel generation of CO2 absorption capture systems. Energy Procedia 4, 282e290. Palma-Flores, O., Flores-Tlacuahuac, A., Canseco-Melchor, G., 2014. Optimal molecular design of working fluids for sustainable low-temperature energy recovery. Computers and Chemical Engineering 72, 334e339. Papadokonstantakis, S., Badr, S., Hugerbuhler, K., Papadopoulos, A.I., Damartzis, T., Seferlis, P., Forte, E., Chremos, A., Galindo, A., Adjiman, C.S., Jackson, G., 2015. Towards sustainable solvent-based post combustion CO2 capture: from molecules to conceptual flowsheet design. Computer Aided Chemical Engineering 36, 279e305. Papadopoulos, A.I., Linke, P., 2004. On the synthesis and optimization of liquideliquid extraction processes using stochastic search methods. Computers and Chemical Engineering 28 (11), 2391e2406. Papadopoulos, A.I., Linke, P., 2009b. A decision support grid for integrated molecular solvent design and chemical process selection. Computers and Chemical Engineering 33 (1), 72e87. Papadopoulos, A.I., Linke, P., 2005. A unified framework for integrated process and molecular design. Chemical Engineering Research and Design 83 (6A), 674e678. Papadopoulos, A.I., Linke, P., 2006a. Multiobjective molecular design for integrated processesolvent systems. AIChE Journal 52 (3), 1057e1069. Papadopoulos, A.I., Linke, P., 2006b. Efficient integration of optimal solvent and process design using molecular clustering. Chemical Engineering Science 61 (19), 6316e6336. Papadopoulos, A.I., Linke, P., 2009a. Integrated solvent and process selection for separation and reactive separation systems. Chemical Engineering and Processing 48, 1047. Papadopoulos, A.I., Stijepovic, M., Linke, P., 2010a. On the systematic design and selection of optimal working fluids for organic Rankine cycles. Applied Thermal Engineering 30, 760e769. Papadopoulos, A.I., Stijepovic, M., Linke, P., Seferlis, P., Voutetakis, S., 2010b. Power generation from low enthalpy geothermal fields by design and selection of efficient working fluids for organic Rankine cycles. Chemical Engineering Transactions 21, 61e66. Papadopoulos, A.I., Stijepovic, M., Linke, P., Seferlis, P., Voutetakis, S., 2013a. Toward optimum working fluid mixtures for organic Rankine cycles using molecular design and sensitivity analysis. Industrial and Engineering Chemistry Research 52, 12116e12133. Papadopoulos, A.I., Stijepovic, M., Linke, P., Seferlis, P., Voutetakis, S., 2013b. Molecular design of working fluid mixtures for organic Rankine cycles. Computer Aided Chemical Engineering 32, 289e294. Papadopoulos, A.I., Stijepovic, M., Linke, P., Seferlis, P., Voutetakis, S., 2012. Multi-level design and selection of optimum working fluids and ORC systems for power and heat cogeneration from low enthalpy renewable sources. Computer Aided Chemical Engineering 30, 66e70. Pavurala, N., Achenie, L.E.K., 2014. Identifying polymer structures for oral drug delivery e a molecular design approach. Computers and Chemical Engineering 71, 734e744. Pereira, F.E., Keskes, E., Galindo, A., Jackson, G., Adjiman, C.S., 2011. Integrated solvent and process design using a SAFT-VR thermodynamic description: high-pressure separation of carbon dioxide and methane. Computers and Chemical Engineering 35 (3), 474. Pierobon, L., Casati, E., Casella, F., Haglind, F., Colonna, P., 2014. Design methodology for flexible energy conversion systems accounting for dynamic performance. Energy 68, 667e697.

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The Signature Molecular Descriptor in Molecular Design: Past and Current Applications D.P. Visco, Jr. 1 and J.J. Chen The University of Akron, Akron, OH, United States 1 Corresponding author: E-mail: [email protected]

1. MOLECULAR DESCRIPTORS All chemical substances have qualities that determine their behaviors in different environments and conditions. These qualities, unique to that substance, are accessible to the scientist and help them make sense of their observations and experiments. Transformations are often required, however, to turn these qualities into quantitative information. The vast field of molecular descriptors is an end result of this transformation, capturing structural and chemical information into a quantitative form that allows scientists to use the information in a logical and mathematical manner (Todeschini and Consonni, 2008). Molecular descriptors allow scientists to apply an algorithmic, repeatable process in the exploration of molecular space in the form of numerical values as a way to discriminate between the inherent qualities within two substances. There is a vast array of molecular descriptors that exist, with several taxonomies for their grouping. However, a common approach is to classify molecular descriptors by their dimensionality: zero-dimensional descriptors (0D), one-dimensional descriptors (1D), two-dimensional descriptors (2D), and three-dimensional descriptors (3D) (Faulon and Bender, 2010; Todeschini and Consonni, 2009). 0D descriptors only depend on the molecular formula of a molecule without any knowledge of structure, such as molecular weight or molecular net charge. 1D descriptors are lists of substructures in the molecule and describe properties requiring some knowledge of the molecular structure but not full knowledge, like dipole moments, partition coefficients, and hydrogen acceptors and donors. Most descriptors tend to be 2D, accounting for Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00011-3 Copyright © 2016 Elsevier B.V. All rights reserved.

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the topology in the molecule and utilizing graph theory in some way. 3D descriptors take into consideration the 3D spatial features of a molecule and, thus, have the ability to contain more information than 2D descriptors.

2. INTRODUCTION TO SIGNATURE MOLECULAR DESCRIPTOR 2D molecular descriptors consider the entire 2D structure of the molecule and account for all the atoms and bonds contained within the molecule. This is handled using graph theory, a branch of mathematics that documents the pairwise relations of a group of objects. To create a molecular graph, which documents how atoms are connected to each other in a molecule, we declare the atoms are nodes and the bonds are edges and create a graph that captures all the pairwise relations (bonds) of the atoms (Todeschini and Consonni, 2008). Deleting edges and/or parts of the entire molecular graph creates fragments, which, when combined, are a representation of the 2D molecule. While common fragments can be identified a priori (e.g., functional groups) in deconstructing a molecular graph, this is not a requirement and allows for the free creation of fragments open to several deconstruction algorithms. The set of fragments for a molecule (or set of molecules) can be used as independent variables when creating quantitative structure-property relationships (QSPRs), with the occurrence of that fragment in a molecule taken as the value of the independent variable (Duchowicz et al., 2008; Huang et al., 2013; Gharagheizi et al., 2013; Mattei et al., 2013). A topological index (TI) is a class of molecular descriptor that is based on the molecular graph and records the local topological environment of an atom, if using a fragment of the molecular graph, or a molecule, if using the whole molecular graph (Todeschini and Consonni, 2008). For example, Randic (1975) examines molecular connectivity, c, focusing on the carbon atoms and its branching in a molecule. Kier and Hall build on Randic’s c connectivity index by incorporating nonhydrogen atoms when documenting molecular connectivity (Kier and Hall, 1976, 1977, 1981, 1990). Among the many 2D fragmentebased TIs that exist (Devillers and Balaban, 2000), there is one that systematically captures the structural information of a 2D structural formula, known as the Signature molecular descriptor (Visco et al., 2002; Faulon et al., 2003a, 2004). Functionally, Signature is an operation on the 2D graph of a molecule that deconstructs the molecule into smaller fragments of a predetermined size (known as a height). Designating an atom in the molecule as the root atom, Signature creates the fragment by starting at the root atom and follows the bonds out to a predetermined height without backtracking, while taking note of all the atoms, including hydrogen, and bond types along that path. This fragment, known as an atomic Signature, captures the atoms and bonds in that path from the root atom. The process is repeated so that all of the atoms in the molecule,

The Signature Molecular Descriptor in Molecular Design Chapter j 11

FIGURE 11.1 Signature example: acetic acid. We start at the root atom (designated here by the star), go out a predetermined distance (i.e., height), and record how the atoms encountered on that path are connected to the root atom to determine the atomic Signature. The process is repeated for all atoms in the molecule to obtain the molecular Signature. Using acetic acid as an example, we show the distances from the root atom in: (A) the molecule itself, (B) tree form (C) the resulting Signatures from height ¼ 0, height ¼ 1, and height ¼ 2. The atoms found further down the tree of a branch point atom are denoted by the nested parenthesis. Single bonds between atoms are assumed in atomic Signatures when bonding is not specified. Otherwise, it is presented as follows (“]” is a double bond; “t” is a triple bond; “p” is an aromatic bond).

including hydrogen, become the root atom in turn. Once exhausted, the resulting collection of atomic Signatures for the molecule is then known as the molecular Signature. Occurrence numbers are used to denote how often a particular atomic Signature appears in a molecule. Since fragments change depending on the distance from the root atom, heights for atomic and molecular Signatures need to be specified when describing a molecule. To demonstrate how atomic and molecular Signatures are calculated at various heights, Fig. 11.1 is provided using acetic acid as the example. While Signature, as a fragmental descriptor, is related to other fragmental descriptors, it is useful to contrast Signature to a popular fragmentation approach, such as Joback and Reid’s group contribution method for estimating thermodynamic properties of pure compounds (Joback and Reid, 1987). Unlike Joback and Reid’s approach where functional groups or other group types

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FIGURE 11.2 Functional group fragmentation versus signature fragmentation. In Joback and Reid’s approach, there are two identified groups: (A) the carboxylic acid group and the methyl group. In Signature at height-1 (B), each atom in the molecule in turn becomes the root during fragmentation, resulting in an overlap between fragments.

are specified a priori, the atomic Signatures are unique to the set of molecules used in a particular study. For example, consider once again acetic acid. The Joback and Reid approach, as captured in Fig. 11.2A, deconstructs the molecule into two fragments: one methyl group and one carboxylic acid group. On the other hand, there are three unique atomic Signatures for acetic acid at height-0, six unique atomic Signatures at height-1, and six unique Signatures at height-2 (see Fig. 11.1B). If we focus on height-1 for a moment, we see that the Signature fragments (i.e., the atomic Signatures) have overlap (Fig. 11.2B). This overlap is a key feature of Signature that tends to extend the set of independent variables used to describe a molecule (i.e., six unique height-1 atomic Signatures versus two Joback-Reid groups for acetic acid), but provides an ability to capture all of the local bonding interactions (i.e., the carbonecarbon bond in acetic acid). Such finer-grained detail in Signature has several benefits, one of which is to allow QSPRs the opportunity to identify the most impactful bonding interactions in a molecule as it relates to training a model against a certain molecular property (Visco et al., 2002; Faulon et al., 2003a). Note that the “local” aspect of the bonding is tuned/defined by the selection of the Signature height. For example, the number of unique height-2 atomic Signatures in a molecule will always be greater than or equal to the number of unique height-1 atomic Signatures. Likewise, you will have at least as many unique height-3 atomic Signatures as you will have height-2 atomic Signatures, and so on. Of course, the greater the Signature height used, the more expansive the definition of “local” environment becomes.

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3. ADVANTAGES OF SIGNATURE When compared to other molecular descriptors, Signature possesses several advantages that arise from how the atomic Signatures are generated. Historically, Signature was first developed in 1994 as a tool for computer-aided structural elucidation studies (Faulon, 1994). The conventional approach towards structural elucidation was to infer a structural formula from the analytical data and then, as new analytical data was added, iterate the structural formula to account for the new data. Computer-aided algorithms, on the other hand, allowed for a deterministic approach of building all possible structural formulas corresponding to the analytical data and removing ones that do not conform to new analytical data until only one is left, or a stochastic approach of building molecules that have structural features indicated by the analytical data. Signature was developed as a tool to explore the stochastic approach. Signature, as a structural elucidation tool, accomplished five different tasks: develop all the fragments and bonds indicated by analytical data, construct a structural formula from those fragments and bonds, optimize the 3D structure, predict physical properties from the 3D structure, and calculate the requisite number of test samples for statistical significance (Faulon, 1994). The features of Signature that made it powerful as a structural elucidation tool also allowed for its use as a molecular descriptor. Before introducing the advantages of Signature, it is useful to know how structural information is decomposed and transformed into Signature. Initially, the structure of a compound is captured in a chemical table file containing all the bonds, bond types, atoms and atomic 3D coordinates. This information, normally in a .mol or .sdf file type, is stored either individually (one file per compound) or combined (one file for the entire compound set). In either format, a computer script extracts the atomic connectivity information to create the atomic signatures for a given compound. A user-controlled parameter selects the desired atomic Signature height. There are three main outputs: a .scan file (per compound) that contains the atomic Signatures of a given compound and two data files for the entire compound set. The first data file is a compilation of all atomic Signatures for the set of compounds (the atomic Signature database), and the second data file is a matrix (called the descriptor matrix) whose entries are occurrence numbers; each column corresponds to a unique atomic signature in the set, and each row corresponds to a compound in the set.

3.1 Advantages of Signature: Complete Documentation of Atomic Topography The first advantage of Signature, as shown in Fig. 11.2 and its discussion, is the complete documentation of the atoms and bonds in a molecule by identifying each atomic Signature and tabulating the number of each atomic Signature in a molecule (Visco et al., 2002; Faulon et al., 2003a,b, 2004). With this complete

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accounting of the available 2D structural information, we can use any combination of atomic Signatures to develop quantitative structure-activity relationships (QSARs) or QSPRs (Visco et al., 2002; Faulon et al., 2003a), which are correlations of structural features to an observed chemical property. Indeed, Signature has been shown to create QSPRs as accurate as many other types of molecular descriptors and has a benefit of reduced correlation between the independent variables (Faulon et al., 2003a; Visco et al., 2002).

3.2 Advantages of Signature: Canonical Representation of Molecule Signature, as it is canonical (Faulon et al., 2003a, 2004), can be considered the basis set for the development of all other 2D descriptors. As has been previously shown (Visco et al., 2002; Faulon et al., 2003a), all other 2D classes of descriptors can be written in terms of Signature. Thus, we can use atomic Signatures to create QSARs directly or to derive other molecular descriptors using Signature. This can be beneficial, as preexisting models using other molecular descriptors can be transformed into models using Signature, though minimal effort has been explored in this area.

3.3 Advantages of Signature: Tunable Specificity/Degeneracy Another advantage of Signature concerns degeneracy (Faulon et al., 2003b, 2005). The Signature height selected controls the area Signature covers from the root atom. We can imagine that with larger height values, the structural area covered by the atomic Signature fragment would be large. Thus, the larger the height value, the larger the area overlap is, as noted in Fig. 11.2B, which results in a more specific molecular Signature. Therefore, height is a parameter that controls degeneracy. Accordingly, larger Signature heights (e.g., 2) might be used for a QSPR where specific bonding interactions among multiple atoms is of interest to capture in the correlation/prediction of the property of interest. On the other hand, Signature used in computer-aided molecular design (CAMD) might find more value in a smaller height (e.g., 1) in order to allow for the creation of many candidate molecules. Indeed, Signature becomes virtually nondegenerate at height-3, meaning there is one molecular Signature for a given 2D structure (Faulon et al., 2003b). Therefore, computer-aided molecule design studies using Signature have focused mainly on heights-1 (Weis et al., 2005) and, on occasion, height-2 (Jackson et al., 2008).

3.4 Advantages of Signature: Efficiently Combine Atomic Signatures to Form New Structures An additional key advantage of Signature is that efficient algorithms exist to combine atomic Signatures together in a systematic and exhaustive way to

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create molecular structures (Churchwell et al., 2004; Martin, 2012; Faulon et al., 2003b). Accordingly, Signature is readily applicable to CAMD (Churchwell et al., 2004; Weis et al., 2005; Weis and Visco, 2010). In order to create 2D structures, atomic Signatures are combined into different molecular Signatures that solve a set of equations based on connectivity and valence. The equations are Diophantine in nature, meaning they have integer coefficients and integer solutions (the solutions being the occurrence of that atomic Signature in a molecule). The degeneracy of Signature at height ¼ 0 (which are just atom types, see Fig. 11.1) or height ¼ 1 means that there will often be many 2D structures that correspond to a solution. The algorithm enumerates and creates all structures that have a given molecular Signature. Such an approach allows for the creation of novel compounds since the atomic Signature fragments can be combined in all possible ways to create nonintuitive molecules. The connectivity and valence equations (generally called “consistency equations”) for a particular problem are underspecified, meaning that the solution set to the consistency equations is infinite. To constrain the solution set, it is typical to force the atomic Signatures to have ranges that are mapped from the problem of interest. In other words, if a particular atomic Signature has an occurrence range of 0e5 from the data set of interest, then solutions to the consistency equations must only range from 0 to 5 for that atomic Signature. This constraint is imposed not only to generate a finite number of solutions, but prevents extrapolation from the QSAR/QSPR when scoring the generated solutions from the consistency equations for fitness.

4. APPLICATIONS OF SIGNATURE After the development of Signature as a computer-aided structure elucidation tool, Signature was formally explored as a molecular descriptor and found to be comparable to other molecular descriptors used in generating QSPRs (Faulon et al., 2003a). While fulfilling its original purpose as a structural formula elucidation tool (Diallo et al., 2003), Signature was formalized, characterized, and described as a tool for chemical structure enumeration (Faulon et al., 2003a,b). Since its development in 1994, Signature has been used in many different applications. We summarize those uses in the next subsections.

4.1 Applications of Signature: QSARs The most direct application of Signature is as a molecular descriptor in QSARs and QSPRs to correlate structural features with observed properties. Signature was first used in a QSAR during a test study on HIV-1 protease inhibitors (Visco et al., 2002) (Faulon et al., 2003a). Signature was also used at varying heights to determine those heights that provide the most correlative QSARs for

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small molecule ligands and for metabolites (Faulon et al., 2008). In addition, Signature was used to analyze the effect of different substituent groups on a central scaffold (Chen et al., 2013) and to create an interpretable QSAR in order to inform structural modifications on substituent groups applied to a common central scaffold (Eriksson et al., 2014). Also, to meet the EU’s European Chemicals Agency and the US Organization for Economic Cooperation and Development’s guidelines to identify and quantify the applicability domains (ADs) of work environment toxicity QSARs (EU; OECD; OECD; Norinder et al., 2015), Signature-based QSARs have been developed to study the AD of toxicity QSARs (Norinder et al., 2015). Signature-based QSARs were also developed to study the AD of industrial drug discovery QSARs (Eklund et al., 2012). Signature has also been used to characterize proteineprotein interactions. For example, Signature was used to predict proteineprotein/peptide interactions in human, mouse, yeast and Helicobacter pylori datasets (Martin et al., 2005). Additionally, Signature has been applied to characterize more complex proteineprotein interactions, such as predicting and characterizing the factors of protein beta sheet formation (Brown et al., 2006a) as well as predicting protein promiscuity and the contributing active groups/fragments (Carbonell and Faulon, 2010). In 2015, Signature has been used to identify molecular fragments contributing to or inhibiting bloodebrain barrier permeability (Varadharajan et al., 2015). While the previous examples are all biological in nature, Signature has also been used to create QSPRs in nonbiological contexts. For example, with other molecular descriptors, Signature was used to create QSPRs predicting the electronic properties of organic semiconductors (Misra et al., 2011) and to describe the photovoltaic performance of phenothiazine dyes (Venkatraman and Alsberg, 2015).

4.2 Applications of Signature: QSAR/QSPR and Molecular Design From its inception as a computer-aided structure elucidation tool (Faulon, 1994), Signature has been used to build molecules from fragments. In this context, Signature is used both to create molecules (new or otherwise) and to predict the properties of interest for these created molecules (normally facilitated by a model using atomic Signatures as independent variables). Originally formulated as an inverse QSAR approach [i.e., solving a QSAR for the set of independent variables given a desired dependent variable value (Visco et al., 2002; Faulon et al., 2003a)], Signature was ultimately employed in molecular design through an approach that first creates molecules and then scores the molecules using a model for a property (or properties) of interest. Signature has been used in this fashion to design and characterize environmentally friendly hydrofluoroether foam blowing agents (Weis et al., 2005), polymers (Brown et al., 2006b), and green industrial solvents (Weis and Visco,

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2010). Signature was also used to design and characterize possible glucocorticoid receptor structures with pulmonary selectivity as possible new asthma treatments (Jackson et al., 2008). In Eden’s reverse problem formation (RPF), he applied Signature to redefine the TIs in QSPRs and the fragments used to design optimal compounds according to given process conditions (Chemmangattuvalappil et al., 2009a,b, 2010). Additionally, to find optimal compounds across a multitude of requirements and determine trade-offs that are made to optimize one property over another, the Signature-based RPF was combined with a fuzzy logic algorithm to design and characterize, via QSPR, the compounds describing the Pareto front in a given situation (Ng et al., 2014a,b, 2015a).

4.3 Applications of Signature: QSAR/QSPR, Molecular Design, and Experimental Validation In the previous subsection, we identified examples of Signature used in molecular design, though published work to evaluate the efficacy of the predicted structures has not been provided in the public domain for a variety of reasons, for example, intellectual property rights or corporate/trade secrets. However, some examples of molecular design with Signature have been published that include a loop closure step, in other words, where the results of the design approach can be evaluated through experimental verification of the predicted properties for the “new” molecules selected. One of the earliest examples is the use of Signature to create inhibitors for a protein called ICAM-1. Here, Signature was not employed in an all-atom form, but at an amino acid level. Thus, rather than a fine-grained approach that deconstructs amino acids into their atomic constituents, the amino acids themselves were the labels in constructing a chemical graph for the proteins of interest (Churchwell et al., 2004). QSARs were developed and the inverse design problem solved to predict active ICAM-1 inhibitors. A subset of those predicted to be most active against ICAM-1 were synthesized, tested in vivo, and were confirmed to be active, demonstrating the validity of Signature in a molecular design approach. We provide a more detailed example of this loop closure step in a case study on cement admixture development (Kayello et al., 2014; Shlonimskaya et al., 2014) in Section 5.3.

4.4 Applications of Signature: QSAR/QSPR and Classification In the previous subsection, we described the use of Signature in molecular design where a relatively small dataset of compounds were deconstructed into atomic Signatures, the fragments combined to make new compounds, and the resulting compounds scored with a QSAR/QSPR to identify those with the most promise associated with a property of interest. On the other hand, Signature has also been used as a screening tool for very large databases without the molecule design component. In these applications, Signature is the independent variable for model creation, whether through a QSAR/QSPR or in

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a classification scheme (i.e., active versus inactive). For example, Signature was used as a descriptor to identify small molecule ligands for Factor XIa inhibitors through a classification and screening approach (Weis et al., 2008; Li et al., 2014); we provide this as a case study detailed in Section 5.1. Signature has also been used to find ligands for enzymes in a study that combines molecular dynamics, docking algorithms, and QSAR screening (Martiny et al., 2013).

4.5 Applications of Signature: Inclusion in Biological Software Many users of Signature have recognized its ability as a structural enumeration tool. To facilitate this application, Signature has been included as a molecular descriptor or protocol in several biological problem analysis and ligand prediction software packages (Spjuth et al., 2013). Signature was cited in a patent for software packages that identify active sites in proteins that may be possible drug targets (Zhou et al., 2008) and was the basis for a drug-likeness filtering system (Ursu and Oprea, 2010). The Bioclipse package uses Signature as a descriptor for creating QSARs (Spjuth et al., 2013), while the CDK-Taverna 2.0 package uses Signature for natural product/molecule similarity searching (Truszkowski et al., 2011; Vanii et al., 2012). Both of these applications are tools for users to apply as they will; more specific applications include structure enumeration for QSARs predicting protein phosphorylation sites (Gray et al., 2010) and the classification of Cytochrome P450 isoform inhibitors (Lapins et al., 2013; Rostkowski et al., 2013). Signature’s structural enumeration abilities have even extended to RNA and the prediction of RNA structures from RNA fragments and sequences (Bindewald et al., 2008).

4.6 Applications of Signature: Industrial Bioreaction Pathway Design Industrial bioreactors and cell cultures make biological products or byproducts of interest, and, on that front, Signature has contributed to the identification and mapping of reaction pathways (Carbonell et al., 2011), the design and optimization of pathways for a product of interest (Carbonell et al., 2014), the monitoring of bioreactors and reactor streams for changes of intermediates, products (Ahlberg et al., 2014), and the inclusion of possible toxic compounds, such as mutagens and carcinogens (Spjuth et al., 2011). Signature was also used to scan through reaction pathways to identify conserved classes of reaction pathways, conserved actors, or conserved reactants that appear in multiple pathways to create a consolidated network map of reaction pathways (Sorokina et al., 2015). For designing optimal reaction pathways, reactants, and products, Eden’s RPF uses Signature to identify the static and reactive fragments and constrain the reactants and products in the reaction to have fragments that participate in the reaction, as well as optimal properties for

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reactor conditions (Chemmangattuvalappil et al., 2012; Dev et al., 2013; Chemmangattuvalappil and Eden, 2013; Ng et al., 2015b).

4.7 Applications of Signature: Signature as a 3D Molecular Descriptor One limitation of Signature is that it has been developed as a 2D descriptor. Thus, as a 2D descriptor, it cannot (for example) discriminate between active and inactive stereoisomers, whose biological activities against a certain protein target can differ by orders of magnitude. When evaluated by Signature, these two stereoisomers would possess the same molecular Signature. Extending Signature from 2D to 3D for some applications is an area of active research. For example, Signature has been updated to include stereochemistry as part of its structure enumeration process (Carbonell et al., 2013). Briefly, the full geometry of a molecule is analyzed to identify stereo centers, the priorities determined using full-molecule trees rooted by the stereo atom according to CahneIngoldePrelog rules [International Union of Pure and Applied Chemistry (IUPAC)], and the configuration is noted by substituting different symbols for the original bond symbols found in Fig. 11.1 (i.e., /¼\ for E, /¼/ for Z, @@ for R, and @ for S) (Carbonell et al., 2013). Another approach utilizing Signature in 3D was developed by Eden in his reverse problem formulation (RPF) technique. Here, the 2D Signature fragments (i.e., atomic Signatures) are optimized in 3D and used to describe 3D TIs in QSARs (Herring et al., 2012). Eden and his colleagues also use spatial Signatures to build and optimize 3D structures of molecules (Herring and Eden, 2014a,b, 2015), detailed in a case study in Section 5.2.

5. COMPUTER-AIDED MOLECULAR DESIGN: SIGNATURE CASE STUDIES To provide the reader with a deeper view on the application of Signature as a molecular design tool, we present three distinct case studies that show the utility of Signature: (1) virtual high-throughput screening (vHTS), (2) molecular and process design, and (3) interpretable QSPR/CAMD development. We have chosen these examples, as they show the breadth of usage of Signature in molecular (and process) design and span multiple areas (i.e., biological/pharmaceuticals, construction products, and the chemical process industry).

5.1 CAMD: Signature Case Study: Virtual High Throughput Screening vHTS is an approach that allows the search of a compound database against a computational model that evaluates candidates for fitness (Bleicher et al.,

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2003). This approach is virtual since it is done on a computer as opposed to typical HTS processes where many compounds are evaluated experimentally (in small quantities) against a target. Functionally, CAMD in the ways presented in Sections 4.2 and 4.3 can also be considered vHTS. In those applications, the database of compounds identified as the training set ultimately form the basis for the compounds that can be created from the atomic Signatures in that training set. Then, the scoring function effectively “screens” these solutions to identify the best candidates to move forward for additional evaluation, synthesis, and, ultimately, testing. This CAMD approach, however, can be very costly since almost all of the compounds that can be created from the molecular design process done in this way have never been synthesized before. On the other hand, the use of large, preexisting chemical databases whose compounds have already been synthesized (and, in many cases, commercially available) facilitates the solution process. We provide an example of this latter approach through this case study. The National Center for Biotechnology Information curates the PubChem Compound database of submitted chemical information and the PubChem Bioassay database of submitted experimental data (Kim et al., 2015; Wang et al., 2014). With the available experimental and chemical data, Weis et al. (2008) created a classification model from a particular PubChem Bioassay dataset and screened the PubChem Compound database for novel compounds using the trained model. Such vHTS approaches, in general, take known experimental data and extend their utility in a virtual way to identify compounds in the database that are predicted to have activity against a protein of interest. This approach is in contrast to large (>100,000 compounds) exploratory bioassays handled by robots that yield a small percentage of actual active compounds (Pereira and Williams, 2007; Dobson, 2004). At the time of the published study of Weis et al. (2008), the PubChem Compound database contained information on 17 million compounds, while the PubChem Bioassay database contained 800 HTS datasets. With the available data, Weis et al. screened for Factor XIa inhibitors, a protein involved with the clotting process, using the related PubChem Bioassay AID 846 as the training dataset. The process flowchart is shown in Fig. 11.3. Weis et al. (2008) used atomic Signature fragments directly to create a model (a support vector machine classifier) to correlate the observed activity of compounds in the training set to the atomic Signatures present in the compounds. Atomic Signatures of height 0, 1, and 2 were used, generating 865 unique atomic Signatures. In order to limit the number of atomic Signatures available to the model, filters and wrappers were used. Filters identified those atomic Signatures that were considered for model analysis a priori. Wrappers worked with the model creation process to select the most impactful atomic Signatures for the data set of interest. Weis et al. used Furey’s u coefficient as the filter and K-means clustering as the wrapper.

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FIGURE 11.3 Process Weis et al. followed to conduct the virtual high-throughput screening for Factor XIa inhibitors. From Weis, D.C., Visco Jr., D.P., Faulon, J.L., 2008. Data mining PubChem using a support vector machine with the Signature molecular descriptor: classification of factor XIa inhibitors. Journal of Molecular Graphics and Modelling 27, 466e475. With permission. Copyright 2008 Elsevier.

Both filter and wrapper models were created. While the u coefficient filter models were developed more quickly, w10 min versus 4 days with K-means clustering, they performed worse in tenfold cross-validation tests, 80% versus 89% accuracy with K-means clustering. The authors posit while the time saved is significant, the final model is created only once while the decrease in accuracy affects the results hereafter. Thus, the increase in accuracy warrants the larger time requirement. After creating the support vector machine classification model, the authors proceeded to screen the PubChem Compound database for possible Factor XIa inhibitors. The PubChem Compound’s structures were transformed into height ¼ 0, 1, and 2 Signatures and passed to the K-means clustering model. To maximize the predictive power of the model, they limited considerations to compounds whose atomic Signatures are all found in the training dataset,

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which resulted in a total of 31,267 compounds. Since the focus was finding biologically active compounds, only compounds believed to be active (i.e., a classification score from the model >0) were considered, reducing 31,267 compounds to 1300 compounds. To increase the confidence of identifying active compounds, compounds with classification scores >1 (298 compounds) were screened using the Autodock (Morris et al., 1998) docking software to verify if the resulting complex was energetically favorable. The resulting binding energies ranged from 5.48 to 9.84 kcal/mol for all 298 compounds examined. The verification of the model predictions (i.e., the vHTS) were carried out in 2013 in a separate investigation (Li et al., 2014). Here, of the 298 predicted active compounds, 21 were selected that span the similarity range from the original bioassay (i.e., from very similar to very dissimilar, using the Tanimoto coefficient to describe structural similarity). The compounds were experimentally tested based on the protocol used in original PubChem Bioassay Aid 846. Of the 21 identified compounds, 7 were confirmed active for a discovery rate of 33% (Li et al., 2014). Such rates are an order of magnitude greater than typical high-throughput screening approaches, which demonstrate the value of vHTS in this capacity. The seven active compounds are shown in Table 11.1.

TABLE 11.1 Seven Active Compounds From Factor XIa screening. The structures Shown Below Were Among the 296 Compounds Identified as Active by the Screening Done by Weis et al. and Are Confirmed as Active by Li et al. (2014) Structure

PubChem Compound ID

Exp. IC50 (mM)a

2211745

1.7

976343

21.13

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TABLE 11.1 Seven Active Compounds From Factor XIa screening. The structures Shown Below Were Among the 296 Compounds Identified as Active by the Screening Done by Weis et al. and Are Confirmed as Active by Li et al. (2014)dcont’d Structure

PubChem Compound ID

Exp. IC50 (mM)a

1144816

24.34

710799

29.89

710710

35.31

977731

36.16

1288249

40.40

a IC50 is the concentration of the compound required to reduce the biological response by 50%. With permission. Copyright 2014 AIChE J.

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5.2 CAMD: Signature Case Study: Reactant, Product, and Reaction Pathway Design Mario Eden, Nishanth Chemmangattuvalappil, and their colleagues are at the forefront of reactant, product, and process design for industrial processes. This initiated with the formulation of the RPF technique (Eden et al., 2004). Traditional process and product design in industry was decoupled with little feedback of one to the other, shown in Fig. 11.4. RPF models the situation as a coupled problem where the two different problems together guide the resulting solutions, shown in Fig. 11.5. Eden applied Signature to the RPF, redefining molecular groups for the molecular and process properties for optimum performance using Signature (Chemmangattuvalappil et al., 2009b). This allowed more integration between the two problems since the same atomic Signatures that are used as molecular groups for molecular design are now variables used to describe process properties. Previously, the two problems were integrated and solved together, but each part of the problem used different descriptors/molecular groups for each problem. Now, both problems are expressed using the same variables. It is also important to note that in this application of Signature, the heights are not predetermined. The height(s) necessary to capture the molecular descriptors used to create the process design QSPRs were calculated and then used to create all of the atomic Signatures used for molecular design. Signature’s canonical aspect enabled application of the RPF algorithm to different design problems regardless of the TIs used to create the QSPRs describing the process properties (Chemmangattuvalappil et al., 2009a, 2010).

FIGURE 11.4 The traditional formulation of process and product design. Traditionally, the processes were formulated and solved independently. MSA, mass separating agent. From Eden, M.R., Jørgensen, S.B., Gani, R., El-Halwagi, M.M., 2004. A novel framework for simultaneous separation process and product design. Chemical Engineering and Processing: Process Intensification 43, 595e608. With permission. Copyright 2003 Elsevier.

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FIGURE 11.5 The RPF of process and product design. RPF couples the two problems together and solves them simultaneously for solutions that solve both problems. MSA, mass separating agent. From Eden, M.R., Jørgensen, S.B., Gani, R., El-Halwagi, M.M., 2004. A novel framework for simultaneous separation process and product design. Chemical Engineering and Processing: Process Intensification 43, 595e608. With permission. Copyright 2003 Elsevier.

2D structural fragments were optimized into 3D fragments and used to redefine 3D TIs (Herring et al., 2012; Herring and Eden, 2014a,b). To optimize molecular design in the 3D application of the RPF algorithm, the genetic algorithm (GA) was included in the process and detailed as follows (Herring and Eden, 2015). Herring and Eden believed a spatial Signature based on 2D Signatures would retain all of the benefits of Signature (Visco et al., 2002; Faulon et al., 2003a) while including some of the discriminating power 3D molecular descriptors possess (Herring et al., 2012). The extension of 2D Signature into a spatial Signature involved taking 2D fragments and performing conformal studies on them. Spatial orientation is important when trying to design 3D molecular structures, leading to the discrimination between identical fragments with different orientations. From this, they established the spatial Signatures they used for their molecular design later in the algorithm. When creating 3D molecular structures from spatial Signatures, ideally a full conformal study based on the compounds in the training set is conducted to exhaustively search the chemical space described by the training set (Herring and Eden, 2015). However, this is computationally unfeasible. To attack the problem, Herring and Eden stochastically searched the chemical

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FIGURE 11.6 Genetic operators deletion, mutation, and insertion. The genetic operators (A) deletion, (B) mutation, and (C) insertion are demonstrated in a molecular context on the circled C. Deletion is the removal of a non-hydrogen atom, mutation is changing the bond type and/or the bonded atom, and insertion is the adding of a non-hydrogen atom. From Herring, R.H., Eden, M.R., 2015. Evolutionary algorithm for de novo molecular design with multidimensional constraints. Computers and Chemical Engineering 83, 267e277. With permission. Copyright 2015.

space using the GA. The GA allows Herring and Eden to sample different parts of the chemical space (via an initial population of different structures) and apply various genetic operators (e.g., mutation, insertion, deletion, crossover) to find some optimal 3D structures. The genetic operators are shown in Fig. 11.6 and Fig. 11.7. After each structure is generated, it undergoes conformational analysis to examine the differences between different structures. They are all oriented based on the same reference to identify the deviations of not only fragments,

FIGURE 11.7 Genetic operator: crossover. The genetic operator crossover is demonstrated in a molecular context on the circled C. Complementary parts of A and B (A1 and B2 respectively) are combined to form the child C. From Herring, R.H., Eden, M.R., 2015. Evolutionary algorithm for de novo molecular design with multidimensional constraints. Computers and Chemical Engineering 83, 267e277. With permission. Copyright 2015.

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but also the orientation of each fragment. Structures whose difference is below a threshold are considered the same structure, and the predictions from the QSPRs are averaged over the ensemble to account for the differences in geometries. As a proof-of-concept case study, Herring and Eden (2015) attempted to design molecules with boiling points between 75 C and 80 C and the target boiling point of 77.5 C. Using on a QSPR Basak et al. (1996) previously created with 2D and 3D molecular descriptors, they implemented the aforementioned process to remake the structureeproperty relationship in terms of spatial Signatures. From a database of 1023 compounds (Basak et al., 1996), 245 were chosen to make a training set. The 245 compounds had 194 unique height-2 signatures. After optimization and conformational analysis, the 245 height-2 signatures were transformed into 582 spatial signatures. The compounds listed in Table 11.2 had structure occurring most often in multiple rounds of structure creation and had experimental boiling points closest to the range of desired boiling points. The fitness value metric used expresses how close the predicted and desired boiling points are according to Eq. (11.1) from Venkatasubramanian et al. (1995): "  2 #! n X Pi  Pi;bar fi ¼ exp a (11.1)  2 Pi;max  Pi;min i

TABLE 11.2 Best Solutions From Study. Several Best Solutions Appeared Multiple Times Over Multiple Runs and Are Listed Here Solution

Predicted Boiling Point ( C)

Fitness Value

Ethyl acetate

77.3

0.99

2,2-Dimethylpentane

77.8

0.99

Isopropyl alcohol

78.0

0.99

3,4-Dimethyl-1-pentene

78.1

0.98

2,3-Dimethyl-2-butene

76.7

0.97

2,3,3-Trimethyl-1-butene

78.3

0.97

2-Methyl-1,3-pentadiene

76.4

0.95

Ethanol

78.7

0.94

1,3,5-Hexatriene

78.8

0.93

Carbon tetrachloride

75.9

0.9 Continued

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TABLE 11.2 Best Solutions From Study. Several Best Solutions Appeared Multiple Times Over Multiple Runs and Are Listed Heredcont’d Solution

Predicted Boiling Point ( C)

Fitness Value

2,2,2-Trifluoroethanol

79.3

0.87

4,4-Dimethyl-2-pentene

79.4

0.86

2-Butanone

79.5

0.85

2-Methyl-2-propanol

79.5

0.85

1-Butanal

75.5

0.85

Acetonitrile

79.7

0.82

1,2-Hexadiene

75.0

0.77

2,2,3-Trimethylbutane

80.0

0.77

2,4-Dimethylpentane

80.1

0.76 

Fitness value from Eq. (11.1) and the parameters are: Pi,min ¼ 75 C, Pi,max ¼ 80 C, Pi,bar ¼ 77.5 C, and a ¼ 1. From Herring, R.H., Eden, M.R., 2015. Evolutionary algorithm for de novo molecular design with multi-dimensional constraints. Computers and Chemical Engineering, 83, 267e277. With permission. Copyright 2015.

where a is the Gaussian decay rate, controlling width of the Gaussian distribution of values, Pi is the property of interest, Pi,min is the minimum acceptable value, Pi,max is the maximum acceptable value, and Pi,bar is the targeted value and the average of Pi,max and Pi,min. The function scores values close to Pi,bar highly and vice versa. It is important to note the equation is for properties in general, but is applied to boiling points in this specific instance.

5.3 CAMD: Signature Case Study: Ideal Structure Similarity Searching In the previous two case studies, the focus was on the outcome of the molecular design algorithm (Herring and Eden, 2015; Weis et al., 2008; Li et al., 2014). The work of Kayello et al. (2014) in developing cement shrinkage reducing admixtures (SRAs) is different in its approach. Instead of developing the models first and the associated interpretations later, Kayello et al. (2014) developed conjectures about behavior based on observations of the structure of the training set compounds and their properties, and then identified compounds to test in order to verify the conjectures.

The Signature Molecular Descriptor in Molecular Design Chapter j 11

To develop the conjectures about SRAs, a review of the available literature yielded information about the properties of compounds as chemical admixtures for use in concrete. In this field, the reduction of the surface tension of water will lower the stress in the concrete pores and, thus, reduce the risk of concrete cracking through the shrinkage process. Therefore, surface tension reduction can serve as a quickly evaluated proxy for the potential of a compound to act as an SRA. From a literature review, Kayello et al. (2014) created a training set of 12 compounds, shown in Table 11.3, and developed four conjectures regarding a compound’s reduction on the surface tension in a dilute mixture with water (Kayello et al., 2014): 1. Surface tension linearly varies with respect to alkyl group length attached to amines.

TABLE 11.3 The 12 compounds used to derive the 4 conjectures. Compound name, structure, and slope are provided. Slope is the change in surface tension as mole fraction changes with pure water as solvent. A more negative slope indicates the compound is more effective at effective at reducing surface tension at lower compositions. Compound

Structure

Monoethanolamine

Diethanolamine

Triethanolamine

Slope (mN/m)

H 2N

160

OH

HO

NH

HO

N

OH

OH

192

286

OH

2-(Methylamino)ethanol

H3C

Dimethylethanolamine

H3C H3C

NH

N

OH

OH

253

485

Continued

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SECTION j II Molecular Design

TABLE 11.3 The 12 compounds used to derive the 4 conjectures. Compound name, structure, and slope are provided. Slope is the change in surface tension as mole fraction changes with pure water as solvent. A more negative slope indicates the compound is more effective at effective at reducing surface tension at lower compositions.dcont’d Compound

Structure

2-(Ethylamino)ethanol

H3C

2-(Diethylamino)ethanol

Slope (mN/m) 486

NH

OH

N

H3C

CH3

716

OH

Methyldiethanolamine

334

OH N

H3C

1-Amino-2-propanol

OH

279

OH NH2

H3C

3-Amino-1-propanol

2-Amino-2-methyl-1-propanol

OH

H2N

508

CH3

HO

150

NH2

CH3

2-Methoxyethanol

H3C

O

OH

308

From Kayello, H.M., Tadisina, N.K., Shlonimskaya, N., Biernacki, J.J., Visco, D.P., 2014. An application of computer-aided molecular design (CAMD) using the signature molecular descriptorddpart 1. Identification of surface tension reducing agents and the search for shrinkage reducing admixtures. Journal of the American Ceramic Society 97, 365e377. With permission. Copyright 2014.

The Signature Molecular Descriptor in Molecular Design Chapter j 11

2. Surface tension varies with respect to how amines are positioned. 3. Surface tension increases when nitrogen atoms at the molecular core are replaced with alkyl groups. 4. Surface tension increases when hydroxyl groups are replaced with alkyl groups. Fourteen compounds were identified in order to evaluate the four conjectures. Experiments on surface tension reduction of these 14 compounds confirmed the four conjectures. The experiments evaluated “slope,” defined as the change in surface tension of the pure water solvent as a small amount of solute is added. A more negative slope indicates a compound is more effective at reducing surface tension at dilute compositions and, thus, may be more desirable as an SRA. Following this experimental evaluation, a QSPR was created for this surface tension reduction (i.e., an approximation of the limiting slope) using the

TABLE 11.4 Admixture Confirmatory Study Results. Admixtures, Group, and Microstrain Are Reported. Note the Maximum Strain Is Realized When No Admixture is Present. Upon Introduction of an Admixture, Strain Is Reduced. The Computer-Aided Molecular Design (CAMD) Compounds Are Those Identified in This Study and Compare Favorably With the Commercial Set Admixture

Group

7 Day Net m-Strain

None

Control

559

C1

Commercial

261

C2

Commercial

239

2-Propoxyethanol

Training set

319

2-Ethoxyethanol

Training set

480

2-Butylaminoethanol

Computer-aided molecular design (CAMD)

308

Butylmethylamine

CAMD

229

Diethylmethylamine

CAMD

288

3-Ethoxypropylamine

CAMD

352

3-Propoxypropylamine

CAMD

252

From Shlonimskaya, N., Biernacki, J.J., Kayello, H.M., Visco, D.P., 2014. An application of computer-aided molecular design (CAMD) using the signature molecular descriptorepart 2. Evaluating newly identified surface tension-reducing substances for potential use as shrinkagereducing admixtures. Journal of the American Ceramic Society, 97, 378e385. With permission. Copyright 2014.

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14 compounds with the independent variables as height-1 atomic Signatures. The resulting QSPR, which was developed using a forward-stepping multiple linear regression approach, identified four atomic Signatures as independent variables. The regression coefficients of these four atomic Signatures were all supported by the previous conjectures as well (Kayello et al., 2014). At this point, the 14 compounds tested and evaluated experimentally for surface tension reduction in water were used as the training set for the inverse design problem. Thus, Diophantine equations were created from the height-1 atomic Signature fragments for these 14 compounds and solved using a brute force algorithm (Weis et al., 2005). The solutions were then scored by the previously developed QSPR for surface tension reduction. The promising solutions (i.e., molecular Signatures) were then transformed to structures (Churchwell et al., 2004; Martin, 2012; Weis et al., 2005; Weis and Visco, 2010). Some of the structures that showed strong reduction in the surface tension of water were then subject to actual shrinkage tests (among other evaluations) and performed comparable to commercially available products (Shlonimskaya et al., 2014). Results are shown in Table 11.4 and compare all of the admixtures to the blank (i.e., no admixture present).

6. CONCLUSION Signature was introduced about in 1994 as a tool for structural elucidation studies. In 2003, Signature was explored as a molecular descriptor in QSAR/ QSPR studies. When this was proven successful, Signature emerged as the key part of molecular design algorithms across a variety of areas, including as the descriptor in various biological platforms and has evolved to include a way to discriminate between stereoisomers, a known limitation of the original 2D Signature formulation. As more researchers employ the Signature molecular descriptor in their work across many fields, its usage within CAMD and in related areas should grow accordingly.

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Chapter 12

Integrated Process and Product Design Optimization F.P. Bernardo University of Coimbra, Coimbra, Portugal E-mail: [email protected]

1. INTRODUCTION Integrated chemical product and process design may be understood as the specification of a chemical-based product together with the design of the correspondent manufacturing process. The product/process specification should take into account product functionalities and attributes valued by customers, as well as feasibility and profitability of production at a commercial scale. Generic methodologies to guide the solution of such an integrated problem along the way from customer needs to product manufacturing have already been proposed (Cussler and Moggridge, 2011), as well as procedures more focused on particular product categories (Wibowo and Ng, 2001, 2002; Fung and Ng, 2003; Fung et al., 2007; Cheng et al., 2009; Martı´n and Martı´nez, 2013). The basic idea under these methodologies is to drive decisions by product quality factors related to customer satisfaction that, once identified, are then translated to a product/process technical specification. Consumer formulated products, relevant in different economic sectors (agrochemical, pharmaceutical, cosmetic, food), are mixtures of several ingredients combined in microstructured systems, such as gels, emulsions, pastes, powders, or foams. Their specific microstructure is recognized as a central aspect in their design, linking product and process decisions: initially created by the manufacturing process, product structure influences product functionalities, expressed during product use (Hill, 2004, 2009). For relatively simple molecules and homogeneous mixtures with welldefined target properties, there are design methods, known as CAMD (computer-aided molecular design), able to systematically explore a large design domain through the combination of a reduced set of fundamental units, often molecular groups (Achenie et al., 2002; Gani, 2004; Samudra and Sahinidis, 2013). The extension of these systematic searches to microstructured formulations is a challenging problem, mainly due to the difficulty Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00012-5 Copyright © 2016 Elsevier B.V. All rights reserved.

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in defining basic units and predicting relevant properties (Gani and Ng, 2015). Some contributions to effectively solve it have already been proposed (Conte et al., 2011; Mattei et al., 2012). In this chapter, we first present a recently published conceptual model for chemical product/process design (Bernardo and Saraiva, 2015), which we believe is a necessary basis to develop more systematic design methods, namely for consumer formulated products. The model is basically a block diagram linking what we call the three central design functions (quality function, product function, and process function), and will be presented in Section 2. Although basic, such model may be useful to clearly state the design problem, organize available information, and identify important variables and relationships. On top of this basic structure, we then propose (Section 3): (1) general optimization formulations integrating both product and process decision variables; (2) a two-stage decomposition of the product design problem, useful to search for new ingredients of formulated products; and (3) optimization formulations to systematically study product/process interactions and trade-offs. Finally, in Section 4, three examples are provided: (1) liquid perfumes, (2) a cosmetic emulsion, and (3) a pharmaceutical ointment.

2. CONCEPTUAL MODEL In this section, we first try to settle and define basic concepts in chemical product design, which are then organized in the form of a simple block diagram identifying key variables and relationships. The domain of chemical products under consideration includes molecules, formulations, and physicochemical devices. A common aspect to this wide range of products is that they are designed and then manufactured to provide certain functionalities under a given use environment and thus satisfy customers’ needs. The product itself is defined by a given compositiondentities that constitute the productdand structuredhow those entities are organized in space. Composition and structure may then refer to different product attributes at different scales, from the molecular to the product scale: composition may refers to the molecular entities in a liquid mixture or the several materials and components of a discrete assembled product, and structure may refer to the specific microstructure of a colloidal system or the architecture and geometry of a macroscopic device. The specific composition and structure of the product is in part the result of its manufacturing process, which then should also be considered as part of the product design problem. Product/process integration is particularly relevant when specific product microstructural attributes strongly depend on the selected manufacturing technologies and respective operating conditions. Product functionalities and performance should be equated using quantifiable and measurable indices, preferably having physicochemical meaning. Performance metrics are either constitutive properties, more directly related to product composition and structure (e.g., viscosity of a liquid mixture), or

Integrated Process and Product Design Optimization Chapter j 12

operational properties, which are the result of the product use process and thus a more direct measure of product functionality (e.g., soil solubilization capacity of a detergent). Operational properties depend on constitutive properties and also on specific conditions of the product use process, which then also plays an important role in the design problem. In the case of industrial products, such as solvents or surfactants, the product use process is a downstream chemical process, while in the case of consumer products, it is the final use of the product in a specific environment, which in the case of foods, cosmetics, and pharmaceuticals, includes the human body. When human senses play an important role, it may be hard to define operational properties in precise physicochemical terms. In such cases, one has to rely on sensorial assessment by customers, which in general is more expensive and less accurate than physicochemical analytical techniques. Given the discussion above, three key components of the product design problem are distinguished: the product itself, its manufacturing process, and its use process. Fig. 12.1 gives a symbolic representation of this trio. The complete definition of these three components is made over five different design domains, as follows: 1. product manufacturing process: how the product is produced; 2. product composition and structure: what the product is at the molecular and/or supramolecular scales; 3. product use conditions: how the product is used in a given environment and the conditions imposed by that environment; 4. product performance: how the product performs in terms of constitutive and/or operational properties; 5. product quality: how the product is valued by customers in terms of qualitative product attributes, also known as quality factors (e.g., skin feeling of a cosmetic cream, cleaning power of a detergent).

FIGURE 12.1 Symbolic representation of three key components of the product design problem. The manufacturing process (I), driven by the inward arrows, confers a given composition and structure to the product, which then attains a given state (II); product final functionality (e.g., release of an active ingredient) is expressed during product use (III), where external conditions, represented by the outer circumference, play an important role.

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These five domains are related through three basic design functions, which constitute the backbone of our conceptual model for chemical product design, as depicted in Fig. 12.2: 1. the process function, which relates product composition and structure (pair {d1,x1}) with manufacturing process variables (design variables d2 and operating variables z2); 2. the property function, which relates product performance metrics (p) with product composition and structure (pair {d1,x1}) and product use conditions (z1); and 3. the quality function, which relates product quality factors, directly valued by customers, with product performance metrics (p), also designated as quality variables. The block diagram of Fig. 12.2, when read from left to right, represents the analysis of the product/process system: (1) the manufacturing process, given particular values of the design variables d1 and d2 and operating conditions z2, produces a product with the state x1; (2) this product, under conditions z2, has properties p; and (3) some of these properties are performance metrics that determine product quality in terms of quality factors directly valued by customers. A first sketch of this model was previously presented by us and our collaborators (Bernardo and Saraiva, 2005; Costa et al., 2006), now being refined and simplified. Cisternas and Ga´lvez (2006) and Cisternas (2007) also proposed a fundamental description of the chemical product design problem that shares several aspects with our model, namely that the product is a system depending on a set of components, their organization (structure), and a specific interaction with the environment. In other words, this is our property function, with the performance p being a function of the sets of variables d1, x1, and. z1. A distinctive and important feature of our model is the differentiation between product design variables d1, which are process independent, and product

index 1 refers to the product and index 2 to its manufacturing process d1 – Product design variables (process-independent) d2 – Process design variables x1 – Product state variables (process-dependent) z1 – Product operating variables (use conditions) z2 – Process operating variables p – Product performance metrics (including constitutive and operational properties)

FIGURE 12.2 Conceptual model for chemical product design.

Integrated Process and Product Design Optimization Chapter j 12

state variables x1, which depend on the manufacturing process. Product composition and structure variables belong to sets d1 or x1, depending on whether or not these variables are process independent. If the process confers structure to the product but does not alter its global composition, such as in the production of a structured formulation from individual ingredients, then set d1 includes that ingredients and their global proportion, and x1 represents product structural attributes (e.g., droplet size distribution of an emulsion). If, however, the process determines both product composition and structure, then set x1 includes both types of variables. For instance, in the production of a crystalline solid, both purity and crystal size are process-dependent variables. Table 12.1 clarifies the meaning of all variable sets by using three simple examples, corresponding to three basic product/process typologies: (1) process does not affect product global composition nor its structure, (2) process affects product structure but not its global composition, and (3) process affects both product composition and structure.

2.1 Decomposition of the Property Function for Product Operational Properties In the case of operational properties, the property function may be decomposed into constitutive models, describing more fundamental properties of the materials from which the product is made, and product use models, describing physicochemical processes that take place during product use (Fig. 12.3). These depend on properties of the materials that make up the product (constitutive properties q1), and also on characteristic materials and conditions of the surrounding environment or resulting from specific product/environment interactions (parameters q3; index 3 refers to the surroundings). In the example given in Fig. 12.3 (pharmaceutical ointment applied on skin), a key process is the transport of a drug molecule from the ointment to the outer surface of the skin and then across several skin layers. The drug diffusion coefficient across the ointment layer is an example of a constitutive parameter q1, while the mass transfer resistances of the several skin layers are important parameters within the set q3. The product/environment interaction may function in both ways: product composition and structure may change during product use, and on the other hand, product use may induce alterations in the surrounding environment. An example of the first case is the change in the ointment microstructure after application on skin, such as partial destabilization of droplets (it is an emulsion-type ointment). Interaction in the reverse way occurs when the ointment is formulated with permeation enhancers, which are specific molecules that interact with skin lipids, disordering them and thus enhancing drug diffusion through skin (Hadgraft, 2001). With this description of the property function, the product/process design problem may be viewed as the design of two processes in series from which

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Product/Process Typology

Liquid Mixture/Trivial Mixing Process

Structured Formulation/Process Affects Product Structure but Not Its Global Composition

Structured Formulation/Process Affects Product Composition and Structure

Product example

Perfume

Cosmetic emulsion

Microcapsules containing a drug solution enclosed by a polymeric wall

d1

Individual components and their proportion

Individual components and their proportion

Drug, solvent, polymer

d2

Process configuration and equipment design

x1

Empty set, since product state is processindependent (assuming negligible losses during processing)

z2

Process degrees of freedom and input conditions

z1

Conditions affecting fragrance evaporation and dispersion

Shear stress during application on skin

External conditions affecting drug release

p

Concentration of fragrances in inhaled air

Emulsion rheology during application on skin

Rate of drug release from the capsule

Quality factor

Perceived odor

Skin feeling

Controlled drug delivery and effects thereafter

Droplet size

Capsule size, wall thickness, drug concentration inside capsule

SECTION j III Customer Products

TABLE 12.1 Examples of Variable Sets in the Proposed Conceptual Model (Fig. 12.2) for Different Product/Process Typologies

Integrated Process and Product Design Optimization Chapter j 12

Example of an emulsion-type pharmaceutical ointment for systemic drug absorption d1 – drug + excipients and corresponding mass fractions. x1 – droplet size z1 – ointment volume applied on skin, area of application, patient blood volume, time between consecutive applications. θ 1 – drug partition coefficient between dispersed and continuou s phases of the ointment, diffusion coefficient in continuous phase, partition coefficient between skin outer layer and continuous phase,... Product use model: mass transfer model describing transdermal drug delivery from the emulsion vehicle. θ 3 – mass transfer resistance of the several skin layers, drug pharmacokinetic parameters. p – temporal profile of drug concentration in plasma, mean deviation of this profile from a target value.

FIGURE 12.3 Structure of the property function in the case of operational properties and exemplification of variable and parameter sets with the case of a pharmaceutical ointment.

final product performance results: the product manufacturing process, upstream of the product itself, and the product use process, downstream of the product itself, this last one incorporating materialeproperties relationships (constitutive models). This perspective therefore stresses the importance of traditional chemical process engineering in the design of new chemical products.

2.2 Basic Formulation of Product Design Problems The process function is implicitly represented by the set of equations: f2 ðd1 ; d2 ; z2 ; x1 Þ ¼ 0:

(12.1)

The number of equations is n2 ¼ dim(x1), and product state variables x1 are a set of dependent variables. In a similar manner, the property function is stated as n1 ¼ dim(p) equations: f1 ðd1 ; x1 ; z1 ; pÞ ¼ 0:

(12.2)

Using the decomposition of Fig. 12.3 above, one has: 1. constitutive models defined by n1c ¼ dim(q1) equations: f1c ðd1 ; x1 ; q1 Þ ¼ 0;

(12.3)

2. product use models defined by n1 equations: f1u ðd1 ; x1 ; z1 ; q1 ; q3 ; pÞ ¼ 0:

(12.4)

Eqs. (12.4) and (12.2) are equivalent forms of the property function. Both representations (12.1) and (12.2) are here given in a generic form without making distinction between algebraic and differential equations or

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between continuous and discrete variables. Set d1, for instance, may include binary decisions relative to the presence of a particular chemical species in a formulation, and set f2 may include differential equations modeling the temporal evolution of a particular process step. Also, intermediate state variables are not specified: in the process function (12.1), these may refer to intermediate product states during processing, while the property function (12.2) may involve primary material properties q1 affecting the final property of interest p. Globally, once the degrees of freedom d1, d2, z1, and z2 are specified, the model (12.1) þ (12.2) may be solved to predict product properties p. The quality function does not have a complete quantitative description since quality factors (or customer needs) are, by definition, qualitative propositions stating product attributes as valued by customers. These attributes must first be translated into objective product performance specifications of the type p w p*, where p* are target values for the performance metrics p. In some cases, this translation of customer needs into quantitative specifications is fairly well understood, such as for industrial products with well-defined target performance (e.g., solvents, surfactants, flocculants) or in the case of some attributes of consumer products [e.g., consistency of semisolid products, related to rheologial properties (Wibowo and Ng, 2001); performance of detergents, well-defined by measurable indices such as the critical micelle concentration (Fung et al., 2007); sprayability of liquid formulations, determined by properties such as surface tension and viscosity (Conte et al., 2011)]. More difficult situations are often related to human sensorial attributes that are hard to define in physicochemical terms, such as “smoothness of a cosmetic cream” or “mouthfeel of a food product.” Human perception of color and sound is fairly well understood, while touch, taste, and smell are poorly understood senses. It is thus still difficult to define adequate metrics p to describe product quality factors related to these senses (Cussler and Moggridge, 2011; Cussler et al., 2010). One then has to rely on sensory panel testing, where product samples are directly evaluated by users in terms of a sensorial performance index p, often defined along an arbitrary scale (e.g., appraisal from 1, unsatisfactory, to 5, very good). The obtained classifications should then be correlated with known properties and/or composition of the samples, using specific methods and statistical tools (Civille and Carr, 2015). These sensory tests and analysis should be viewed as a last resort since product direct assessment through indexes p measurable in the laboratory is more systematic, cheaper, and faster, particularly in earlier stages of conceptual and exploratory product design. Once quality factors are effectively translated into a set of performance metrics, a quantitative treatment of the quality function is relatively simple. For each performance metric p, one may define rigid restrictions of the type jp  p*j  d, with d being a given tolerance, or having the more general form g(p,p*)  0. In alternative, a continuous perspective of quality loss may be

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adopted using Taguchi loss functions that usually have a quadratic form: loss L equals to k(p  p*)2, where k is a loss coefficient estimated from customer satisfaction data (Phadke, 1989; Bernardo et al., 2001). Ultimately, a global loss function L(p,p*) may be constructed (or a complementary function of customer satisfaction), integrating individual metrics pi, using, for instance, a weighted sum. The weights attributed to each quality factor must be determined from carefully designed customer tests (Bagajewicz, 2007; Smith and Ierapetritou, 2009). Back to Fig. 12.2, we can now read it from right to left, which is the natural design route, and thus formulate the product design problem as a series of the following three subproblems: Problem 1. Translate product quality factors, as valued by customers, into a set of product performance metrics p, preferably with physicochemical meaning. Then, quantify desired product performance using restrictions of the type g(p,p*)  0 or associated loss functions L(p,p*). Problem 2. Given the above quantitative models and restrictions for product quality, find {d1,x1} (and eventually a subset of z1), such that f1(d1,x1,z1,p) ¼ 0. This is called the inverse search problem or the inversion of the property function, which aims to find a material or product with prespecified properties. Problem 3. Find {d2,z2}, such that f2(d1,d2,z2,x1) ¼ 0. This is the classical process design problem whose goal is to specify a manufacturing process able to produce product state x1. In short, these three problems may be simply stated as the inversion of the quality, the property, and the process functions, as depicted in Fig. 12.2 when read from right to left. A detailed discussion of each one of them falls outside the scope of this chapter, being given in Table 12.2 a summary of key aspects. As can be seen from the table, a diverse blend of sciences and methods may be required, usually going beyond traditional chemical engineering domains. Regarding problem 2, it should be stressed that the initial domain of interest may be quite large and embrace very diverse alternatives, since in an early design stage we are seeking for basic product concepts and associated technologies able to provide functionalities p, while materials to be used and other product details are still unknown. Overall, and except for routine simple cases, the solution of problems 1, 2, and 3 does not proceed as a linear sequence. After a first product performance specification and a first generation/selection of product concepts, one often has to refine the analysis of selected alternatives, and thus, referring to Fig. 12.2, proceed from left to right. Specifications p* are then revised, and a new, more focused, design route (from right to left) is initiated. These alternate routes in opposite directions, synthesis/analysis cycles, are repeated until a satisfactory solution is attained, subject to time and budget limitations. In the next section, basic optimization formulations of these design problems will be presented and some issues regarding their application to the design of formulated consumer products discussed.

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Problem 1: Inversion of the Quality Function

Problem 2: Inversion of the Property Function

Problem 3: Inversion of the Process Function

Input information

Quality factors, organized and ranked (from marketing studies)

Specification of product performance (p variables with target values p*)

Specification of the product to be produced {d1,x1}

Solution

Function of global quality loss L(p,p*)

Product {d1,x1,z1} with performance close to p*

Manufacturing process {d2,z2} able to produce product with state x1

Subproblems

l

l

l

Hard issues

l

l

Useful sciences and methods

l

l

l

translate quality factors into performance metrics p determine individual loss functions L for each metric pi construct global model integrating all individual metrics pi

l

objectify complex and/or subjective attributes specify product performance without restricting the domain of the product itself

l

processual analysis of product use consumer evaluation tests and statistical analysis of results science of human perception

l

l

l l

l

l

l l

l

delimit domain of interest generate plausible alternatives within that domain select the most promising ones detailed design of winning alternatives

l

large and diverse domain (product concepts and materials) how to generate alternatives (random, combinatorial, or incremental strategies) how to gradually “sieve” alternatives (hierarchical design strategy)

l

synthesis, design, and scale-up of structuring processes (at the nano- and microscales)

techniques of creative problem solving combinatorial and discrete optimization several methods to estimate materials properties analysis and modeling of the product use process

l

traditional chemical engineering sciences and methods

l l

select raw materials, technologies, ancillary materials process synthesis process analysis and optimization

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TABLE 12.2 General Characteristics of the Three Central Design Problems

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3. OPTIMIZATION FORMULATIONS FOR PRODUCT/ PROCESS DESIGN Given the previously mentioned representations for the process function, Eq. (12.1), the property function, Eq. (12.2), and a quantitative model of product quality (restrictions g(p,p*)  0 and/or global loss function L(p,p*)), it is simple to write a mathematical formulation for simultaneous product/process design optimization, at a higher level of abstraction. Let F be a global objective function to be maximized, accounting for loss of product quality L and manufacturing process costs. The optimization problem is then: max Fðd1 ; d2 ; z1 ; z2 ; p; p Þ ½product=process performance

d1 ;d2 ;z1 ;z2

(12.5)

s.t. f1 ðd1 ; x1 ; z1 ; pÞ ¼ 0 ½property function f2 ðd1 ; d2 ; z2 ; x1 Þ ¼ 0 ½process function gðp; p Þ  0 ½product performance restrictions hðd1 ; d2 ; z1 ; z2 ; x1 Þ  0 ½other restrictions: The design degrees of freedom are here sets d1, d2, z1, and z2, i.e., product and process design and operating variables. If product and process design problems are decoupled, one obtains a sequence of two problems. First, the product design problem, without considering limitations imposed by the process function: max F1 ðd1 ; x1 ; z1 ; p; p Þ ½product performance

d1 ;x1 ;z1

(12.6)

s.t. f1 ðd1 ; x1 ; z1 ; pÞ ¼ 0 ½property function gðp; p Þ  0 ½product performance restrictions hðd1 ; x1 ; z1 Þ  0 ½other restrictions: The result of this problem is the optimal product fd1 ; x1 ; z1 g, for which one then looks for an optimal manufacturing process: max F2 ðd2 ; z2 Þ ½process performance d2 ;z2

s.t.

  f2 d1 ; d2 ; z2 ; x1 ¼ 0½process funtion hðd2 ; z2 Þ  0 ½other restrictions:

(12.7)

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The practical concretization of these formulations poses two main difficulties, particularly in early design stages. First, when alternative basic product concepts and principles of functioning are still being explored, a comprehensive definition of the search domain {d1,x1,z1} is still lacking, and thus systematic searches are hard to perform. Second, even when the design domain is clear, quantitative property functions may be very hard to construct. In the development of a dermal product, for instance, one may be initially open to different physical forms of the product, including paste, cream, lotion, gel, spray, or patch. This set of physical systems corresponds to a large and diverse physicochemical domain {d1,x1,z1}, difficult to enumerate and even more difficult to explore in a systematic and efficient way. The analogous problem in process design is to choose basic technologies, unit operations, and their arrangement. In this case, however, there are more developed tools to describe basic processing units, in particular for fluid phase processing, and thus solve problem (12.7) performing a systematic search within the domain {d2,z2} (Biegler et al., 1997). For relatively simple molecules with well-defined target performance (e.g., solvents for liquideliquid extraction), a systematic approach is possible if property functions can be equated based on a finite number of fundamental units whose different combinations produce alternative molecules. If those fundamental units are molecular groups, then the property functions are group contribution methods, already developed in different domains (solvents, polymers, and even more complex molecules). The design problem then reduces to find combinations of those fragments that produce molecules with good performance, which may be formulated as a discrete optimization problem. This is a particular case of problem (12.6) for which the design variables d1 are the number of fragments of the type k in the molecule (integer variables), with k ¼ 1,., K, and K being the number of fundamental units considered. In the chemical engineering literature, this approach to molecular design is known as computer-aided molecular design (CAMD) (Achenie et al., 2002). The extension of CAMD to fluid phase mixtures is, in principle, simple, with the set d1 now including molar fractions of the several species in the mixture (continuous variables). Naturally, one here needs reasonable models to estimate mixture properties. On the other hand, the extension of CAMD methods to more complex formulations having specific and complex ingredients and characteristic nano- or microstructures is still a new territory to be explored. Formulated consumer products most often belong to this category, including a diverse range of colloidal and/or dispersed systems such as gels, emulsions, pastes, powders, and foams. In these complex domains, besides molecular species and their concentration, design variables {d1,x1} need to include a representation of the several possible microstructural attributes, such as size and shape of dispersed phases or thickness of a nanolayer. Further, one then needs to estimate how composition and structure affect key product properties, which clearly may be hard to accomplish, even in relatively narrow

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product domains. We believe that an effective approach to this problem should begin with the definition of tractable product subdomains of interest (e.g., oilin-water emulsions with a thickened aqueous phase) and incorporation of specific knowledge from corresponding industrial sectors, including databases of common ingredients and their main functionalities, and also qualitative formulation rules (Wibowo and Ng, 2002; Fung et al., 2007; Cheng et al., 2009). These efforts have already began, both using systematic searches in particular subdomains (liquid formulations, Conte et al., 2011; emulsion-based products, Mattei et al., 2012), or through knowledge-based approaches that incorporate knowledge gained in previous development cases (Lee et al., 2014). The two following subsections further explore formulations (12.5) to (12.7): Section 3.1 presents a decomposition of problem (12.6) that may be helpful to guide the selection of ingredients for a formulated product, and Section 3.2 purposes some simple optimization tools to systematically study product/process interactions and trade-offs. Finally, Section 3.3 briefly discusses the selection of computational platforms to efficiently solve the proposed optimization problems.

3.1 Two-Stage Approach to Invert the Property Function When operational properties may be equated independently of {d1,x1} (structure of Fig. 12.3 without dashed arrow), the following decomposition of the product design problem (12.6) into two subproblems may be useful (Eden et al., 2004). First, we find constitutive properties q1 and use conditions z1 corresponding to the desired functionality (here restrictions h($)  0 are omitted): max F1 ðz1 ; p; p Þ ½product performance z1 ;q1

(12.8)

s.t. f1u ðz1 ; q1 ; q3 ; pÞ ¼ 0 ½product use models gðp; p Þ  0 ½product performance restrictions: Then, we look for a product composition and structure {d1,x1} matching those constitutive properties. If q1 is the solution of the first problem, and using a quadratic deviation criterion, the second problem is:  2 min q1  q1 (12.9) d1 ;x1 ;q1

s.t. f1c ðd1 ; x1 ; q1 Þ ¼ 0 ½constitutive models gðp; p Þ  0 ½product performance restrictions:

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For the sake of simplicity, problem (12.9) considers a single parameter q1, but clearly several parameters may be handled, using, for instance, a weighted sum of quadratic deviations. Problems (12.8) and (12.9) are thus a two-stage approach to invert the property function, using constitutive properties q1 as intermediate guiding parameters. This decomposition strategy is of direct application in the case of industrial products whose performance may be equated without specifying their molecular composition (e.g., solvents, antisolvents, refrigerants). For instance, in the design of a solvent for liquideliquid extraction, one may first determine what should be the solvent solubility properties q1 in order to attain a given extraction efficiency p*, and without specifying the solvent moleculed problem (12.8). Then, in a second stage, we look for a molecule or mixture of molecules having those solubility propertiesdproblem (12.9). The application of this two-stage approach to more complex formulated products and respective use processes is an issue that has not yet been fully explored. Referring to the ointment example of Fig. 12.3 and with the drug molecule already chosen, such an approach corresponds to first determine what should be the drug equilibrium and kinetic parameters in order to attain a target drug concentration in plasma, and only after that to choose an adequate ointment microstructure and composition. In practice, this strategy may not be fully applicable due to difficulties in solving problem (12.8) independently of all variables {d1,x1}. Nevertheless, it may be possible to apply it partially, solving problem (12.8) for some key parameters q1 that will then serve as a guide to select a related subset of design variables {d1,x1}. An example of this kind will be presented in Section 4.3, where the substitution of some ingredients of a pharmaceutical formulation is equated in the form of a pair of problems like (12.8) and (12.9).

3.2 Integrated Product/Process Design Once a basic product concept is selected, further development should integrate the process function and thus consider product/process interdependency. In terms of the optimization problems previously presented, it is likely that one begins with a sequential approach, first solving the product design problem (12.6) and then using its solution S1 ¼ fd1 ; x1 ; z1 g as input to problem (12.7), of which solution S2 ¼ fd2 ; z2 g is the first design of the manufacturing process. In a later, more detailed design stage, both property and process functions are completely quantified, and one may then fully integrate both problems in a single problem like (12.5), of which solution S12 corresponds to an optimal balance between product and process aspects. The solutions resulting from the sequential approach S1 and S2 clearly make up a feasible solution to the integrated problem (12.5). Therefore, the integrated solution S12 is better than or equally good as the sequential solutions. In terms of the global objective F, one may then write: F(S12)  F({S1,S2}).

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Product/process interactions and trade-offs may be systematically studied using multiobjective optimization techniques applied to the integrated problem (12.5). In particular, nondominated (Pareto) solutions, regarding two competing objectives, such as product quality L versus manufacturing costs C, may be obtained using two common techniques: the method of weights or the ε-constraint method. In the first case, L and C must be expressed in the same basis (e.g., EUR per kg of product), and a global objective is defined as a weighted sum of the two conflicting objectives [this approach is already somehow implicit in formulation (12.5)]. The product/process optimization problem is then solved for different values of the weights. In the ε-constraint method, one solves the problem: min C

(12.10)

s.t. L  ε; for different values of ε ( or, equivalently, the problem min L, subject to C  ε). When using this approach, besides the Pareto curve, one generates additional relevant information. First, the Lagrange multiplier of the constraint L  ε at the optimum solution C* (where the constraint is active) is l ¼ dC*/dε. This is a rigorous measure of the price one has to pay to produce a product with higher performance. Second, when problem (12.10) is solved for decreasing values of ε, one may reach a limit below which the problem is infeasible. This is the maximum product performance (minimum quality loss) that is attainable with the production process being considered. These topics will be illustrated by the example of Section 4.2.

3.3 Computational Implementation Both the property and the process function may consist of a complex system of algebraic and/or differential equations that have to be included as equality restrictions in problems (12.5) to (12.9). There are two main approaches to handle these large-scale systems of equations: (1) equation-oriented approach, where all equations are explicitly handled as equality constraints [formulation (12.5) above], and (2) modular approach (also known as black-box optimization), where dependent variables p and x1 are calculated in external modules [formulation (12.5) above, but with p ¼ f1(d1,x1,z1) and x1 ¼ f2(d1,d2,z2), f1 and f2 being external black-box functions]. The equation-oriented approach may be more effective (in terms of global optimality) and also more efficient (less computational time), since all equations are explicitly handled by the optimization algorithms used. A general platform like general algebraic modeling system (GAMS) may then be used, taking advantage of state-of-the-art optimization algorithms, including global

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optimization solvers for nonlinear programming (NLP) and mixed-integer nonlinear programming problems (GAMS Development Corporation, 2015). The downside is that all equations have to be programmed and differential equations decomposed into algebraic ones (GAMS only handles algebraic equations). On the other hand, the modular approach facilitates the use of previously programmed models to predict product properties p or product states x1, including large-scale models involving differential equations and models available in commercial software. The drawback is in the use of black-box functions, which may render in more computational time and added difficulties in assuring global optimization (because the optimization solver is blind to the analytical form of black-box functions). In sum, the equation-oriented method is better to perform a rigorous optimization, but it may be harder to implement in practice. The modular approach is more flexible and easier to implement, but global optimization guarantees are weaker. The example of Section 4.2, presented as follows, resulted in a relatively small problem (74 variables and 85 restrictions). An equation-oriented method was thus adopted and the problem formulated and solved in GAMS. The example of Section 4.3 handles a large-scale mass transfer model, previously implemented in Mathematica (Wolfram MathWorld, 2015), and thus a modular approach was adopted. The optimization layer was also implemented in Mathematica, using the internal function NMinimize (in particular, the NeldereMead method). All calculations were made in a PC with an Intel Core2 Quad Processor Q9400 at 2.66 GHz.

4. EXAMPLES Three examples are here provided. The first one, liquid perfumes, only aims at illustrating how design variables and relationships are organized according to our conceptual model. The second one, a cosmetic emulsion, is a relatively simple case where fully quantitative models have been constructed (but only regarding a single aspect of product quality), and thus interactions and trade-offs between product quality, product composition, and manufacturing costs may be fully explored. Finally, in the third example, formulation of a pharmaceutical ointment, one has a detailed property function based on which a base formulation may be optimized and the substitution of some of its ingredients equated.

4.1 Perfumes The quality of liquid perfumes and other products containing volatile fragrances (e.g., home fragrance diffusers, textiles) obviously depends on the odors that are perceived and its intensity and duration. A simple model of perception is based on a single parameter, the odor value OV, which is the ratio between the effective concentration of a given fragrance i in the air (Ci) and a

Integrated Process and Product Design Optimization Chapter j 12

threshold value (Thi), above which the fragrance is perceived by humans (determined from standard perception tests) (Mata et al., 2005): OVi ¼

Ci Thi

(12.11)

The perception model then states that the fragrance more strongly perceived by the human nose is the one having the highest odor value. For a liquid perfume with components i, i ¼ 1,., N, including fragrances, solvents, and eventually other auxiliary substances, the perceived component is then component i*, such that OVi ¼ maxi ðOVi Þ: The odor value may be defined as a function of time t after fragrance evaporation and distance z from source. The corresponding perceived substance is thus i*(t,z). This function is an important component of the quality function, relating objective performance metrics (OVi) with a product characteristic directly perceived by consumers (perceived fragrance i*). Moving now to the property function, we need to relate the performance metrics OVi with the product composition and use conditions. Maximum values of Ci and OVi are attained close to the product/air interface and, in the case of a liquid product, may be estimated through a vaporeliquid equilibrium model: p M i 1 (12.12) OVmax;i ¼ gi xi i Thi RT Here, xi is the molar fraction in the liquid phase, gi the activity coefficient in the liquid phase, pi the vapor pressure of pure i, Mi the molar mass, T the temperature, and R the ideal gas constant. Actual values of OVi(t,z) may be estimated with a transient model of fragrances evaporation and subsequent transport in the gas phase. If only maximum values of OV are considered, Eq. (12.12) is already the desired property function, where: l

l l

Product design variables d1 are components i and their molar fraction in the liquid xi. The only product use variable z1 is the temperature of use T. Parameters gi, pi , Mi, and Thi depend on the above variables.

Liquid perfumes are made by a trivial mixing process, and hence, assuming evaporation losses are negligible during processing, molar fractions xi are not altered by the process and thus belong to the set of process-independent design variables d1. The set of process-dependent state variables x1 is then empty, and the process function does not influence product formulation.

4.2 A Cosmetic Emulsion A moisturizing lotion is an oil-in-water emulsion with around 10e20% of occlusive and emollient oils and a thickened aqueous phase. Here, we only focus on one quality factor, the so-called skin feeling, which refers to the

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sensations experienced during lotion application on skin (Bernardo and Saraiva, 2005). Sensorial tests indicate that customer evaluation of skin feeling has a strong correlation with lotion viscosity (Brummer and Godersky, 1999). More precisely, the ideal product should have an initial viscosity m1 of around 400 Pa, corresponding to the onset of flow of the product under low applied stresses, and a much lower final viscosity m2 of around 0.02 Pa s, when the product is spread over large areas and subject to much higher stresses (the emulsion has a strong shear-thinning behavior). From customer assessment data, two loss functions, L1 and L2, measured in % of product lost value, are constructed, quantifying the loss of quality associated with deviations of initial and final viscosity from the respective ideal values m1 and m2 . Another component of skin feeling is the perceived smoothness of the lotion. Data regarding smoothness is scarce, but it is known that emulsions with smaller droplets are perceived smoother (Wibowo and Ng, 2001). The mean droplet diameter Dd is then chosen as a performance metric. The corresponding loss function L3 is constructed, assuming that below 10 mm, there is no loss, and above 10 mm, the loss is L3 ¼ k3(Dd  10)2. The loss coefficient k3 is calculated assuming a 10% loss for a mean droplet diameter of 20 mm, which results in k3 ¼ 0.1. It should be noted that Dd also belongs to the set x1 of product state variables since it clearly depends on the emulsification conditions. Therefore, the property function regarding smoothness is not defined. Back to performance metrics m1 and m2, we need a property function to predict them as a function of emulsion composition. Viscosity is in great part controlled by the continuous phase that usually contains a thickener, often a synthetic polymer or a natural gum, which confers to the final product its characteristic pseudoplastic behavior: a first plateau for low shear rates, with a nearly constant high viscosity m1, followed by a strong shear-thinning region where viscosity decreases several orders of magnitude, and then a final plateau for high shear rates with a low m2. We thus consider a base formulation with an aqueous phase thickened with xanthan gum, and also containing glycerine as a humectant. Glycerine also contributes to increase emulsion final viscosity m2 for high shear rates. Oil phase viscosity (md), for now, is considered a free constitutive parameter to be optimized within feasible limits. In a second phase, oil phase composition will be adjusted to attain the desired viscosity. The following information and models are conciliated to obtain a final model for emulsion viscosity: (1) available experimental data for xanthan gum aqueous solutions (Pal, 1995), (2) a Carreau model to fit these data (this is a two-plateau model; Tanner, 2000), (3) watereglycerine viscosity data to account for glycerine contribution to m2, and (4) the theoretical model of Yaron and Gal-Or (Pal, 2001) to predict emulsion viscosity from continuous and dispersed phase viscosities, mc and md, and oil phase volume fraction f. The final inputeout format of the viscosity model is: _ m ¼ f ðwT ; wG ; f; md ; gÞ;

(12.13)

Integrated Process and Product Design Optimization Chapter j 12

where wT is the mass fraction of thickener in the continuous phase, wG the mass fraction of glycerine (in the continuous phase) and g_ the shear rate corresponding to the conditions of emulsion application on skin. This model is a property function with: l l l

product design variables d1: wT, wG, and f constitutive property q1 : md _ Product use variable z1 : g:

Initial viscosity m1 is estimated using this model and, with the initial shear rate g_ 1 calculated as the transition point between the first plateau of high viscosity and the strong shear-thinning region (the point of onset of flow). Final viscosity m2 is evaluated with the typical value g_ 2 ¼ 5000 s1 , calculated based on sensorial tests (Brummer and Godersky, 1999). The lotion manufacturing process is a relatively simple, nearly sequential batch process, comprehending: (1) prepreparation of aqueous and oily phases in separate stirred tanks, (2) addition of the oily phase to the aqueous phase with formation of a preemulsion, (3) closed-loop recirculation of the preemulsion through a colloid mill with fine emulsion formation, and (4) filling of bottles with the final product, using a filling machine. A process model is constructed for a production of 1000 ton/year in batches of 1 ton of product and operation from Monday to Friday (13 shifts ¼ 104 h, per week). Besides mass and energy balances, the model includes simplified descriptions of droplet breakup that estimate the maximum droplet diameter that subsists under the mechanical stress provided by the equipment: (1) in the preemulsification tank, the maximum (viscous) stress in the boundary layer near the impeller blades is calculated; and (2) in the colloid mill, the flow in the narrow gap between the stator and the rotor is modeled as a simple shear flow with a corresponding mean viscous stress (Shimizu et al., 1999; Wieringa et al., 1996). Manufacturing costs are then estimated, including raw materials, energy, and labor. The final process function has the following inputeout structure: fDd ; x2 g ¼ f ðwT ; wG ; f; md ; d2 ; z2 Þ;

(12.14)

where: l l l

l

l

l

product design variables d1:wT, wG, and f; product constitutive property q1:md; process design variables d2 (here considered fixed): annual production, batch size, and equipment dimensions; process operating variables z2: speed of mixing equipment (and other operating degrees of freedom); product state variable x1: droplet diameter Dd (in rigor, an estimate of the maximum diameter of the droplet diameters distribution); and process state variables x2: results from mass and energy balances, cycle time, annual operating time (AOT), and estimate of manufacturing costs (C).

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Based on the property function (12.13) and process function (12.14), one then formulates the integrated product/process design problem as follows: find wT, wG, f, md, and process degrees of freedom z2 that minimize manufacturing cost C and also take into account product quality. Using a formulation like (12.10) and assuming a global loss function L ¼ L1 þ L2 þ L3, the optimization problem is then: min

wT ; wG ;f;md ;z2

Cðx2 Þ ½manufacturing cost

(12.15)

s.t. _ ½property funtion m ¼ f ðwT ; wG ; f; md ; gÞ fDd ; x2 g ¼ f ðwT ; wG ; f; md ; z2 Þ ½process funtion Lðm1 ; m2 ; Dd Þ  Lmax hð:Þ  0 ½other restrictions: This is a nonconvex NLP problem with 74 variables and 85 restrictions. The problem is formulated and solved in GAMS, explicitly handling all model equations, and for different values of Lmax. Equal solutions are obtained using the local solver CONOPT (0.1 s of CPU time) and the global solver MSNLP (1 s of CPU time), meaning that the global optimum has probably been reached. Table 12.3 shows results for two values of Lmax. The main effect observed is that the production of a thinner emulsion (case B) requires higher viscous stresses in the mechanical mixing equipment, which, in turn, can only be obtained increasing product viscosity for high shear rates. This is accomplished by TABLE 12.3 Optimal Product/Process Design Solutions: Maximum Quality Loss of 30% (A) and 2% (B) A

B

wT (%)

0.90

0.87

wG(%)

7.2

15.0b

f

0.050a

0.124

a

md (cP)

30

63.3

Dd (mm)

22

13

L1,L2,L3(%)

0, 16, 14

0, 1, 1

AOT (h)

4779

4776

C (EUR/ton)

783

1212

a

Lower bound. Upper bound.

b

Integrated Process and Product Design Optimization Chapter j 12

increasing the oil and glycerine content of the emulsion. The downside is an increase in manufacturing costs, mainly due to the use of more expensive raw materials (namely oily components). Fig. 12.4 shows the complete set of optimal product/process solutions, obtained varying Lmax between 0.5% and 30%. This figure represents rigorously the price one has to pay to increase product quality and how that price varies when quality requisites are more demanding. In mathematical terms, this is the marginal value associated with the restriction L  Lmax, equals to l ¼ dC*/dLmax, where C* is the minimum manufacturing cost. Since the restriction is active in the optimum, Lmax is the abscissa in Fig. 12.4, and the marginal value is the slope of the curve. As quality requisites are more demanding (as L decreases), the cost of decreasing L in one unit increases (slope of the curve increases). For instance, for L ¼ 10%, that cost is 20 EUR/ton per percentage point reduction in quality loss, while for L ¼ 1%, that value increases to 65 EUR/ton. This analysis is here made for cost versus overall product quality loss L, but can easily be done for each one the quality components (L1, L2, and L3). Still regarding Fig. 12.4, problem (12.15) becomes infeasible for L values below 0.5%, since no further reduction in the emulsion droplet size Dd is possible. The minimum attainable value is 12 mm, obtained with both decision variables wG and f saturated at their upper bounds, 15% and 0.15, respectively.

4.3 Formulation of a Pharmaceutical Ointment In the design of a pharmaceutical ointment for transdermal delivery of a particular drug molecule, the following base formulation is first considered: 1: drug (2%), 2: propylene glycol (18%), 3: lanolin (14%), 4: petrolatum (59%), 5: paraffin (5%), and 6: Span 83 (2%). The ointment is of the emulsion type with a liquid mixture of drug and propylene glycol dispersed over the semisolid matrix of oily excipients. A detailed description of this example may be

FIGURE 12.4 Set of Pareto optimal solutions of problem (12.15): product quality versus manufacturing costs.

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found in Bernardo and Saraiva (2008, 2015), while here, we will only focus on a subproblem of ingredients substitution. The only quality factor here considered is the sustained release and systemic delivery of the drug molecule. After ointment application on skin, the drug molecule crosses several skin layers and reaches the blood circulation system. Here, drug transport and metabolism is fast enough so that a homogenous drug concentration in plasma (CP) may be considered. This concentration varies with time, depending on the dynamics of transport across skin and of internal metabolism. A sustained drug delivery may then be quantified as the mean deviation of the temporal profile CP(t) from a target value CP , which should be as low as possible (see Fig. 12.5). For a period T after ointment application, one then defines the performance metric p1 as: 11=2 0 Z T   1 2 CP ðtÞ  CP A p1 ¼ @ (12.16) T 0 Profile CP(t) is predicted from a model of drug transfer along a single direction (perpendicular to skin surface) and comprising four compartments: ointment layer applied on skin (dispersed and continuous phases), two different skin layers, and the blood circulation system. Drug transfer through these compartments is modeled as a series of interphase equilibria and diffusion processes. Some of the transport parameters are estimated as a function of ointment composition. In mathematical terms, the model consists of a system of partial and ordinary differential equations. After spatial discretization using orthogonal collocation in finite elements, one obtains a system of 15 linear ordinary differential equations. The integration of this system results in the temporal

FIGURE 12.5 Predicted temporal profiles of drug concentration in plasma (CP) after three consecutive ointment applications on skin: horizontal line, target concentration; dashed line, base ointment formulation (2% drug, 18% PG, 14% lanolin, 59% petrolatum, 5% paraffin, and 2% Span 83); full line, optimized formulation with new drug solvent (3.7% drug, 21.3% DEG, 7.3% lanolin, 60.7% petrolatum, 5% paraffin, and 2% Span 83).

Integrated Process and Product Design Optimization Chapter j 12

profile CP(t) from which the performance metric p1 is then computed. The system of equations is solved in Mathematica (Wolfram MathWorld, 2015). A single simulation takes about 0.05 s of CPU time. Simulation results indicate that the key parameters affecting drug transport are two drug partition coefficients: Kcd, referring to drug partition between continuous and dispersed phases of the ointment, and KSC,c, between the outermost layer of the skin (SC, stratum corneum) and the ointment continuous phase. These partition coefficients are estimated based on regular solutions theory, known values of the solubility parameter d for each component of the ointment, and also empirical equations regarding partitioning into SC that take into account specific drug/SC interactions. The key ingredients affecting Kcd and KSC,c are the drug solvent (S, propylene glycol in the base formula) and the oily aqueous excipient (E3, lanolin in the base formula). It is then convenient to write the performance index p1 as a function of the solubility parameters of these two key species, dS and dE3, and also mass fractions w for all species: p1 ¼ f ðw; dS ; dE3 Þ:

(12.17)

This property function is inverted using the two-stage approach of Section 3.1. First, we look for optimum values for solubility parameters dS and dE3: min p1

w;dS ;dE3

(12.18)

s.t. p1 ¼ f ðw; dS ; dE3 Þ gðw; dS ; dE3 Þ  0: This NLP problem is solved in Mathematica with p1 being calculated by an external black-box function (see Section 3.3). The solution found is dS ¼ 29.7 (lower bound) and dE3 ¼ 20.4 (J/cm3)1/2 (solution obtained in about 10 min of CPU time). The second stage of the problem is to look for molecular species having d values close to these ones. Consulting a database with d values and also using additional criteria (miscibility with ointment components and viscosity), the candidates in Table 12.4 are selected (the table also shows the base case, where S ¼ propylene glycol and E3 ¼ lanolin). A more exploratory search could be made using a group contribution method to estimate d values and a set of molecular groups covering a plausible larger chemical domain (e.g., fatty alcohols, fatty acids, and their esters). Overall, there are 12 pairs {S,E3}. For each one, the composition w that minimizes p1 is calculated [problem (12.18) with dS and dE3 fixed]. The base solution (pair PG/lanolin, w ¼ {0.02, 0.18, 0.14, 0.59, 0.05, 0.02}) has a performance p1 ¼ 0.0357 ng/cm3. Nine of the twelve pairs, after optimizing w, have a significantly better performance with p1 around 0.022 ng/cm3, and are thus selected for further analysis, including experimental tests. Using some additional criteria, the pair diethylene glycol (DEG)/lanolin seems to be the

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TABLE 12.4 Possible Candidates for Drug Solvent and Oily Aqueous Excipient

Drug solvent

Oily aqueous excipient

Species

d [(J/cm3)1/2]a

PG e propylene glycol (base case)

30.7

DEG e diethylene glycol

29.1

BG e butylene glycol (1,3-butanediol)

28.1

Lanolin (base case)

18.1

Lauryl alcohol

20.0

Myristyl alcohol

19.2b

Cetyl alcohol

18.8b

a

Barton (1991). Estimated conciliating values from Vaughan (1985) with d ¼ 20.0 for lauryl alcohol.

b

most promising (optimized mass fractions w1 to w4 equal to 0.037, 0.213, 0.073, and 0.607; w5 and w6 fixed at base values). Fig. 12.5 compares the predicted profiles of drug concentration in plasma for this solution and the base case, clearly showing the significant improvement in terms of a more sustained drug delivery. It should be noted that the solutions here calculated are partial solutions in the sense that they are focused on a single objective (minimize p1), and thus significant adjustments may be needed in order to attain a reasonable equilibrium between all quality factors of the product.

5. CONCLUSIONS We have presented a simple and schematic conceptual model for chemical product design, interlinking three central design functions (quality function, property function, and process function) through five design domains (product quality, performance, use conditions, composition and structure, and manufacturing process). On top of this basic structure, we have then proposed general optimization formulations integrating both product and process decision variables and discussed still open problems in order to effectively apply those formulations to the design of formulated consumer products. Three examples were provided, illustrating how the conceptual model functions as a working platform and how optimization tools may assist the solution of some subproblems.

REFERENCES Achenie, L.E.K., Gani, R., Venkatasubramanian, V. (Eds.), 2002. Computer Aided Molecular Design: Theory and Practice. Elsevier, Amsterdam.

Integrated Process and Product Design Optimization Chapter j 12 Bagajewicz, M.J., 2007. On the role of microeconomics, planning, and finances in product design. AIChE Journal 53, 3155e3170. Barton, A.F.M., 1991. Handbook of Solubility Parameters and Other Cohesion Parameters. CRC Press, Boca Raton. Bernardo, F.P., Saraiva, P.M., 2005. Integrated process and product design optimization: a cosmetic emulsion application. In: Puigjaner, L., Espun˜a, A. (Eds.), ESCAPE-15, Computer-Aided Chemical Engineering, vol. 20B. Elsevier, pp. 1507e1512. Bernardo, F.P., Saraiva, P.M., 2008. A theoretical model for transdermal drug delivery from emulsions and its dependence upon formulation. Journal of Pharmaceutical Sciences 97, 3781e3809. Bernardo, F.P., Saraiva, P.M., 2015. A conceptual model for chemical product design. AIChE Journal 61, 802e815. Bernardo, F.P., Pistikopoulos, E.N., Saraiva, P.M., 2001. Quality costs and robustness criteria in chemical process design optimization. Computers and Chemical Engineering 25, 27e40. Biegler, L.T., Grossmann, I.E., Westerberg, A.W., 1997. Systematic Methods of Chemical Process Design. Prentice-Hall, London. Brummer, R., Godersky, S., 1999. Rheological studies to objectify sensations occurring when cosmetic emulsions are applied to the skin. Colloids and Surfaces A 152, 89e94. Cheng, Y.S., Lam, K.W., Ng, K.M., Ko, R.K.M., Wibowo, C., 2009. An integrative approach to product development e a skin-care cream. Computers and Chemical Engineering 33, 1097e1113. Cisternas, L.A., Ga´lvez, E.D., 2006. Principles for chemical products design. In: Marquardt, W., Pantelides, C. (Eds.), ESCAPE-16 þ PSE 2006, Computer-Aided Chemical Engineering, vol. 21. Elsevier, pp. 1107e1112. Cisternas, L.A., 2007. Nature of chemical products. In: Ng, K.M., Gani, R., Dam-Johansen, K. (Eds.), Chemical Product Design: Toward a Perspective Through Case Studies. Elsevier, pp. 459e472. Civille, G.V., Carr, B.T., 2015. Sensory Evaluation Techniques. CRC Press, Boca Raton. Conte, E., Gani, R., Ng, K.M., 2011. Design of formulated products: a systematic methodology. AIChE Journal 57, 2431e2449. Costa, R., Moggridge, G.D., Saraiva, P.M., 2006. Chemical product engineering: an emerging paradigm within chemical engineering. AIChE Journal 56, 1976e1986. Cussler, E.L., Moggridge, G.D., 2011. Chemical Product Design. Cambridge University Press, Cambridge. Cussler, E.L., Wagner, A., Marchal-Heussler, L., 2010. Designing chemical products requires more knowledge of perception. AIChE Journal 56, 283e288. Eden, M.R., Jørgensen, S.B., Gani, R., El-Halwagi, M.M., 2004. A novel framework for simultaneous separation process and product design. Chemical Engineering and Processing 43, 595e608. Fung, K.Y., Ng, K.M., 2003. Product-centered processing: pharmaceutical tablets and capsules. AIChE Journal 49, 1193e1215. Fung, H., Wibowo, C., Ng, K.M., 2007. Product-centered process synthesis and development: detergents. In: Ng, K.M., Gani, R., Dam-Johansen, K. (Eds.), Chemical Product Design: Toward a Perspective Through Case Studies. Elsevier, pp. 239e274. GAMS Development Corporation, http://www.gams.com, (accessed April 2016). Gani, R., Ng, K.M., 2015. Product design e molecules, devices, functional products, and formulated products. Computers and Chemical Engineering 81, 70e79.

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SECTION j III Customer Products Gani, R., 2004. Computer-aided methods and tools for chemical product design. Chemical Engineering Research and Design 82, 1494e1504. Hadgraft, J., 2001. Skin, the final frontier. International Journal of Pharmaceutics 224, 1e18. Hill, M., 2004. Product and process design for structured products. AIChE Journal 50, 1656e1661. Hill, M., 2009. Chemical product engineering-the third paradigm. Computers and Chemical Engineering 33, 947e953. Lee, C.K.H., Choy, K.L., Chan, Y.N., 2014. A knowledge-based ingredient formulation system for chemical product development in the personal care industry. Computers and Chemical Engineering 65, 40e53. Martı´n, M., Martı´nez, A., 2013. A methodology for simultaneous process and product design in the formulated consumer products industry: the case study of the detergent business. Chemical Engineering Research and Design 91, 795e809. Mata, V.G., Gomes, P.B., Rodrigues, A.E., 2005. Engineering perfumes. AIChE Journal 51, 2834e2852. Mattei, M., Kontogeorgis, G.M., Gani, R., 2012. A systematic methodology for design of emulsion based chemical products. In: Karimi, I.A., Srinivasan, R. (Eds.), PSE 2012, Computer-Aided Chemical Engineering, vol. 31. Elsevier, pp. 220e224. Pal, R., 1995. Oscillatory, creep and steady flow behavior of xanthan-thickened oil-in-water emulsions. AIChE Journal 41, 783e794. Pal, R., 2001. Evaluation of theoretical viscosity models for concentrated emulsions at low capillary numbers. Chemical Engineering Journal 81, 15e21. Phadke, M.S., 1989. Quality Engineering Using Robust Design. Prentice Hall, New Jersey. Samudra, A.P., Sahinidis, N.V., 2013. Optimization-based framework for computer-aided molecular design. AIChE Journal 59, 3686e3701. Shimizu, K., Minekawa, K., Hirose, T., Kawase, Y., 1999. Drop breakage in stirred tanks with Newtonian and non-Newtonian fluid systems. Chemical Engineering Journal 72, 117e124. Smith, B.V., Ierapetritou, M., 2009. Framework for consumer-integrated optimal product design. Industrial & Engineering Chemistry Research 48, 8566e8574. Tanner, R.I., 2000. Engineering Rheology. Oxford University Press, Oxford. Vaughan, C.D., 1985. Using solubility parameters in cosmetics formulation. Journal of the Society of Cosmetic Chemists 36, 319e333. Wibowo, C., Ng, K.M., 2001. Product-oriented process synthesis and development: creams and pastes. AIChE Journal 47, 2746e2767. Wibowo, C., Ng, K.M., 2002. Product-centered processing: manufacturing of chemical-based consumer products. AIChE Journal 48, 1212e1230. Wieringa, J.A., van Dieren, F., Janssen, J.J.M., Agterof, W.G.M., 1996. Droplet breakup mechanisms during emulsification in colloid mills at high dispersed phase volume fraction. Transactions of the Institution of Chemical Engineers A 74, 554e562. Wolfram MathWorld. http://mathworld.wolfram.com/. (accessed November 2015).

Chapter 13

Tools for Formulated Product Design M. Martı´n*, 1 and A. Martı´nezx

*Universidad de Salamanca, Salamanca, Spain; xProcter and Gamble, Brussels Innovation Center, Strombeek-Bever, Belgium 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION: FORMULATED PRODUCTS AND RAW MATERIALS Products that are a mix of ingredients are an important part of everyday life, such as food, beverages, cosmetics, detergents, lotions, drugs, etc. While the properties of the products are their specialties, they are actually the result of the interaction among ingredients, for instance, the taste, texture, fragrance, cleaning performance, or action on a certain illness. The market value of the industry dealing with these products is huge; some of the largest companies, such as pharmaceuticals, customer products, and fuels, are in this sector. On the one hand, the product can be a mix of ingredients. On the other hand, many raw materials, like biomass, are comprised of a number of major components. For instance, lignocellulosic biomass consists of cellulose, hemicellulose, and lignin. If we go down to the elementary analysis, we can talk about carbon, hydrogen, and oxygen, mainly. Depending on their availability, a number of products can be built out of the raw material. Another example is algae, consisting of lipids, starch, and protein. The different components can be raw materials for a wide range of chemicals. Chemical complexes are integrated systems that make full use of the raw material to produce a large portfolio of products to maximize the benefit. Sometimes the raw material has a fixed composition; however, in some others, the production process or the growing process can be altered to modify that composition. By using the right raw material, our chemical integrated complex can be more efficient, and thus process system engineering analysis and approaches can provide the tools for the design of such products and raw materials. In this chapter, we consider both ends. The first case corresponds to the design of formulated products from a number of ingredients, determining the amount of each ingredient to be mixed for the optimal performance of the final Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00013-7 Copyright © 2016 Elsevier B.V. All rights reserved.

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products at the minimum price and environmental impact. As a case of study, we consider laundry detergents, which have been evaluated by Martı´n and Martı´nez (2013, 2015). The industrial importance of this formulation is due to the volatile prices of ingredients, their availability, and the ever-changing environmental regulations. Industry needs tools to readapt the composition of their final products with no impact on their performance, no matter the changes in prices and availability of the raw materials or the new regulations limiting a particular ingredient. On the other end, we consider the possibility of tuning the composition of the raw material for the optimal operation of a chemical integrated process. Martı´n and Grossmann (2013) presented a work where algae composition was tuned for the optimal simultaneous production of ethanol, biodiesel, and fatty acid ethyl ester (FAEE) so that part of the ethanol is used as a transesterifying agent for the oil accumulated by the algae, and the rest can be sold as biofuel. The advantage of this formulation is that it guides biotechnology research to focus the efforts on algae growing while the result is of interest to avoid the use of fossil-based raw materials, i.e., methanol, in the production of biodiesel. The chapter is organized as follows. In Section 2, we present the mathematical formulations used to address these two problems. Next, in Section 3, we present the application of the tools for the solution of both problems, and we draw some conclusions in Section 4.

2. MATHEMATICAL FORMULATIONS 2.1 Pooling Problem 2.1.1 State of the Art The pooling problem is a generalization of the blending problem that combines features of both the classical network flow problem and the blending problem. In plain words, it can be formulated as follows: Given a list of available suppliers (ingredients) with raw materials containing known specifications (specs), what is the minimum-cost way of mixing these materials in intermediate tanks (pools) so as to meet the demand and spec requirements at multiple final blends (products)? The ingredients can be mixed in the pools, intermediate tanks, and mixed again to generate the final products, but it is also allowed to mix ingredients to obtain the final product. The flows from each source to either pools and/or final products are decision variables in the model; these are the mass balances that hold for the network. Moreover, the products must meet certain specifications. It is here where bilinear terms appear in the formulation, i.e., concentration levels. Therefore, the pooling problem is a bilinear programming problem. In particular, because of the bilinearities, we can also define it as a nonconvex quadratic program with quadratic constraints (QCQP). This is the major difference compared to the blending problem since the absence of mixing leads to a linear problem (LP).

Tools for Formulated Product Design Chapter j 13

The mathematical form of the problem makes it hard to solve. The first efforts to solve the pooling problem were not able to solve it to global optimality. Among them, in chronological order, we find the use of recursive LP (Haverly, 1978) and successive LP (Baker and Lasdon, 1985) which consists of approximating the bilinear terms using a first-order Taylor expansion obtaining a new feasible point, linearize again, and iterate. In 1990, Floudas and Aggarwal presented Benders’ decomposition-based algorithms for addressing the pooling problem. In order to evaluate the goodness of the local solution found, several studies evaluated the sensitivity of the solution with respect to the parameters of the problem (Greenberg, 1995). Based on the limitations of local solvers to deal with the problem, various global optimization algorithms have been proposed to tackle this kind of problem. For instance, Visweswaran and Floudas (1990) developed “GOP,” which stands for global optimization algorithm, based on duality theory and Lagrangian relaxations. The algorithm alternates between solving a projection of the primal problem and a series of relaxed dual problems. The global solution is obtained when the upper bound, given by the projection of the primal, converges to the lower bound, given by the relaxed dual problems. Fould’s et al. (1992) used a branch and bound algorithm where they first implemented McCormick envelopes within a global optimization algorithm to relax the bilinear terms. Another alternative comes from Ben-Tal et al. (1994), who reformulated the pooling problem using a duality-based approach. Quesada and Grossmann (1995) implemented the reformulation-linearization technique (RLT) within a branch and bound optimization algorithm. This technique consists of adding redundant constraints to the nonlinear programming (NLP) pooling problem so that when relaxed, the underestimation is tighter. The use of the Lagrangian-based method was also proposed by several authors (Adhya et al., 1999; Almutari and Elhedhli, 2009). Audet et al. (2004) used a branch and cut algorithm developed for nonconvex QCQPs using four different types of RLT. The cuts generated are McCormick envelopes that are activated for sections of the domain. BARON, a global optimization software, was also tested over this particular problem (Tawarmalani and Sahinidis, 2002). BARON software is based on the branch and cut algorithm for nonconvex problems that currently includes convexity identification and automatic convexification. Karuppiah and Grosmann (2006) developed piecewise linear relaxation of the convex envelopes for the bilinear terms and implemented them within a branch and bound algorithm, reducing the solution time. Misener and Floudas (2009) classified the pooling problems based on the type of mathematical modeling of the blending: (1) linear blending and one layer of pools where the mass balances to the pools are the only source for bilinear terms, the standard pooling problem; (2) the generalized pooling problem, where the existence of pools is an alternative, converting the problem in a mixed-integer nonlinear program (MINLP); and (3) the extended pooling problem that is applied to emission control (Misener et al., 2010).

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Although the study of pooling problems started in the context of refineries, other fields, such as wastewater treatment (Ahmetovic and Grossmann, 2011), emission regulations (Furman and Androulakis, 2008), and lately, formulated product design (Martı´n and Martı´nez, 2013, 2015), have benefited from the idea.

2.1.2 Formulation The basic formulation for a pooling problem is presented as follows and represents the mass balances to a flowsheet, such as given by Fig. 13.1. The basic mathematical model for the pooling problem is given by Eqs. (13.1)e(13.8): Min Cost Production ðraw materialsÞ þ Pools

(13.1)

Assuming that the labor, maintenance, and utility costs are similar, no matter the product. S.t. Feed availability X X ALi  xi;l þ zi;l  AU ci (13.2) i Tx

Pool capacity

Tz

X

xi;l  Sl

cl

Tx

FIGURE 13.1 Structure of the pooling problem.

(13.3)

Tools for Formulated Product Design Chapter j 13

Product demand DLj 

X

yl; j þ

X

Ty

Material balance

X

X

cj

(13.4)

Tz

xi;l 

X

Tx

Quality balance

zi; j  DU j

yl; j  0 cl

(13.5)

Ty

Ci;k $xi;l  pk;l

Tx

X

yl; j  0

cl; k

(13.6)

Ty

Product quality P

zi; j 

Tz

P Tz

Hard bounds

P Ty

zi; j 

P Ty

pk;l $yl;j  PU j;k

cl; k

pk;l $yl;j  PLj;k

cl; k

8
0 (18.2) þ xm i

Experimental method

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TABLE 18.5 Mathematical Constraint Models With Target Values

Decomposition-Based Optimization Chapter j 18

Subtask 1.2.2. Development of the unavailable property models is not considered in this case study.

3.3 Phase 2, Task 2.1: The Feasible Blends Candidates Subtask 2.1.1. A total number of 6822 compounds that meet the blending agent constraints (see Table 18.3) were generated using computer-aided molecular design technique software (ICAS-ProCAMD). Therein, five biochemicals are selected to illustrate the design algorithm proposed in this book chapter: butanol (BU), pentanol (PEN), hexanol (HE), ethyl levulinate (EL) and butyl levulinate (BL). Subtask 2.1.2. The miscibility of each biochemical with B5 components is examined using the Gibbs free energy of mixing, and the result is presented in Table 18.6. Only the miscible (M) and the partial miscible (P) blends are considered in the next task. TABLE 18.6 The Results of the Stability Test of Each B5 Component With the Selected Bio-Compounds Bio-Compounds Diesel Component

EL

BL

BU

PEN

HE

n-Decane

P

M

M

M

M

n-Undecane

P

M

M

M

M

n-Dodecane

P

P

M

M

M

n-Tetradecane

P

P

M

M

M

n-Pentadecane

P

P

M

M

M

n-Hexadecane

P

P

M

M

M

n-Octadecane

P

P

M

M

M

n-Icosane

P

P

M

M

M

Methyl laurate

M

M

M

M

M

Methyl myristate

M

M

M

M

M

Methyl palmitate

M

M

M

M

M

Methyl stearate

M

M

M

M

M

Methyl oleate

M

M

M

M

M

Methyl linoleate

M

M

M

M

M

Methyl linolenate

M

M

M

M

M

Methyl arachidate

M

M

M

M

M

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3.4 Phase 2, Task 2.2: The Feasible Blends Subtask 2.2.1. The miscible and the partial miscible blend candidates generated in the Task 2.1 were further examined using linear (Eqs. (18.3)e(18.6)) property models. All the possible binary and ternary green diesel blends could meet the target linear properties in appropriate composition range. Subtask 2.2.2. The search space obtained in subtask 2.2.1 was further narrowed down by matching the nonlinear property constraint: flash point. Only one ternary blend: B5 þ BU þ PEN is rejected here as it failed to meet the flash point value set in Table 18.5. Subtask 2.2.3. The stability of the partial miscible blends containing EL and BL is rechecked using Eq. (18.2). Based on the previous studied, EL (Wang et al., 2012b) and BL (Christensen et al., 2011) are expected to mix well with B5 up to 10% and 20% by mass without phase separation at room temperature. Meanwhile, alcohol could be the co-solvent for B5-EL and B5-BL blends. The feasible composition range for each binary (with the composition of biochemical i: xNLbio,i) and ternary green diesel blends (with the composition of biochemical m and n: xNLbio,m and xNLbio,n), which meet the linear, nonlinear, and stability constraints, are listed in Table 18.7. These composition ranges were the upper bounds of each biochemical present in the respective blends. For ternary blends, free bound (F.B) is assigned when the nonlinear property constraint (flash point) is satisfied in the entire composition range that was obtained in subtask 2.2.1 (means at the composition where all the linear property constraints as satisfied).

TABLE 18.7 The Feasible Region of Each Green Diesel Blend Binary Blend

xNLbio,i

Ternary Blend

xNLbio,m

xNLbio,n

B5 þ EL

0.100

B5 þ EL þ BL

0.100

0.200

B5 þ BL

0.173

B5 þ EL þ BU

F.B

0.008

B5 þ BU

0.008

B5 þ EL þ PEN

F.B

0.039

B5 þ PEN

0.038

B5 þ EL þ HE

F.B

F.B

B5 þ HE

0.264

B5 þ BL þ BU

F.B

0.008

B5 þ BL þ PEN

F.B

0.040

B5 þ BL þ HE

F.B

F.B

B5 þ BU þ PEN

Reject

B5 þ BU þ HE

0.005

F.B

B5 þ PEN þ HE

0.010

F.B

Decomposition-Based Optimization Chapter j 18

3.5 Phase 2, Task 2.3: The Optimum Green Diesel Blends Subtask 2.3.1. The objective in this case study is to optimize the OC of green diesel blend. Oxygenated green diesel fuel blend is able to enhance fuel combustion. In most cases, the higher the oxygen content is, the more reduction to the harmful exhaustions, especially particulate matters (Wang et al., 2012a), unburned hydrocarbon, and soot (Ng et al., 2012). The optimum green diesel blend should consist of at least 1.0% by mass of each different biochemical. Meanwhile, the total biochemical content should not exceed 30% by mass to ensure the designed green diesel blends are compatible with the existing diesel engine. Only 5% loss of higher heating value is allowed in this case. The optimization problem is mathematically formulated as follows: X Fobj ¼ min xi OCi subjected to P 1. P xi  1 ¼ 0 2. xbio;i  0:3 of the upper bound listed in Table 18.7 3. HHV  43 MJ=kg 4. xbio,i  0.01 5. all linear property constraints Subtask 2.3.2. The optimum solutions of each green diesel blend obtained were ranked according to their oxygen content as shown in Table 18.8. There are five blends rejected in this optimization step: binary blends of B5 with BU and PEN; ternary blends of B5 with EL-BU, BL-BU; and BU-HE because they fail to meet the optimization constraints. Fig. 18.3 plots the cost and the oxygen content of the optimum blends listed in Table 18.8. Apparently, GD4 and GD6 are the most promising optimum solutions in this case. Both GD4 and GD6 have higher oxygen content and lower cost compared to the other green diesel options. Please note that the cost evaluated here is based on the retailing price from local chemical suppliers in small quantity; thence, a much higher cost is obtained compared to the conventional B5 palm oil biodiesel (around 0.44 USD/L in December 2015, based on Malaysian market price). Despite this, the example shown here is to serve a concept on how to select the best optimum green diesel blends.

3.6 Phase 3, Task 3.1: The Fuel Additives Subtask 3.1.1. The selected GD4 and GD6 blends are further evaluated in this task to enhance their fuel quality using suitable fuel additives. The fuel qualities needed to enhance include emission, engine performance, and storage stability as B5 consisting unsaturated fatty acid methyl esters. Engine performance and emission could be improved simultaneously using cetane

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TABLE 18.8 The Optimum Green Diesel Blends Ranked According to the Oxygen Content Formulation (B5 þ % by Mass of Biochemical)

OC (%)

r (kg/ m3)

ƞ (mm2/ s)

HHV (MJ/ kg)

CN

FP ( C)

GD1

B5 þ 17.3 BL

5.3

864

3.53

43

50

81

GD2

B5 þ 26.4 HE

4.6

834

3.88

44

49

61

GD3

B5 þ 10.0 EL

3.9

858

3.60

43

52

79

Blend

Estimated Property

Binary Blend

Ternary Blend B5 þ 9.7 HE þ 13.3 BL

5.7

857

3.59

43

49

67

GD5

B5 þ 9.6 HE þ 11.0 EL

5.7

858

3.54

43

49

67

GD6

B5 þ 15.3 BL þ 4.0 PEN

5.5

861

3.52

43

49

60

GD7

B5 þ 12.7 EL þ 3.9 PEN

5.4

862

3.45

43

49

60

GD8

B5 þ 1.0 EL þ 16.1 BL

5.3

864

3.52

43

50

77

GD9

B5 þ 1.0 PEN þ 25.2 HE

4.6

836

3.87

44

49

61

6

30

5

25

4

20

3

15

2

10

1

5

0

0 GD1

GD2

GD3

GD4

GD5

Oxygen Content

GD6

GD7

GD8

GD9

Cost (USD per L)

FIGURE 18.3 The cost and the oxygen content of the optimum green diesel blends.

Cost

GD4

Oxygen Content, %

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Decomposition-Based Optimization Chapter j 18

improver, while antioxidant is supposed to improve oxidation stability for storage purposes. Unfortunately, due to the limitation on information/experimental data, storage stability could not be considered further in this case study. Subtask 3.1.2. The suitable cetane enhancer is retrieved from the additive database. 2-Ethylhexyl nitrate (2EHN) is selected, as it is the common and cost-effective cetane enhancer, while it has higher flash point (65 C) compared to the standard target value (60 C) (Oxley et al., 2000). Subtask 3.1.3. The miscibility of 2EHN with GD4 and GD6 blends is primary investigated by the knowledge base. As 2EHN is miscible with diesel, it is considered to mix well with GD4 and GD6 blends because the petro-diesel is still the major component in these blends (by assuming “like dissolves like”). Theoretically, 0.1% by mass of 2EHN is sufficient to increase cetane number as much as 6 (Oxley et al., 2000). Hence, the final green diesel formulation is designed by adding 0.1% by mass of 2EHN into GD4 and GD6 to increase the cetane number up to 52, which is the minimum target value of the EU4 emission reference diesel fuel.

4. RESULTS AND DISCUSSIONS Initially, the possible binary and ternary blend candidates were around 49,000 for B5 blending with BU, PEN, HE, EL, and BL with the variation of 1% blending mass changed. The search space for the feasible blends was successfully narrowed down phase by phase with the aid of the decompositionbased computer-aided approach. In this case study, GD4 and GD6 with 0.1% by mass of 2EHN were proposed as the most promising optimum blends as they have higher oxygen content with lower cost compared to the other shortlisted green diesel blends. The oxygen content of B5 (0.62% by mass) was successfully elevated by blending it with the oxygenated biochemical. Less biochemical is required to achieve the green fuel blends with higher oxygen content if compared to the blends that are using the blending agent with lower oxygen content (e.g., HE, PEN, and BU). The oxygen content is used as an indicator for the ability of a green diesel fuel in reducing the harmful exhaustions, such as oxides of nitrogen (NOx), carbon dioxide (CO2), carbon monoxide (CO), unburned hydrocarbon (UHC), particulate matter (PM), and smoke. Occasionally, some adverse effects may induce the emission issues as the oxygen content is increased. For example, the emission of NOx may become worse when using oxygenated diesel fuel (Varatharajan et al., 2011). However, this problem could be solved by increase the cetane number (for better fuel combustion) using a suitable fuel additive. Other fuel properties like oxidation stability and hydrophilic behavior are needed to be examined experimentally due to missing prediction models. The last phase: experimental validation is important for making the final adjustment (using fuel additive or slightly altering the blend composition) to further improve and develop the selected base formulations.

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5. CONCLUSIONS This book chapter proposed a systematic tailor-made green diesel blend design algorithm to solve the MINLP problem using a decomposition-based computer-aided strategy. The design algorithm integrates a computer-aided approach with experimental study in four main phases: (1) mathematically formulate the design problem, (2) optimize the green diesel blends, (3) enhance the blends using fuel additives, and (4) experimental validation. In this algorithm, the optimum green diesel blends are obtained using a reliable and efficient computer-aided approach in advance. Subsequently, the experimental validation is employed to validate and do the appropriate adjustments (if necessary) to further improve the final base formulations. A case study: optimize the oxygen content of the binary and ternary blends of B5 with biochemical (e.g., BU, PEN, HE, EL, and BL) is described to illustrate the application of the blend design algorithm. Only nine out of 15 different feasible blends (counted as the difference in biochemical/s used) that satisfied all the design constraints are shortlisted at the end of this study. By comparing the cost and the oxygen content, GD4 and GD6 are the most promising solutions. Proposed is 0.1% by mass of 2EHN to enhance their cetane number for better combustion quality and, hence, further reduce the harmful emissions (e.g., NOx). There are a few limitations of the presented design algorithm: 1. Only binary and ternary blends are considered here; multicomponent mixtures (referring to the blends with three and above blending agents or main ingredients) should be addressed in the future to check the functionally and the reliability of this green diesel blends algorithm, particularly in Phase 2. 2. The usage of fuel additives mainly relies on the knowledge base at this moment. More information such as solubility/miscibility and their effects to the designed fuel’s physicochemical properties are needed. This information is important to expand the additives database and accurately trace the effects of the additive toward the engine performance and emissions. 3. Some of the important properties like oxidation stability, hydrophilic behavior, and the details on engine emissions are only evaluated at the experimental stage. Additional efforts should be focused to develop these missing property prediction models. The inclusion of these property models at the initial computer-aided design phase could save more valuable resources in the later experimental validation phase.

ACKNOWLEDGMENTS The valuable guidance and advice provided by Professor Dr. Rafiqul Gani at the Technical University of Denmark (DTU) are gratefully acknowledged. Finally, the financial support provided by Ministry of Higher Education (MOHE) Malaysia and the Universiti Teknologi Malaysia (UTM) under the Vote No. Q.J130000.2644.11J19, Q.J130000.2544.10H67, R.J. 130000.7344.4J150 is highly acknowledged.

Decomposition-Based Optimization Chapter j 18

REFERENCES Ariffin Kashinath, S.A., Abdul Manan, Z., Hashim, H., Wan Alwi, S.R., 2012. Design of green diesel from biofuels using computer aided technique. Computers & Chemical Engineering 41 (0), 88e92. Chen, Z., Ma, X., Yu, S., Guo, Y., Liu, J., 2009. Physical-chemical properties of ethanol-diesel blend fuel and its effect on the performance and emissions of a turbocharged diesel engine. International Journal of Automotive Technology 10 (3), 297e303. Christensen, E., Williams, A., Paul, S., Burton, S., Mccormick, R.L., 2011. Properties and performance of levulinate esters as diesel blend components. Energy & Fuels 25 (11), 5422e5428. Conte, E., Gani, R., Ng, K.M., 2011. Design of formulated products: a systematic methodology. AIChE Journal 57 (9), 2431e2449. Fredenslund, A., Jones, R.L., Prausnitz, J.M., 1975. Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE Journal 21 (6), 1086e1099. Fredenslund, A., Gmehling, J., Michelsen, M.L., Rasmussen, P., Prausnitz, J.M., 1977. Computerized design of multicomponent distillation columns using the UNIFAC group contribution method for calculation of activity coefficients. Industrial & Engineering Chemistry Process Design and Development 16 (4), 450e462. Liaw, H.-J., Lee, Y.-H., Tang, C.-L., Hsu, H.-H., Liu, J.-H., 2002. A mathematical model for predicting the flash point of binary solutions. Journal of Loss Prevention in the Process Industries 15 (6), 429e438. Magnussen, T., Rasmussen, P., Fredenslund, A., 1981. UNIFAC parameter table for prediction of liquid-liquid equilibriums. Industrial & Engineering Chemistry Process Design and Development 20 (2), 331e339. Ng, J.-H., Ng, H.K., Gan, S., 2012. Development of emissions predictor equations for a light-duty diesel engine using biodiesel fuel properties. Fuel 95, 544e552. Oxley, J.C., Smith, J.L., Rogers, E., Ye, W., Aradi, A.A., Henly, T.J., 2000. Fuel combustion additives: a study of their thermal stabilities and decomposition pathways. Energy & Fuels 14 (6), 1252e1264. Phoon, L.Y., Hashim, H., Mat, R., Mustaffa, A.A., 2016. Flash point prediction of tailor-made green diesel blends containing B5 palm oil biodiesel and alcohol. Fuel 175, 287e293. Varatharajan, K., Cheralathan, M., Velraj, R., 2011. Mitigation of NOx emissions from a jatropha biodiesel fuelled DI diesel engine using antioxidant additives. Fuel 90 (8), 2721e2725. Wang, X., Cheung, C.S., Di, Y., Huang, Z., 2012a. Diesel engine gaseous and particle emissions fueled with diesel-oxygenate blends. Fuel 94, 317e323. Wang, Z.-W., Lei, T.-Z., Liu, L., Zhu, J.-L., He, X.-F., Li, Z.-F., 2012b. Performance investigations of a diesel engine using ethyl levulinate-diesel blends. BioResources 7 (4), 5972e5982. Wei, L., Cheung, C.S., Huang, Z., 2014. Effect of n-pentanol addition on the combustion, performance and emission characteristics of a direct-injection diesel engine. Energy 70, 172e180. Yunus, N.A., Gernaey, K.V., Woodley, J.M., Gani, R., 2012. An integrated methodology for design of tailor-made blended products. In: Ian David Lockhart, B., Michael, F. (Eds.), Computer Aided Chemical Engineering. Elsevier.

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Chapter 19

Strategies for Structured Particulate Systems Design C. Amador1 and L. Martin de Juan1 P&G Technical Centres Limited, Newcastle Upon Tyne, United Kingdom 1 Corresponding authors: E-mail: [email protected]; [email protected]

1. RELEVANCE OF STRUCTURED PARTICLE PRODUCTS IN INDUSTRY Particle products play a critical role in the manufacturing industry across key sectors such as chemical, pharmaceutical, biotechnology, metallurgical, ceramic, household, and food industries. A good example of how particle systems are relevant across industries was the foundation in 1979 of the International Fine Particle Research Institute (IFPRI) that is a global network of companies and academics aimed to define and influence long-term (precompetitive) research in particle science and engineering aligned with the industry needs. IFPRI members represent some of the world’s largest manufacturing industries in bulk and specialty chemicals, pharmaceuticals, minerals, enzymes, catalysts, food, and household products (further information at www.ifpri.net). The focus of industries handling and producing particle products can be classified in three big topics: l

l

Transport and storage of particulate solid raw materials, intermediates, and products. Aims to design the equipment that ensure adequate dosing as well as preservation of the original structure of the particulate system, which could be modified as a result of caking, attrition, and/or segregation during the handling of the bulk solid. Design of cost-efficient processes that enable development of particle systems with the desired structure. In many cases, there is not only one way to manufacture a product that presents the required performance vectors. As it is discussed later, structured particle systems present multiple degrees of freedom to generate alternative structures that meet success criteria for performance. In addition, there is a wide variety of processes for granulation, classification, mixing, coating, and comminution available in the

Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00019-8 Copyright © 2016 Elsevier B.V. All rights reserved.

509

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SECTION j IV Design of Structured Products

l

market. One of the key challenges for industry is identifying which process is the most cost effective and how it can be implemented in a time/resource efficient manner. As the world evolves toward globalization, there is a growing need by those industries that want to be successful to accelerate innovations delivered to the market. Design of particle systems that present a structure such that product meets the performance vectors defined by a given application. Product design activity is defined as the design of a product whose structure meets or exceeds performance vectors declared as success criteria to go to market. This process is quite complex and, in many applications, classified as an art because it requires relating a set of performance vectors with a given structure, and modeling capability may not be available. As it was previously indicated, particulate systems may present alternative structures that meet declared performance vectors. Selection of optimal structure is conditioned by factors such: capital investment, processing cost, and environmental footprint. As such, aims of industry are (1) development of structures that maximize performance vectors to grow share in its specific market, and (2) modify existing structures to others that are more cost effective or present less environmental impact.

Previous paragraphs have highlighted the relevance of particle structure to meet key performance vectors to enable the production of the product (processability), its maintenance and safe use (stability), and satisfaction by final user (product specifications and quality). Usually, there are some core performance vectors that are common across industries: l

l

l

Appearance: although it is typically associated with products that are exposed to consumers, some of the properties that define appearance such as color, shape, size distribution, and bulk density are also important for the development of products not exposed to the consumer. Properties such as bulk density, size distribution, or shape may impact handling, storage, and manipulation by product users if their current equipment is designed for different particle properties. Dosing: is related with flow properties of the particulate system as well as the homogeneity of the product as it is dosed at the final application. Product is expected to present these attributes at end use. Therefore, evolution of structure as a result of caking and segregation needs to be considered when designing robust products. Mass transfer: describes the dynamics of the product on the final application; it may include (1) dissolution rate of the system, (2) triggered release of certain components, (3) reaction rate of components on the actives sites deposited on the particles, and (4) swelling rates of the system, i.e., all processes that are controlled by the mass transfer from the particulate system to the medium or from the medium to the particulate system.

Strategies for Structured Particulate Systems Design Chapter j 19

l

Breakage propensity: related with how initial structure is preserved at point of application. It is related to the attrition of the particulate system during handling, storage, and final use.

2. SCALES OF STRUCTURED PARTICLE PRODUCT Previous section highlighted the relevance of structure in particle systems. Term structure is widely used across different disciplines and typically refers to the way in which the parts of a system or object are arranged or organized (Cambridge dictionaries online). In the case of particulate systems (Fig. 19.1), it is proposed to define structure at four different scales: 1. supramolecular scale: the way in which molecules are organized within a domain, 2. particle scale: the way in which its domains are organized within a particle, 3. mesoscale: the way in which particles are organized within a volume, 4. macroscale: the way in which volumes of particles with different properties or composition are arranged within a unit operation. Authors often refer to the combined supramolecular/particle scales as microstructure. Particulate systems final properties are designed and also manipulated at three different scales: (1) supra molecular, (2) particle, and (3) mesoscale, whereas macroscale differences are typically the result of nonhomogeneity within the unit operation. As a result, particulate systems provide higher degrees of freedom to design a formulated product than other systems, and this is one of the reasons why they are so widespread across industries and

FIGURE 19.1 Classification of structure in particulate systems.

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SECTION j IV Design of Structured Products

applications. Particulate systems allow (1) formulating incompatible chemistries, (2) controlled release of actives as function of time, pH, temperature, stress, etc., and (3) relatively easy separation from a continuous medium. Another aspect that is important in the previous classification is the dependency between different types of structure. Supramolecular structure of different domains influences particle structure properties, and mesostructure properties are impacted by the different particle structures that constitute the bulk solid. Next, two examples of particulate products with complex particle structure are introduced, which is referred to during the chapter: (1) detergent particles produced via spray drying at high temperatures and (2) milk powder produced via spray drying at low temperatures.

2.1 Spray-Dried Detergent Particles Fig. 19.2 represents the three different domains within a detergent spray-dried particle. Domain A contains inorganic, organic, and dissolved air phases that are formed by spray drying a well-mixed slurry of a colloidal dispersion of surfactant micelles and surfactant/polymer lamellar liquid crystals in a saturated inorganic solution with entrained air. The shape of the micelles depends on hydrophobic group and ionic head that determines the packing of monomers with the sequence sphere / rod / disc as the surface area of the head group decreases (Ramaraju, 2006). Surfactant monomers start interacting with themselves forming micelles and more complex liquid crystal arrangements when their concentration goes above the critical micelle concentration (Fig. 19.3). The properties of this domain, heterogeneous but relatively uniform, are determined by its supramolecular structure. Domain B is composed of undissolved solids in the inorganic saturated slurry, which can also have its own

Inorganic/organic/porous domain A Undissolved solids domain B

Steam/Air domain C

FIGURE 19.2 Representation of three domains within spray-dried particle: (A) inorganic/ organic/porous domain formed from a slurry dispersion of surfactant lamellar lyotropic liquid crystals in a concentrated inorganic solution; (B) large solids that were undissolved in the presprayed detergent slurry; (C) large porosity domain.

Strategies for Structured Particulate Systems Design Chapter j 19

FIGURE 19.3 Representation of ideal structures of water and surface-active mixes as surfaceactive concentration increases, which controls the rheological properties of the mixture. Neat phase represents a surfactant lamellar liquid crystal with a bilayer arrangement of surfactant molecules. From Corkill, J.M., Goodman, J.F., 1969. The interaction of non-ionic suface-active agents with water. Advances in Colloid and Interface Science 2 (3), 298e330, with permission.

supramolecular structure depending on the composition and formation process of those inorganic solids. Domain C is porosity due to both entrained air and steam formation, which depends on boiling point, heat rate during drying process, and additive materials. The combination of the three distinct domains within the particle is referred to as particle structure, which is studied in Section 4. The surfactant phase chemistry presents complex interactions that can limit the levels of certain ingredients in the slurry and powder to deliver processability (inability to mix, pump, or spray) and key powder properties such as physical stability, flowability, solubility, and strength. Steward et al. (2009) identified three different surfactant phases in a system of linear alkylbenzene sulfonate (LAS) in water depending on temperature and surfactant concentration, namely, L1 micellar isotropic phase, La lamellar lyotropic liquid crystal, and La0 , a swollen lamellar liquid crystal phase with a larger d-spacing of the lamellar bilayers due to water uptake (see Fig. 19.4). He also observed biphasic regions L1 þ La and L1 þ La0 . Ramaraju et al. (2006) identified similar phases, apart from La0 , for a system of water and dodecyl-p-benzene sulfonic acid. Steward et al. (2011) found that in the presence of electrolyte solutions, LAS could yield a multiple-lamellar region L1 þ La þ La0 . Liu et al. (2016) analyzed a ternary system containing alkyl ethoxysulfate surfactant (AES), ethanol, and water identifying similar L1 and La phases, with

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FIGURE 19.4 (A) Surfactant phases in waterealkylbenzene sulfonate system, (B) d-spacing increase in lamellar phase. From Steward, J.A., Saiani, A., Bayly, A., Tiddy, G.J.T., 2009. The behaviour of lyotropic liquid crystals in linear alkylbenzene sulphaonate (LAS) systems. Colloids and Surfaces A: Physicochemical and Engineering Aspects 338, 155e161, with permission.

the addition of an undesired hexagonal or middle liquid crystal phase H at low ethanol concentrations and middle AES concentrations, with very high viscosity.

2.2 Spray-Dried Milk Powder Dry milk particulate products have complex supramolecular and particle structures. Milk has a dispersion of fat globules in a water-based solution of carbohydrates (lactose), minerals, soluble proteins and a colloidal suspension of casein protein micelles and particulate whey proteins (Beckman Coulter, 2015). Lactose can form crystals or be amorphous. Four types of insoluble casein proteins (as1, as2, b, k) form large w100 nm spherical colloidal micellar structures of several thousand protein molecules built from casein sub-micelles, which are interconnected by colloidal calcium phosphate nanoscale particles. Casein protein comprises w80% of the protein content with the remaining 20% being a mixture of soluble globular proteins referred to as whey protein. Fat globules range from 0.1 to 15 mm to and have a protective membrane that impedes them from coalescing. Milk plasma is what remains after fat globules are removed, while milk serum is what remains after both fat globules and casein micelles are removed. A negative surface charge on the casein micelles prevents coagulation (Aguilera and Stanley, 1999). When milk is spray dried to produce milk powder, its emulsion functionality has to be conserved by protecting fat globule membranes, embedding them into a fully amorphous matrix to limit free fat (Vuataz, 2002).

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3. SUPRAMOLECULAR STRUCTURE Supramolecular structure refers to the molecular structure present across the different liquid and solid domains that conform a material. It determines physical properties of that domain such as true density, color, surface energy, strength, toughness, ductility or hardness, which are critical in the final bulk product. When studying the properties of the different domains within a material, it is important to understand how that domain has been formed. The next section introduces key features and properties that relate and help describe the supramolecular structure of particulate products, indicates why they are relevant in product processability and final key attributes such as stability, solubility, or flowability and how they can be measured and modeled.

3.1 Crystalline and Amorphous Structure Phase Composition Gases, liquids, and solid amorphous materials show isotropic properties, uniform properties along spatial directions. Crystals, instead, have highly ordered structures of atoms, molecules, and ions that show anisotropy in mechanical, electrical, magnetic and optical properties. Crystals are classified into seven systems, namely regular, tetragonal, orthorhombic, monoclinic, triclinic, trigonal, and hexagonal depending on the angles and lengths between crystal axes. Crystals are built up from a large number of unit cells or space lattices, which have a regular arrangement of points (atoms/molecules/ions) in the space. Every point sees the same environment. There are 14 Bravais lattices that form the seven crystal systems and different unit arrangements can macroscopically show the same crystal (e.g., both body-center or face-center cubes yield regular (cubic) crystals) (Mullin, 2001). Crystalline phases are responsible for defining key material properties such as melting point, critical in chocolate making, for example, where different polymorphic forms are impacting texture and at what point during use chocolate melts (Loisel et al., 1998). Fully crystalline powders generally have improved bulk properties such as stability and flowability versus amorphous ones, which have a larger adsorptive capacity (Chan and Chew, 2003). Palzer (2011) proposes the following classification Fig. 19.5 for the supramolecular structure according to its polarity and the molecular assembly order: l l l l

polar amorphous solids (e.g., carbohydrates and amorphous organic acids) apolar amorphous solids (e.g., polystyrene, polypropylene, and waxes) polar crystalline solids (e.g., mineral salts, crystalline organic acids, urea) apolar crystalline solids (e.g., mono- and triglycerides)

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FIGURE 19.5 Classification of supramolecular structure according to polarity and order. From Palzer, S., 2011. Agglomeration of pharmaceutical, detergent, chemical and food powders e similarities and differences of materials and processes. Powder Technology 206, 2e17, with permission

Solid true amorphous materials can also be presented as highly viscous liquids because they can flow under pressure and do not show ordered microscopic structure of atoms/molecules. However, many traditional “amorphous” materials have been shown to have some degree of regular molecular arrangement or crystallinity. Liquid crystals (LC) are liquids that show anisotropic properties just above their melting point because of regular molecular arrangement, either induced by temperature (thermotropic, e.g., LCDs) or molecular self-assembly in a solvent (lyotropic, e.g., surfactant lamellar crystal as in Fig. 19.3). Crystal size and ratio of different polymorphs impact rheology (processability) and quality of foods in relation to stability, texture, taste, and melting point. Briggs and Wang (2004) show that chocolate rheology, applied shear rate, and time have an effect on crystallization kinetics, crystal size (larger sizes at low shear), and polymorphs during chocolate tempering, and rheology measurements can be used to aid investigation of crystallization processes. Vuataz (2002) shows that two different lactose crystals can be formed during spray drying of milk (a hydrate lactose crystals in a supersaturated milk concentrate and b anhydrous crystals in a rubbery-glassy powder state) depending on process conditions impacting droplet temperature and solids content (see Fig. 19.6). Lactose crystallization should be minimized during spray drying, and b anhydrous crystals (preferred over a hydrate lactose crystals because of improved

Strategies for Structured Particulate Systems Design Chapter j 19

FIGURE 19.6 The state diagram of WM (lactose and water phase transitions). Vuataz G., 2002. The phase diagram of milk: a new Tool for Optimising. Lait 82, 485e500, with permission.

solubility) can be induced within the stored milk powders by subjecting them to heat shocks. A review of organic crystal polymorphs prediction via computer modeling is described by Price (2004). Most methods of crystal structure prediction start by seeking the crystal structure that corresponds to the global minimum in the lattice energy. This assumes that thermodynamics controls crystallization and that all temperature effects and zero-point energies can be neglected. Thus, the method seeks the static 0K crystal structure that gives the most energetically favorable packing. If there are local minima in the lattice energy that are within the energy range of possible polymorphism, then these are energetically feasible as polymorphs (Price, 2004). Crystal polymorphism formation has been modeled using traditional chemical reaction equations coupled with differential heat transfer equations as presented by Bakalis et al. (2011) to model the different crystal polymorphs in cocoa butter, which plays a crucial role in delivering the preferred taste, texture, and melting point of chocolate. X-ray diffraction (XRD) and differential scanning calorimetric (DSC), discussed later, provide the required data. Optical microscopy uses a glass or quartz lens and has a resolution of up to 200 nm. There are several contrast-inducing techniques that enhance LM such as polarized optical microscopy (POM), phase/differential interference contrast (sample staining), fluorescence microscopy, hot stage microscopy, microspectrophotometry, and confocal microscopy (Aguilera and Stanley, 1999). In POM, polarized light, which vibrates in a single plane, is directed

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toward the sample, with the rotation angle and intensity of the reflected light being a function of the anisotropicity and birefringent structures (able to rotate the light plane). It is an ideal technique to visualize complex surfactant lyotropic liquid crystal structures conducting a penetration scan (Fig. 19.7) where a surfactant mix and an electrolyte solution are put into contact and the boundary is observed, as conducted by Ramaraju et al. (2006), Steward (2008), or Liu et al. (2016). Confocal optical microscopy eliminates out of focus light at the confocal plane, enabling one to generate three-dimensional (3D) images of surface features or thin, translucent particulates. McKenna et al. (1999) (Fig. 19.8) used confocal microscopy of whole milk powder to identify differences in the

FIGURE 19.7 (A) Penetration scan using polarized light microscopy for wateredodecyl-pbenzene sulfonic acid system at (A) 2.7 C and (B) 18.1 C. Ramaraju, S.M., Carroll, B.J., Chambers, J.G., Tiddy, G.J.T., 2006. The liquid crystalline phases formed by lineardodecylbenzene sulphonic acid during neutralization with sodium carbonate. Colloids and Surfaces A: Physicochemical and Engineering Aspects 288, 77e85, with permission.

FIGURE 19.8 Confocal photographs of whole milk powders showing surface and internal distribution of fat globules in two commercial milk powders. McKenna, A.B., Lloyd, R.J., Munro, P.A., Singh H., 1999. Microstructure of whole milk powder and of insolubles detected by powder functional testing. Scanning 21, 305e315, with permission.

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radial distribution and size of fat globules within the particles of four commercial milk powders that could not be observed with traditional particle size distribution data. Electron microscopy uses a beam of accelerated electrons as the illumination source to achieve a greater magnification of 0.1 nm for transmission electron microscopy (TEM) and 3 nm for surface electron microscopy (SEM). SEM sample preparation is easy and is mainly used to study surface and particle structure (Lin, 1985). TEM, instead, requires a more complex sample preparation (see Fig. 19.9) with methods such as shadow casting,

(A)

(B)

(C)

(D)

(E)

(F)

FIGURE 19.9 TEM of casein micelles by (A) shadow casting, (B) negative staining, (C) cryomicroscopy, (D) freeze fracturing and unidirectional shadowing, (E) freeze-fracturing and rotary shadowing, and (F) freeze-etching and rotary shadowing; scale bars ¼ 100 nm. Schmidt, D.G., Buchheim, W., 1992. The application of microscopy in dairy research. Journal of Microscopy 167 (1), 105e121, with permission.

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negative staining, thin-sectioning, or freeze fracturing (Schmidt and Buchheim, 1992) and is generally used to identify individual powder constituents such as casein micelles and fat globule particles (Kalab and Emmons, 1974; Caric and Kalab, 1987). X-ray microtomography is mainly used for particle structure and is discussed in Section 4. XRD techniques comprise wide-angle x-ray scattering (WAXS) and small-angle x-ray scattering (SAXS). XRD methods use a collimated beam of X-rays that is diffracted into many different directions (diffraction patterns) where their angles and intensities are used to generate a picture of the electron density, which is correlated to the atomic and molecular structure of a crystal. Each crystalline solid is characterized by a unique d-spacing pattern with short and long spacing (powder pattern), which can be used to differentiate two chemically identical solids with different crystal polymorphs (Birkholz, 2006). WAXS (10e90 degrees diffraction angle) is used to identify short d-spacing distances in detailed crystal studies detecting ordering of individual atoms. SAXS (0.1e20 degrees diffraction angle) is used to explore larger length scales and longer d-spacing than WAXS to identify large structures in nonhomogeneous systems such as dispersed LC in amorphous matrix. It has a resolution that goes from a few to hundreds of angstroms, providing information about the shape and size of macromolecules. Amorphous materials show a continuous intensity curve versus angle (2q) with no peaks. Many current equipment can do both WAXS and SAXS with the same sample. Hicklin et al. (1985) used XRD to identify short and long spacing for six different crystal polymorphs in blends of cocoa butter and hydrogenated fats. Steward et al. (2009) applied SAXS to measure d-spacing of LAS surfactant bilayer LC in water showing that the separation between bilayers decreases with an increase in surfactant concentration and a decrease in temperature (see Fig. 19.4). Raman spectroscopy is an inelastic scattering technique (energy of incident bean is not conserved) versus XRD, where the incident laser light interacts with the material molecules emitting electromagnetic radiation. It can be used to analyze composition of materials, and Mazurek et al. (2015) has applied it to analyze the full composition of milk with small standard relative errors 3.4e6.1%. A variant of Raman also allows measuring orientation of crystals in solid samples and can complement XRD studies by providing more dynamic data information about the chemical events (e.g., ligand binding, enzymatic reactions) that take place in the crystals prior to flash freezing and X-ray analysis (Carey, 2006). PH O ðTÞj ERH aw ¼ 2  Material ¼ (19.1) 100 PH2 O ðTÞ

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3.2 Water Activity (aw) Water activity (aw) is a measure of how bound water molecules are to the supramolecular structure of a material and is defined as the material partial pressure of water divided by the saturation pressure of water at a given temperature PH2 O ðTÞ (see Eq. (19.1)). In percentage, it is often referred to as equilibrium-relative humidity of the material. When aw is 1, water inside the structure is as free as pure water. The water activity (aw) of a material is one of the most important properties, a result of the underlying material supramolecular structure. Water can be bound via physical sorption onto surfaces and molecular bonds, which can lead to low water activities. For example, linear alkylbenzene sulfonate surfactant lamellar liquid crystal bilayers found in detergent slurries can swell with water, above certain temperatures (Steward et al., 2011). This feature, which depends on the mixture of surfactant, polymer, and electrolyte, can be crucial in defining rheology and drying kinetics as well as the physical stability of the product. In addition, as specific surface area of the material increases due to intraparticle porosity and surface roughness, water physically adsorbs stronger to the surface (thinner layer), increasing the desorption heat needed and reducing water activity. Water activity aw often correlates with other key properties of the processing intermediate product such as phase transition points, viscoplastic, and mechanical properties that impact processability. For example, a reduction in water activity correlates with an increase in material boiling point and a reduction in water diffusivity (Stockdale, 1978), which determine heat and evaporation rates during drying, which in turn impacts supramolecular structure. It also impacts flowability, glass transition temperature, mechanical properties, and crystal formation (Jakubczyk et al., 2008), which can lead to product stickiness and biological stability (see Fig. 19.10 for dairy products by Roos, 2002). Jakubczyk et al. (2008) showed that increasing water activity led to an increase of fracture stress (hardening) in rye and fiber crisp breads due to the adsorbed water inducing a new matrix of proteins and carbohydrates. A water sorption isotherm is the correlation of the material water content (often X (g water/g solids)) with water activity see Fig. 19.11 Adsorption and desorption curves often show hysteresis. Menkov and Durakova (2007) discussed five different sorption isotherm models for fitting experimental data of sesame flour. Li et al. (2003) applied an additive model to predict sorption isotherms of multi-ingredient tablets from sorption isotherms of each of the ingredients to find that none of the tested processes (wet granulation, drying, compression, and coating) impacted the final isotherm of the resulted product. Freezing/unfreezing a food material does not change the water activity (Aqualab, 2011), although water activities of frozen materials are lower (Chen, 1987). Clausius-Clapeyron (Eq. (19.2)) describes the required energy per mass to undergo a physical phase transition (i.e., adsorption) as a function of the

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FIGURE 19.10 Stability map for dairy powders. Critical water activity corresponds to the glass transition depression of amorphous lactose to 24 C, which may enhance deteriorative changes and loss of quality. Roos, Y., 2002. Importance of glass transition and water activity to spray drying and stability of dairy products. Lait 82, 475e484, with permission.

temperature of the system and only applies for a constant amount of adsorbed material G:   Dh_T;G v ln½p ¼ (19.2)  vT RT 2 G where p is the numerical value of the equilibrium pressure corresponding to the surface excess concentration G ¼ ns/A, and Dh_T;G is the differential enthalpy of adsorption, also defined as Dh_T;G ¼ Du_T;G  RT, where Du_T;G is the differential energy of adsorption, which is the change of internal energy of the complete adsorption system, produced by the adsorption of an infinitesimal surface excess amount dns when temperature T, Volume V, and A (surface area) are held constant (Rouquerol et al., 1999). This equation can be integrated and used to predict water activity at any temperature if the adsorption heat, water activity and saturation pressure at a reference temperature are known (Eq. (19.3)).     Dh_T;G Dh_T;G ln aw ðTÞ$PH2 O ðTÞ ¼ ln PH2 O ðTREF Þ$aw ðTREF Þ þ (19.3)  R$TREF R$T Water activity aw can be measured using capacitance hygrometers, resistive electrolytic hygrometers, or dew point hygrometers, while water sorption isotherms for a material can be generated using a dynamic vapor sorption system, where the weight of the sample is measured over time as it is exposed to a controlled relative humidity environment.

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3.3 Thermal Phase Transitions Glass transition Tg is the temperature region at which an amorphous material (e.g., polymers in detergent granules or carbohydrates in milk) reversibly transitions from a hard and glassy state to a soft, rubbery state and only refers to the amorphous portion of a semicrystalline solid. An increase in water activity aw leads to a reduction in Tg via a plasticizing effect (see Fig. 19.11), which can be modeled using the Gordon-Taylor Eq. (19.4), shown next, where w refers to mass fraction, 1 refers to the mixture of solids, 2 refers to pure water for which Tg2 is w135 C, and k is a constant (Roos, 2002). Tg ¼

w1 $Tg1 þ k$w2 $Tg2 w1 þ k$w2

(19.4)

Vuataz (2002) developed a universal correlation of glass transition temperature Tg for milk powders as a function of water activity, which is fairly linear for 0.12 < aw < 0.65, by applying Gordon-Taylor Eq. (19.5) with a sorption isotherm BET equation. Vuataz (2002) indicates that heating an amorphous milk powder above Tg leads to lactose nucleation/crystallization and that the time required for it to happen is dependent on (T-Tg). Glass transition of a material can be measured according to different methods. As temperature is scanned, a volumetric, mechanical or thermodynamic change linked to the phase transition is monitored, and the temperature (or temperature range) at which the change occurs is identified as Tg. The glass transition using these methods is a kinetic and relaxation transition and, as

FIGURE 19.11 Correlation of glass transition temperature Tg of two polysaccharides (maltodextrin DE12 and DE21) with water activity aw and water content in droplets via sorption isotherm. From Gianfrancesco, A., Turchiuli, C., Dumoulin, E., Palzer, S., 2009. Prediction of powder stickiness along spray drying process in relation to agglomeration. Particulate Science and Technology 27, 415e427, with permission.

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such, depends on the method and the temperature scanning rate (Carter and Schmidt, 2012). Methods to characterize the Tg of a material are classified according to following categories: l

l

l

l

volumetric methods: to characterize Tg based on volume changes are dilatometry and thermal mechanical analysis, mechanical or dielectric changes: to characterize Tg based on change in storage modulus and maximum in loss modulus or when dielectric loss constant goes through a maximum, moisture sorption techniques: characterize Tg by change on moisture uptake as a result of moisture sorption switch from mainly adsorption to absorption, thermodynamic changes: DSC.

DSC is a simple method used to identify the temperature at which a phase change such as Tg or Tmelting takes place and also to measure thermal properties such as specific heat Cp or phase change latent heat l. In DSC, the difference in the heat required for increasing the temperature of a sample and a reference is measured as the temperature is ramped over time. Fig. 19.12 shows a representation of the method and typical curves expected for different phase changes (Ho¨hne et al., 1996). The slight slope in the heat flux curve indicates a continuous increase in specific heat of the sample as temperature increases, while at the glass transition there is a step change in the specific heat of the sample. Steward (2009) uses DSC to obtain the temperature at which the surfactant mixture goes from a biphasic liquid crystal region L1 þ La to an isotropic solution L1 via an endothermic process (boundary in Fig. 19.4). DSC measurements can be combined with thermogravimetric analysis (TGA) measurements, where the mass of the sample is measured over time to provide additional information on loss of inorganic/organic material content as a result of oxidation or thermal degradation processes (Fo¨ldva´ri, 2011). Sticky point temperature Ts is the temperature at which an amorphous or hygrothermal-sensitive material with a given moisture content starts to

FIGURE 19.12 Representation of DSC operation and typical graphs for glass transition (endothermic), crystallization (exothermic), and melting point (endothermic).

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FIGURE 19.13 Relationship between sticky point and glass transition temperature at different contact times for different materials. From Palzer, S., 2005. The effect of glass transition on the desired and undesired agglomeration of amorphous food powders. Chemical Engineering Science 60, 3959e3968, with permission.

agglomerate. Sticky point is related to the glass transition temperature Tg. Palzer (2005) applies sinter technology equations to explain how, depending on the application (contact time and applied force between particles), adhesion forces between particles resulting from viscous flow is relevant for a given process (agglomeration, tableting, caking, etc.).    2 5pd2 X t¼ 10½CðTsTgÞ=½BþðTsTgÞ (19.5) m 4gpd þ 2Ft g d According to this expression, the contact time t required to develop adhesion forces due to particle sintering depends on the surface tension g, the particle diameter d, the applied force Ft, and the material dynamic viscosity mg (z1012 Pa s) at glass transition temperature Tg, where X/d represents the diameter of sinter bridge to the diameter of the particle (typical value 0.1), and C and B are coefficients from the William-Landel-Ferry equation that relates the viscosity for the material at glass transition temperature with viscosity at sticky point temperature (see Fig. 19.13). Jaya and Das (2009) provide (Ts  Tg) values for fruit powders that go from 3e5 C (pineapple powder) to 10e20 C (mango powder) depending on moisture content. An increase in moisture can lead to both an increase and a decrease of the

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FIGURE 19.14 Representation of glass transition temperature Tg, sticky point curve, and sticky region. Adapted from Kudra T., 2003. Sticky region in drying e definition and Identification. Drying Technology 21 (8), 1457e1469.

(Ts  Tg) difference. The sticky region goes above the sticky point temperature up to an upper boundary when the material fully transitions into a liquid state (see Fig. 19.14). Gianfrancesco et al. (2009) studied stickiness of two polysaccharides model solutions (maltodextrin DE 12 and D21) with different Tg/Ts values during spray drying at different conditions, showing that maltodextrin DE12 (higher Tg/Ts) droplets were only sticky close to the atomizing nozzle, while maltodextrin D21 droplets were also sticky along the drying chamber (see Fig. 19.15). This analysis can be used to select fines return to controlled

FIGURE 19.15 Evolution of drop properties during spray drying of both maltodextrin DE12 and DE21. Gianfrancesco, A., Turchiuli, C., Dumoulin, E., Palzer S., 2009. Prediction of powder stickiness along spray drying process in relation to agglomeration. Particulate Science and Technology 27, 415e427, with permission.

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atomization. Goula and Adamopoulos (2008a,b) showed that the addition of maltodextrin to tomato pulp during spray drying acted as a caking agent, altering the surface stickiness of the tomato pulp droplets entering the safe drying regime earlier (no buildup of powder or excessive agglomeration), which led to improved product properties such as powder hygroscopicity, caking, and solubility. The sticky point can be measured using multiple techniques. Boonyai et al. (2004) classify the techniques as follows: l

l

Direct methods involve measuring shear force, viscosity, optical property, cohesion, and adhesion of the material powder sample as it changes from a free-flowing state to a sticky state as a function of moisture and/or temperature. Direct methods are subclassified into (1) conventional (propeller driven, shear cell, ampule, and optical probe); (2) pneumatic (blow, fluidization, and cyclone tests); and (3) in situ stickiness test. Indirect method sticky temperature is inferred from measurement of glass transition temperature once correlation between sticky temperature and glass transition temperature is known.

One of the most common direct methods is the propeller (Kudra, 2003; Jaya and Das, 2004) where a powder sample is placed in a heated, stirred flask. As the temperature of the bath increases, the sticky point is reached when the sample starts to resist movement and the impeller torque raises. Bhadra et al. (2013) successfully applied a standard rheometer with a cup and vane configuration to measure Ts. Boiling point is the temperature at which the partial pressure of water in the material reaches the total pressure of the system PT (100 C for PT ¼ 1 atm and aw ¼ 1) as per Eq. (19.6). Boiling point is important during drying processes at high temperature, defining droplet/material temperature, which increases as water evaporates and water activity aw decreases. TBoiling is T such that PH2 O ðTÞ ¼

PT aw

(19.6)

Water sorption isotherms at different temperatures can be used to estimate the adsorption heat via Eq. (19.3) as a function of water content, which then can be used to extrapolate different temperatures to estimate boiling point.

3.4 Mechanical Properties, Viscoplasticity, and Rheology Mechanical properties of supramolecular structure influence the mechanical properties of the granule that determines particle deformation, attrition, flowability, build up deposition, etc. Mechanical properties of particulate products are important in processability issues such as powder buildup or lumping during pneumatic transport or dosing under high stresses. A

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stressestrain curve represents the correlation between an applied normal stress (s) and the deformation strain (ε). The linear portion of the curve is characterized by the Young’s modulus E, which represents the material elastic (reversible) deformation, which is time and strain-rate independent. The point at which the material starts to deform plastically (non-reversibly) is defined by the yield stress sYield (correlated to aw and Tg), which can be strain-rate dependent and is often correlated to water activity aw. The point at which the material fails is called fracture point. When materials have a viscous-like component, that is, both strain-rate and time-dependent, a viscosity value (consistency l and power index n) is also needed to represent the material. These elastic (spring), plastic (sliding friction), and viscous (dashpot) components can be combined, as in a BinghameMaxwell model, for an elastic, perfectly viscoplastic solid where a spring component is in series with parallel sliding friction and dashpot components (see Fig. 19.16). Strain hardening, creep, and relaxation tests can be carried out to fully characterize the viscoplasticity of a material. In particulate products, it is possible to remove the porosity by compacting the material at high pressure into a tablet on which an unconfined compression test can be conducted to measure Young’s modulus E and yield stress sYield of the material (see Fig. 19.9 Fig. 19.17). During drying processes and pneumatic transport of particulates, the kinetic energy of the impacting droplets/particles should be lower than sYield to avoid agglomeration or sticking of particles to walls. Woo et al. (2010) proposed a model based on the viscoelastic rheological properties of amorphous materials to describe the particle wall collisions. This approach has the advantage of considering the effect of impacting velocity, particle size, and particle rigidity to be incorporated on models for deposition versus a classical approach of sticky temperature criteria. Unconfined compression tests on tableted powder can be carried out with a dynamic mechanical analyzer, where temperature and humidity can be controlled, or using a materials testing machine. However, mechanical

FIGURE 19.16 Representation of elastic, plastic, and viscous components defined by Young’s modulus (E ), yield stress sYield, consistency (l), and power index (n) to model viscoplasticity.

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FIGURE 19.17 Unconfined compression of detergent powder tablet (strain hardening) after removing porosity. Yield stress shows strain-rate dependency.

properties of materials at smaller length scales cannot generally be derived from bulk properties determined by ordinary macroscale methods (Pantano et al., 2012). In addition, the standard well-assessed techniques for mechanical characterization at the macroscale cannot be transferred to the micro- or nanoscale since the machinery and equipment they involve are not suitable for manipulating components with submillimeter size. Therefore a set of mechanical techniques have been developed over the last 25 years for determining mechanical properties such as Young’s modulus, Poisson’s ratio, yield strength, fracture strength, hardness, and endurance limit. Pantano et al. (2012) provide a review of the different test methods developed and establish the following classification: (1) static methods (compression, bending, tension, and torsion tests) and (2) dynamic methods (fatigue test and resonant tests). Table 19.1 provides a comprehensive description of the different test techniques and the relevant properties.

3.5 Particle Size Distribution (PSD) The PSD of emulsions and colloidal/particulate suspensions present in the mixes used to produce particulate products impacts both processability and final product properties. Milk flavor, emulsion stability, and mouth feel depend on the particle size of the fat droplets, and large fat droplets can lead to creaming and a greasy taste (Beckmancoulter, 2015). PSD in liquids and slurries can be measured via laser diffraction (LD) technique where the spatial distribution of scattered light is a function of the particle size in the analyzed sample. The interpretation of data is not straightforward because the phenomenon of light diffraction by particulates is

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Young’s Modulus

Poisson’s Ratio

Shear Modulus

Yield Strength

Fracture Strength

Creep

X

X

Tension

X

X

Compression

X

X

Bending

Axisymmetric

X

X

Bulge

X

MDE

X

Microbeam

X

X

M-Test

X

X

X

X

Wafer curvature

Torsion

Residual Stress

X

X

X

X

X

X

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TABLE 19.1 Mechanical Tests and Determinable Properties

Nanoindentation

Resonant

X

Beams

X

Plates or films

X

X

RUS

X

X

AFAM

X

X

X

SeN curves

Fatigue damage

Crack growth rate

Uniaxial tension

X

X

X

Bending

X

X

X

Thermal

X

X

X

Adapted from Pantano, M.F., Espinosa, H.D., Pagnotta, L., 2012. Mechanical characterization of materials at small length scales. Journal of Mechanical Science and Technology 26 (2), 545e561, with permission.

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Fatigue

Sonic

X

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very complex, and the reader is referred to a review on the subject by Stojanovic and Markovic (2012).

4. PARTICLE STRUCTURE Particle structure is defined as the spatial disposition and volume concentration distributions of the different domains that conform the particle as well as its shape, size, porosity, and roughness. Particle structure properties influence the performance vectors identified in Section 1 for a particle system: appearance, dosing, mass transfer, and breakage propensity. However, the extent to which a given particle structure present in a particle system influences those vectors depends on the mesostructure (next section). Particle structure can be manipulated by the selection of the process and operating conditions to form the particle structure and the domains that constitute it or that are precursors of the final domains that constitute it. Borchers (2005) presents an overview of alternative granulation processes (Fig. 19.18) that may be considered for the formation of particle structures depending on the initial domains selected as well as the desired attributes for the particle. A review of granulation processes and their fundamentals is out of the scope of this chapter, and Salman et al. (2007b) is highly recommended. Selection of the domains that constitute the particle structure may attend to different criteria: 1. function in the particle (e.g., active ingredient, binder material, stabilizing agent) 2. stability through the product life cycle: production, storage, and final use 3. toxicity, environmental footprint, and cost An example of influence of particle structure in fertilizers is presented by Brockel and Hahn (2004). In this article, the authors highlight the roles of a domain that is located at the surface of the particle. Depending on the properties of this domain, such as thickness, uniformity, and porosity, the role of the domain may be (1) carrier of active ingredients for their fast release (domain is not required to cover the full surface of the core); (2) a protective barrier against wear and environment conditions (this domain covers all the surface of the core, but it does not need to present a constant thickness); or (3) a control release shell where the domain is homogenously distributed all along the surface of the core (depending on its thickness and porosity the actives at the core are released over long periods of time). Fill formers, fillers, plasticizers, lubricants, dyes, anticaking agents, and surfactants are part of the composition of this domain and influence its supramolecular structure and therefore its properties. Frantisek Stepanek has devoted a lot of studies to the characterization and modeling of particle structure and its impact on product properties. Modeling

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FIGURE 19.18 Granulation processes and product appearances. Borchers, G., 2005. Design and manufacturing of solid detergent products. Journal of Surfactants and Detergents 8 (2), with permission.

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of particle structure has been done by Ansari and Stepanek (2006) following two approaches: 1. The stochastic design method considers a random distribution of domains in the particle. The particle is contained in a computational unit cell consisting of a cubic grid of voxels. Structure is modified in an iterative way according to the Metropolis algorithm. In every iteration step, two voxels within the particle are randomly chosen and their phase function swapped. The resultant particle structure is evaluated versus a model defined by the user. The user-defined model may refer to particle structure descriptors (e.g., two-point correlation function; Yeong and Torquato, 1998) or particle attributes (e.g., dissolution rate; Ansari and Stepanek, 2006). Voxel change is accepted depending on the results of the evaluation. After that, the next iteration is started. The algorithm ends when no significant change in the evaluation of particle structure is observed over a specified number of successive iterations. 2. In the variational design method (Fig. 19.19), particle structure is the result of the optimization process against an objective function defined by the user (as in the previous approach). Particle structure is generated from its

FIGURE 19.19 Variational approach for modeling of particle structure. Stepanek, F., Ansari, M.A., 2005. Computer simulation of granule microstructure formation. Chemical Engineering Science 60, 4019e4029, with permission.

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domains according to the “granulation formation model.” The particle structure is maintained in a computational unit cell consisting of a cubic grid of voxels. Each voxel carries information about the phases present in the volume it covers. the granule formation process is constituted by a set of granulation process parameters such as primary domain sizes, sequence of primary domains addition, binder domain primary size, and solidification rate. These parameters are systematically varied till an optimum structure against the objective function defined by user is achieved. Domain size and morphology are encoded using the volume-of-fluid method generalized to n domains. As indicated by Ansari and Stepanek, a stochastic approach led to discovery of new unexpected particle structures; however, there is not information about how to physically make these structures, whereas the variational method provides optimal solutions within the boundaries of the process parameters and supramolecular structure properties of the domain. Particle structure may be characterized by the properties discussed in the subsequent subsections.

4.1 Volume Fraction and Size Distribution of the Domains That Constitute the Particle Structure Particle structure is the result of the volume fraction and size distribution of the domains present in the particle. Performance vectors of a given particle structure depend on the supramolecular structure and the concentration of the domains. As the proportion of a given domain increases, the properties of this domain tend to control the behavior of the particle. For example, as the proportion of a domain that presents low values of the diffusion coefficient and solubility increases, the particle dissolution rate decreases significantly (Ansari and Stepanek, 2006). Similar trends can be observed in other properties of particles such as breakage propensity, for which (Fu et al., 2005) observed that as the ratio between binder and particles in granular structures increases, the breakage propensity for a given particle size decreases. Concentration of domains in a particle depends on the ratio of initial materials, equipment design, and processing conditions. Domains that constitute the final particles are the result of the different transformations that take place along the process. Phenomena such as decomposition, reaction, phase change (e.g., crystallization), drying, size exclusion, and agglomeration modify the final concentration of domains within a given particle versus the initial proportion of materials introduced in the process. Size distribution of domains versus final particle size of the granule impacts not only the properties of the particle structure but also the volumetric fraction that can be achieved at a certain size that is conditioned by processes of size exclusion and agglomeration.

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Size exclusion process was analyzed by Glaser (1989), Mulhem et al. (2003, 2006), and Mulhem (2004) who describe the separation of the solid particles from the carrier liquid (SLS) as a result of the relative size of solids in the slurry and the resultant droplet size distribution. Variables such as solids concentration and size of solids play a critical role in the relative proportion of binder and solid domains within a given droplet (Fig. 19.20). Similar principles to size exclusion in atomization processes can be reapplied to comminution of particle structures that present domains that are attrition resistant (Gentzler and Michaels, 2004) at the resulting stress conditions of the process. In agglomeration processes, binder distribution tends to present a different profile from the one resultant from disruption processes (atomization, breakage). In this case, small particles tend to be preferentially primary particles of solids that have not agglomerated or where the extend of agglomeration is below

FIGURE 19.20 Binder and solids fraction as a result of solids exclusion for different macroscopic proportions of binder and solids as well as different undissolved solids size. The top graphs present 50% volume concentration of binder and undissolved solids domain; bottom graphs present 80% volume concentration of binder and 20% volume concentration of undissolved solids. Graphs on the left present a mean particle size of undissolved solids of 150 mm, and graphs on the right a mean particle size of 300 mm.

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average. On the opposite side, large-size particles may be generated as a result of poor distribution of binder in the process, which tends to have average binder content higher than the one that would result from the initial proportion of materials introduced in the granulator. Smirani-Khayati et al. (2009) have studied the binder distribution during granulation processes across different particle size and granulation times. A domain’s size and shape distributions impact internal packing when those domains do not coalesce within the particle. As a result, size and shape distribution of the domains can be critical for particle structure properties such as intraparticle porosity and particle permeability. As the packing of the domains increases, both the intraparticle porosity and permeability decrease. This usually results in particles that exhibit poorer mass transfer properties and higher stiffness. The size distribution of the domain also determines its surface area and therefore impacts the particle reactivity. As the size of the domain decreases, the particle structures typically present higher performance on mass transfer vectors (Ansari and Stepanek, 2006). Characterization of the volume fraction of the domains may be done by measurement of the concentration of the chemicals present. Alternatively, there are some other techniques that allow the characterization of particle structure considering volume, size, and spatial distribution of the domains such as scanning electron microscopy, TEM, magnetic resonance imaging, X-ray microtomography, and X-ray nanotomography. The first two techniques, previously discussed, are “destructive” techniques, as the granule must be modified to study the internal structure. Noninvasive and nondestructive techniques have become more popular over the last 25 years. Nuclear Magnetic Resonance (NMR) imaging consists of the application of a large static magnetic field to the sample of interest to remove the degeneracy of the nuclear spin states of any nucleus of nonzero nuclear spin (Gladden, 1995). An electrical current is then applied to induce transitions between the nondegenerate spin states of the particular nucleus to be studied. The frequency of the radiation that must be applied to satisfy this resonance condition is related to the static magnetic field and the gyromagnetic ratio of the nucleus of interest. Each nucleus has a different gyromagnetic ratio and, hence, a different resonance frequency, thereby explaining the element-specific nature of the NMR technique. To observe the magnetic resonance phenomena of nuclei as a function of their spatial position, a small magnetic field gradient is applied in addition to the uniform polarizing field (Gladden, 1995). One of the major limitations of this technique is the inability to study ferromagnetic materials and samples containing significant amounts of paramagnetic species. However, as previously indicated, one of the key advantages of this technique is the ability to distinguish between states of matter and different chemical species. X-ray tomography is also a nondestructive noninvasive imaging technique that is able to obtain 3D images of a scanned sample from a series of X-ray

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shadow images (Moreno-Atanasio et al., 2010). When X-rays pass through matter, the amount of X-ray photons absorbed by the material depends on the material density, atomic number, and beam energy. Focus and image contrast have been improved in certain applications with the use of a higher beam intensity and a higher degree of collimation from X-ray synchrotron radiation (Moreno-Atanasio et al., 2010). Most of the examples in literature that use X-ray tomography to characterize particulate structures are based on the use of X-ray microtomography (Dadkhah et al., 2012; Rajniak et al., 2007; Stepanek et al., 2005; Farber et al., 2003). With the relatively recent advent of the ultrahigh-resolution Nano XCT, microscopic samples can now be visualized in 3D and down to 2D spatial resolutions of 50 nm at a field of view of 16.6 um (Wong et al., 2014). Some of the limitations of this technique are (1) time resolution to study dynamic behaviors (typically a scan lasts from 30 to 120 min); (2) size restriction for high-resolution studies; and (3) ability to distinguish between materials with similar absorption coefficients.

4.2 Spatial Distribution of the Domains that Constitute the Particle Structure If we consider a particle structure constituted by two domains with constant volume concentration, alternative spatial distribution of domains can be described as in Fig. 19.21. Spatial distribution of domains within a particle is critical in the design of advanced particle structures to (1) protect active ingredients against attrition, poisoning, and humidity or (2) mass transfer control of reactive molecules diffusing into or active ingredients diffusing out of the particle. These types of structures can be found in catalyst, fertilizers, food, biotechnological, pharmaceutical, or detergent particles. Ansari and Stepanek (2006) studied the influence of these structures on dissolution rate of particles. Depending on the physicochemical properties of the two domains, dissolution rate of structures may be significantly impacted by spatial distribution of their domains. As indicated by Knight (2001), starch-based powders are used as thickening agents in food preparation. Starch grains swell and partially dissolve in the temperature range of 55e75 C, which results in an increase of the viscosity of the liquid where the powder is dispersed. During heating, it is essential to maintain suspension of the granules to avoid formation of lumps, which can be achieved by mechanical dispersion. Food products such as gravy granules, custard powder, and snack soups are starch-based products that are treated in such a way that formation of lumps is minimized by modification of particle structure. One of the routes consists of coating starch with highly soluble components such as electrolytes (e.g., sodium chloride) and/or nonionic materials (e.g., glucose, fructose, or maltodextrose). Stepanek et al. (2009) studied the relationship between the volumetric composition of wet granules and the amount of binder available on the surface

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FIGURE 19.21 Spatial distribution of two domains along a particle structure in 2D (left) and 3D (right). Cases (A)-(C) show a random dispersion of normal, milled, and pre-agglomerated particles of the active. Cases (D)-(F) show the active located in the shell, in an intermediate layer, and in the core of the granule. Ansari, M.A., Stepanek, F., 2006. Design of granule structure: computational methods and experimental Realization. AIChE Journal 52 (11), 3762e3774, with permission.

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for different domain morphologies. They showed that the fractional coverage of wet granules follows a bilinear dependence on the binder/solids ratio that corresponds to the pendular and capillary state of granules.

4.3 Porosity and Pore Size Distribution Considering the role of the domain’s volume fraction, size distribution, and spatial distribution, the influence of porosity and pore size distribution on particle structure can be interpreted as the presence of a gas domain within the particle. Therefore as particle porosity increases, mechanisms of mass transfer are enhanced (assuming the same pore size distribution) as a result of an increase on the external and overall specific surface areas of the particle. As described by Ansari and Stepanek (2008), the impact of porosity depends on the properties of the other domains, and it can have a very strong impact when primary particles are fast dissolving, or it can have very small impact when primary particles dissolve slowly. On the other hand, interpretation of porosity as a gas domain that is compressible shows why mechanical properties such as particle stiffness or particle breakage are influenced by the porosity of the granule as indicated by Subero and Ghadiri (2001), who identified different regimes of breakage depending on the granule porosity, and Bonakdar et al. (2016), who showed the relevance of particle porosity on the extent of breakage of spray-dried particles. As previously indicated, bulk density of a particle system is an important property that influences storage volume, transport cost, reactor size, or product appearance. Particle porosity is therefore a critical product attribute for particle systems and needs to be controlled during the manufacturing process. Granules with large porosity are typically generated by spray drying, whereas to achieve low porosities, granulation processes that expose granules to high stress are considered (e.g., agglomeration, extrusion, roller compaction). Pore size and spatial distribution influence mass transfer of material within the particle. These properties have been exploited on catalyst design to improve the selectivity of a specific reaction toward certain compounds that can diffuse more effectively and therefore access to the active sites on the catalyst that are disposed spatially at the core of the particle. They are also used to control the release of nutrients in fertilizers by controlling the pore size distribution of the coating covering the nutrient Brockel and Hahn (2004). Particle wetting is influenced by the pore size distribution: 1. When the contact angle between the fluid and the surface of the pore is higher than 90 degrees, as pore size distribution decreases, the pressure required for a fluid to penetrate within a given pore increases.

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2. When the contact angle between the fluid and the surface of the pore is below 90 degrees, the pressure at the pore increases as pore size decreases. This relationship for capillary pressure is described by the Young-Laplace Eq. (19.7) assuming cylindrical pores. This equation is used to measure porosity and pore size distribution of particle systems via porosimetry. DP ¼

4s cos q dpore

(19.7)

where DP is the pressure gradient across the gas fluid interphase within the pore, s is the surface tension of the fluid, q is the angle of contact between liquid and particle, and dpore is the diameter of the pore. Particle porosity can be estimated using several techniques such as mercury porosimetry, X-ray micro CT tomography, gas sorption isotherm, or image analysis. A conventional technique to characterize porosity and pore size distribution is mercury porosimetry, which allows characterizing pores between 500 um to 3.5 nm. In this technique, a volume penetration of a fluid (typically mercury) into the pore structure of the sample is monitored at different pressures. Based on Eq. (19.7), the diameter of the pore corresponds to a given pressure assuming cylindrical pores. When pore size is smaller than 50 nm, gas sorption isotherms may be considered for the determination of the pore volume and the pore size distribution, as is discussed in the next section.

4.4 Specific Surface Area The specific surface area of a particle is a function of porosity, pore size distribution, shape, size, and roughness. The role of the specific surface area is critical in the design of a heterogeneous catalyst where typically a domain with high specific surface area (e.g., g-alumina, silica, zeolites) denominated carrier is included in the structure of the catalyst. An actual catalyst (e.g., platinum, rhodium, palladium) is deposited on the surface of the carrier to maximize the yield of the desired reaction and reduce the use of catalyst. Catalyst performance is therefore related with the specific surface area of the carrier. A similar case is when substrates are used in absorption columns where the surface area of the particles used in the packed bed influences the yield and the time required to deactivate the column. Depending on the porosity and pore size distribution of the particle, the specific surface area is influenced by size, shape, and roughness. When the particle structure presents nil or low porosity, the specific surface area of the particle is a function of these other attributes. Under these circumstances the specific surface area typically presents a stronger correlation with dissolution rate of the particle if the dissolution rate is controlled by external mass transfer.

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The specific surface area is typically characterized by the physical adsorption of a gas (argon, krypton, or nitrogen) on the surface of the sample at cryogenic temperature. Gas adsorption can be determined by volumetric, gravimetric, or flux methods. The volume of gas adsorbed on a monolayer over the surface of the particles is determined according to the BET equation (Brunauer et al., 1938), and the specific surface area is calculated based on molar volume of the gas and the average area occupied by the gas molecule.

4.5 Surface Energy The surface energy of a particle influences adhesion forces between particles as well as the wettability of particles with fluids. The contact angle between a fluid and a particle is determined by the relative surface energies of the system’s particleeliquid, liquidegas, and particleegas. It therefore influences properties of the particle such as dissolution rate by modifying wetting and particle dispersion. Thielmann et al. (2008) have studied the impact of surface energy on agglomeration both experimentally and via modeling. Hydrophilic particles were found to yield a narrower granule size distribution than hydrophobic ones. This is due to several aspects such as poorer agglomeration of primary hydrophobic particles and less uniform spreading of the binder on their surface, leading to a wider size distribution. Shat et al. (2014) showed how the influence of both surface energy and shape of crystals impact the cohesion of particle systems. Surface energy can be measured via contact angle measurements of tablets produced with particles or by capillarity of packed beds using the YoungLaplace equation described before. However, inverse gas chromatography (IGC) presents fewer issues, and it is a preferred technique as it allows the characterization over a wider range of temperatures without the modification of the particle structure (e.g., by compression due to tableting). In IGC (Mohammandi-Jam and Waters, 2014), a particulate system is placed in a column where a low concentration of a well-characterized single gas or vapor of a volatile substance is injected via an inert carrier gas through the column. The volatile substance is typically identified as a probe molecule. Different probes with different known characteristics such as polarity, acidity, or molecular area are used. The respective properties of the stationary phase can be determined by analyzing the retention data resulting from the interaction of a well-defined probe with the stationary phase.

4.6 Surface Forces Surface forces of particles play a critical role on the properties of particulate systems such as caking, flowability, and rheology of solids suspensions. Therefore, understanding the surface forces between particles provides the

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basis for understanding of the overall system. Most common adhesive forces between particles can be classified as follows: l

l

l

Van der Waals forces based on electric dipoles of atoms and molecules. Their intensity depends on the particle size, interparticle distance, and composition of the domain at the surface of the granule. Electrostatic forces are based on different electric potential of particle surfaces. Liquid bridges are a result of capillary forces exerted by liquid in the zone of contact between particles.

Particle surface forces are influenced by supramolecular properties of the domains situated at the surface of the particle, particle size, shape, and roughness. Advanced surface force measurements are most often conducted on model systems using model materials such as mica, gold, and silica in atomic force microscopes (AFM). AFM are composed of a microscale elastic cantilever with a sharp tip. When the tip is brought into proximity to a sample, surface adhesive forces between the tip and the sample lead to deflection of the cantilever. The forces acting on the tip are dependent on its distance to the surface. Topography of the sample can be determined by moving the tip across the surface and measuring the distance dependence. A bulk technique that is less resource intensive consists of the use of centrifuges. A certain amount of particles is initially pressed by use of centrifugal force against a rigid wall. Subsequently, the wall is reversed, and the centrifugal force is modified to pull the particles out of the wall. The measurement of force required to pull the particles out is correlated to the adhesion forces.

4.7 Surface Roughness Surface roughness plays a critical role on the interaction between the particle and other particles and fluids. This influences cohesion and wettability of the particles and therefore has some influence on performance vectors such as dosing or mass transfer. Particle interactions are impacted by surface roughness as it leads to a reduction of adhesive forces via an increase of the distance between particles. Several authors such as Rumpf (1990), Rabinovich et al. (2000), and Laitinen et al. (2013) have provided equations that relate the adhesion forces due to Wan der Vaals forces with the particle roughness. " # A rR R Fad ¼ þ (19.8) 6H02 r þ R ð1 þ ðr=H0 ÞÞ2 where Fad is the adhesion force, A is the Hamaker constant, R is the radii of the particle, and r is the radii of the asperity.

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Roughness also impacts particle adhesion controlled by other adhesion forces such as electrostatic and liquid bridges. Impact of wall roughness is small in comparison to its influence on Van der Waals forces, especially as the amount of liquid increases (Schulze, 2008). As previously discussed, roughness can significantly increase the specific surface area, which has a significant impact on mass transfer and product attributes. Roughness also influences the interaction with fluids in different ways. l

l

l

Depending on the surface tension and contact angle between the fluid and the domain at the surface of the particle, wettability of the particles may change significantly by varying roughness (Hassas et al., 2016; Xia et al., 2016). Particle roughness is known to impact the boundary layer of liquid flowing around it and therefore impact the drag coefficient between the particles and the fluid as well as the heat and mass transfer particle-bulk coefficients. So it can be manipulated to enhance transport phenomena processes between particle system and fluid. Capillary condensation of vapors in the gas phase takes place at the surface of the particle, which may impact the adhesion forces between particles and with the container. Contact of particles with liquid condensed on the surface is dominated by the interaction between condensed fluid and the particles.

Characterization of particle surface can be performed using atomic force microscopy.

4.8 Formation of Particle Structure During Drying Some of the granulation processes introduced previously such as spray drying and fluidization systems present drying as a critical transformation to modify the properties of the particulate system. Both the original supramolecular structure of the domains and the particle (droplet) structure evolve as a result of drying: 1. The volatile solvent (typically water) activity of the domains is reduced. This results in the modification of the mechanical properties of the domain as well as precipitation of new domains as crystalline or amorphous supramolecular structures. 2. Particle size evolves as a result of particle shrinking during the initial stages of drying till the formation of a shell or crust at the surface of the particle. During the latest stages of the drying process, mechanisms such as particle inflation, imploding, or shattering result from (1) gradients of pressure between core and surface of the particle and (2) mechanical properties of the shell. 3. Particle shape is influenced during the initial stages of drying by the domain’s surface tension and viscosity as well as the flux of thermal energy to the particle. During the latest stages of drying, particle shape is also impacted by diverse mechanisms such as inflation, collapse, imploding, or shattering.

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4. Particle surface properties are also conditioned during drying. On one hand, the spatial distribution of domains defines which domains are present at the surface of the particle; on the other hand, some mechanisms that control particle shape may also impact particle roughness. 5. The spatial, volumetric, and size distribution of the different domains is a function of transfer phenomena such as flux of thermal energy to and within the droplet and mass transfer of components and/or domains within the particle. Vehring (2008) presents a simple way to estimate the distribution of components in the droplet based on Fick’s second law of diffusion in absence of capillarity and internal convection effects: cs;i ¼ cm;i

e0:5Pei 3bi

(19.9)

where cs,i is the concentration of component i at the surface, cm,i is the average concentration of the component i in the droplet, and Pei is the Pe´clet dimensionless number defined as the ratio between external mass transfer of solvent that controls the velocity of the receding interface and mass transfer by diffusion of the component i in the droplet. bi is a function that must be integrated numerically for each Pe´clet number: Pei ¼

4 8Di

(19.10)

where Di is the diffusion coefficient of component i in the droplet and 4 is the convective evaporation term that can be approximated in case of forced convection according to the equations defined by Ranz and Marshall (1952) as   Mw;l Ys ðTe Þ h i 4kg ln 1 þ Mw;g 1þYs ðTe Þ 1=3 4¼ 2 þ 0:6Re0:5 (19.11) d Prg rl c p where kg is the external heat transfer coefficient between the droplet and the gas phase, rl is the density of the solvent, cp is the specific heat of the gas, Ys is the equilibrium molar fraction of the solvent at the surface. Ys depends on the equilibrium temperature at the surface (Te). Expression (19.11) also considers the following dimensionless numbers: Red is the droplet Reynolds number, Prg is the gas phase Prandtl number phase and Mw,l /Mw ,g is the ratio of the molecular weight of the solvent and the gas. The expression (19.11) assumes that the concentration of solvent in the gas phase is very small in comparison with concentration at the surface of the droplet (Ys(Te)  YN) ¼ Ys(Te). The determination of Ys can be done by solving iteratively Clausius Clapeyron equation:   Ys ðTe Þ ¼

e

v ln Pv;ref DH R

Pt

1 Te

þ

1 Tref

(19.12)

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and lg ðTN  Te Þ ¼  DHv Ys ðTe Þ Mw;l M kg

(19.13) w;g

where lg, the external mass transfer constant of the solvent in the gas phase and kg can be estimated from Ranz and Marshall equations, DHv is the enthalpy of evaporation, TN is the temperature of the drying media, R is ideal gas constant and Pvref and Tref are respectively the reference equilibrium temperature and the vapour pressure data for the solvent. These equations are useful to understand how process conditions such as temperature TN and particle dispersion Red, drying media properties lg, kg, Prg and domain and/or component properties Di, DHv influence the spatial location of components or domains within the particle. When Pe´clet number Pei is smaller than 1, the domain and/or component diffusion is relatively fast compared to the radial velocity of the receding droplet surface. Therefore, domains and/or components remain fairly evenly distributed in the droplet during drying. On the other hand, when Pe´clet number Pei is larger than 1, the surface moves faster than the domains or dissolved components. As a result, the surface becomes enriched with the components and/or domain that present a high Pe´clet number. Formation of shell or crust at the particle surface is triggered by packing or coalescence of domains or by precipitation of new domains that may present crystalline or amorphous structure. Large Pe´clet numbers reduce the time required to reach the critical concentration of domains or saturation of components that result on the formation of the shell at the surface of the granule. Therefore large Pe´clet numbers typically result in large particle porosity. The composition of volatile components in each domain, the solubility of components in volatile solvents, and the interdomain forces (Van der Walls, electrostatic) all influence the mass transfer phenomena within the particle and the generation of new domains. Particle morphology resulting from droplet drying has been studied in literature both from characterization and modeling points of view. Several conceptual maps (Charlesworth and Marshall, 1960; Hassan and Mumford, 2007; Handscomb and Kraft, 2010) have been used in the literature to describe how process conditions (e.g., drying temperature history) and domain properties impact particle morphology during drying (Fig. 19.22).

4.9 Modeling of Particle Structure During Drying The modeling of particle structure during drying includes up to five (Nesic and Vodnik, 1991) different stages. Depending on the particle properties and drying conditions, some of these stages may not be relevant to simulate drying

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FIGURE 19.22 Conceptual map of mechanism for droplet drying on droplets containing dissolved solids or solids suspensions. From Handscomb, C.S., Kraft, M., 2010. Simulating the structural evolution of droplets following shell formation. Chemical Engineering Science 65, 713e725, with permission.

kinetics and morphology evolution of a specific system. The proposed stages are these: 1. At induction period, surface droplet temperature evolves from the initial temperature to the wet bulb temperature so that the external mass and heat transfer rates between droplet and drying medium are balanced (heat of evaporation equals the convective heat due to the T e Tbulb temperature gradient). 2. During the constant drying rate period, the droplet surface is saturated with volatile solvent, and the droplet temperature remains constant at the wet bulb temperature. Drying rate is controlled by external heat and mass transfer rates between droplet and drying medium. During this stage the droplet shrinks according to D2 law. 3. Falling rate period is achieved when the droplet surface is not saturated anymore, and drying is controlled by internal mass transfer of the volatile solvent to the surface. A shell or crust is formed at the surface of the particle and droplet diameter remains constant or presents a relatively

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small shrinkage. As a result of the reduction on the evaporation rate, the droplet temperature increases until the heat and mass transfer rates are balanced again. 4. Bubble nucleation and inflation period. Those systems that present bubbles of gas within the droplet experience internal expansion forces due to the increase in pressure at those bubbles. The resulting pressure is mainly controlled by the vapor pressure of the volatile solvent, which is a function of the droplet temperature. When the vapor pressure of the volatile components equals the internal pressure at the bubble, the components evaporate instantaneously, and the temperature is equal to the boiling temperature of the solvent in this system. Boiling temperature may increase as volatile concentration decreases, therefore temperature is defined by the moisture content and pressure. The final morphology of the system depends on the properties of the shell and the temperature history of the droplet. 5. Dried particle. Once volatile solvent is completely removed, temperature of the droplet evolves to the temperature of the drying medium until equilibrium is reached. There are different approaches in the literature in relation to the modeling of particle structure during drying.

4.9.1 Models Considering Mass Transfer of Volatile Components Modeling of induction and constant drying rate stages are neglected in some cases depending on the system studied. The approach used to model these initial stages is well established. Two different strategies are often used to model the drying stage with a falling rate: 1. Effective diffusion models (Kentish et al., 2005) assume that moisture transport within a drying droplet can be described by an effective diffusion coefficient, which has a strong relationship with moisture content and temperature. 2. Shrinking core models (Farid, 2003) assume that the solutionecrust interface recedes into the porous particle. Evaporation occurs at the receding interface, and water mass transfer is controlled by vapor diffusion through the shell. The modeling of the nucleation and inflation period assumes the presence of a bubble at the core of the droplet that changes in size as a result of the force balance between bubble pressure and surface tension and/or mechanical properties of the shell. Hecht and King (2000) consider two scenarios: (1) the bubble changes volume at constant pressure so the final bubble volume is defined by the thermodynamic equilibrium; (2) the bubble changes pressure at constant volume. Then the pressure difference between the gas in the bubble

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FIGURE 19.23 Modeling strategy for drop drying considering mass transfer of volatile solvent, solute in the solvent, and discrete phase. From Handscomb, C.S., Kraft, M., 2010. Simulating the structural evolution of droplets following shell formation. Chemical Engineering Science 65, 713e725, with permission.

and the drying gas is converted into an expansion or contraction velocity. This velocity is multiplied by the magnitude of the time increment to determine how much the bubble grows or shrinks.

4.9.2 Models Considering Mass Transfer of Volatile Solvent and Discrete Phase This approach (Sydel et al., 2006) models the radial distribution of components and domains throughout the particle as a result of mass transfer of the continuous (volatile solvent) and discrete phases (solids). Modeling of the discrete phase is done via population balances that may consider convection, diffusion, nucleation, and particle growth mechanisms. The modeling of the continuous phase (volatile solvent) may also consider convection, diffusion, and crystallization. During the drying falling rate period, mass transfer throughout the shell is considered to be controlled by vapor diffusion through the porous structure. Handscomb et al. (2009a,b) and Handscomb and Kraft (2010) follow this approach with the incorporation of additional sub-models that define the evolution of the particles after the formation of the shell. The criteria for the application of sub-models is based on the relative magnitudes of the capillary pressure in the surface of the pores, the strength of the growing shell, and the pressure drop across the shell (Fig. 19.23).

5. MESOSTRUCTURE Mesostructure is defined as the spatial disposition and arrangement of particles and liquids along a volume that is representative of the bulk product or a region of it. Mesoscale manipulation is essential to define the properties of particulate systems, either multi- or single component. Most of the processes to produce

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particles, especially granulation ones, generate particles that are not identical to each other. As a result, particle properties need to be defined as distribution functions that are representative of a specific volume within the bulk. Mesostructure may be manipulated by modification of the particulate system at different scales: 1. supramolecular structure: drying, crystallization of components, composition, glass transition 2. particle structure: comminution, agglomeration 3. particle distribution within a given volume: classification, mixing, segregation, fluidization, addition of particles or liquids As a result of mixing and segregation, not only the mesostructure evolves, but the macroscale structure (unit operation scale) does as well. In a homogeneous system, macroscale structure can be characterized by mesostructure, whereas in a heterogeneous system, macroscale is described by multiples mesostructures distributed within the unit operation. Macroscale structure is equipment dependent, and it is not considered within this work. Mesostructure can be characterized by the properties described in the subsequent sections.

5.1 Size and Shape Distribution of Each of the Different Particulate Components This is one of the key properties in a particle system that influences most of the performance vectors. Ratio surface/volume of a particle increases as particle size decreases. Therefore all processes that are influenced by particle surface to volume ratio, such as dissolution or adsorption, are enhanced as particle size of the population decreases. Also, as particle size decreases, the range of particle interaction forces such as Van der Waals and electrostatic become of the same order of magnitude as gravity and the number of particle contacts per unit of volume increases. This has a strong influence on packing (Kojima et al., 2013), flow (Capece et al., 2015, Fig. 19.24), attrition (Ghadiri and Zhang, 2002), and fluidization behavior (Geldart classification) of the particle system. Ratio of cohesive to gravitational forces can be characterized by the granular bond number: Bo ¼

Fcohesion Weight

(19.14)

Addition of flow aids, lubricants, or flow agents to improve flow properties and packing of cohesive particle systems is a common practice in industry to modify mesostructure of particle systems. These flow aids may have different roles depending on the type of interaction between particles: (1) when the bond number is large, lubricants are introduced to reduce the adhesion forces

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FIGURE 19.24 Influence of granular bond number on bulk flow function coefficient. From Capece, M., Raimundo, H., Strong, J., Gao, P., 2015. Prediction of powder flow performance using a multi-component granular Bond number. Powder Technology 286, 561e571, with permission.

between particles and with the wall, and (2) when the particle system exhibits a tendency to caking, anticaking agents create a physical barrier between particles minimizing the number of direct contacts. The selection of the flow aid depends on the size distribution of the original system and the required function: anticaking or flow agent. The size ratio between the flow aid and the particle system needs to be large enough to reduce adhesion forces between particles but not too large so that it enhances particle forces (Fig. 19.25). Both the concentration of the flow agent used and the mixing time enhance the coverage of original particles by the flow aid (Kojima et al., 2013) to a point when most of their surface is covered by the flow aid. At this point, the flow agent interparticle contacts start to be dominant, resulting in a reduction of the flow properties of the material. Particle systems are characterized by particle size defined as distributions that can be based on volume, number, or surface. These distributions can be represented as frequency distribution or cumulative curves and can be described by different descriptors: 1. Single parameters that correlate well with a performance vector. For example, Sauter mean diameter (diameter of a representative particle for which its surface/volume ratio equals that of the distribution of particles) is used to characterize a distribution with regard to dissolution rate.

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FIGURE 19.25 Influence of particle diameter of flow aids on interparticle Van der Waals forces. From Schulze D., 2008. Powder and Bulk Solids. Behaviour, Characterization, Storage and Flow. Springer, with permission.

2. Parameters that characterize distribution functions that are adjusted from experimental characterization data. The most common functions are normal distribution, logarithmic normal distribution, Rosin Rammler, and logarithmic Rosin Rammler. These distributions are usually defined by two parameters: a characteristic size and a representative parameter of the population spread. The spread of the size distribution is a very important parameter that impacts several performance vectors. Narrow distributions have a smaller packing and exhibit fewer contacts per particle than wider distributions (Mort et al., 2004). In addition, the tails of wide distributions have more influence on certain particle system attributes, due to the size of the particles changing by more than one order of magnitude from the large to the small particles. Size characterization may be done via different methods (Rhodes, 2008), of which the most common ones are sieving, image analysis, and laser diffraction. The characteristic dimension of the particles is a function of the technique used and the shape of the particles. Sieve analysis had been a classical method to characterize PSD until the introduction of more advance techniques such as image analysis and laser diffraction. It provides a mass distribution as a function of the characteristic length of the sieves used for the analysis.

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Image analysis (via one or two cameras) characterizes individual particles and provides precise morphological information. This technique is more resource intensive as it characterizes individual particles, and therefore a small sample size is typically used. The size distribution obtained by image analysis is based on a number size distribution, and therefore it is very sensitive to the presence of very fine particles. Laser diffraction provides bulk material properties and volume size distributions; therefore this technique is less resource intensive and can handle a larger amount of material with rapid characterization. This technique is very sensitive to the presence of very coarse particles. Laser diffraction is a preferred technique for very fine size distributions or continuous monitoring, whereas image analysis is preferred for coarser size distributions. Although it is possible to obtain information about particle shape with laser diffraction, only image analysis allows the true characterization of particle size and shape (Califice et al., 2013). Shape is another relevant distribution property of mesostructure that influences performance vectors related with surface/ volume ratio (Tseng et al., 2015), flow (Sandler and Wilson, 2009; Johanson, 2009), and packing Yu et al., 1996 (Fig. 19.26). The prediction of particle size and shape distribution resulting from the formation, manipulation, and handling of particulate systems is typically approached by population balance modeling (PBM). Smoluchowski (1916) is considered to be the first work to formally use population balances for polydispersed particle dynamics. Since this work, PBM has been used in many branches of engineering and science such as polymerization, aerosol, crystallization, emulsification, boiling, chemical reactors, or separation. The processes modeled by the population balance equation are characterized by the presence of a continuous phase and a dispersed phase comprising of entities

FIGURE 19.26 Influence of particle size volumetric mean (B) and size distribution (A) spread on packing. From Zou, R.P., Gan, M.L., Yu, A.G., 2011. Prediction of the porosity of multi-component mixtures of cohesive and non-cohesive particles. Chemical Engineering Science 66, 4711e4721, with permission.

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with a distribution of properties, such as size, shape, or composition. The different terms of the population balance equation PBE take into account that the entities of the population can change their properties due to various physical phenomena (Solsvik and Jakobsen, 2014). The particle phase space constitutes the internal and external particle coordinates. External coordinates refer to the spatial distribution of the particles, whereas the internal coordinates refer to those properties associated to each individual particle such as volume, diameter, composition, or shape. A population balance equation presents the following terms: Accumulation: it is applicable to transient models to express the variation over time of the number of particles that have common internal coordinates (e.g., size, shape, etc.) l Convection and diffusion: in external coordinates, it refers to the continuous change of position of particle entities as a result of convection or diffusion processes. In the case of internal coordinates, this term is also used as to refer to those evolutions that are continuous and gradual along these internal coordinates such as expansion, compression, or evaporation (Solsvik and Jakovsen, 2014) l Source: it refers to sudden rate of appearance of disappearance at a point in the internal coordinates. These phenomena are referred to as birth and death of particles. Breakage of a given particle results in a death event of the original particle and birth events of the resulting particle entities. Birth and death events are typically defined by kernels. A kernel is the key phenomenological instrument in a PBE, as it gives the functional dependence of the aggregation or breakage rate as a function of the particle properties and process conditions. A kernel may be based on (1) a physical model and knowledge of all the variables, (2) a semiempirical approach where a mechanistic insight is applied, or (3) purely empirical approach fitted from experimental data. Accumulation þ Spatial convection þ Internal convection ¼ Source l

vfn ðr; X; tÞ þ Vr ½ fn ðr; X; tÞvr ðr; X; tÞ þ VX ½ fn ðr; X; tÞvX ðr; X; tÞ ¼ Jðr; X; tÞ vt (19.15) where fn is the number density function that depends on the spatial position r and, internal property X, vr, and vX are the convective velocities along space r and internal property X, and J is the source term (Solsvik and Jakovsen, 2014). There are some situations where spatial variation may be neglected and where the interest lies in studying the global behavior of the system. In this case, Eq. (19.15) may be simplified: X Q k nk vnðX; tÞ vlogðVÞ þ VX ½nðX; tÞvX ðX; tÞ þ n ¼ JðX; tÞ  vt vt V k

(19.16)

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where n is the number of particles with property X, and Q is the volumetric flow rate across the k input and output streams to the unit operation of volume V. The application of PBM to different processes is reviewed by Ma et al. (2016) in the case of crystallization and (Salman et al., 2007b) when applied to agglomeration. In addition, different applications of PBM to predict particle size in different operations are described by Vogel and Peukert (2005) for impact mills, Nijdam et al. (2006) and Verdurmen et al. (2004) for spray drying towers, Chaudhury et al. (2015) for reactive granulation, and Meyer et al. (2015), Vreman et al. (2009), and Tan et al. (2005) for fluid bed granulation.

5.2 Contact Points Contact mechanics between particles within a volume conditions packing, flow, and attrition of a particle system (Fig. 19.27). Properties such as coordination number and contact density define the yield strength of a cluster of particles as well as the transmission of stress along a given system. Rumpf et al. (1976) proposed that the tensile strength of a cluster of spherical particles could be estimated according to the following equation: st ¼

1  ε Fa n 2 p d

(19.17)

FIGURE 19.27 Network of normal contacts in a polydisperse system. From Tsoungui, O., Vallet, D., Charmet, J.C., 1998a. Use of contact area trace to study the force distribution inside 2D granular systems. Granular Matter 1, 65e69; with permission.

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where (1 e ε) refers to particle packing, Fa is the adhesion force between particles, d is the particle size, and n is the mean coordination number. Based on this equation, the tensile stress is proportional to the coordination number. As particle systems get more complex and polydispersity is present (Tsoungui et al., 1998b), a new parameter is introduced in the equation, which is a function of the variation of the packing density with the mean particle volume. In general, this parameter presents a weak dependency with the particle size ratio. Mort et al. (2004) performed simulations to predict the distributed structural and compositional features of the mesostructure, based on predefined packing values. This approach allowed defining the correlations to determine average coordination number and number density of contacts based on packing and size distribution. Mort et al. (2004) also studied impact of an anticaking agent (addition of a particle 100 times smaller than the primary system) on the reduction of the number of particle contacts. As it can be seen in Fig. 19.28, only when the level of the fines (caking agent) exceeds a critical value does the reduction in the number of contact points between the coarse particles start to be effective. Experimental characterization of the coordination number may be assessed by X-ray microtomography (Nguyen et al., 2011). However, this technique (Kalender, 2011) is still very resource intensive and can be challenging when the mesostructure features distributions of shape, size, and components. An alternative approach is to infer the average number of contacts from the properties of the particle system via the application of a model, as shown by Mort et al. (2004).

FIGURE 19.28 Effective reduction in coarseecoarse particle contacts as the addition of fines (caking agent) reaches a critical value f*. (A) full mean contact distributions as a function of fines level; (B) trend of mean coarse contacts with the mean size of the coarse particles (dgv) as a function of fines level. From Mort, P.R., Greene, G., Pillai, S., Popov, G., Riman, R.E., 2004. A multi-scale approach to modelling of particle assemblies in materials. Journal of the Ceramic Society of Japan, Suppl. 112-1, PacRim5 Special Issue, 112 (5), 271e274, with permission.

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5.3 Particle Spatial Distribution The proposed definition of mesostructure includes particle systems with different materials that can be present as particles or fluids. Those components may be introduced as random mixtures or as ordered structures. An ordered structure presents fluids or particles spatially distributed on fix locations versus reference particles (e.g., coatings). One of the key performance vectors for particle structured systems described at the beginning of the chapter was dosing, referring to the ability to consistently provide accurate amounts of homogeneous chemistry. This is critical in applications such as pharmaceuticals, fertilizers, detergents, or advanced ceramics. Therefore, one of the key aspects of dosing refers to the characteristic length scale used to describe a volume within which a homogenous mixture of components is found. Mort and Riman (1995) derived a general equation for multicomponent mixtures: "     X  # n sxðiÞ 2 6 1  2Vi s2i s2k ¼ Vk w k þ wi þ þ (19.18) pD3 ð1  εÞ Vi Vi wi wk k¼1 where D is the characteristic length scale of the volume of particles studied, and sx(i) represents the value of the mixing standard deviation with respect to the ith component. V is volume fraction excluding packing (1 e ε), w is the mean particle volume per component, and s is the standard deviation of the particle volume distribution. It can be inferred from this equation that variability of a given particle increases as follows: l

l l l

as characteristic length of the system (D) decreases; related to dose or sample size, as volume fraction of the particle decreases (Vi), as particle size of the component increases (wi), as packing of the system decreases (1 e ε).

The previous equation does not take into consideration segregation mechanisms and assumes a random mixing of the components. However, it highlights some of key strategies when designing a structured particle system: l

l

l

Minor active components are typically incorporated into particles that are present at a significant volume proportion in the mixture to reduce dose variability. As particle size of the system decreases, the variability also decreases as long as segregation mechanisms do not become dominant. Ordered structures tend to be an efficient method to ensure that minor components distribution during mixing is more effective.

Modeling work performed by Mort et al. (2004) on the average radial composition of random and ordered particle structures is able to differentiate, in coated particles, the presence of the monolayer of coated material at the

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FIGURE 19.29 Impact of mixing time on the distribution of flow aid nano particles on the surface of particles. From Kojima, T.J., Elliot, J.A., 2013. Effect of silica nanoparticles on the bulk flow properties of fine cohesive powders. Chemical Engineering Science 101, 315e328, with permission.

surface of the core and then an additional monolayer corresponding to the neighbor particles. On the other hand, the random mixture of material of the same size shows a radial probability function that oscillates as it converges to the bulk fines composition. Both the volumetric concentration and also the distribution of materials impact the properties of the mesostructure. As previously discussed, the introduction of flow aids or anticaking agents are good examples of the effects on flow, packing, and caking propensity of a given system as a result of the addition of a new particle component. The impact of mixing time on flow and packing after the addition of flow aids is related to the evolution of flow agents from a random to a more ordered structure (Kojima and Elliot, 2013) (Fig. 19.29). Particle composition within mesostructure may evolve as a result of segregation mechanisms during transport and handling of the particulate system. Some of the factors that influence segregation are differences in size, density, shape, and particle roughness. Johanson (1996) distinguishes between five primary mechanisms of segregation: trajectory, sifting, fluidization, air current, and angle of repose, and Tan and Puri (2004) (Fig. 19.30) establish a new segregation classification based on the role of particle size in the mechanism of segregation that allows identifying segregation patterns and determine solutions. Segregation mechanisms are equipment dependent (e.g., silos, chutes), and therefore a great effort needs to be done on designing processes that minimize

FIGURE 19.30 Classification of segregation mechanisms. From Tan, P., Puri, V.M., 2004. Methods for minimizing segregation: a review. Particulate Science and Technology 22, 321e337, with permission.

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it (Tan and Puri, 2004). However, in many situations, the design of the process may not be sufficient or cannot be modified (e.g., existing process or product to be used in a process owned by a customer of product). In this case, the design of mesostructure needs to consider the major factors that influence segregation and minimize its influence. Size ratio between particles is typically one of the most critical parameters, and thus it is a good practice, whenever possible, to design particle systems whose mesostructure presents a narrow size distribution. Modeling of particle segregation can be done via continuum modeling (Combarros et al., 2016; Fan et al., 2014) or discrete element modeling (Combarros et al., 2014; Ketterhagen et al., 2009). Discrete element modeling has been used to understand the fundamentals of the segregation mechanism by studying the relationship between the particle structure properties and the evolution of the mesostructure (Bhattacharya and McCarthy, 2014). Modeling of the macroscale has been done via two approaches: (1) continuum modeling where mass transfer parameters may be estimated from experiments or from discrete element modeling work (Fan et al., 2014) and (2) discrete element modeling by applying scale-up rules that allow one to decrease the number of particles to be simulated versus the real case (Feng et al., 2009).

5.4 Liquid Spatial Distribution The spatial location of fluid incorporated into a particle system depends on multiple factors that can be classified as follows: 1. equipment and operating conditions during fluid incorporation: spray flux number, droplet size, shear stress distribution, mixing profile, ratio fluid/ particle system, and residence time; 2. fluid properties: surface tension, viscosity, melting point, and wetting angle; 3. particle system (substrate) properties: PSD, surface energy of different particles, porosity, and specific surface area. According to these conditions, the fluid may be located at different positions: 1. within the pore structure of one or multiple particle components, 2. homogenously distributed along the surface of one or multiple particle components, 3. heterogeneously distributed on the surface of one or multiple particle components, 4. as agglomerated lumps of fluid with small particles embedded. The impact of incorporating a fluid into a particle system on its mesostructure properties tends to be less significant when the fluid is distributed within the pore structure of the particle system. Variables that influence the

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penetration time of the fluid into the pore structure can be inferred from Washburn equation: t¼

4mL2 dpore gLV cos q

(19.19)

where m is the fluid viscosity, dpore is the diameter of the pore, gLV is the liquid surface tension, Q is the contact angle, L is the penetration length of the pore, and t is the penetration time. Fluid distribution on the surface of the particles may lead to the formation of liquid bridges that influence appearance (lumps, size distribution) as well as flow and packing properties by increasing particle cohesion. Liquid bridges may evolve to solid bridges when the temperature of the system falls below the melting point of the fluid (hot melts) or when some components of the particle system are soluble within the liquid deposited on the surface (Rock and Schwedes, 2005). Finally, the fluid may absorb the particles and modify the rheological properties of the microstructure at the surface of the granule (e.g., phase change or modification of glass transition temperature) leading to a mechanism of caking by viscous flow of the material at the surface of the particle (Hartman and Palzer, 2010). Hapgood et al. (2008) provide a detailed review of wetting mechanisms for particle systems applied to granulation processes.

5.5 Particle Packing Particle packing is a property of mesostructure that defines the bulk density and therefore influences cost of transport, storage, equipment design, appearance, and fill volume of the final package (over- or under-fill of final container). Bulk density is the result of the manipulation of these: l l l

microstructure: characterized by the true density of the domains rtrue particle structure: characterized by the intraparticle porosity εparticle mesostructure: characterized by the packing (1  ε) rbulk ¼ rtrue ð1  εparticle Þð1  εÞ

(19.20)

As it was previously indicated, particle packing is defined by the PSD, shape, and cohesion forces. Typically, particle packing is estimated from bulk density measurements when the particle density is known by applying the previous equation. Particle packing also influences the pressure drop of fluids through packed beds (e.g., filtering media, catalyst beds) as shown by Ergun’s equation:   rf 1  ε 2 vP mv ð1  εÞ2 ¼ 150 2 þ 1:75 (19.21) v vx d ε3 ε3 d

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where m is the viscosity, rf is the fluid density, v is the superficial velocity through the bed, and d is the equivalent diameter of the particles. Modeling of particle packing has been reported in the literature since 1928e32 with the work by Furnas (1928) and by Westman and Hugill (1931). The models formulated along the years can be classified into three types (Prior et al., 2013): l

l

l

Analytical models: the linear packing model is the most popular approach where the specific volume of the system is the sum of the contributions of the specific volume of each component of mixtures. The individual contribution of each component depends of the abundance and size of the component when compared to the others (Zou et al., 2011). Geometrical models: these estimate the packing porosity of a mixed bed from the size distribution function of the solid particles (Suzuki and Oshima, 1985). Spatial distribution: the use of advanced numerical simulation techniques (Abreu et al., 2003) or discrete element modeling (DEM) (Caukin et al., 2015) to predict the packing of particles with complex shape as well as interaction of particles with the containers (wall effects) has been developed over the last two decades. Software specific for these applications is commercially available (e.g., DigiPac or DigiDEM, Caulkin et al., 2009, 2015).

5.6 Permeability and Wetting Permeability is defined from Darcy’s law, relating the velocity of the fluid through a porous media with the pressure drop required (static, capillary) in laminar flow. vP 1 ¼ vm vx k

(19.22)

It can be derived from the Kozeny Carman equation for pressure drop of fluids across packed beds under laminar flow conditions: vP mv ð1  εÞ2 ¼ 180 2 vx d ε3

(19.23)

Thus, permeability is a function of packing and size distribution of the particle system. k¼

d2 ε3 180 ð1  εÞ2

(19.24)

Therefore, the ability of a fluid to penetrate or wet a particle system can be controlled by modification of mesostructure parameters such as particle

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packing, size, and/or incorporation of particles with a lower contact angle with the fluid (capillarity). To further influence wettability of the particle system, surface energy of the particles would have to be modified (particle structure and supramolecular structure). A common industrial issue is the incorporation of bulk solid particles into liquids. Dissolution rate of particle systems may be controlled by different mechanisms: wetting, dispersion, breakage, and dissolution. Control of the mesostructure influences overall dissolution rate when wetting is the controlling factor.

5.7 Bulk Flow Properties Dosing is an essential performance vector for any particle system; as such, the product is expected to discharge from its container at a steady flow. In addition to the relevance of flow properties during discharge, equipment design and flow properties influence homogeneity, stress profile, and energy requirements during manipulation of particle systems under transformations such as mixing, coating, and granulation. Tardos et al. (2003) distinguishes different bulk flow regimes: l

l

l

l

l

Static: this is characteristic of zero shear rate. The determination of the distribution stress along the unit and the yield condition are critical for this regime. Yield condition defines the point where the bulk powder starts to flow and is conditioned by cohesion forces, packing, size distribution, and coordination number. Slip and stick: this regime is characterized by large swings in stresses as the material flows and stops repeatedly as a result of different mechanisms (Shultze, 2008). Slow frictional (quasi-static): during this regime, frictional and cohesion forces between particles predominate. Shear rate is small, characteristic of the discharge of powder out of a container. In general, flowability under this regime increases as particle size increases and spread of the distribution decreases. Intermediate: under this regime, all collisional, cohesion, and frictional forces between particles are relevant. Low shear mixers and granulators operate under this regime. Rapid granular flow: this is characteristic of very high shear rates (e.g., high shear mixers) where short collisions between particles determine the character of the flow.

Fig. 19.31, contains Tardos classification of particle flow regimes, where d is the particle diameter, g is gravity, and g_ is the characteristic shear rate of the process. Therefore, it can be inferred from this map that PSD (mesostructure) has a significant impact on the behavior of a given particle system when exposed to the same shear rate. Schulze (2008), Levy and Kalman

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FIGURE 19.31 Schematic representation of different regimes in powder flow. From Tardos, G.I., McNamara, S., Talu, I., 2003. Slow and intermediate flow of a frictional bulk powder in the Couette geometry. Powder Technology 131, 23e39, with permission.

(2001), and Neddermann (1992) provide very comprehensive discussions on the fundamentals of static and dynamic behavior of particle systems as well as principles and methodology to characterize flow. Properties of mesostructure are strongly dependent on deformation history, and they exhibit anisotropic behavior. Therefore, any test performed to characterize the flow properties of a powder needs to take into account how the analysis performed at mesostructure reflects the actual conditions at large scale. The most accepted tests to characterize flow properties of bulk solids systems are uniaxial compression and shear tester (Fig. 19.32). Both tests provide values of unconfined yield stress and packing, corresponding to the principal stress and consolidation time characteristic of the test. As it was previously indicated, as particle systems exhibit strong dependency with deformation history, test results may differ depending on the test used. Flowability tests are performed at different consolidation stresses and consolidation times characteristic of the process. The ratio of consolidation stress to unconfined yield stress (ffc) is used to characterize flowability of the system according to the Jenike classification: ffc < 1 not flowing. 1 < ffc < 2 very cohesive.

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2 < ffc < 4 cohesive. 4 < ffc < 10 easy flowing. 10 < ffc free flowing. Shear testers are typically used for advance characterization of bulk solids as they are able to measure additional parameters to flow function and packing such as effective internal friction and wall friction angles that are used in the design of silos. Other parameters that can be characterized with shear testers include angle of the linearized yield locus, angle of internal friction at steady state flow, cohesion, and uniaxial tensile strength. On the other hand, unconfined yield stress analysis is common as routine analysis in industries to characterize the flowability of the particle systems as it is a less timeconsuming and relatively more robust method. Common issues when storing particle systems within silos include arching, funnel flow, rat-holing, flooding, nonuniform discharge, buckling, or vibrations. As it was highlighted during the discussion on particle segregation, the best approach consists of designing a process (container design, storage time, storage conditions) that is able to handle the particle systems with desired properties. However, this is neither always possible nor affordable, and therefore modification of the structure of the particle system needs to be considered. The introduction of flow aids and anticaking agents as well as the control of the PSD are typical interventions that can be performed at mesoscale.

5.8 Compaction Curves: Elastic and Plastic Deformation of Particle Systems Compaction curves are used for determination of yield points as well as characterization of the structure of particle systems resulted from granulation processes (Mort, 2001). The compaction curve of granular materials typically presents three regions (Fig. 19.33). The first region is mainly dominated by packing rearrangement, the second region is mainly controlled by granule deformation to fill interstitial voids, and the third region corresponds to the reduction of particle porosity. This last region is also called the elastic region. Mort (2001) defines the transition between different regions as the onset of plastic yield and join point that can be determined by onset analysis. As demonstrated by Mort (2001), compaction curves are highly influenced by supramolecular and particle structure parameters, especially on the second and third regions, whereas mesostructure mainly influences the first region. Modifications of the procedure proposed by Mort (2001) based on uniaxial test compaction curves have also been reported in different ways for model calibration of mesostructure both in continuum Sinka (2007) and DEM (Thakur et al., 2014) (Fig. 19.34).

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FIGURE 19.33 Regions in the compaction curve of granular materials. From Mort, P.R., 2001. Analysis and application of powder compaction diagrams. In: Handbook of Conveying and Handling of Particulate Solids. In: Handbook of Powder Technology, vol. 10. Elsevier Science, with permission.

5.9 Particle Attrition Particle attrition may present different types of issues regarding quality vectors such as appearance (e.g., dusty material), performance (e.g., in catalyst with actives deposit on the surface), or particle contamination. However, one of the most relevant issues associated with attrition is the generation of dust that represents a health and safety risk due to the generation of airborne material

FIGURE 19.34 Compaction curves applied to detergent powders with different porosity. Confined stress-strain (A) and porosity-stress behavior (B). From Thakur, S.C., Ahmadian, H., Sun, J., Ooi, J.Y., 2014. An experimental and numerical study of packing, compression and caking behaviour of detergent powder. Particuology 12, 2e12, with permission.

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that can get in contact with skin or be inhaled (e.g., sensitizers such as enzymes, Ahmadian and Ghadiri, 2007) and/or form explosive dust when concentrations exceed the lower explosive limit. Attrition is affected by particle structure variables such as size, shape, surface, porosity, hardness, or presence of cracks. According to Ghadiri et al. (2000), attrition in process equipment may occur by high-energy particle collisions or by quasi-static bulk compression and shear deformation, involving two simultaneous processes of surface damage and body fragmentation. The surface damage occurs by chipping and wear. In this case the surface layers, edges, or corners are removed from the particles, resulting in the generation of fines. In the case of fragmentation, the parent particles are broken into a number of fragments whose sizes may be comparable to the parent particle, although extensive fragmentation may also produce fines that are similar to the debris produced by chipping. Bemrose and Bridgwater (1987) provide a review of the most relevant type of attrition test available: l

l

l

Single particle: they provide information on fragmentation, crushing, and single particle tests. Multi-particles: they provide information on both fragmentation and abrasion, fluidized bed, shear cell, rotating rum, grindability, vibration, paddle wheel, and enhanced sieving. Others include chemical reaction, pressure change, heating, and fluid transport.

The single particle impact test is typically regarded within the literature as a more fundamental test. There are several correlations available in the literature. In the case of semi brittle particles, Ghadiri and Zhang (2002) derived the following equation: 4f

rlHv2 Kc2

(19.25)

where 4 represent the fractional loss per impact that is a strong function of particle structure properties such r particle density, l characteristic size, H particle hardness, and Kc fracture toughness and the impact velocity v. Particle Breakage by Salman et al. (2007a) is recommended for a comprehensive reading on particle breakage mechanisms, models, and measurement techniques. Gentzler and Michaels (2004) analyzed impact attrition of three brittle porous pharmaceutical structured particles in a laboratory vibrational impact tester. Results obtained show that the transition to gross fragmentation is influenced by particle structure parameters such as the size of attritionresistant primary particles in the agglomerate (link with size exclusion phenomena described previously) as well as the point at which existing flaws become available.

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Subero and Ghadiri (2001) proposed a map of breakage for agglomerates subjected to a single impact particle test. They observed two regimes: (1) localized disintegration where the damaged is restricted to the impact area and (2) fragmentation that consists of the local disintegration of the impact site and the propagation of large cracks into the body of the agglomerate. These two regimes coexist for identical assemblies tested in identical conditions; however the frequency of each depends mainly on the impact velocity and the particle porosity (Fig. 19.35). Modeling of the impact of particle structure on attrition has been done by several authors via DEM modeling. Typical simulations are based on a single impact test of dense agglomerates. Granule fracture is the result of the manner in which strong interparticle forces are transmitted into the agglomerate and the consequent development of a heterogeneous distribution of primary particle velocities. Thornton et al. (1999) shows that most of the input energy is dissipated due to plastic deformation of the particle structure within the damage zone. Thornton et al. (1999) distinguishes two stages: (1) loading stage, which is irreversible deformation of the microstructure, sliding, and randomly distributed microcrack formation along sets of half-meridian planes, and (2) unloading stage where the agglomerate undergoes a selection process in which certain preconditioned half-meridian planes experience further microcrack formation and coalescence leading to subsequent fracture along these planes. The agglomerate creates its own flaw population during the loading stage, and preexisting flaws do not have a significant effect on the agglomerate “strength.” Single impact test simulations performed at different

FIGURE 19.35 Map of breakage for agglomerates. From Subero, J., Ghadiri, M., 2001. Breakage patterns of agglomerates. Powder Technology 120, 232e243, with permission.

Strategies for Structured Particulate Systems Design Chapter j 19

impact angles show that the normal component of the impact velocity is the dominant factor in controlling the breakage contacts (Moreno et al., 2003). Those breakage contacts are more prevalent in the back side of the agglomerate with respect to the direction of the impact with the wall. Based on this work, the pattern of breakage depends on the impact angle for the same value of damage ratio. The influence of particle shape on single impact tests shows that agglomerates experience a large plastic deformation before disintegrating into small debris (Zheng et al., 2015). Most of the small debris after breakage is primarily near the agglomerateewall interface, whereas fragments are created at the top of the agglomerate. The influence of granule shape depends on the nature of the impact: face, edge, or vertex. However, in most cases, the damage ratio in non-spherical particles is larger than that experienced by spherical agglomerates.

6. THE GRAND CHALLENGE ON STRUCTURED PARTICLE PRODUCT DESIGN: AN INTEGRATED APPROACH As indicated by O’Driscoll (2002), many companies follow the sequential approach for product development that does not recognize the impact that product and process design has on downstream functions (manufacturing and sales). This approach typically designs a poor process that results in added design, manufacturing, and engineering redesign costs. Although product design cost only represents 10% of the total budget, manufacturing costs that represent 50e80% are also determined by the design of the product. Therefore a strategy for product design that has manufacturing in mind is key to developing successful products in current market conditions where products are more complex, required in increasingly larger numbers, intended to satisfy a wide variation in user population, required to compete aggressively with similar products, and required to be of a consistently high quality. Impact of structure in particulate products has been highlighted in previous sections. Sometimes the role of particle structure tends to be underestimated on the design and development of formulated products. This typically happens at the early stages of the development, during the molecule or formula design process, and it can be the source of re-work on the development of new products. Principles of design for manufacture DFM (O’Driscoll, 2002) (Fig. 19.36) need to be implemented at the early stages of the process and need to consider both complete product and manufacturing designs. The role of the particle process designer is the development of a particle system whose structure: (1) meets performance vectors defined by user and manufacturing requirements (ability for processing) and (2) ensures that defined chemistry by the formula or molecular designer is active at the point of application.

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FIGURE 19.36 Design for manufacture work process. From O’Driscoll, M., 2002. Design for manufacture. Journal of Materials Processing Technology 122, 318e321, with permission.

This implies that the particle process designer needs to do the following: 1. Define the set of structures that meet performance vectors at application. 2. Study the impact that storage, transport, and manipulation before use has on particle structure (caking, attrition, segregation) and chemistry activity. 3. Define the process that generates the desired structure and chemistry activity in a cost-efficient way. Some examples of manipulation of structure of particle systems applied to food, fertilizers, polymers, and detergent products is presented by Knight (2001), Borchers (2005), and Brockel and Hahn (2004).

6.1 Modeling Approach on Structured Particle Product Design A common industry approach for the development of particle systems consist of empirical procedures based on the product and process designer expertise.

Strategies for Structured Particulate Systems Design Chapter j 19

The usual procedure consists of a systematic set of experiments on different types of equipment and under different process conditions to develop particle systems that are evaluated against a set of defined performance vectors. From this, empirical statistical models that correlate process and formulation variables with performance vectors are developed. These models usually neglect the role of structure and therefore present a limited capacity for optimization and reapplication. An efficient approach for the design of particle products has been proposed by Frantisek Stepanek across several articles (Stepanek and Ansari, 2005) (Fig. 19.37). The procedure consists of defining: (1) process functions that relate process and formulation variables to a set of parameters that describe the structure of the product and (2) property functions that relate the structure parameters to the performance vectors. Once these functions are determined, the procedure consists of identifying the set of structures that according to the property functions would satisfy the success criteria defined for each of the performance vectors. Process functions for the different processes and operating conditions can then be used to optimize the full system of equations to minimize cost, including constraints related to environmental footprint, safety, or capital. Ansari and Stepanek (2006) have demonstrated the basis for this approach on a layering agglomeration model to produce particles with a desired dissolution rate profile. The great challenge for the design of particle products is to extend this work to additional performance vectors and expand the structure properties to include supramolecular structure and mesostructure properties presented in this work.

FIGURE 19.37 Inclusion of particle structure on the modeling of product performance vectors as a function of process conditions and formulation.

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Key challenges: l

l

l

l

l

definition of structure of particle systems and characterization of relevant parameters at different scales: supramolecular structure, particle structure, and mesostructure, development of multiscale models that relate properties across different structure levels, development of process functions for relevant processes that relate operating conditions and formulation with structure, development of property functions for key performance factors of a product, development of an optimization process that considers the relevant process and property functions.

These challenges require expertise across multiple disciplines such as chemical engineering, chemistry, physics, physical-chemistry, mechanical engineering, characterization-instrumentation, and optimization, and thus a common effort is required to develop work processes, models, and optimization procedures. The amount of effort and resources required to solve these challenges is quite significant for a single organization (industry or academia) to tackle on its own. A well-coordinated effort across multiple organizations is required.

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SECTION j IV Design of Structured Products Stepanek, F., Ansari, M.A., 2005. Computer simulation of granule microstructure formation. Chemical Engineering Science 60, 4019e4029. Stepanek, F., Rajniak, P., Mancinelli, C., Chern, R.T., Ramachandran, R., 2009. Distribution and accessibility of binder in wet granules. Powder Technology 189, 376e384. Steward, J.A., Saiani, A., Bayly, A., Tiddy, G.J.T., 2009. The behaviour of lyotropic liquid crystals in linear alkylbenzene sulphaonate (LAS) systems. Colloids and Surfaces A: Physicochemical and Engineering Aspects 338, 155e161. Steward, J.A., Saiani, A., Bayly, A., Tiddy, G.J.T., 2011. Phase behaviour of lyotropic liquid crystals in linear alkylbenzene sulphonate (LAS) systems in the presence of dilute and concentrated electrolyte. Journal of Dispersion Science and Technology 32, 1700e1710. Steward, J.A., 2008. Engineering the Properties of Spray-Dried Detergent Granules (Thesis). School of Materials, University of Manchester. Stockdale, M., 1978. Water diffusion coefficients versus water activity in stratum corneum: a correlation and its implications. Journal of the Society of Cosmetic Chemists 29, 625e639. Stojanovic, Z., Markovic, S., 2012. Determination of particle size distributions by laser diffraction. Technics-New Materials 21, 11e20. Subero, J., Ghadiri, M., 2001. Breakage patterns of agglomerates. Powder Technology 120, 232e243. Suzuki, M., Oshima, T., 1985. Verification of a model for estimating the void fraction in a three component randomly packed bed. Powder Technology 43, 147. Sydel, P., Blomer, J., Bertling, J., 2006. Modeling particle formation at spray drying using population balances. Drying Technology 24, 137e146. Tan, P., Puri, V.M., 2004. Methods for minimizing segregation: a review. Particulate Science and Technology 22, 321e337. Tan, H.S., Salman, A.D., Hounslow, M.J., 2005. Kinetics of fluidised bed melt granulation V: simultaneous modelling of aggregation and breakage. Chemical Engineering Science 60 (14), 3847e3866. Tardos, G.I., McNamara, S., Talu, I., 2003. Slow and intermediate flow of a frictional bulk powder in the Couette geometry. Powder Technology 131, 23e39. Thakur, S.C., Ahmadian, H., Sun, J., Ooi, J.Y., 2014. An experimental and numerical study of packing, compression and caking behaviour of detergent powder. Particuology 12, 2e12. Thielmann, F., Naderi, M., Ansari, M.A., Stepanek, F., 2008. The effect of primary particle surface energy on agglomeration rate in fluidised bed wet granulation. Powder Technology 181, 160e168. Thornton, C., Ciomocos, M.T., Adams, M.J., 1999. Numerical simulations of agglomerate impact breakage. Powder Technology 105, 74e82. Tseng, S., Lin, T., Hsu, J., 2015. Chemical Engineering Science 123, 573e578. Tsoungui, O., Vallet, D., Charmet, J.C., 1998a. Use of contact area trace to study the force distribution inside 2D granular systems. Granular Matter 1, 65e69. Tsoungui, O., Vallet, D., Charmet, J.C., Roux, S., 1998b. Partial pressures supported by granulometric classes in polydisperse granular media. Physical Review E 57 (4), 4458e4465. Vehring, R., 2008. Pharmaceutical particle engineering via spray drying. Pharmaceutical Research 25 (5), 999e1023. Verdurmen, R., Menn, P., Ritzert, J., Blei, S., Nhumaio, G.C.S., Sorensen, T.S., Gunsing, M., Stratsma, J., Verschueren, M., Sibeijn, M., Schulte, G., Fritsching, U., Bauckhage, K., Tropea, C., Sommerfeld, M., Watkins, A.P., Yule, A.J., Schonfelt, H., 2004. Simulation of agglomeration in spray drying installations: the EDECAD project. Drying Technology 22 (6), 1403e1461. Vogel, L., Peukert, W., 2005. From single particle impact behaviour to modelling of impact mills. Chemical Engineering Science 60, 5164e5176.

Strategies for Structured Particulate Systems Design Chapter j 19 Vreman, A.W., van Lare, C.E., Hounslow, M.J., 2009. Chemical Engineering Science 64 (21), 4389e4398. Vuataz, G., 2002. The phase diagram of milk: a new tool for optimising. Lait 82, 485e500. Westman, A.E.R., Hugill, H.R., 1931. The packing of particles. Journal of American Ceramics Society 13, 767. Wong, J., D’Sa, D., Foley, M., Gar Yan Chan, J., Chan, H.K., 2014. NanoXCT: a novel technique to probe the internal architecture of pharmaceutical particles. Pharmaceutical Research 31, 3085e3094. Woo, M.W., Mujumdar, A.S., Daud, W.R.W., 2010. Spray Drying Technology 1. ISBN:978-98108-6270-1. Xia, W., Ni, C., Xie, G., 2016. The influence of surface roughness on wettability of natural/goldcoated ultra-low ash coal particles. Powder Technology 288, 286e290. Yeong, C.L.Y., Torquato, S., 1998. Reconstructing random media. Physical Review E 57 (1), 495e506. Yu, A.B., Zou, R.P., Standish, N., 1996. Modifying the linear packing model for predicting the porosity of nonspherical particle mixtures. Industrial Engineering Chemical Research 35, 3730e3741. Zheng, K., Du, Ch, D., Li, J., Qiu, B., Fu, L., Dong, J., 2015. Numerical simulation of the impactbreakage behaviour of non-spherical agglomerates. Powder Technology 286, 582e591. Zou, R.P., Gan, M.L., Yu, A.G., 2011. Prediction of the porosity of multi-component mixtures of cohesive and non-cohesive particles. Chemical Engineering Science 66, 4711e4721.

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Chapter 20

Computational Tools for the Study of Biomolecules P.G. Jambrina* and J. Aldegundex, 1

*Universidad Complutense de Madrid, Spain; xUniversidad de Salamanca, Spain 1 Corresponding author: E-mail: [email protected]

1. INTRODUCTION In the advent of the computational era during the 1960s, Mulliken claimed in his Nobel lecture, “I would like to emphasize my belief that the era of computing chemists (.) is at hand.” Mulliken’s vision became truth, and now computational tools are able to faithfully predict the behavior of chemical systems, and even to replace experiments in those situations in which they are difficult to carry out. Nowadays, computational approaches are widely used to assist researchers in drug discovery or the development of materials with desired properties. Moreover, computer simulations allow us to elucidate reaction mechanisms that experimentally can only be inferred using indirect techniques (such as isotopic substitution). The computational prediction of chemical properties is very demanding from the computational point of view. Although the theoretical tools required to perform exact calculations have been known since the early decades of the 20th century, such types of calculations are only possible for the simplest chemical systems, i.e., those involving few electrons and/or atoms. Hence, for the study of most relevant systems in chemistry, biology, or material science, approximations have to be invoked. The nature of those approximations is size dependent; the larger the system is, the cruder the approximations are to keep computational cost at a manageable level. The purpose of this chapter is to introduce the reader to the computational study of biomolecules. From among the large amount of existing computational approaches, we will restrict ourselves to the study of atomistic simulations, i.e., to those methods that model the system at an atomic level. To this aim, we have divided the chapter into two different parts. The first one (Sections 2 and 3) is devoted to the exploration of the techniques used to study individual chemical structures (nuclear geometries) of molecular systems. We Tools for Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00020-4 Copyright © 2016 Elsevier B.V. All rights reserved.

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will start our presentation with the ab-initio and DFT methods, which require very few experimental or empirical inputs (DFT) or none at all (ab-initio). Although the use of these methods is unfeasible for most biologically relevant problems, they are at the core of some of the approaches that are commonly used for their treatment, such as the hybrid quantum mechanical/molecular mechanics (QM/MM) methods. Finally, we will conclude this part of the chapter with a brief description of the force field methods routinely applied to the study of biosystems. The second part of the chapter (Section 4) is dedicated to the study of the nuclear dynamics or, in other words, of the nuclear motions. The characterization of the dynamic evolution of the nuclei is crucial because it is behind chemical reactions and spectroscopy. As pure quantum mechanical treatments of nuclear dynamics are only feasible for very small systems, we will focus on the description of methods where the classical equations of motion are used instead of the quantum mechanical ones, with special attention to the dynamics in condensed phases.

1.1 The Ideal Scenario: Quantum Mechanical Treatment If we could disregard the computational limitations highlighted in the previous paragraphs, the rigorous treatment of any molecular problem would be performed in a quantum mechanical context, and its starting point would be the time-independent Schro¨dinger equation: Hb ðr; RÞJðr; RÞ ¼ EJðr; RÞ

(20.1)

where Hb ðr; RÞ is the Hamiltonian operator, Jðr; RÞ, and E represent its eigenfunctions and eigenvalues, and r and R denote the whole set of electronic and nuclear spatial coordinates. All the information accessible about the stationary states, i.e., states characterized by well-defined values of the energy E, of the system would be contained in the wave functions Jðr; RÞ. In a nonrelativistic context, and considering only the Coulombic interactions that dominate the molecular Hamiltonian except when heavy atoms are involved, the Hb operator for a molecule formed by N nuclei and n electrons can be written as (Zhang, 1998; Domcke et al., 2011) shown: Hb ¼ TbN þ Hb el ¼ TbN þ Tbe þ Vbee þ VbeN þ VbNN N n n X n X X Z2 2 Z2 2 X e2 ¼ VR a  Vr i þ 2Ma 2me 4pε0 jri  rj j a¼1 i¼1 i¼1 j>i 

N X n X a¼1 i¼1

2

N N X X

(20.2)

2

Za e Za Zb e þ 4pε0 jRa  ri j a¼1 b>a 4pε0 jRa  Rb j

where the first term ð TbN Þ represents the nuclear kinetic energy and the second one ð Hb el Þ the electronic Hamiltonian formed, in turn, by the addition of the

Computational Tools for the Study of Biomolecules Chapter j 20

operators corresponding to the electronic kinetic energy ð Tbe Þ and the electroneelectron ð Vbee Þ, electronenuclear ð VbeN Þ, and nuclearenuclear ð VbNN Þ interactions. Indexes denoted with Greek symbols and capital letters refer to nuclei so that, for instance, Ma represent the mass of the a nucleus and Za its atomic number. Regarding electrons, they are referred to with Latin lowercase letters, with me indicating their mass and e the absolute value of its charge. The vacuum permittivity is represented as ε0 . We will assume throughout the chapter that the preceding Hamiltonian is written in the center of a mass system. Strictly speaking, this would imply to add an extra contribution called a “mass polarization term” that stems from the impossibility to separate rigorously the relative and center of mass motions for more than two particles. Such contribution is commonly very small and will be hereafter omitted. Eq. (20.1) can be solved (Zhang, 1998; Domcke et al., 2011) by expanding the total wave function Jðr; RÞ in a basis set formed by the adiabatic electronic functions ð4ðr; RÞÞ defined as the solution of the electronic Schro¨dinger equation: Hb el 4n ðr; RÞ ¼ εn ðRÞ4n ðr; RÞ; (20.3) where the semicolon in 4n ðr; RÞ indicates that Eq. (20.3) is solved for every nuclear configuration of interest, and the nuclear coordinates only play a parametric role. The eigenvalues εn ðRÞ are hypersurfaces representing the electronic energy and are crucial when it comes to determining the nuclear dynamics. Depending on whether the expansion of the total wave function is performed in terms of the adiabatic functions for an arbitrary nuclear geometry, X Jðr; RÞ ¼ cn ðRÞ4n ðr; RÞ (20.4) n

or a fixed one ðR0 Þ, Jðr; RÞ ¼

X

cð0Þ n ðRÞ4n ðr; R0 Þ

(20.5)

n

one obtains the adiabatic and diabatic representations (Zhang, 1998; Domcke et al., 2011), respectively. While the information about electronic structure, stable geometries, etc., is contained in the 4n ðr; RÞ functions, the nuclear ð0Þ dynamics can be studied through the nuclear functions cn ðRÞ or cn ðRÞ. The adiabatic and diabatic representations are equivalent as long as a complete basis set of electronic states is used. However, they lead to systems of coupled differential equations for the determination of the nuclear wave functions that differ largely in complexity. In the adiabatic case [Eq. (20.4)], the potential term of the coupled equations is diagonal and formed by the adiabatic electronic eigenstates εn ðRÞ. The kinetic energy term, in turn, includes nondiagonal elements whose evaluation requires computing the derivatives of the electronic wave functions 4n ðr; RÞ with respect to the nuclear coordinates. Regarding the diabatic representation [Eq. (20.5)], nondiagonal

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elements only appear in the potential term. The evaluation of these elements is much simpler than in the adiabatic case as it only requires the electronic wave functions calculated at the geometry R0 and does not involve derivatives but only the electronenuclear interaction. This difference determines that, in most practical scenarios, the diabatic representation is chosen when it comes to solving problems where more than one electronic state is coupled (nonadiabatic problems). In those situations where the nuclear adiabatic functions ðcn ðRÞÞ are needed, they can be easily calculated from their diabatic counð0Þ terparts ðcn ðRÞÞ as both sets are connected by a unitary transformation. If nonadiabatic effects were negligible, the integration of the coupled equations could be facilitated by disregarding the nondiagonal terms connecting different electronic states. For the adiabatic representation, this is meaningful when the nuclear kinetic energy is small compared to the energy difference between neighboring electronic states εn ðRÞ and leads to the adiabatic approximation. For the diabatic representation, in turn, neglecting the nondiagonal terms of the coupled equations is valid when the electronenuclear interaction is small compared to the nuclear kinetic energy and leads to the diabatic approximation. The adiabatic/diabatic approximations can be therefore considered as the small/large nuclear kinetic energy limits of the nonadiabatic problem. From a time-dependent (dynamic) perspective, the adiabatic approximation is applicable when the nuclei are moving slowly enough as to permit the electrons to adapt instantaneously to the nuclear configuration and the diabatic approximation when the nuclear motions take place at such speed that the electrons cannot respond, and their spatial arrangement remains “frozen” at the distribution corresponding to R0 . Overall, the adiabatic approximation is more useful in practical situations in chemistry as the conditions under which it is valid are more easily found. In this context, the nuclear motions take place on a single electronic state, and the total wave function Jðr; RÞ can be written as cðRÞ4ðr; RÞ. The nuclear dynamics is described by the equation:   b T N þ εðRÞ þ UðRÞ cðRÞ ¼ EcðRÞ (20.6) where the potential energy surface on which the nuclei move is given by the sum of εðRÞ, the electronic energy corresponding to 4ðr; RÞ, and a term UðRÞ called diagonal Born-Oppenheimer correction that involves the diagonal second-order nuclear derivatives of the electronic wave function 4ðr; RÞ. If UðRÞ, which is commonly much smaller than εðRÞ, is neglected, one obtains the famous Born-Oppenheimer approximation (Born and Oppenheimer, 1927; Zhang, 1998; Domcke et al., 2011). Unfortunately, purely quantum mechanical treatments are only affordable for a handful of systems, those formed by very few atoms (typically three or four). This not being the case, other approximations than the aforementioned ones are needed. As the number of atoms gets larger and the electronic states

Computational Tools for the Study of Biomolecules Chapter j 20

necessary to describe properly a certain process increase, such approximations become more numerous and drastic. Following this idea, this chapter will describe the evolution of the methodologies employed to determine the equilibrium geometries, properties, and time evolution of molecular systems as their size and complexity increase and render it more difficult to carry out a fully rigorous treatment.

2. ENERGY CALCULATIONS FOR MOLECULES As it stems from the discussion unfolded in the preceding section, to solve the electronic Schro¨dinger Eq. (20.3) or, at least, to calculate the energy for fixed geometries of the nuclei is a requisite for the study of nuclear dynamics. In this section, we will briefly describe the methodologies used to that end, moving from those that have a purely quantum mechanical nature to less computationally expensive approaches amenable to being applied to larger systems. The first methods that will be described form what is known as “electronic structure methods” and will be divided into three categories: ab-initio, DFT, and semiempirical methods. All of them are quantum mechanical in essence as they focus on solving the electronic Schro¨dinger equation. To this end, these methods make use of different approximations that get cruder as we move from the ab-initio to the semiempirical group. Electronic structure methods are computationally expensive and cannot be directly applied to most biological systems due to the large number of atoms involved. The methodologies used to cope with these problems do not concentrate on solving the electronic Schro¨dinger equation but in calculating a molecular energy that could be later used to perform dynamic studies. Among the different approaches to the description of very large systems of biological relevance, we will introduce the force field, QM/MM, and coarse-grained methods.

2.1 Ab-Initio Methods Ab-initio methods (Szabo and Ostlund, 1996; Helgaker et al., 2013) solve the electronic Schro¨dinger Eq. (20.3) from first principles using the charges and masses of the electron and nuclei as the only empirical input. This feature, together with the fact that these are the only electronic structure methods for which a completely unambiguous and systematic procedure to improve the results exists, determines that the ab-initio methods are the most accurate ones. As a matter of fact, high-level ab-initio calculations render the best possible computational results and rarely fail in reproducing experimental results. However, this high accuracy is reached at the expense of grueling computational requirements that may render these methods unaffordable when the number of atoms and/or electrons scales.

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2.1.1 Hartree-Fock Approximation Most of the difficulties that characterize the solution of the Schro¨dinger equation for a system formed by n electrons stem from the electroneelectron interaction, which renders Eq. (20.3) nonseparable. The simplest way to overcome this hurdle is to use an independent particle model where, for every electron, such interactions are represented by means of an average potential that only depends on the electron position. The methodology so derived, known as self-consistent field (SCF) or Hartree-Fock method (Szabo and Ostlund, 1996; Helgaker et al., 2013), is at the very heart of ab-initio techniques both by its simplicity and because it serves as starting point for more advanced treatments of the electronic problem. In the context of the Hartree-Fock approach, it is assumed that the electronic wave function for the system ground state at an arbitrary nuclear geometry R can be expressed as a single Slater determinant:  c ð1Þ c ð2Þ / c ðnÞ   1  1 1    1  c2 ð1Þ c2 ð2Þ / c2 ðnÞ  p ffiffiffiffi 4HF ¼ jc1 ; c2 ; /; cn i (20.7) ðr; RÞ ¼ 0  « « «  n!  «   cn ð1Þ cn ð2Þ / cn ðnÞ formed by molecular orbitals (MO) ci ðjÞ where the indexes i and j label the molecular orbital (i) and the electronic coordinates ( j ), respectively, and run from 1 up to n, the number of electrons. Each c function, in turn, consists of the product between a spatial orbital and a spin function (a or b, depending on whether the spin projection of the electron is þ1=2 or 1=2). The variational principle ensures that the electronic energy for the Slater determinant, hc1 ; c2 ; /; cn j Hb el jc1 ; c2 ; /; cn i, will be above the exact energy of the ground state of the electronic Hamiltonian no matter which molecular orbitals ci are used in (20.7) and what nuclear geometry is being considered. It can be proven that the optimum molecular orbitals, i.e., those which minimize this energy, are eigenfunctions of a monoelectronic and Hermitian operator Fb1 : Fb1 ci ð1Þ ¼ ei ci ð1Þ

(20.8)

called the Fock operator and whose explicit expression is as follows: b þ vHF ð1Þ Fb1 ¼ hð1Þ

(20.9)

b While the Hamiltonian hð1Þ is a monoelectronic operator given by the following: N N X N 2 X X Za e2 Za Zb e2 b ¼  Z V2  þ hð1Þ r1 2me 4pε0 jRa  r1 j a¼1 b>a 4pε0 jRa  Rb j a¼1

(20.10)

that accounts for the electronic kinetic energy, the electronenuclear attraction, and the nuclearenuclear repulsion; the electroneelectron repulsion is represented by

Computational Tools for the Study of Biomolecules Chapter j 20

vHF ð1Þ ¼

n  X

Jbj ð1Þ  Kbj ð1Þ

 (20.11)

j¼1

Jbj ð1Þci ð1Þ ¼ ci ð1Þ Kbj ð1Þci ð1Þ ¼ cj ð1Þ

Z Z

cj ð2Þ

e2 c ð2Þdq2 ð4pε0 Þr12 j

cj ð2Þ

e2 c ð2Þdq2 ð4pε0 Þr12 i

where Jbj and Kbj are the Coulomb and exchange operators, respectively. The q2 symbol groups the spatial r2 and spin u2 coordinates of the electron labeled as “2.” As vHF ð1Þ depends on the coordinates of a single electron, it necessarily accounts for the effect of the electroneelectron repulsion in an averaged fashion. The molecular orbitals fulfilling Eq. (20.8) are called canonical orbitals and their eigenvalues ðei Þ orbital energies. The electronic energy corresponding to the Slater determinant defined through the canonical orbitals is shown: εHF ¼

n X

ei 

i¼1

where Jij and Kij  Z Jij ¼ ci ð1Þ cj ð2Þ Z Kij ¼



ci ð1Þ cj ð2Þ



n X n 1X ðJij  Kij Þ 2 i¼1 j¼1

 e2 c ð1Þcj ð2Þdq1 dq2 ð4pε0 Þr12 i  e2 c ð2Þcj ð1Þdq1 dq2 ð4pε0 Þr12 i

(20.12)

(20.13)



(20.14)

are the Coulomb and exchange integrals, respectively, and the c orbitals are the canonical ones. Unfortunately, Eq. (20.8) is difficult to solve because the Fock operator is defined in terms of the canonical orbitals, which, in turn, only can be determined once the Fock operator is well defined. The solution to this catch-22 situation is to use an iterative method where an initial guess of the canonical orbitals is the starting point for successive calculations of new Fock operators and canonical orbitals based on the precedents ones until convergence is attained. To facilitate the procedure, the linear combination of atomic orbitals (LCAO) approximation is invoked at this point; the molecular orbitals are expanded in terms of M functions fa : ci ¼

M X

cai fa

(20.15)

a¼1

which are commonly chosen to represent atomic orbitals, although they are not obtained as the solution of the atomic Schro¨dinger equation. In this way, the

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Virtual orbitals

iterative procedure is expressed in terms of the unknown cai coefficients and leads to the Roothaan and Pople-Nesbet-Berthier equations. The first ones appear in the context of restricted Hartree-Fock calculations for closed-shell systems, where the computational effort is reduced by imposing that the same spatial orbital is shared by two electrons (one with a and another one with b spin). The Pople-Nesbet-Berthier equations are the Roothaan equations counterparts for unrestricted Hartree-Fock (UHF) calculations where the aforementioned restriction on the form of the spatial orbitals is lifted. Although UHF calculations are better suited for the treatment of open-shell systems, they are not exempt from problems as the UHF determinants do not possess a well-defined multiplicity and include spurious contributions from excited states (Jensen, 2007). If M atomic orbitals are used in the expansion (20.15), the self-consistent procedure described in the previous paragraph will render the approximated form of an equal number of canonical orbitals. Among these, the n orbitals of lowest energy will be occupied and form the best possible representation of the electronic wave function as a single determinant (20.7). The remaining M  n orbitals, termed as virtual orbitals, will be empty (see Fig. 20.1). The computational effort associated to an HF calculation mainly stems from the evaluation of the Coulomb and exchange integrals and scales as wM 4 . Although the use of symmetry may reduce this effort for small molecules, a convenient selection of the basis functions is always crucial to keep the calculation time at bay and to facilitate the convergence of the process. A detailed description of the huge number of different basis sets used in actual calculations is out of the scope of the chapter as their development is an art in itself. However, it is worth mentioning that the atomic orbitals used in the expansion (20.15) can be divided in two groups: Slater (SO) and Gaussian (GTO) orbitals. The first ones are more accurate because they mirror the linear exponential decay that characterizes the exact solution of the Schro¨dinger equation for the hydrogen atom. However, their usage involves that

.. .. .

Occupied orbitals

590

.. .. .

χΜ χΜ−1 χn+3 χn+2 χn χn−1 χ3 χ2 χ1

FIGURE 20.1 Occupied and virtual canonical orbitals as derived from a Hartree-Fock calculation.

Computational Tools for the Study of Biomolecules Chapter j 20

the three- and four-center two-electron integrals that appear in connection to the Coulomb, and exchange integrals must be evaluated numerically, which increases the computation time. To circumvent this problem, most calculations expand the SO as fixed linear combinations of Gaussian orbitals where the exponential decay is represented through a quadratic (Gaussian) dependence. This leads to the worst description of the electron density both in the vicinity of the nuclei and in the asymptotic region, and to the necessity of increasing the number of basis functions to reach a level of accuracy comparable to that offered by Slater orbitals. However, this drawback is more than offset by the time savings derived from the possibility of calculating analytically the three- and four-center integrals if Gaussians are used. Basis sets can be classified according to the type and number of atomic orbitals included in the calculation and by the way in which they are represented (Jensen, 2007; Lewars, 2011). The choice of a particular basis set for a certain problem reflects a trade-off between accuracy and computational cost. In general, minimum basis sets, i.e., including the minimum number of atomic orbitals necessary to accommodate the electrons of each atom and representing such orbitals through a single function (SO, GTO, or a fixed combination of GTOs), are computationally cheap but lead to poor quality results. Whenever possible, the results are improved by expanding the basis set through the inclusion of (1) more than one function in the expansion of each atomic orbital and (2) some extra functions that improve the description of the bond directionality (polarization functions) and the lack of compactness of the charge distribution in anions (diffuse functions). Although one could reduce the calculation time by describing different atoms with different basis sets depending on their chemical relevance for the process under study, this practice is rarely used for small- and medium-size molecules, as it tends to create artifacts.

2.1.2 Correlation Energy If the atomic basis set used in the LCAO approximation [Eq. (20.15)] were complete, i.e., infinite, we would obtain the exact eigenfunctions and spectra of the Fock operator at each nuclear geometry, and the energy of the Slater determinant formed by the occupied orbitals so obtained is known as the Hartree-Fock limit (see Fig. 20.2). In spite of having used a complete basis set, the Hartree-Fock limit would always be above the exact ground state energy of the electronic Hamiltonian (20.2) (εexact in Fig. 20.2) due to an inherent limitation of the HF method: it does not account properly for the correlation between the electrons. Using a single Slater determinant to describe the electron wave function implies that the electroneelectron interaction is represented through an average potential ðvHF ð1ÞÞ where the instantaneous correlations between the electronic motions are not taken into account. This leads to nonzero probabilities of finding two electrons occupying simultaneously the same point of the space and, in general, magnifies the importance of electronic

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Energy

592

Electronic energy (εHF) calculated with a base of M atomic orbitals

Hartree-Fock limit Correlation energy

εexact M FIGURE 20.2 Hartree-Fock limit and exact energy of the ground state for the electronic Hamiltonian (20.2) at a fixed nuclear geometry and as function of the number of basis functions (M). The correlation energy is defined as the difference between these two values.

arrangements that are energetically unfavorable from the point of view of the electroneelectron interaction. This determines that the Hartree-Fock limit will always be above the exact energy of the ground state by an amount called the correlation energy (Szabo and Ostlund, 1996; Jensen, 2007; Lewars, 2011; Helgaker et al., 2013), which, although small compared to the Hartree-Fock limit, typically only a small fraction of its value, is extremely important from the chemical point of view. The inability of the Hartree-Fock calculations to incorporate the effect of the instantaneous interactions between electrons is the main drawback of this methodology and makes it necessary to use more sophisticated approaches to account for the correlation energy. Next, we will describe these methods, grouped under the name of post-HF methods (Szabo and Ostlund, 1996; Jensen, 2007; Lewars, 2011; Helgaker et al., 2013) and used to recover the correlation energy and to generate electronic energies and wave functions that improve those provided by HartreeFock calculations. In all cases, it will be necessary to reduce the size of the basis sets with respect to the Hartree-Fock case to make the computational cost affordable. This means that, even for the best methodologies, total energies will not be exact by a significant amount. In practice, the difficulty of implementing the Hartree-Fock scheme and all the other techniques and approaches that will be presented in this chapter is such that using commercial software packages for their application, usually developed by very large teams and evolved and improved over the years, is a must. For ab-initio methodologies, as well as for those based on DFT (see Section 2.2) and semiempirical approaches (see Section 2.3), a nonexhaustive list of such packages includes GAUSSIAN (Frisch et al., 2015), MOLPRO (Werner et al., 2015), GAMESS (Schmidt et al., 1993; Gordon and Schmidt, 2005), ORCA (Neese, 2012), ADF (Baerends et al., 2016), Q-Chem (Krylov and Gill, 2013), and TURBOMOLE (University of Karlsruhe & Forschungszentrum Karlsruhe GmbH, 2010).

Computational Tools for the Study of Biomolecules Chapter j 20

2.1.3 Configuration Interaction The most general method to account for the correlation energy is called configuration interaction (CI) (Szabo and Ostlund, 1996; Jensen, 2007; Lewars, 2011; Helgaker et al., 2013). It uses a Hartree-Fock calculation as starting point and works on the fact that the electronic wave function for any state of an n-electron system can be rigorously written as shown:   XX r r X X r s  r s  c a  4a þ c a b  4a b þ j4i ¼ c0 4HF 0 þ

XX

a



r

cra sb tc 4ra sb tc



ab

þ/

rs

(20.16)

abcrst

 regardless of the chosen atomic basis set. In this expression, 4HF 0 i is the Hartree-Fock wave function, i.e., the Slater determinant formed by the n occupied canonical orbitals, the indices a; b; c; . and r; s; t; . run over the occupied and virtual orbitals, respectively, and 4ra s. b. i represents a Slater determinant (a configuration) where the electron in the a b. occupied orbitals has been promoted to its r s. virtual counterparts. The CI methodology truncates expansion (20.16) to include only D determinants and applies a variational method using the cra s. b. coefficients as parameters. The diagonalization of the D  D matrix so obtained renders an upper approximation to the energies of the first D electronic states. In particular, full configuration interaction calculations (full CI) are CI calculations where the aforementioned truncation is not performed and all the excited determinants are considered. A full-CI method based on an HF wave function obtained from a complete basis set would recover all the correlation energy and lead to the exact solution of the electronic problem, as illustrated in Fig. 20.3. Although this limiting case is unreachable because it implies M/N, see Eq. (20.15), and D/N, its existence provides a systematic way of improving electronic wave functions and energies just based on increasing the size of the basis set and the number of determinants used in the CI calculation. The number of determinants for a system formed by n electrons, D¼

M! n!ðM  nÞ!

(20.17)

scales quickly with the number of basis functions M and always fulfills D[M. An equilibrium between accuracy and computational effort is reached by keeping only those determinants corresponding to single and double excitations, where the double ones are those that contribute the most to the wave function of the electronic ground state. Calculations following these premises are called CISD (configuration interaction singles and doubles) and are characterized by a computational effort that scales as wM 6 . Except for very small systems where higher excitations can be included, the CISD method represent the form in which CI is most commonly applied. A particularly

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Exact soluon

D

M

Hartree-Fock limit

FIGURE 20.3 Graphical representation of the calculations accuracy as more determinants (D) and larger basis sets (M) are used in the expansion (20.16).

unwelcome consequence of truncating the Eq. (20.16) is that, while the full-CI methodology is size-extensive and size-consistent, any truncated form of CI does not possess these properties. In particular, this means that CISD recovers a smaller fraction of the correlation energy as the number of atoms increases (not size-extensive) and that the sum of the energies calculated for noninteracting molecules or atoms does not coincide with the energy calculated when the system is treated globally (not size-consistent).

2.1.4 Møller-Plesset Perturbation Theory A completely different approach to the problem of recovering the correlation energy is based on perturbation theory. In these methods, the total Hamiltonian 0 is decomposed as the sum of a zeroth-order Hamiltonian Hb and a perturbation Hb . This division should be such that (1) the eigenvalues and eigenfunctions of 0 Hb are known, and (2) the overall influence of Hb on the state of the system is small. Under this proviso, the eigenvalues and eigenfunctions of the total 0 Hamiltonian can be written as a series where the first term is the Hb contribution, and the remaining ones incorporate progressively the influence of the perturbation and, ideally, become increasingly small. The only methodology following this scheme and widely used in Chemistry is the Møller-Plesset perturbation theory (MP) (Szabo and Ostlund, 1996; Jensen, 2007; Lewars, 0 2011; I. N. Levine, 2013), where Hb is chosen as the sum of the monoelectronic Fock operators defined in Eq. (20.9), and the perturbation Hb is defined as the difference between the exact electroneelectron interaction ð Vbee Þ and its aver-

aged counterpart vHF summed for all electrons. With this definition, the first-

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order Møller-Plesset (MP1) energy is nothing but the Hartree-Fock one given in Eq. (20.12). The correlation energy is gradually recovered at second (MP2), third (MP3), fourth (MP4), and successive orders. In practice, only MP2 and MP4 are used, as empirical evidence suggests that MP3 offers little improvement with respect to MP2 and MP5 uses to be computationally unaffordable. MP2 is able to recover around 80% of the correlation energy, and its computational requirements scale as wM 5 , which makes this method the most economical one for including electronic correlation. While MP2 includes double excitations, MP4 incorporates besides single, triple, and quadruple ones. It scales as wM 6 if the triple excitations are not taken into account and as wM 7 otherwise, in which case accounts for around 95% of the correlation energy. Although MP methods are size-extensive and MP2 and MP4 may lead to accurate results, they are lagging behind other methodologies. This is due to convergence problems derived from the fact that the Hamiltonian Hb may not really represent a small perturbation, which would lead to a very erratic or nonexistent convergence if Hartree-Fock were not a good starting point, and from the nonvariational nature of the method, which leads to oscillations in the calculated properties that make it difficult to extrapolate.

2.1.5 Coupled Clusters Another nonvariational and size-extensive hierarchy of methods are the coupled clusters (CC) ones (Jensen, 2007; Lewars, 2011; I. N. Levine, 2013). This group includes some of the most successful methodologies to recover correlation energy, and it is based on the expression b 40 ¼ e T 4HF 0

(20.18)

where 40 is the exact electronic wave function for the ground state of the molecule, 4HF is the Hartree-Fock approach to 40 , and Tb is the cluster 0 b operator. T consists of a sum of operators Tb1 þ Tb1 þ . þ Tbn whose effect on the determinant 4HF 0 is to generate a linear combination of determinants where 1 ð Tb1 Þ, 2 ð Tb2 Þ, etc., electrons have been promoted from occupied canonical orbitals that participate in 4HF into virtual orbitals. If the co0 efficients of these combinations could be determined from a calculation performed with a complete atomic basis set and including all the possible Tbi operators, the resulting combination of determinants would be equivalent to a full-CI expansion of the 40 wave function or, in other words, would be the exact 40 . In practice, only an approximation to such coefficients can be evaluated, as the basis must be truncated, and only some Tbi operators can be incorporated to the calculations. Among these, the most important one is Tb2 , and the method resulting of including only its contribution is called coupled clusters doubles (CCD). It is worth highlighting that CCD accounts for the double excitations in an exact way and for the quadruple, sextuple, etc., ones in an approximated way. If Tb1 is also included the resulting method is called

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CCSD, and if Tb3 is also considered, one gets CCSDT. This last method gives very accurate results but is too computationally expensive (it scales as wM 8 ); instead, a less demanding version termed CCSD(T) is used. In CCSD(T) calculations the contribution of the triple excitations is only estimated so that it scales as wM 7 . In spite of this, it provides excellent results, and it is rarely necessary to go beyond it, to the point that it is considered the reference method for molecules with up to 10 nonhydrogen atoms. Above this size, some of the less demanding procedures introduced before should be used ðCCSDðwM 6 Þ or MP2ðwM 5 ÞÞ.

2.1.6 Multiconfigurational SCF The post-HF methods described so far are oriented to the analysis and determination of the features of the ground electronic state and work on the basis that mono-determinantals SCF calculations produce qualitatively correct approximations to the electronic wave function that can be later used as starting point for most sophisticated and correct treatments of the electronic problem. When these assumptions are not valid either because the ground state is nearly degenerate or because one is interested in an excited electronic state, a different approach is in order. The one usually adopted is called multiconfigurational SCF (MCSCF) (Jensen, 2007; Lewars, 2011; Levine, 2013). It works by adopting a trial wave function formed by several, far less than in the CI case, Slater determinants where both the spin-orbitals that form the determinants and the coefficients of the multideterminantal expansion are optimized simultaneously through an iterative procedure. In this context, all the configurations are treated equally, and no one of them occupies a preeminent position, as is the case for HF-based methods. The main difficulty when performing an MCSCF calculation derives from the choice of the configurations included in the expansion because such a choice may be strongly dependent on the nature of the problem under consideration, and it is difficult to establish general rules. The MCSCF approach most commonly used is the complete active space self-consistent field (CASSCF) methodology (Jensen, 2007; Lewars, 2011; Levine, 2013), where the molecular orbitals are divided into an active and an inactive space. The inactive space includes the occupied and virtual orbitals with the lowest and largest energy, respectively. The active space, in turn, includes the remaining orbitals, both occupied and virtual. Next, an MCSCF calculation including all the possible excitations that imply orbitals in the active space is performed, in such a way that the active space is treated at a full-CI level and the inactive one at a Hartree-Fock level. Further modifications of this method make it possible to shrink the computation time by reducing the number of excitations and by introducing a more complex partitioning of the molecular orbitals. MCSCF calculations provide qualitatively good electronic functions in those cases where Hartree-Fock calculations fail. However, they only recover a

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small fraction of the correlation energy, typically called “static” correlation energy, and they are later combined with CI or perturbative methods to make up for this limitation. In this connection, the combination of an MCSCF reference function with a CI scheme gives rise to the multireference configuration interaction (MRCI) methods (Jensen, 2007; Lewars, 2011; Levine, 2013). Equally, perturbation theory calculations performed on a CASSCF wave function originate the multiconfigurational second-order perturbation (CASPT2) method (Jensen, 2007; Lewars, 2011). The extra flexibility for the definition of the molecular orbitals and the “equalitarian” status assigned to more than one configuration intrinsic to this manifold of techniques render them especially well suited for the calculation of excited electronic states. While methods built on the Hartree-Fock solution tend to be mainly focused on the electronic ground state, the MRCI and CASPT2 approaches are the best choice for studies involving excited electronic states.

2.2 Density Functional Theory (DFT) In spite of being very accurate, the applicability of the manifold of ab-initio methods is limited by their computational requirements. This fact restricts their usage to systems consisting of few electrons and/or atoms. Although the exact figures behind the somewhat undefined adjective “few” are experiencing an upward evolution as computers become more powerful, post-HF methods are not a realistic option for the majority of systems of pharmacological or biological interest.

2.2.1 General Formulation of the Density Functional Theory The DFT (Jones and Gunnarsson, 1989; Parr and Yang, 1989; Kohn, 1999; Koch and Holthausen, 2001) represents a completely different approach to the treatment of the correlation energy and electronic structure problems that can be applied to medium-size molecules while keeping computational time at a manageable level so that, nowdays, systems formed by up to 100 atoms can be routinely treated using this methodology. DFT exploits the fact that, while the electronic Hamiltonian [see Eq. (20.2)] only contains mono- and bi-electronic terms, the electronic wave function depends on the coordinates of the n electrons included in the molecule. This suggests that the electronic wave function contains more information than necessary when it comes to solving the electronic problem (20.3) so that those methods, (HF and post-HF) that focus on the electronic wave function are somehow using an unnecessarily large amount of resources. Following this idea, DFT calculations will not make emphasis on the determination of the wave function but seek to obtain all molecular properties from the electronic density, Z Z rðr1 Þ ¼ n . 4 ðq1 ; q2 ; .; qn Þ$4ðq1 ; q2 ; .; qn Þdu1 dq2 .dqn (20.19)

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which represents the probability density of finding any of the n electrons that form the molecule at the position r1 and whose integration over the whole space gives as a result n. The qi symbol in Eq. (20.19) groups the spatial ri and spin ui coordinates of the ith electron, which implies that in Eq. (20.19) we are integrating overall the spin coordinates and all the spatial coordinates but r1 . As compared to the wave function, using the electronic density has three main advantages: it is a measurable property, it is more manageable from a mathematical point of view, and it possesses an intuitive meaning. DFT calculations are based on the two Hohenberg-Kohn theorems (Hohenberg and Kohn, 1964). The first one establishes that the electronic density for a nondegenerate ground electronic state of a molecular system ðr0 ðrÞÞ determines the wave function and energy of the ground state and any exited state of the system. In particular, the exact ground state energy ðε0 Þ can be written as a functional, a rule that maps a function into a real number, ε½r0  given by ε½r0  ¼ ε0 ¼ Te ½r0  þ Vee ½r0  þ VeN ½r0  þ VNN |ffl{zffl}

(20.20)

Constant

In this expression, the nuclearenuclear repulsion VNN is constant for a given nuclear geometry, the functional VeN ½r0  accounts for the expectation value of the electron-nuclear interaction: ! Z Z N X Za e2 VeN ½r0  ¼ r0 ðrÞ  (20.21) dr ¼ r0 ðrÞnðrÞdr 4pε0 jRa  rj a¼1 and the functionals Te ½r0  and Vee ½r0  correspond to the expectation values of the electron kinetic energy and electroneelectron repulsion, respectively. If the electronic density r0 ðrÞ and the functionals Te ½r0  and Vee ½r0  were known, Eq. (20.20) would render ε0. Unfortunately, this is not so simple because theorem does not give a single hint about the nature of the functionals Te ½r0  and Vee ½r0 , but it merely proves their existence. The second Hohenberg-Kohn theorem states that the energy calculated for any trial density function ðrt Þ fulfilling the conditions Z rt ðrÞ  0 cr and rt ðrÞdr ¼ n; is above the exact value for the electronic ground state: ε½rt  > ε½r0  ¼ ε0

(20.22)

This result, however, does not mean that actual DFT calculations will be variational because Eq. (20.22) implies that the correct, exact functional is being used. As discussed earlier, some parts of such functional are unknown and must be approximated (see later), which will render the resulting calculations nonvariational. While Hohenberg and Kohn demonstrated their theorems to

Computational Tools for the Study of Biomolecules Chapter j 20

nondegenerate ground states, this restriction was later proved to be unnecessary (Parr and Yang, 1989). The basis of current DFT calculations is the methodology devised by Kohn-Sham (KS) (Kohn and Sham, 1965) to transform Eq. (20.20) into a practical tool for calculating electronic energies. The KS approach uses a fictitious reference system formed by noninteracting electrons and whose electronic density coincides with that of the real system ½r0 ðrÞ to recast ε0 as follows: Z Z Z 1 r0 ðr1 Þr0 ðr2 Þ ref ε0 ¼ r0 ðrÞnðrÞdr þ Te ½r0  þ dr1 dr2 2 ð4pε0 Þ2 r12 (20.23) þ VNN þ EXC ½r0  where the first term represents the electronenuclear interaction, the second one the kinetic energy of the noninteracting electrons forming the fictitious system, the third one the classical Coulomb repulsion between two electron clouds described through r0 , and the fourth one the constant nuclearenuclear repulsion. The fifth contribution, termed the exchange-correlation energy ðEXC ½r0 Þ, includes all the corrections to its precedent counterparts necessary to keep expression (20.23) exact, i.e., the kinetic correlation energy, the electronic correlation and exchange energies, and a correction to prevent the self-interaction energy that stems from treating the electrons as classical clouds of charge. Although they are in principle equivalent, Eq. (20.23) has multiple advantages with respect to (20.20). The first three contributions in (20.23) have been chosen keeping in mind that the procedure to evaluate them from r0 ðrÞ is simple and well defined and that they are large compared to the exchangecorrelation energy. In this way, the lack of information about the exact nature of the energy functional ε½r0  has been encapsulated into EXC ½r0 , in the hope to minimize the errors derived from any approximation used to estimate its value. On the other hand, r0 ðrÞ can be exactly written as follows:  n  X  KS 2 r0 ðrÞ ¼ (20.24) ci ðrÞ  i¼1 that describe the electrons of the in terms of the Kohn-Sham orbitals cKS i noninteracting reference system. By substituting this expansion into (20.23), it is possible to employ a self-consistent procedure similar to that used in Hartree-Fock calculations to solve the electronic problem for any nuclear geometry: the Kohn-Sham orbitals are expanded in the same atomic basis sets used in ab-initio calculations and chosen to make minimum the energy. Following an initial guess of the electronic density, the overall procedure is then reduced to a succession of iterations where the coefficients of the expansions are progressively improved until convergence is obtained. Once the optimum Kohn-Sham orbitals are known, Eqs. (20.23) and (20.24) render the

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energy and ground state electronic density, respectively. It is extremely important to point out that this procedure would be variational if the correct expression for the exchange-correlation energy were known and, besides, exact in the limit were the basis set to become complete. In other words, all the post-HF corrections described in connection to ab-initio methodologies would be unnecessary as the energy obtained from (20.23) would include the totality of the correlation energy with a computational cost similar to that of a HartreeFock calculation. Unfortunately, the exact form of the functional EXC ½r0  is unknown. This fact, together with the absence of a systematic and unambiguous way of improving the approximated forms for the exchange-correlation energy used in actual DFT applications, is the main drawback of DFT calculations. As a response to this difficulty, the quest for the “divine functional” (Mattsson, 2002; Jensen, 2007) has occupied most of the efforts of the DFT community throughout time and produced an innumerable number of approximations to this ideal (Perdew et al., 2005; Sousa et al., 2007; Zhao and Truhlar, 2007, 2008; Jensen, 2007; Lewars, 2011; Levine, 2013). In the present work, we will just briefly described the main families of functionals. A matter of controversy in connection with DFT calculations is whether or not they can be considered as ab-initio methods. If the exact form of the exchange-correlation energy functional were known, DFT calculations would be ab-initio without any doubt. However, our lack of information about the exact nature of this functional forces us to employ approximated representations that depend on parameters that, many times, are chosen to fit and reproduce sets of experimental results. Although this would disqualify DFT as ab-initio, the truth is that the number of parameters is much lower than in the semiempirical and force fields methodologies that will be presented later, which leaves the question open.

2.2.2 Local Density Approximation The local density approximation (LDA) (Parr and Yang, 1989) represents the simplest approach to EXC ½r0 , which, in the context of this model, would be given by Z LDA EXC ½r0  ¼ r0 ðrÞεXC ðrÞdr (20.25) where εXC ðrÞ is the exchange-correlation energy per electron of a homogenous electron gas (a system formed by uniformly distributed electrons moving on a positive charge background so that the system is electrically neutral) whose electronic density is precisely r0 ðrÞ at each point r. The term “local” refers to the absence of any r0 ðrÞ derivative in the expression for EXC ½r0  given by Eq. (20.25), which implies that the LDA approximation will be valid when the electronic density varies very slowly with the position (see next paragraph). If the exchange and correlation contributions are considered separately, the first

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one can be computed analytically. The correlation energy, in turn, lacks an analytical expression and is represented as a complicated function of r0 depending of parameters whose values are fitted (Vosko et al., 1980) using accurate simulations for the energy of the homogeneous electron gas as reference. The local spin density approximation (LSDA) (Parr and Yang, 1989) is an extension of the LDA methodology that conceptually resembles UHF calculations as it treats differently the electrons depending on their spin projection a or b. It is equivalent to the LDA approximation for closed-shells systems near the equilibrium geometry, but it works better for nonequilibrium geometries, and besides, it can handle open-shell systems. In any case, both LDA and LSDA functionals lead to poor results when applied to molecules and have been replaced for most accurate functionals. Improvements on LDA and LSDA functionals proceed (1) by separating EXC into two contributions, one for the exchange and another one for the correlation energy, that are modeled separately in an attempt to reach exact and compatible expression for both contributions and (2) by including corrections that impose nonlocality. This last condition implies that the contribution of a point to EXC depends on what happens at other points at finite distances to reflect the fact that the exchange and correlation energies are, in fact, nonlocal properties. Among the corrections that impose nonlocality, the simplest one is to acknowledge that the exchange-correlation energy EXC should take into account the derivatives of the electronic density r0 when calculating the contribution of a point to EXC , which includes information about the immediate neighborhood of the point.

2.2.3 Generalized Gradient Approximation The generalized gradient approximation (GGA) improves the LSDA definition of the exchange-correlation energy by including the first derivatives of the electronic density: h i Z

GGA a b EXC r0 ; r0 ¼ f ra0 ; rb0 ; Vra0 ; Vrb0 dr (20.26) GGA used to be split into separate exchange and correlation In practice, EXC functionals. An example of the first class is the B88 (Becke, 1988a) functional, which can be combined with any of their correlation counterparts belonging to this family, for instance the LYP (Becke, 1988b) and P86 (Perdew, 1986) functionals, to form the global exchange-correlation energy. One example of such mixing is the BLYP functional, which merges B88 for the exchange energy and LYP for the correlation contribution. The commonly used PW91 (Ziesche and Eschrig, 1991; Perdew et al., 1992, 1993; Perdew et al., 1992) and PBE (Perdew et al., 1996, 1997) correlation and exchange functionals also belong to the GGA manifold. If second-order derivatives are included in the expression (20.26), one gets the meta-generalized gradient approximation (MGGA).

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2.2.4 Hybrid Functionals GGA and MGGA functionals can be improved by calculating a fraction of the exchange energy included in EXC according to the exact expression derived from Hartree-Fock theory but using the Kohn-Sham orbitals instead of the Hartree-Fock molecular orbitals for its evaluation. The rest of the exchange and correlation energy is accounted for through LDA, GGA, or MGGA functionals. The most representative member of this family, termed hybrid functionals, is the B3LYP one (Becke, 1993), which holds for “Becke threeparameter Lee-Yang-Parr functional” and is by far the most commonly used representation for the exchange-correlation energy, to the point that it is considered the standard choice for the average quantum chemistry problem. Most functionals, although not the totality of them, of the M06 group devised by Zhao and Truhlar (2006, 2007, 2008) also belong to the hybrid family as they combine an MGGA scheme with different fractions of Hartree-Fock exchange. Their flexibility, good performance for different tasks, the inclusion in some of them of nonlocal contributions, and the ensuing capability of describing properly dispersion forces, deficiently described by the majority of functionals, will probably generalize the usage of M06 functionals and lead them to contest with B3LYP for the “everyday functional” position in the near future. The most accurate functionals currently available are those called double hybrid, which refine the hybrid-GGA ones by including some correlation energy calculated through second-order perturbation theory, typically employing an MP2 scheme based on the Kohn-Sham orbitals. Examples of these functionals are the B2-PLYP (Grimme, 2006) and mPW2-PLYP, which use an exchange-correlation energy with the following structure: DH EXC ¼ ð1  a1 ÞEXHF þ a1 EXDFT þ ð1  a2 ÞECGGA þ a2 ECMP2

(20.27)

where the values of the parameters a1 and a2 and the concrete nature of EXGGA and ECGGA change depending on the functional. Given the nonlocal character of the MP2 correlation energy incorporated in these functionals, they represent a step forward in the quest for the perfect functional and will improve the description of long-range interactions and dispersion forces. Regarding their performance, B2-PLYP and mPW2-PLYP lead to the best agreement in systematic comparisons with experimental results, but they do so to the expense of a significant increase in computational time compared to their hybrid counterparts, which may set limits to their applicability. A thorough discussion of the performance of the existent functionals for different tasks would exceed the purpose of this chapter and can be found elsewhere (Sousa et al., 2007; Zhao and Truhlar, 2007; Jensen, 2007; Lewars, 2011). As an average, results based on DFT calculations are of a quality similar to MP2 with smaller basis sets and less computational effort. However, although some functionals as B3LYP and the M06 ones offer good results for a

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variety of properties, no functional can be qualified as “the optimum one” regardless of the property considered. In other words, this means that finding the best functional for a particular study does not ensure that such functional will continue offering the best results if the property or system under consideration changes. As it was indicated several times before, the inability to obtain a proper description of the long-range interactions in zones where no overlapping of the electronic clouds of the fragments exists was one of the most serious flaws of the majority of the existing functionals. Only recently, general methodologies to tackle this problem efficiently have been devised. Among these, dispersion corrected DFT (DFT-D) (Grimme, 2006; Grimme et al., 2010) is the most commonly used and consists of adding a correction term to the exchangecorrelation functional. Such a term depends on certain parameters whose values vary with the functional that is being corrected and are calculated by fitting to high-quality ab-initio interaction and conformational energies. It is worth mentioning that the dispersion term does not alter the outcome of the SCF procedure inherent to the KS-DFT methodology, so overall, it affects molecular optimizations but not the value of the electronic density, from which any other molecular property is calculated.

2.2.5 Time-Dependent DFT The DFT methodology presented earlier focuses on the resolution of the timeindependent electronic Schro¨dinger equation to determine the ground electronic state and its properties. The extension of DFT theory to the time domain, called time-dependent density functional theory (TDDFT) (Runge and Gross, 1984; Dreuw and Head-Gordon, 2005; Ullrich, 2011), makes it possible to apply the DFT methodology to the study of electronic excited states. The most common implementation of this technique is the linear-response time-dependent density functional theory (LR-TDDFT), which employs perturbation theory to evaluate the response of the ground state electronic density when a weak external electric field is applied and renders the energies of the excited electronic states as the poles of the response function. Although of general applicability, LR-TDDFT calculations are especially suited to the study of radical cations as they work better for low-lying excited states below the first ionization energy of the molecule.

2.3 Semiempirical Methods The ab-initio and DFT methods described so far require an intense computational effort due to the necessity of calculating a soaring number of integrals between base functions centered at different atoms. Semiempirical methods reduce such effort by invoking certain approximations to shrink the number of integrals that need to be calculated and by using simplifications and

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experimental data to estimate their values. This combination of physical theory and experimental information reduces the computational requirements so drastically that semiempirical methods can even be applied to biomolecules. However, it is important to highlight that, in spite of the drastic character of some of the approximations that accompany semiempirical calculations, to solve the electronic Schro¨dinger Eq. (20.3) always remains as the final motivation of the overall process.

2.3.1 p Electrons Methods The first semiempirical methods were devised for the treatment of conjugate planar molecules. The simple Hu¨ckel method (SHM) (Hu¨ckel, 1931a,b, 1932, 1933; Levine, 2013; Lewars, 2011) dates from the early 1930s, well before the ab-initio calculations came into play. The method is based on the separation of the molecular orbitals into two groups, s and p, depending on whether the wave function remains unchanged or not under reflection in the molecular plane, and it concentrates exclusively on the second ones, whose form and energy are calculated by expanding the molecular orbitals into a minimum basis set of atomic functions with the right symmetry and by using the variational principle. The SHM method employs a Hamiltonian for the p electrons that consists of the sum of monoelectronic terms, whose concrete definition is not specified, and neglects the matrix elements of the Hamiltonian between not-adjacent atoms as well as the overlap between basis functions centered in different atoms. Besides, it assumes that the value of the nonzero elements of the Hamiltonian representation only depend on whether or not they are diagonal, which reduces the problem of determining the molecular orbitals to the solution of a particularly simple set of secular equations. The results so obtained make it possible to calculate the charge densities, bond orders, and molecular dipole moments attributable to p electrons and express the corresponding energy levels as a function of just two parameters, a and b, the second of which can be determined experimentally by comparing with spectroscopic data. Although the SHM method provides with theoretical support to the Hu¨ckel rules as well as physical insight about certain molecular properties and it works surprisingly well given the crudity of some of the approximations involved in the model (it disregards electronic spin, does not consider s electrons, and does not account properly for the interaction of the p electrons), the description of the molecular structure that it offers is only qualitative. The Pariser, Parr, and Pople (PPP) method (Pariser and Parr, 1953a,b; Pople, 1953) represents an evolution of the SHM theory devised in 1952 where the electronic repulsion between the p electrons is better described through the consideration of a more realistic Hamiltonian in which such interaction is explicitly considered. The details of the expansion of the molecular orbitals in a minimal basis set of atomic orbitals are determined following a procedure similar to that employed in the Hartree-Fock calculations. This leads to

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equations equivalent to the Roothaan equations of the HF theory, which are simplified by neglecting a significant part of the integrals and solved through an SCF procedure whose starting point is an SHM calculation. The PPP method succeeds in describing the electronic spectra of many aromatic hydrocarbons, but it is rarely used nowadays as it has been superseded by the more general methods described next.

2.3.2 All Valence Electrons Methods The first semiempirical method of general applicability was the extended Hu¨ckel method (EHM) (Hoffmann, 1963, 1964a,b,c). As suggested by the name, it is a modification of the SHM method that includes new features and improvements that make it suitable to treat all kind of molecules and not only the conjugate planar ones. In common with their SHM counterparts, the EHM calculations employ a simplistic form of the Hamiltonian formed by undefined monoelectronic terms, represent the molecular orbitals as an expansion of atomic orbitals, and use the variational method to reduce the problem of calculating the molecular orbitals and their energies to the solution of a set of secular equations, in such a way that no iterative process is necessary. However, both methods differ in several crucial aspects; the EHM method takes into account all the valence electrons, includes all the valence atomic orbitals in the expansions, does not neglect the overlapping between base functions centered in different atoms, which is calculated in each case, and considers all the elements of the Hamiltonian representation for those atoms whose overlapping is not zero. The importance of the EHM method does not lie in the quantitative agreement between its predictions and experimental data but in the insight of certain chemical concepts provided by the qualitative analysis of its results. Besides, and very importantly, the iterative process involved in ab-initio and DFT methods commonly uses an EHM calculation as starting point. Following the same spirit that led from the SHM to the PPP method, Pople et al. developed the complete neglect of differential overlap (CNDO) (Pople et al., 1965; Pople and Segal, 1965, 1966; Santry and Segal, 1967), the intermediate neglect of differential overlap (INDO) (Pople et al., 1967), and the neglect of diatomic differential overlap (NDDO) (Pople and Beveridge, 1970) methods as SCF improvements of the EHM approach that take into account explicitly the electron repulsion and simplify the solution of the Roothaan-like equations by neglecting, simplifying, or fitting to experimental data many of the integrals involved in the process. The three methods differ in the extent to which they use the zero differential overlap (ZDO) (Jensen, 2007) approximation, which consists of neglecting all the products, and therefore the corresponding integrals, involving atomic functions depending on the same electronic coordinates when such functions are centered on different atoms. While CNDO calculations apply this approximation for the totality of

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overlap and electron repulsions integrals, the INDO and NDDO methods make allowance for an increasing number of exceptions to this receipt. In general, the CNDO, INDO, and NDDO methods work relatively well for the calculation of equilibrium geometries and dipole moments, while the results are quite poor for dissociation energies. Their importance, however, stems from the fact that NNDO served as inspiration for the first successful semiempirical method: the modified neglect of diatomic overlap (MNDO) (Dewar and Thiel, 1977; Levine, 2013) developed by Dewar et al. As its forerunners, MNDO is a SCF procedure that uses an LCAO expansion of the molecular orbitals in a minimum basis set and only considers explicitly the valence electrons. However, in this methodology the ZDO approximation is only applied to those integrals involving three and four centers, which are neglected. All the information about each type of atom necessary to obtain the remaining integrals and to form the Roothaan-like equations is contained in six parameters (four for the hydrogen atom) whose values are determined by comparing with experimental geometries, dipole moments, and thermochemical properties and minimizing the corresponding errors. This method, in turn, triggered the development of a plethora of semiempirical approaches built following the same scheme used by Dewar et al. for MNDO and whose improvements were based on (1) including more flexibility through the introduction of new parameters, (2) adding d orbitals to the atomic basis sets to describe transition metals, (3) increasing the sample of molecules used for the determination of the parameters, (4) employing more sophisticated expressions to approach the value of certain integrals, and finally, (5) including dispersion and hydrogen-bonding corrections to describe noncovalent interactions. A discussion of the features and differences between these methods can be found in references (Jensen, 2007) and (Levine, 2013). Among them, the PM6 method (Stewart, 2007), where PM stands for “parametrization method” and the number “6” indicates the existence of several forerunners, is highly accurate when it comes to determining energetic properties and molecular geometries, and when corrected to account for dispersion and hydrogen bond interactions (Korth, 2010; Rezac and Hobza, 2012), it excels in the determination of intermolecular energies. The results produced by the best semiempirical methods like PM6 do not reach the accuracy of DFT calculations, and besides, they should be used and interpreted with care. As they follow a Hartree-Fock scheme, some correlation energy can be recovered and introduced into the model through the parametrization process. However, this also means that extreme precautions are necessary in those situations where the electronic wave function would not be properly described by a single Slater determinant. Semiempirical methods can be used as starting point to develop methodologies suitable to cope with molecules containing up to thousands of atoms (Levine, 2013) where the description of bond-breaking and bond-forming

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processes is naturally included in the model, which represents a huge advantage with respect to the force field approach described in the next section. In this scenario, most of the computational effort of semiempirical methods is connected to the diagonalization of matrices during the iterative process, and therefore, the majority of efforts devoted to extend the semiempirical approaches to the biological realm concentrate on obtaining molecular orbitals while skipping this mathematical step.

2.4 Force Fields When studying systems of biological interest, such as proteins or DNA chains, we often have to deal with more than 105 atoms. The large size of these systems restricts the kind of computational methods that can be used to evaluate the energy, and even the cheapest semiempirical methods soon become unfeasible. On top of this, simulations of biologically relevant transformations, such as ligand binding or protein folding, require simulation times from nanoseconds to microseconds or beyond, which actually means that the potential energy, which is a function of the coordinates of all the atoms, has to be calculated billions of times.

2.4.1 Empirical Force Fields Hence, to study biological systems, we require a potential energy function that could be evaluated really fast while still being accurate enough to provide a reliable outcome. The most widely used methods to evaluate the energy for these systems are the empirical force-fields1, also known as molecular mechanics methods. There are many robust and reliable force field methods for the study of biological systems such as CHARMM (Brooks et al., 2009), AMBER(Salomon-Ferrer et al., 2013), and GROMOS (Oostenbrink et al., 2004). There are also force fields especially devised to cope with small organic molecules and fully compatible with one of their biomolecular counterparts. For instance, the CGENFF force field (Vanommeslaeghe et al., 2010) is compatible with CHARMM. The size and complexity of the problems treated by means of force fields determines that any direct reference to the electronic Schro¨dinger Eq. (20.3) has been abandoned. Their purpose is to account for the overall potential energy function of the system, so as we will discuss in the second part of the chapter, it can be used in combination with the classical equations of motion to describe the nuclear dynamics. In particular, every force field expresses the overall potential energy function of the system as the sum of different potentials with an intuitive chemical interpretation such as bond stretchings,

1. A force field is defined both by the functional form of the potential energy function and by a set of parameters of which its different contributions depend.

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bending of angles, etc. For example, the form of the CHARMM potential energy function is given by X X X E¼ Kr ðr  req Þ2 þ Kq ðq  qeq Þ2 þ Kf ½1 þ cosðnf  dÞ bonds

þ

X



angles

Kc c  ceq

2

dihedral

þ Enonbond

impropers

(20.28) where Kr , Kq , Kf , and Kc are constants that measure the extent of the different contributions.

2.4.2 Bonding Terms for Empirical Force Fields Leaving aside for the moment Enonbond , which accounts for the electrostatic and Van der Waals interactions, the remaining terms of Eq. (20.28) are termed “bonding terms.” They include a sum of mostly harmonic terms for fictitious entities2 such as bonds, angles, dihedrals, and out-of-plane distortions (improper dihedral angles that are used, for instance, to maintain the planarity of the peptide bonds). All of these fictitious entities have to be listed beforehand. This means that the energy depends not only on the position of the nuclei as in the ab-initio methods but also on the connectivity of the system, which remains unchanged throughout the simulation. Let us focus on the first term of Eq. (20.28); for any two atoms that form a chemical bond and are located at a distance r, the interaction potential is given by Kr ðr  req Þ2, where Kr is the spring constant and req the equilibrium distance. This harmonic potential provides a good approximation of a realistic Morse-like potential for values of r close to req . However, the energy of the system monotonically rises for r > req, which means that no dissociation can take place and that, in consequence, bonds cannot be broken. On the other hand, since the connectivity of the system is not updated during the simulation, there is not substantial stabilization energy when two atoms approach each other in the right orientation to form a chemical bond, i.e., no new bonds are formed. Here lies the main limitation of standard force fields: they cannot describe chemical reactions. This limitation also accounts for protonation and deprotonation, so the protonation state of every titratable group also has to be specified beforehand. The angular terms in Eq. (20.28) also depend on two parameters: the spring constant Kq and the equilibrium angle qeq . This is also the case of the improper dihedral terms, which depend on its spring constant Kc and the corresponding equilibrium value ceq , typically 0 or 180 degrees to keep the planarity of 2. The adjective “fictitious” is used because, rigorously speaking, a molecular system is only defined by the nature of the nuclei that form it and by their position. In this context, bonds, angles, etc., are just artifices we use to facilitate our description and understanding of the system.

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certain groups. For the purely dihedral terms the energy depends on three parameters, the spring constant Kf , a phase shift d, and the multiplicity n, which accounts for the presence of many energy minima throughout the interval of allowed values for the dihedral angle. The values of Kf are typically small compared with the other spring constants so that the system can populate states characterized by significantly different dihedral angles during a simulation. As the barriers existing between those states do not have to be the same, sometimes multiple dihedral terms with different multiplicity have to be included to properly described the height, width, and location of the energetic barriers. On top of this, when dealing with proteins, some force fields as CHARMM add a cross-term energy term between the backbone dihedral angles that aims to improve the conformational properties of the polypeptide (Best et al., 2012). An interesting consequence of the use of harmonic potentials is that in a force field every atom is distinguishable. Therefore, the swap of two identical atoms involves a huge increase in the energy. The concrete values of the parameters that characterize the different terms of the force field form part of its definition as they are necessary to evaluate the energy. Such values are carefully chosen to reproduce different sets of experimental results. If the systems treated by means of force fields would involve just a few dozens of atoms, it would be possible to identify each atom by means of a single number. However, for biological polymers (such as proteins or nucleotide chains), it is more convenient to identify the atoms using at least three labels that correspond to the name of the monomer (hereinafter residue), to the number of that residue in the chain, and finally, to the name of the atom as a part of the residue. As an example of the third kind of label, in the left side of Fig. 20.4, we show the atomistic representation of an Alanine residue, where every atom has been assigned a different name: the methyl carbon is named CB and is bonded to three hydrogens named HB1, HB2, HB3, and another carbon CA, etc. It is worth mentioning that the properties of a bond, angle, and dihedral term depend not only on the atoms that form them but also on their electronic state, charge, surroundings atoms, etc. For example, the CeO bond and HeCeO angle have very different properties in an aldehyde than in an alcohol. Thus, the force field is designed to identify the kind of CeO bond and HeCeO angle we are dealing with in each case. Accordingly, every atom in the simulation has to be linked to an atom type and, ideally, the force field should contain individualized sets of parameters for each combination of atom types. Following the Alanine example, Fig. 20.4 shows not only the atom names but the whole topology table for the residue within the CHARMM force field. Such a table establishes a correspondence between the name of the atom (first column) with the atom type (second column), and finally, it specifies a list with all the chemical bonds that are present in the residue where, as the red cross indicates, the proximity between atoms does not involve that they should

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FIGURE 20.4 Topology of the alanine residue in the CHARMM force field (Best et al., 2012). Force fields require as input not only the position of the atoms but also the atom types and their connectivity.

necessarily bond together. The Ca (CA) and the Cb (CB) atoms belong to a different type, and the CAeHA bond and the CBeHB1 bonds will be described through different parameters. However, HB1, HB2, and HB3 belong to the same atom type, and the three CBeHB1e3 bonds will be equivalent. We do not need to specify any list of angles and dihedral angles present in the molecule because that list can be directly obtained from the bond connectivity. However, we do have to specify a list of improper dihedral angles to enforce the planarity of certain groups of atoms during the simulation.

2.4.3 Nonbonding Terms for Empirical Force Fields We will discuss now the features of the nonbonding term in Eq. (20.28), whose form is    X X 1  R0;ij 12 R0;ij 6 qi qj Enonbond ¼  εij þ εij (20.29) 2 rij rij εrij i jsi and where the indexes i and j run, in principle, over all the atoms that form the system; the double sum accounts for every possible pair of atoms, and rij is the distance between the atoms that form the pair. The first two terms in Eq. (20.29) correspond to the Van der Waals interaction, which is usually represented by a LennardeJones potential, where εij is the well-depth, and R0;ij is the internuclear distance for which the value of the potential is zero. The third contribution to Eq. (20.29) is the electrostatic term, which for the majority of the force fields, is approximated as the Coulombic interaction between point partial charges, qi and qj , located in the position of each nucleus. ε is the

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dielectric constant, which is set equal to ε0 (its vacuum value) for calculations where the solvent molecules are treated atomistically (explicit solvent). Typically, the force fields do not include values of εij and R0;ij for any possible atom pair combination, but they are calculated from the εi and R0;i values that characterize the interaction of two atoms of i-type. The expressions that relate εij and R0;ij with εi and R0;i are these:

1 R0;i þ R0;j 2 pffiffiffiffiffiffiffi εij ¼ εi εj

R0;ij ¼

(20.30) (20.31)

To gain flexibility, the partial charges qi are not included as parameters of the force field, but they are specified in the corresponding topology table (see Fig. 20.4). This means that even atoms belonging to the same atom type may have different charges. Those atoms that are directly bonded, or separated by two or three covalent bonds, interact simultaneously through bonding and nonbonding terms. In those cases, the force fields sometimes neglect the nonbonding interactions, which are excluded from the summations of Eq. (20.29). However, this is not a general rule as other force fields like AMBER (Salomon-Ferrer et al., 2013) apply scaling factors to the nonbonding interactions of those atoms separated by three covalent bonds. The number of nonbonding terms in Eq. (20.29) is much larger than the number of bonding terms in Eq. (20.28) because, while the second interactions require connectivity between the atoms, this is not the case for their nonbonding counterparts. Therefore, when calculating the potential, most of the computational power is used to evaluate the nonbonding interactions. To speed up the calculations, it is therefore convenient to apply strategies that lighten the calculation of those terms. As the intensity of the LennardeJones term evolves as 1=rij6 , the simplest strategy would consist of neglecting such interaction at very large distances and to consider its effect just between atoms that are located at distances below some cut-off value (w12  A). However, an alternative procedure consisting of using a switch function is commonly applied to avoid an abrupt truncation of the LennardeJones interaction. In any case, it should be stressed that, although the LennardeJones terms are very small at large distances, all of them are attractive, and the overall contribution could be significant. Regarding the electrostatic term, it evolves as 1=rij and cannot be truncated. To speed up its calculation, the particle-mesh ewald (PME) method (Darden et al., 1993) is typically used. The PME method makes use of the Fourier transform and divides the electrostatic term into two contributions. The first one is short range (can be neglected at large distances), varies quickly, and is evaluated in the direct space. The second contribution is long range, has a smooth behavior, and is calculated as an interpolation of the potential and the

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charge density in the reciprocal space, where it converges quickly. As the longrange part of the potential is not expected to change significantly between consecutive steps in the propagation, its evaluation is performed only every few steps. One limitation of the PME method is that it requires the system to be translationally symmetric and should be applied in combination with periodic boundary conditions (see later). As the computational cost depends on the number of atoms, it is convenient to reduce this number as much as possible. However, biomolecules cannot be treated as isolated objects because they interact with each other and with the solvent molecules. It is therefore customary to define a “simulation box” that contains the molecule or molecules whose behavior is analyzed and the minimum number of solvent molecules necessary to account properly for its effect. This, however, presents one problem: while atoms located well inside the simulation box have all their internuclear forces equilibrated, atoms close to the “walls” of the box do not. This creates an artificial effect, similar to what originates the surface tension in the interphases, which will eventually cause a compression of the simulation box. To overcome this problem, one could artificially fix the position of the atoms in the layers closer to the walls. A more elegant approach, compatible with the PME method, is to use periodic boundary conditions (PBCs). When using PBCs, at every step of the simulation, replicas or images of the system are created periodically along the three dimensions of the cartesian space. As a consequence, an atom close to one of the walls will interact via nonbonding terms with atoms belonging to a neighbor periodic image of the system, which are close to the opposite wall in the original system (see Fig. 20.5). The imaginary boundaries that separate the periodic images are “permeable” and allow molecules to cross them and drift into and adjacent image. If, for instance, the ion A of Fig. 20.5 is pushed by the overall force and goes through the imaginary barrier between the images i and iþ1, that event will be replicated all over the infinite periodic images so that, in particular, the atom A of the i1 image will enter the i image across the opposite wall. This way, the number and type of atoms contained in every image of the system is always conserved. It is important to underline that, when using PBCs, the atomic motions are just propagated in one copy of the system and mimicked in the remaining ones. The size of the simulation box adopted for a calculation should be small to keep the computation time at bay but large enough as to avoid interactions between copies of the biomolecules located in adjacent replicas of the system. Such interactions could originate spurious effects derived from an excessive proximity between the biomolecules, and for most systems, a solvent layer of at least 10  A is recommended to avoid them. For the same reason, simulation boxes are forced to be electrically neutral by adding ions to the solvent if necessary. Moreover, when simulating biological environments, it is common practice to add additional ions to reproduce the ionic strength of the media.

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FIGURE 20.5 Representation of some nonbonding interactions between the ion A in the image i of the system and water and other ions belonging to the images i and i þ 1. The overall force, represented as a green arrow (light gray in print versions), will make A to drift toward the adjacent image. Please notice that, to keep the picture simple, only periodic images along one coordinate are shown.

2.4.4 Polarizable Force Fields As it was mentioned earlier, the majority of the force fields approximate the electrostatic interaction as the Coulombic interaction between point charges located at the nuclei. Although this approach is computationally efficient (compared to the alternatives), it is also quite crude as it does not take into account the polarization effects, i.e., the changes in the charge distribution of a molecule induced by its chemical environment. This effect is particularly relevant when many ions are located nearby, as it is the case of systems that include heavily charged molecules such as the nucleic acids. Polarization is also expected to play a very important role in simulations of lipid bilayers due to the different charge density across the system. To improve the description of this kind of system, polarizable flavors of the standard biomolecular force fields have been recently developed. Of course, a more accurate description of the electrostatic interactions is accompanied by a significant increase in computational cost. As a consequence of this increase, only simulations up to a few hundreds of nanoseconds have been achieved with polarizable force fields, in clear contrast with the microsecond-scale simulations that have been reached using their nonpolarizable counterparts described before. The different strategies used to account for atomic polarization are thoroughly described in (Baker, 2015) and references therein. Next, we enumerate the most important ones: l

Fluctuating charges method: this method (Patel and Brooks, 2004) is based on the idea of chemical potential equalization; the charge is redistributed

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l

l

among the atoms in such a way that the chemical potential at each point is equalized. Within this method, the electrostatic terms between atoms separated by one, two, or three covalent bonds are modified to include the resistance to electron flow from/to an atom (the hardness). The charges, which are considered to possess a fictitious mass, are propagated with constraints that force the chemical potential neutralization at each integration step. This method faces difficulties when trying to account for polarization that does not occur in the direction of atomic bonds. Multiple electrostatic moments method: within this method (Baker, 2015) the electrostatic term is represented not only by point charges located in the atom positions but also through dipole and quadrupole moments, which leads to anisotropic atomic distributions. The polarization is included via the interaction of the different moments that constitute such distributions. Charges on springs methods (or Drude method): in this method (Lopes et al., 2013), each polarizable atom is represented by a point charge that has attached a charged auxiliary particle with a small mass (typically 0.4 amu) that is subtracted from that of the atom. Both particles are linked by a harmonic potential, and its total charge is identical to the unperturbed static partial charge of the atom. Throughout the simulation, the auxiliary particles are cooled to a very low temperature (near 0 K), and they are allowed to move around their atoms. To avoid over-polarization of the auxiliary particles in the neighborhood of an ion, the relative velocity between the parent and the auxiliary particle is reversed if the distance between the couple exceeds a threshold value, typically 0.2  A.

2.4.5 Parametrization Most biomolecules are polymers formed by a small number of similar pieces such as the 20 natural amino acids or the five nucleic acids. Besides, simulations involving such biomolecules also include solvent molecules (water), some ions (Kþ, Naþ, Ca2þ, Mg2þ, Cl, etc.), and eventually, cofactors like ATP or NADPH and/or lipids when simulating a system embedded in a membrane. All the parameters needed to perform simulations for systems including these fragments have been carefully optimized for every reliable force field using different strategies (Mackerell, 2004; Vanommeslaeghe et al., 2010). Among these, comparison with experimental data is always preferred, although the lack of data may make it sometimes unfeasible. The use of QM data calculated using a high level of theory for a set of model systems (as the benchmark penta-alanine peptide) is an alternative option, but the direct use of these results may lead to a wrong parametrization due to inherent differences between the equilibrium geometries in gas and condensed phases. Standard biomolecular force fields include parameters for those molecules and fragments that appear most commonly in simulations. However, if our system includes small organic molecules, something common in drug

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design protocols or in studies focusing on ligand binding, they will probably not be part of the force field database, and the parameters that characterize such molecules should be obtained. This process, known as parametrization, is not simple and one should pay special care to obtain good parameters, as otherwise the results will not be reliable. The golden rule to succeed in this task is to follow the best practice guidelines defined for the force field that is going to be used for the rest of the system. In particular, mixing parameters obtained for different force fields is a highly not recommended practice. The first step when parameterizing a new molecule is the assignment of a type to every atom. Luckily, force fields include hundreds of atom type definitions, so all the atoms in the molecule could probably fit into one of them. There exist many webservers, such as Paramchem (Vanommeslaeghe and MacKerell, 2012; Vanommeslaeghe et al., 2012) or Prodrg (Schu¨ttelkopf and van Aalten, 2004), that provide assistance with that assignment and allocate atom types by analogy with the results of a database of molecules already parametrized. As an input, these programs require the geometry of the molecule, including the connectivity, in any of the formats commonly used to exchange 3D molecular structures, for example, MOL2. Once the atom type has been identified, their parameters will be probably already included in the force field. If, however, this were not the case, the aforementioned webservers can help to fill the gap by providing values for all those data not contained in the force field, including spring constants and the point charges that will be used to evaluate the electrostatic interactions. The constants so obtained are generated by analogy with preexisting data and could not be appropriate for our molecule. Aiming to help in elucidating whether or not this is the case, the predictions provided by these servers are accompanied by a “penalty score” that, when high, indicates a lack of reliability in the data and the necessity to use more complicated fitting procedures to obtain them accurately. Such fitting techniques are not straightforward, and programs such as Antechamber (Wang et al., 2006) (for AMBER) and The Force Field Toolkit (Mayne et al., 2013) (for CHARMM) could be used. Special care should be paid to the optimization of partial charges, as the electrostatic interactions depending on them are responsible of the interaction between our molecule and the rest of the system. Different force fields use very different strategies for the parametrization of partial charges. For example, while in CHARMM the partial charges are chosen to reproduce the quantum mechanical interactions of the molecule with water molecules in a variety of orientations (Mackerell, 2004), within AMBER the partial charges result from fitting the electrostatic potential around the molecule. In particular, for nonpolarizable force fields, it is not just possible to use the point charges obtained from abinitio calculations as the point nature of the charges, and the subsequent nonconsideration of the charge polarizability should be usually corrected through an increase in the atomic charge.

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2.4.6 Reactive Force Fields All the force fields described so far are incapable of describing chemical reactions. This happens, in the first place, because chemical bonds are represented through harmonic potentials than cannot lead to dissociation and, besides, because the connectivity is defined in advance and is not allowed to change throughout the simulation. As it will be discussed subsequently, the description of the formation and breaking of bonds would require significant modifications of the terms included in Eq. (20.28). Many biological processes like ligand binding, protein folding, and protein aggregation, where the system remains close to the equilibrium geometries and the atom connectivity does not change, are not affected by the problem posed in the former paragraph. Even when studying enzymatic reactions, the chemical reaction just takes place at the “active site” of the enzyme, and only very particular and specific bonds could be broken or formed (we will discuss this issue in Section 2.5) in such a way that nonreactive force fields are good enough to describe the majority of the system. However, one could be interested in systems at geometries far from the equilibrium or at very high temperature, as it happens in combustion processes, chemical degradation of nanowires, or reactions at solid/gas or liquid/ gas interfaces. To describe the evolution of these systems, we have to continue dealing with thousands of atoms while considering, in addition, the chemical transformations that can occur at many different sites. None of the existing methodologies discussed in the preceding sections are applicable to these problems: quantum mechanical calculations are too computationally expensive for systems formed by so many atoms, and the empirical force fields are incapable of describing the chemical transformations that will take place. For the study of these systems, it is compulsory to use reactive force fields such as COMB (Liang et al., 2012) or ReaxFF (van Duin et al., 2001). These force fields use an expression for the energy similar to Eq. (20.28), where the energy is described as a sum over bonding and nonbonding terms, but using more sophisticated functional forms for the different terms. The price to pay for such increase in accuracy and complexity is that simulations using reactive force fields are much more expensive and, therefore, restricted to a few nanoseconds timescale. Throughout this section, we will describe these methods focusing on the ReaxFF force field. Reactive force fields make extensive use of the “bond order” concept in a dynamic manner; the bond order of each atom changes throughout the simulation due to modifications in the chemical environment. The main idea behind ReaxFF is that the bonding energy terms in Eq. (20.28) depend on the atomic bond orders, which are not necessarily integer numbers, and there is a direct relationship between the bond order and the internuclear distance between the atom under consideration and those around it. For example, the bond

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order for the interaction between two carbon atoms Ci and Cj at a rij distance will be given by the following (van Duin et al., 2001):    g1    g2    g3  rij rij rij BOðCi  Cj Þ ¼ exp b1 1 þ exp b2 2 þ exp b3 3 r0 r0 r0 (20.32) where bi , gi , and r0i are parameters of the force field, and each of the three exponential terms in Eq. (20.32) corresponds to one of three types of CeC bond mainly differing in their long-range properties. The b parameters in Eq. (20.32) usually take a negative value, so each of the three terms decreases monotonically at large internuclear distances, while at small distances, they remain constant and equal to one. In this way, the maximum bond order per exponential term is one, and the maximum bond order for a CeC bond is three3. In the panel (A) of Fig. 20.6, we show how the bond order depends on the internuclear distance for a CeC bond, using the parameters specified in (van Duin et al., 2001). It should be stressed that the bond order depends only on the distance and not on a previously defined connectivity, so the bonding interactions continue even at relatively large internuclear distances. Accordingly, the bond order between atoms that are separated by two covalent bonds is not necessarily zero. This helps the force field to accurately describe long-range interactions as well as the partially bonded configurations typical of many transition states. For example, the total bond order for a CeC atom pair is 0.1 even at 2.3  A. As the bonding energy terms, including the angular and torsional terms, depend on the bond order, these long-range interactions could lead to an additional stabilization of the system.

(A)

(B)

3.0

total bond order

Bond Order

2.5 2.0

exp 3 1.5

exp 2

1.0

exp 1

0.5 0.0 0.0

0.5

1.0

1.5

2.0

2.5

rij ( Å )

FIGURE 20.6 Bond order characterization in a reactive force field: (A) internuclear distance dependence of the bond order [Eq. (20.32)]; (B) bond order determination for the central carbon of a propene molecule ðC2 Þ. Please note that the overall bond order is calculated as the sum over the partial bond orders, and in this case, it is 4.26 (see text for more details). 3. In general, the number of exponential terms in equations like (20.32) corresponds to the maximum bond order between the two atoms under consideration.

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The bond orders are corrected by the force field at each integration step. In panel (B) of Fig. 20.6, we show the bond order for the central carbon atom of an isolated propene molecule. Please notice that such bond order is due to the interaction with every atom in the molecule and equal to 4.26, which exceeds 4, the maximum value expected according to the octet rule4. Whenever this happens, the force field corrects automatically the bond order by removing part of the long-range interactions. If, for instance, we had a transition state where the H6 atom bonded to C3 had been removed, the system would also apply a correction to the bond order of C2, but not of C3, which would remain with a low bond order value as it corresponds to its radical nature. In this way, the force field would reproduce the high reactivity of this atom by allowing it to have long-range attractive interactions with other atoms from the same or neighboring molecules. There are another two features of the reactive force fields that should be highlighted. First, the atomic charges do not take fixed values as for nonreactive force fields, but they are recalculated at each integration step, which is the most expensive part of the energy calculations. Besides, reactive force fields make use of the hardness and electronegativity of each element in the system to describe the important role played by polarization. Second, and given the reactive character of the field, one atom may belong to many different chemical species throughout the simulation. As, for reactive force fields, the energy of the system must remain constant with respect to the exchange of identical atoms, only one atom type will exist per each chemical element.

2.5 Hybrid Methods: Quantum Mechanics/Molecular Mechanics Quite often, it is convenient to combine different computational methods to improve the description of a particular problem, i.e., to use a hybrid method. A prototypical example of this necessity occurs for enzymatic reactions. The huge number of atoms that forms the enzyme and the solvent molecules around it, which may reach 105 , prevents the use of any accurate quantum mechanical method, although their usage is sometimes ineluctable if one wishes to account properly for the chemical transformation that is going on in the “active site” of the enzyme. The determination of properties of a solute in an explicit solvent is another example where the usage of hybrid methods is necessary. The idea behind the hybrid methods is rather simple: to split the system into at least two subsystems, also called regions or layers, and to study each of them using a different computational method. However, the devil is in the

4. In the case of hydrogen atoms, the maximum bond order would be one.

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details, and in this case, the difficulty arises in how to deal with the interactions between the different subsystems, more so because the layer separation sometimes intersects covalent bonds. This is precisely the case of enzymatic reactions, where some atoms of the protein play an important catalytic role and thus have to be included in the layer described at a higher level of theory. Among the hybrid methods, the most widely used is QM/MM, a two layers method where the first one is treated using an accurate quantum mechanical method (typically DFT), while the energy in the second layer is computed using a cheap empirical force field. This method was described for the first time by Warshel and Levitt in the 1970s (Warshel and Levitt, 1976) and is one of the contributions for which they received the Nobel Prize in 2013. Other hybrid methods include the QM/QM (or even QM/QM/QM) ones where different QM methods of decreasing accuracy are applied to each layer (Chung et al., 2015). In what follows, we will describe the main features of the hybrid methods, paying special attention to the widely used QM/MM methodology. A more detailed description of the latter can be found at the excellent reviews by (Lin and Truhlar, 2007) and (Senn and Thiel, 2009).

2.5.1 Additive and Subtractive Schemes Let us assume that we are studying a system S using a hybrid method. The two layers in which S is split are termed AS (active site) and RS (rest of the system). The description of AS requires higher accuracy and will be performed at a theoretical level L1 , typically a quantum mechanical method (ab-initio or DFT). The RS part, in turn, will be treated at a lower level of theory L2. There are two procedures to express the total energy of the system ES ðhybridÞ in terms of the energies of the layers and the interaction between them: the subtractive and additive schemes. For the subtractive scheme, the energy of the system is given by ES ðhybridÞ ¼ EL2 ðAS þ RSÞ þ EL1 ðASÞ  EL2 ðASÞ

(20.33)

where EL2 ðAS þ RSÞ is the energy of the whole system calculated at a L2 level of theory, and EL1 ðASÞ is the energy of the active site calculated at a L1 level of theory. To avoid counting twice the energy of the active site at a L2 level of theory, EL2 ðASÞ is subtracted. Each energy term on the right side of Eq. (20.33) requires a different calculation. In the particular case of QM/MM methods, where L2 is used to correspond to an empirical force field, one would have ðRS=ASÞ þ ELbond ðRS=ASÞ EL2 ðAS þ RSÞ  EL2 ðASÞ ¼ EL2 ðRSÞ þ ELnonbond 2 2 (20.34) ELnonbond ðRS=ASÞ 2

ELbond ðRS=ASÞ 2

where and are the crossed nonbonding and bonding terms that represent the interaction between both layers of the system calculated at the L2 level. For the simplest case, where the separation between

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AS and RS does not intersect any chemical bond, the interaction energy only includes the nonbonding term. Additive hybrid methods, in turn, calculate the energy according to the following expression: ES ðhybridÞ ¼ EL1 ðASÞ þ EL2 ðRSÞ þ EL1 L2 ðRS=ASÞ

(20.35)

where EL1 L2 ðRS=ASÞ accounts for the interaction between the two subsystems and will be discussed subsequently. If the two layers were independent, EL1 L2 ðRS=ASÞ, ELnonbond ðRS=ASÞ and ELbond ðRS=ASÞ would be null, so both 2 2 schemes would be completely equivalent. Strictly subtractive schemes face one important problem derived from the fact that the interactions between the two layers are described using a force field. For the bonding interaction terms, this means that we would need to know the force field parameters for bonds, angles, and dihedral angles involving atoms that belong to both the AS and RS regions. Some of the atoms of the AS region will not substantially change their positions throughout the chemical reaction, and for them, the bonding terms connecting them with the RS region could be calculated using the standard parameters already incorporated into the force field. This, however, would not be possible for those atoms of the AS region bonded to their RS counterparts that move far from the equilibrium geometry or that are directly involved in the chemical transformation because their motion could not be described by means of the harmonic terms included in standard force fields. The solutions to all these difficulties is, however, simple and consists of using a large AS region, so ideally, this region should be defined in such a way that the atoms that are directly involved in the chemical process are wrapped with a “shell” formed by at least three covalent bonds. However, in practice, the energy contribution due to the dihedral terms is not too relevant, and a shell formed by two covalent bonds used to be large enough. The main drawback of the subtractive QM/MM scheme arises from the nonbonding term and, in particular, can be traced back to the treatment of the electrostatic interactions, whose long-range character make them impossible to neglect no matter how large the AS region is chosen to be. First, the calculation of EL1 ðASÞ in Eq. (20.33) (a quantum mechanical calculation in a QM/MM context) is performed without any information of the surrounding RS region, i.e., the region treated using molecular mechanics would not influence (polarize) the charges in the AS region as EL1 ðASÞ is evaluated5. Second, the charge distribution of the AS region will change during the reaction, in such a way that no unique set of point charges for the atoms of this layer can be used 5. As we will discuss later, this deficiency is solved in the additive scheme by adding an extra term to the AS Hamiltonian operator that represents the polarization of AS by RS at a L1 level of theory. It is worth mentioning that such a solution would not work in the subtractive scheme as it would be lead to counting twice such an effect, already included in ELnonbond ðRS=ASÞ. 2

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when evaluating the electrostatic interaction with the RS region using molecular mechanics. Updating the partial point charges as the reaction evolves would not avoid this problem as it would provoke discontinuities in the potential energy surface. It is worth mentioning that a three-layer method QM/ QM/MM, where the part of the RS system that is closer to the AS one described at a lower quantum mechanical level of theory could overcome or at least minimize this drawback. Due to the aforementioned difficulties, additive schemes are preferred when applying QM/MM methods. Within this scheme, the interaction between the AS and RS parts of the system is decomposed as the sum of three terms: EL1 L2 ðRS=ASÞ ¼ ELbond ðRS=ASÞ þ ELVdW ðRS=ASÞ þ ELElect ðRS=ASÞ (20.36) 2 2 1 The first term describes the bonding terms in which atoms belonging to RS and AS are mixed. This contribution also appeared in Eq. (20.34), and as was discussed above, problems derived from its evaluation could be overcome by choosing an AS region large enough to prevent any interaction of its “active” atoms with those forming the RS subsystem via bonding terms. The contribution ELVdW ðRS  ASÞ accounts for the Van der Waals interaction between the 2 AS and RS systems. In a QM/MM method, it is commonly calculated through the LennardeJones potentials implemented in the force field [see Eq. (20.29)]. Given the short range nature of these interactions and the ensuing approximations adopted to reduce the number of atom couples whose Van der Waals interaction is explicitly considered (see Section 2.4), the choice of an AS layer large enough to describe accurately ELbond ðRS=ASÞ also ensures an unprob2 lematic evaluation of ELVdW ðRS=ASÞ. 2 The main difference between strictly additive and subtractive schemes lies in the third term of Eq. (20.36). In additive QM/MM calculations, the electrostatic interaction between the AS and RS regions is evaluated quantum mechanically, opposite to what happened in the subtractive approach. To this end, the atoms in the RS layer are replaced by the partial point charges and its interaction with the AS atoms is carried out via one additional term in the standard Hamiltonian operator [Eq. (20.2)]. For an AS system formed by N nuclei and n electrons, and a RS system formed by K atoms (here replaced by Elect K point charges), the additional term of the Hamiltonian ( Hb RS=AS ) can be written as shown: Elect Hb RS=AS ¼ 

n X K X i¼1 j¼1

N X K X eqj Za eqj þ 4pε0 jri  Rj j a¼1 j¼1 4pε0 jRa  Rj j

(20.37)

where qj and Za are the partial point charge of the j atom of the RS system and the charge of the a nucleus of the AS layer, respectively. Although the addition of this term to the Hamiltonian fixes one of the problems of the subtractive calculation by accounting for the polarization of the AS region by its RS

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counterpart, we still have to account for the reciprocal effect, the polarization of the RS layer by the AS one. The inclusion of this effect is more complicated as it implies using a polarizable force field and, ideally, letting both layers polarize each other until convergency is reached. Due to the subsequent increase in computation time, most of the QM/MM methodologies simply ignore it and disregard the AS polarization on RS.

2.5.2 Chemical Bonds in the QM/MM Interface We will briefly describe now how to proceed when the separation between the AS and RS subsystems intersects covalent bonds, as it used to be the case when studying enzymatic reactions. For illustration purposes, in Fig. 20.7, we show a simple example of a QM/MM arrangement applied to a biological system: the protonation of a glutamic acid that, for the sake of simplicity, is pointing toward the solvent so it does not interact with any other part of the protein. To speed up the calculations, it is convenient to use an AS (QM) layer that is as small as possible. In principle, the AS region could include just the carboxylate group (COO) that is going to pick up the proton and the water molecule that will donate it. However, as was mentioned before, it is convenient to use a larger AS region so that the closer RS (MM) atoms are more than three covalent bonds away from the atoms that are directly involved in the chemical process. Hence, the CH2eCH2eCOO group will be included in the AS region. Moreover, not only one, but five water molecules

FIGURE 20.7 System separation suitable for the study of the protonation of glutamic acid in a protein environment through a QM/MM calculation. The atoms in the QM layer (AS in the text) are surrounded by an imaginary surface and represented atomistically. This region includes the sidechain of the glutamic acid and some water molecules that surround it and could be deprotonated. Only the atoms of the MM region (RS in the text) that belong to the glutamic acid are represented atomistically in the figure. The bond between the yellow (light gray in print versions) carbon (included in the QM region) and the magenta (dark gray in print versions) carbon (included in the MM region) is split by the separation surface and represented through a discontinuous black line.

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are interacting through hydrogen bonds with the carboxylate group. As these interactions would be seriously modified after the protonation, it is also convenient to include them in the AS region. It is commonly better to define AS regions whose net charge is as low as possible, if not zero. In this example, the charge of the AS region is 1 and, in a real simulation, it might be adequate to include a positively charged residue nearby. Finally, it could be also convenient to include more solvent molecules around the water that experiences the deprotonation, but that would mean an increase in the cost of the calculations. Even in this simple example, the division between the layers intersects a chemical bond, that between the yellow [in the QM (AS) layer] and the purple carbons [in the MM (RS) layer]. If we just included the AS atoms in the quantum mechanical calculation, we would be simulating the behavior of the radical $CH2eCH2eCOO, whose chemical properties are very different from those of the sidechain of the glutamic acid (a closed-shell molecule). There are two main strategies to overcome this difficulty: l

l

Localized orbitals method: this method adds bond orbitals where the intersected bonds were located. These orbitals are obtained using a strictly localized bond orbital scheme that ensures that they only have contributions of those AS and RS atoms that formed the chemical bond. These orbitals are included in the calculation but excluded from the SCF optimization so they will not mix with other basis functions. This was the approach used by Warshel and Levitt when they first used a QM/MM approach (Warshel and Levitt, 1976). Ghost link atoms method: this method has been widely used as it is easier to implement than the localized orbital scheme. The idea behind this approach is to add monovalent atoms (usually hydrogen atoms) to “complete” the broken bonds. This technique works better if the broken bond is a nonpolar single bond, as it is the case in the example of Fig. 20.7. In this example, a CeC bond is broken, and it would be completed by adding a hydrogen atom, in such a way that the AS subsystem would include the HeCH2eCH2eCOO molecule. This additional hydrogen will be initially located in the line between the AS and RS atoms (yellow and magenta carbons respectively), and at every time step, its position will be updated following the same rule. The parameters of the additional hydrogen atom in the force field are set to zero, to make it “transparent” (a ghost atom) for the molecular mechanics calculation.

The main disadvantage of this approach is that the bond between the ghost atom and the corresponding AS atom could be over-polarized by the partner RS atom. Many methods have been designed to solve this problem, the simpler of them consisting of ignoring the charge of this RS atom. A more thorough method (Antes and Thiel, 1998) removes the atomic charge of the group of atoms containing the RS atom.

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2.6 Beyond Atomistic Simulations: Coarse-Grained Methods As it was pointed out above, using force fields, it is possible to carry out simulations of w105 atom systems in the microsecond timescale. However, some biological problems require studies at significantly larger timescales and/ or including millions of atoms. Under these circumstances, even empirical force fields becomes unfeasible. This would be the case, for example, for the study of aggregation problems, protein folding (of some slow-folded proteins), membrane properties, etc. One could think about using a simplified force field where, for example, we could fix some bonds and/or angles at their equilibrium distances. Although that would certainly speed up the calculations to some extent (mainly, as we will discuss in Section 4.4, because it will allow us to use a larger integration step), most of the computational cost of the energy evaluation goes into the calculation of nonbonding terms, which will be unaffected. Hence, to study these systems, we should go beyond all atom simulations and use, for example, coarse-grained methods (Levitt and Warshel, 1975). Although a thorough description of this approach goes beyond the scope of this chapter, we will briefly describe its main features. The interested reader is referred to (Saunders and Voth, 2013; de Pablo, 2011) for more information. Although coarse-grained methods are similar to force fields, they do not include atomistic representations of the systems under study. In a coarsegrained method, an entire group of atoms is represented by a single entity called a pseudoatom. Depending on the particular implementation, which should be chosen in terms of the size of the system and the timescale we are aiming to simulate, one pseudoatom may account for the properties of a few atoms (such as one methyl group), several atoms (the sidechain of an aminoacid), or even many residues. One of the most widely used coarse-grained implementations is the Martini model [see (Marrink and Tieleman, 2013) for a recent review], which can be applied to the study of biosystems like lipids, proteins, and small nucleotide chains. In the Martini model, the backbone of a residue is represented by a pseudoatom, while the sidechain is represented by one to three pseudoatoms (on average four nonhydrogen atoms per pseudoatom). Following the same strategy, one water-pseudoatom would substitute four water molecules and an ionic pseudoatom a real ion and its first solvation shell. Some significative examples are given in Fig. 20.8. The Martini model is defined through a set of parameters that have been obtained by comparison with atomistic simulations and thermodynamic experimental data and, when applied, makes it possible to use time steps of 20 or 30 fs, 10 times larger than using an atomistic force field. The Martini force field faces some important limitations, which may give an idea of the limitations of coarse-grained methods. It was parametrized to accurately represent free energies at a given temperature, so the missing

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(A) Aspartate

(B) Arginine

(C) Phenylalanine

FIGURE 20.8 Pseudoatoms in the Martini model. Nonhydrogen atoms are shown atomistically, while the pseudoatoms used in the Martini model are shown as transparent spheres. To represent an aspartate (panel A) only two pseudoatoms are used: one for the backbone and one for the sidechain (whose charge is 1). For a protonated arginine (panel B), where the polar hydrogens of the sidechain are shown, three pseudoatoms are used: one for the backbone and two for the sidechain. Finally, for a phenylalanine (panel C) the sidechain requires three pseudoatoms to account for the aromatic ring.

entropy, a consequence of the reduction of the number or particles, is balanced out by a reduced enthalpic term. Therefore, the dependence of the free energy on the temperature is inaccurate, and entropies and enthalpies cannot be extracted. Other limitations are the lack of directional hydrogen bonds and the absence of friction from the atomistic degrees of freedom. Martini’s method is not appropriate to the study of changes of the secondary structure of proteins since it applies constraints to keep it unchanged throughout the simulation. However, it is appropriate for the study of conformation changes of the tertiary structure and the interaction between proteins.

3. PREPARING A MOLECULAR DYNAMICS SIMULATION The most crucial, and probably cumbersome, part of carrying out a simulation is to set up the system that is going to be studied. We have to be sure that our system is sensible, reliable, and also representative of the chemical or biological process that we want to simulate. For relatively small systems, those that could be simulated using QM methods, we should scan the energy landscape to be sure that the geometry of the reactants (the reagents valley) is properly described. Let us imagine that we are attempting to calculate the energy barrier for a H2O þ X / HX þ OH reaction. If in our initial structure the H2O were linear, the energy of the reactants would be artificially increased leading to unrealistic smaller barriers.

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The algorithms used for geometry optimization usually succeed in identifying the right structure, except in those cases when our system can be trapped in many local minima. This means, for instance, that they will not predict a linear equilibrium structure for water but may not lead to the lowest energy conformer. A classical example of this failure takes place when studying a monosubstituted cyclohexane, where the minimum that will be identified by the algorithm depends on the position of the hydrogen that is replaced, equatorial, or axial. This kind of problem is so general that even empirical force fields sometimes require more than one harmonic term to describe dihedral angles to account for the local minima present in the potential energy surface. Hence, a careful inspection of the energy landscape is always required as a first step in any simulation. When carrying out simulations of larger biological systems, the very large dimensional phase space impedes a proper scanning of the potential energy surface, and only for small polypeptides is it possible to predict the native tertiary structure of our system using molecular dynamics simulations. Even when that is possible, protein folding is computationally very expensive and involved. Hence, high-quality experimental structures, usually obtained by X-ray crystallography, are a necessary starting point for any simulation. Experimental tridimensional structures are deposited in the RCSB Protein Data Bank [PDB (Berman et al., 2000)], where it is possible to download the resolved tridimensional structure (hereinafter pdb file), the electronic density maps, etc. Moreover, PDB also links to the Universal Protein Resource database [UniProt (The UniProt Consortium, 2015)] containing all sorts of information about the target protein.

3.1 Experimental (Crystal) Structures The header of the pdb file contains information about the experimental conditions in which the structure was obtained (experimental method, resolution, size, and symmetry of the unit cell). It also includes the sequence of amino acids, the primary citation (if the structure has been already published), and the cofactors that are co-crystallized with the protein. After the header, the pdb file contains one line per atom whose position was experimentally determined. Each of these atoms are labeled by an integer number and its atom, chain, and residue names. Following those labels, the cartesian coordinates of the atom, the occupancy, and the temperature factor are displayed. The occupancy will be typically one, except if more than one possible position has been experimentally observed for that atom. If that is the case, the occupancy will provide us the weight of every atomic position in the crystal, so the sum over all the weights must be one. The temperature factor (or b-factor) indicates the displacement of the atomic positions from its average value (disordered regions have higher b-factors). High-resolution experimental structures are preferred, as in those structures the atomic positions will be predicted more

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accurately. The R-factor, which measures the overall agreement between the structure and the experimental density map, should also be examined. Wellrefined structures have low R values. Once a crystal structure has been selected, it is possible to further refine the structure using PDB-redo server (Joosten et al., 2009). Force fields have been prepared to be combined with structures obtained from the PDB. Hence, for standard residues such as the natural amino acids and the most widely used cofactors, the atom and residue names used in force fields match those of the PDB. For titrable residues, the names used in the force field correspond with the presumably most stable protonation state at physiological conditions. For example, ASP corresponds to the negatively charged aspartate (pKa z 3.7), and LYS to the positively charged lysine (pKa z 10.7). For the CHARMM force field, there is not a HIS residue name because the pKa of the histidine is closed to the physiological pKa. Furthermore, a neutral HIS could have two different isoforms (named HSD and HSE). The crystals obtained are not perfect enough to make it possible to elucidate the position of every atom forming the protein. For example, due to the similar electron density between oxygen and nitrogen, the orientation of glutamine and asparagine residues is sometimes uncertain. In fact, there are structures deposited in the PDB that show an asparagine residue coordinating an inorganic cation through its eNH2 group, something that is clearly impossible. Moreover, proteins also have very flexible parts, such as the N and C terminal ends and some flexible loops, whose tridimensional structure could not be experimentally determined. This creates gaps in the protein structure that should be filled using computational tools (Fiser et al., 2000). Hydrogen is a very light atom, and therefore very flexible, so usually its position is not experimentally determined in X-ray crystal structures. Molecular dynamics software is capable of calculating the position of the missing hydrogen atoms based on the position of the heavy atoms they are bonded to. From a practical point of view, the undefined position of the hydrogen atoms is not a significant drawback. The main difficulty arising from this uncertainty is that it implies that the protonation state of the titrable residues is unknown. The pKa of all titrable residues is known, which helps to assign such protonation states. However, the chemical environment is able to considerably shift the pKa values, especially near the active site of the enzyme, so chemical intuition and a deep knowledge of the chemistry of the target protein is sometimes necessary to assign protonation states. For example, even residues that are not considered as titrable, such as cysteine, can be found deprotonated near an inorganic cation, as illustrated in the left panel of Fig. 20.9 (Lee et al., 1989). Another example of nonstandard protonation state has been observed for HIV1protease homodimer, where two aspartates close to the binding site show an asymmetric protonation state (right panel of Fig. 20.9). In fact, the distance between the two aspartates is compatible with an OeH bond (w1  A) and one

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FIGURE 20.9 Left panel: nonstandard protonation state for a zinc finger DNA-binding domain (PDB ID: 1ZNF). The Zn is coordinated by two histidine residues (H19 and H23) and two deprotonated cysteines (C3 and C6). As an SeHeZn bond is not possible, both Cys must be deprotonated. Right panel: asymmetric protonation state in HIV-1 protease (PDB ID: 3TLH). The distance between the oxygen atoms of both aspartates is 2.7  A, which is not compatible with two negatively charged aspartates but with an OeHeO bond, i.e., one negatively charged aspartate that forms a hydrogen bond with an aspartic acid. The hydrogen has been added to display the most likely position of the hydrogen atom.

hydrogen bond between the negatively charged aspartate and the hydrogen of the aspartic acid (w1.8  A) (Li et al., 2000). It is worth noticing that, unlike other crystals, protein crystals have a high containment of solvent molecules (typically water). A few of them are water molecules that form the hydration shell of the protein and may be immobilized due to their direct interactions with the protein, so their position could be experimentally determined. The knowledge of the position of the water molecules in the surface of the protein is not that important since computationally added solvent molecules (explicit solvent) that are included in the simulation will easily reach those positions. However, other crystallized water molecules could be located in pockets buried inside the protein, which are not easily accessed by the explicit solvent, so they should be necessarily included in our simulation. Otherwise, that empty space could be occupied by some atoms of the protein, giving rise to nonrealistic conformations. More importantly, some of those water molecules could play an important role in the catalytic reaction (Rosta et al., 2011). The hardest part of setting up a simulation of a biomolecular system does not lie in the aforementioned technicalities, but in the need of a deep knowledge of the system to simulate. Crystallization is a very cumbersome process, and some inaccuracies could arise from the crystal lattice packing or the supersaturation conditions. In addition, mutations are sometimes introduced either to study some variants or to help crystallization. Nonnatural cofactors or amino acids are also sometimes included to mimic the effect of ligand binding while preventing the enzymatic reaction to happen. Moreover, some posttranslational modifications such as methylation, phosphorylation, or the formation of oligomers could be required for the full activity of the system.

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On top of this, some enzymes could have different stable conformations, and only a prior knowledge of the system would help us to decide which structure we should use and how the experimental structure should be modified to better represent the biological system that we would like to simulate. One text book example of the latter case is found in kinases. Kinases are proteins that transfer a phosphate group from an ATP to a protein substrate and are typically involved in signaling pathways. Kinases are known to have two stable structures, one of them active, where ATP can bind the active site, and another inactive where the ATP pocket is blocked by a phenylalanine. Phosphorylation of at least one residue in its activation loop shifts the equilibrium between those conformations toward the active one, leading to full activation of the enzyme. Different inhibitors can bind either the active or the inactive conformation, and hence, in PDB, it is possible to find many kinase structures in both conformations (Jambrina et al., 2014), so depending on the particular study we would like to carry out, we should select either one conformer or the other. Once we have selected a proper tridimensional structure, we can start the atomistic simulation. Our biological system is placed in a tridimensional box that is usually filled by solvent molecules6. To avoid artifacts if PBCs are used, the overall charge of the system is set to zero by adding counterions to balance the intrinsic charge of the biomolecule. Usually more cations and anions are added to mimic the ionic strength of the physiological media7.

3.2 Homology Modeling In the absence of experimental structures, it is sometimes possible to build reasonable models for one “target” protein based on its functional and sequence similarity with other proteins whose structures are known (called templates). This method is called homology modeling. There are several online tools to carry out homology modeling, such as Phyre2 (Kelley et al., 2015). Homology modeling methods are based on the fact that evolution is more prone to conserve structure than sequence. All homology modeling protocols starts by selecting suitable templates. In fact, several changes in the sequence usually have a very little effect on the 3D structure. This is obvious when scanning a family of proteins. For example, within the kinase family, CAMP and RAF kinase domain only share

6. Implicit solvent models, methods that do not include the solvent molecules in the simulation but model them as a dielectric continuum are widely used for QM calculations of small molecules but not for biomolecular simulations. Nevertheless, implicit solvent methods are included in most packages such as NAMD (Phillips et al., 2005) or CHARMM (Brooks et al., 2009). 7. If the system includes a membrane, it should be also placed in the simulation. That process is very involved and beyond the scope of this chapter. Computational tools such as CHARMM-GUI (Jo et al., 2008) help a lot with that process, and their use is encouraged.

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29% of the sequence while they are structurally analogous. Even the kinase domain of two isoforms of RAF, BRAF and CRAF, share just 81% of their sequence. Actually, a sequence alignment is enough to figure out the residues which play a key functional role, as these are the ones conserved in all the family of proteins. For kinases, some of the conserved residues are the DFG motif, involved in ATP binding, and the H(Y)RD motif, whose aspartate is directly involved in catalysis and whose arginine coordinates phosphorylated residues nearby.

3.3 Docking Sometimes we are interested in the simulation of systems that include different cofactors either natural (such as ATP, or NADP) or “artificial” (as inhibitors). However, we rarely have available experimental structures where our biological system has been crystallized in the presence of the desired or similar cofactors. As a consequence, the location of the cofactor inside the biosystem has to be computationally predicted. That process is called docking and involves (1) the prediction of the binding site and (2) the prediction of the most stable conformation and orientation (also called “pose”). Some binding sites, such as those located in the active site of the enzyme, are identified based on similarity with analogous structures crystallized in the presence of different cofactors. The identification of additional binding sites could be done based on geometric approaches where the binding site is described as a pocket. These methods embed the solvent-free protein in a tridimensional lattice that permits determining which points of the lattice are nonoccupied by the protein but surrounded by it, in such a way that they could host a ligand. Another family of methods locates probes at every point of the aforementioned tridimensional lattice and calculates the interaction energy between the probe and the protein. These methods identify the pockets based on the interaction energy maps so obtained. The interested reader in binding site prediction is referred to (Ghersi and Sanchez, 2011) and references therein. Once the binding site is known, different conformations and orientations (poses) of the ligand within the pocket are generated, and the interaction energy is calculated using scoring functions where the most favorable poses are selected. This process is challenging due to the relatively high number of degrees of freedom of the ligand. Sophisticated docking methods include some flexibility in both the ligand and the protein. Sometimes, we aim to predict which cofactors could be docked in a binding site, a process that is called virtual screening and that is recognized as a powerful technique for drug discovery. For example, Pala et al. (2015) used virtual screening to scan a database of five million chemical compounds to look for influenza virus PA endonuclease inhibitors. Their computational study allowed them to select 15 compounds among them, three of which inhibited virus replication in a virus yield assay.

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4. DYNAMICS SIMULATIONS The information derived from any of the methods described in the previous sections is the starting point for computational studies on spectroscopy and chemical kinetics. The minima of the combined energy of electrons and nuclei correspond to the stable geometries of the system under study, and the analysis of the nuclear motions in the vicinity of any of these minima opens the door to the study of vibrational and rotational spectroscopies. The calculation of the transition probability between electronic states and the determination of the subsequent evolution of the system makes it possible to interpret and predict the electronic spectra of molecular systems and to improve our understanding of many processes of biological interest where nonadiabatic effects are important. Last but not least, a chemical reaction consists of the displacement of the system from one energy minimum to another on the same or a different electronic state. The study of the nuclear motions that match such displacements and the calculation of the probability with which they occur can be used to evaluate the rate coefficients and the rest of properties that characterize any chemical process. Among all the applications described in the precedent paragraph, we will focus on those connected to the study of chemical reactions, as they are more directly related to the general goal of the chapter. Our exposition of the different methodologies employed to study the nuclear dynamics in this context will mimic that followed to describe the alternative approaches to evaluate the molecular energy: we will first present those methods used to cope with small systems, where more rigorous treatments are computationally feasible, and continue with the description of alternative approaches that reduce the computational cost and can therefore be applied to larger systems.

4.1 Purely Quantum Mechanical Techniques Purely quantum mechanical theories (Steinfeld et al., 1998; Levine, 2009; Brouard and Vallance, 2011) for the study of inelastic and reactive collisions concentrate on solving, exactly or approximately, the nuclear Schro¨dinger equation that, under the assumptions of the adiabatic approximation, takes the form given by Eq. (20.6). The exact solution of this equation, whose nature is purely quantum mechanical, is only computationally affordable (Hutson and Green, 1994; Skouteris et al., 2000; Cvitas and Althorpe, 2009, 2011) for collisions involving three or four atoms that, in spite of not having biological interest, are extremely relevant for atmospheric, astrochemical, and purely theoretical studies about reaction dynamics. Such dynamic studies make use of two different approaches, the first of which originates the time-independent (TIQM) methods (Brouard and Vallance, 2011). TIQM calculations consist of solving Eq. (20.6) by propagating the nuclear wave function from the inner

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classically forbidden region of the potential energy surface where it vanishes until the noninteracting regions that correspond to reactants and products. Alternatively, one could use a time-dependent wave packet approach (Tannor, 2007; Brouard and Vallance, 2011) where the reactants are represented by means of a wave packet that is made to evolve in time under a potential defined by the potential energy surface. Both methodologies are equivalent and render the probability amplitudes connecting any possible state of the reactants with their products counterparts for well-defined values of the total energy, total angular momentum, and any other quantity conserved during the collision. From these amplitudes, and averaging over collision energies, one can calculate the macroscopic rate coefficients and compare with experimental results. The computational cost of the purely quantum mechanical calculations described earlier scales so quickly with the number of atoms that they soon become impossible to apply. Although some approximated methodologies like MultiConfigurational Time-Dependent Hartree (Meyer et al., 1990; Beck et al., 2000) make it possible to extend quantum mechanical dynamic studies to systems with up to 12e15 degrees of freedom (Wang, 2015), their range of applicability continues to be too narrow for practical purposes.

4.2 Classical Trajectories The impossibility of performing purely quantum mechanical studies except for very small systems led to the adoption of a more drastic approach consisting of using the classical Hamilton equations instead of the nuclear Schro¨dinger one (20.6) to describe the nuclear dynamics. The Hamilton formalism is a reformulation of the classical Newton equations of motion, which facilitates their application in noncartesian systems of coordinates and whose form is (Goldstein et al., 2013) dpi vH ¼ vqi dt

(20.38)

dqi vH ¼ vpi dt

(20.39)

where qi and pi represent the position and linear momentum of the atoms, and H is the classical Hamilton function that, for the majority of the cases of interest in computational chemistry, coincides with the total energy of the system. As pointed out by Aoiz, Zare et al. (Jankunas et al., 2014), “In this picture, elementary chemical reactions might be regarded as molecular billiards (pool).” This scheme reduces significantly the computational cost, whose origin can be now traced back to the computation of the forces from the potential energy and not to the integration of the Hamilton equations. The accuracy of the

Computational Tools for the Study of Biomolecules Chapter j 20

representation used for the potential and the consequent facility to evaluate its value and its derivatives will therefore set the limit of applicability of this approximation. As was discussed in the first part of the chapter, an increase in the degrees of freedom of the system, i.e., the number of atoms involved in the collision, will require one to adopt less rigorous (nonquantum mechanical) and simpler forms for the potential to keep the computation time at bay. In those cases where the number of atoms is not large enough to make the solution of the electronic Schro¨dinger equation impossible, the integration of the Hamilton equations will make use of its eigenvalues. Otherwise, the energy is provided by a force field type calculation. In any case, the corresponding potential energy surfaces will be fitted to analytical forms or used “on the fly,” i.e., the energy will be calculated as it is needed, whenever such fitting is too complicated or unpractical. Dynamic calculations performed under these premises are termed classical trajectories (Karplus et al., 1965; Bernstein et al., 1979; Steinfeld et al., 1998) and combine a potential that may have a quantum mechanical origin with a classical description of the nuclear motions. For gas phase processes, the procedure is quite simple: once the initial parameters that define the geometry of the reactants and the approaching kinetic energy are fixed, the integration is performed until the distance between the fragments overcomes a threshold, at which point the propagation is halted, and the trajectory is classified according to the nature and properties of such fragments. To make a meaningful comparison with experimental results, it is necessary to integrate as many trajectories as necessary to sample the wide distribution of initial conditions that are relevant for the experiment that is being simulated. For those systems amenable of a quantum mechanical treatment for the nuclear dynamics, classical8 calculations perform surprisingly well (Ban˜ares et al., 2005) given the nature of the approximations adopted: the picture of the reactivity they provide used to be highly accurate and complements quantum mechanical calculations by making available a more visual interpretation of the features of the individual collisions. The only exception to this good behavior takes place when purely quantum mechanical effects, i.e., tunneling, resonances, or threshold effects, are relevant for the collisions, as their description is beyond the possibilities of classical mechanics.

4.3 Nonadiabatic Processes So far, we have implicitly assumed that the system evolves in a single electronic state, which facilitates the dynamic calculations. This, however, is not 8. Actually, for these systems formed by three to six atoms, the calculations are termed “quasi-classical” instead of “classical” because the trajectories are started in a well-defined quantum state and the products state is projected into one of their quantum mechanical counterparts as the quantization is lost as soon as the propagation initiates.

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always the case, and nonadiabatic processes where several electronic states are involved are commonly found in multiple areas of chemistry like photochemistry (Albini, 2015), electron transfer (Mattay, 2013a,b), surface chemistry (Sholl and Tully, 1981), and many biological processes such as those related to vision and photosynthesis. The exact quantum mechanical treatment of nonadiabatic collisions is extremely complicated even for very small systems, as it involves solving a set of coupling differential equations for the nuclear wave functions instead of just Eq. (20.6). Different semiclassical approximations have been devised to describe, at least qualitatively, nonadiabatic effects. All of them analyze the evolution of the population of the electronic states as the nuclei dynamics is propagated classically. The existence of more than one electronic state suggests that the nuclear dynamics should be somehow influenced by all of them. However, the classical equations of motion admit a single potential function acting as a guidance for the nuclear motion. These two contradictory facts can be “juggled” in two different ways. In the Ehrenfest method (Xiaosong et al., 2005), the nuclei are made to evolve classically according to a single potential obtained as an average of all the electronic states involved in the process. Alternatively, the classical equations of motion are propagated as in the adiabatic case but with the inclusion of an algorithm that calculates at any instant the probability of changing to a different electronic state. If the switching takes place, which is more probable as the electronic states come closer, the propagation continues on the new potential. This approach to the multisurface problem leads to the trajectory surface hopping (TSH) methods (Sholl and Tully, 1998). Both the Ehrenfest and the TSH methods are computationally demanding and soon become unpractical as the number of atoms and surfaces increases.

4.4 Canonical Molecular Dynamics Simulations Gas phase reaction studies are based on dynamic simulations that consist of a huge number, rising up to millions, of trajectories that are typically integrated using a microcanonical ensemble, where the total energy is conserved throughout the trajectory and whose information is averaged to obtain the desired dynamic information. The starting and final point of each trajectory is selected in such a way that there are no interactions between the reactants (or products). In liquid simulations, however, the Brownian motion makes it very difficult to define a starting and final point for a trajectory and to employ the conservation energy principle. Instead of using a microcanonical ensemble, liquid simulations use the canonical one, where the temperature and not the energy is conserved. For biological systems, besides, it is computationally impossible to follow the same procedure as for gas phase reactions where millions of trajectories are integrated and analyzed. Instead, dynamic calculations involving large biological systems invoke the ergodic hypothesis, according to which the probabilities obtained from an ensemble of molecules at one instant of time are equal to the probabilities derived from a single molecule simulation that

Computational Tools for the Study of Biomolecules Chapter j 20

propagates for long enough times. This means that we do not need to perform millions of calculations, but we can obtain the same information from a small set of trajectories, or even a single one, propagated for long times.

4.4.1 Langevin Dynamics For liquid simulations, it is convenient to choose between a canonical ensemble where the number of particles, temperature, and volume (NVT) or the number of particles, temperature, and pressure (NPT) are kept constant throughout the simulation. The latter is usually preferred as it is more representative of the experimental conditions. For an N particle system following a canonical distribution, the instantaneous values of the temperature and the system kinetic energy are related as follows: T¼

2Ekin kB N

(20.40)

and the variance of the temporal kinetic energy distribution is given by s2Ekin ¼

3NkB2 T 2 2

(20.41)

where Ekin is the system kinetic energy, and kB is the Boltzmann constant. Hence, conservation of temperature and/or pressure requires the control of the kinetic energy and prevents the total energy from being conserved during the simulation as, if it were conserved, the temperature would increase when it populates internal states characterized by a lower energy. Although a velocity scaling could be enough to keep the temperature constant [Eq. (20.40)], it would not describe properly the kinetic energy fluctuations of a canonical ensemble [Eq. (20.41)]. A useful way of controlling the kinetic energy distribution so that the time average of the instantaneous temperature coincides with the constant value chosen before carrying out the simulation is by using Langevin dynamics or, in other words, by employing the following equation of motion: Fðqi Þ ¼ mi

d 2 qi ðtÞ þ lpi  Ri ðtÞ dt2

(20.42)

where Fðqi Þ is the force experienced by particle i of mass mi whose position and momentum are labeled as qi and pi , respectively. The former equation is nothing but the second Newton’s law modified with two additional terms. The second term of the right side of Eq. (20.42) represents the damping applied to the particle, where l is the damping coupling coefficient. This term plays a frictional role and removes energy from the system, in such a way that high values of l will significantly slow the system. In practice, the l value should be the minimum one suitable to keep the temperature constant (w1 ps1). The third term in Eq. (20.42) is a random force that acts on the particle and, on average, compensates for the loss of energy caused by the damping term. Values of l too large lead to the loss of inertia of the system, whose motion would become

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purely Brownian, overdamped, as the third term in Eq. (20.42) would end up dominating the dynamics. The constant pressure constrain, in turn, requires one to adjust the size of the unit cell during the simulation and scale the atomic coordinates. Such an adjustment is facilitated by the usage of PBCs. A very important parameter when performing any kind of simulation is the value of the time step used for the integration of the equations of motion. Although large time steps will certainly speed up the calculations, they may also affect the accuracy of our simulation. In fact, its maximum recommended value depends on the fastest movements that take place during the simulation. Due to its lightness, hydrogen atoms usually follow almost instantaneously the movement of the atom they are bound to, and accordingly, the maximum value of the time step used depends on the changes experienced by the hydrogen stretching coordinate. Hence, if those distances are kept fixed throughout the simulation, larger time steps can be used, leading to a significant savings of computational resources. This strategy is commonly applied, and it is already available in some dynamic codes such as NAMD (Phillips et al., 2005). Note, however, that the practical implementation of this technique is a bit more complicated than it seems, as it is not enough to freeze the hydrogen-heavy atom distance because that would remove the energy contribution of that degree of freedom. Instead, Lagrange multipliers are used to keep the distance constant while accounting for the energy associated to that stretching, as implemented in the SHAKE algorithm (Tao et al., 2012).

4.4.2 Monte Carlo Methods The Monte Carlo family of methods is an alternative to the molecular dynamics simulations. These methods are not based on trajectories where the position of every atom at a step n depends on the position and velocities at the step n  1. Instead, these are stochastic processes where the position of the system at every step is calculated as follows: l

l

Starting from the geometry at a time step n  1, the three coordinates (x,y,z) of each particle are perturbed by three random values in the [eDd,þDd] interval. In fact, Dd plays the role of the time step size in molecular dynamic simulations; its value should be large enough to speed up the simulations while minimizing the propagation errors that could lead to the appearance of unphysical structures. The energy of the system in its new geometry is calculated. Based on the difference of energies between the previous and the new geometries and the temperature, the probability of acceptance ðPMC Þ is calculated according to the Metropolis algorithm (Metropolis et al., 1953): PMC ¼ min½1; expðDE=kB TÞ  En1

where DE ¼ steps n and n  1. En

(20.43)

is the energy difference between the system at the

Computational Tools for the Study of Biomolecules Chapter j 20

l

A random number in the [0,1] interval is chosen. If that number is larger than PMC , that movement is not “accepted,” i.e., the position that the system at the step n is kept identical to that corresponding to the n  1 step. If, on the contrary, the random number is smaller than PMC , the new geometry is “accepted,” and the system evolves accordingly. This involves that changes to lower energy structures are always accepted.

As it turns out from Eq. (20.43), the velocity does not play any role in Montecarlo simulations. Hence, there is no need to evaluate derivatives of the potential, which makes the calculation cheaper. Monte Carlo simulations do not contain information about time evolution, or any kinematic property, but an ensemble of representative conformations at a given temperature from which thermodynamic properties, such as differences in free energy, can be obtained as the average of the value of that property throughout the simulation. Finally, it should be stressed that both dynamic simulations and Monte Carlo Methods are compatible with the enhanced sampling strategies that we will describe next.

4.5 Enhanced Sampling Methods For most systems of biological interest, the potential energy functions display very complicated topologies. No matter whether we are studying ligand binding, conformational changes, or biochemical reactions, many local minima are usually present and sometimes separated by sharp and high free energy barriers. As a consequence, trajectories could leave some relevant regions of the energy hypersurface barely explored or even unexplored, and even for long simulations, the system could be trapped in a local minimum and not visiting the most stable, and relevant, conformation. On top of this, and due to the aforementioned existence of a manifold of local minima, it is difficult to obtain an ergodic trajectory, i.e., a trajectory where the statistical weights of the different conformers are correct. The methods designed to deal with this problem are termed enhanced sampling methods (also called free energy methods). In what remains of the chapter, we will summarize some of the most relevant ones.

4.5.1 Temperature Replica Exchange There are, in principle, two different strategies to improve the statistics of those regions of interest that are sampled poorly. One could either constrain the sampling of some previously known reaction coordinates or modify the energy expression to reduce the free energy barriers that cause the poor sampling. The temperature replica exchange (Swendsen &Wang, 1986) method belongs to the last family of methods.

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One useful way of reducing the barrier is to increase the temperature, as the available energy is proportional to the temperature; see Eqs. (20.40) and (20.41). However, although simulations carried out at large temperatures will certainly improve the statistics of high energy states, those trajectories will rarely visit low energy states. Moreover, force fields are parametrized to reproduce the chemistry of biosystems at around 300K, and it is not sure they could capture the chemistry at significantly larger temperatures. Hence, the ideal scenario would combine low-temperature trajectories where the minima are properly described with high-energy trajectories that avoid trapping in local minima and are able to sample and overcome free energy barriers between the states of interest, for example, binding and unbinding states or two conformers. Temperature replica exchange achieves such a combination by propagating, in parallel, different independent trajectories (called replicas) at different temperatures. Throughout the simulation, the energies of neighboring replicas are compared, and in principle, larger temperature trajectories should have higher energies. However, due to the kinetic energy fluctuation for a canonical ensemble at its temperature, that is not always the case. Based on the energy difference between the trajectories, the method calculates a swapping swap probability ðPi;j Þ for every pair ði; jÞ of them: Pswap i;j

    1 1 ¼ min 1; exp ½Ei  Ej   kB Ti kB Tj

(20.44)

where Ei ðEj Þ is the energy of the Ti ðTj Þ replica. Eq. (20.44) is analogous to the Metropolis equation used in Monte Carlo simulations (20.43), and its meaning is the following: whenever the energy of the higher temperature replica is swap swap smaller Pi;j ¼ 1, and if that is not the case, the value of Pi;j will be smaller as the energy difference between the two replicas increases. A random number swap in the [0,1] range is calculated, and whenever it is smaller than Pi;j , the temperature of those replicas is exchanged (swapped), so the low-temperature trajectory continues at higher temperature and vice versa. Finally, to compute a certain property at a given temperature, it is enough to average between the values of that property for all the configurations that have been propagated at that temperature in any of the replicas. The swapping between replicas increases enormously the probability of exploring adequately the whole energy surface at a certain temperature because, whenever a swapping occurs, the replicas may be sampling different regions of such surface. It should be stressed that this method is only useful if (1) the difference between the lowest temperature (typically 300K) replica and the highest temperature one is significant (around 100e200K) and (2) if the swapping probability is significant. To increase the swapping probability, it is

Computational Tools for the Study of Biomolecules Chapter j 20

necessary to run several replicas so the temperature difference between neighboring replicas is small9.

4.5.2 Umbrella Sampling The umbrella sampling and metadynamics methods belong to the second family of enhanced sampling methods, where the values of one or a few reaction coordinates (also known as collective variables) are constrained throughout the simulation. The main drawback of these methods comes from the fact that the collective variables should be defined before the simulation begins, which presupposes a deep knowledge about the system. Collective variables can, in principle, correspond to any structural parameter that could be measured throughout the simulation, such as a distance to the binding site or a membrane, a combination of internuclear distances, angles, dihedrals, etc. A good choice of reaction coordinates should encompass all the relevant intermediate states and display very different values for reactants and products. For example, Rosta et al. (2011) used two reaction coordinates for the study of the RNA backbone cleavage by ribonuclease H. The first coordinate accounted for the electron transfer, defined as the difference between two internuclear distances. The second one, in turn, described the coupled proton exchange and was defined as the linear combination of several internuclear distances. The umbrella sampling method (Torrie and Valleau, 1977) consists of constraining the value of the reactant coordinates by adding a biased potential to the Hamiltonian. The biased potential usually consists of a harmonic term per reaction coordinate. For a system characterized by n reaction coordinates (s1 ,.sn ), the biased potential is given by n

2 X Ki si  sref (20.45) Vbias ðs1 ; .sn Þ ¼ i i¼1

sref i

where are the reference values that represent the center of the parabolic potential for each coordinate, and Ki are the spring constants, which may take different values depending on the reaction coordinate. Regardless of the values of the spring constant, it is clear that Vbias forces the system to sample only the region of the potential landscape where the values of the reaction coordinates are close to their reference values. If we perform several simulations (windows) changing the reference values in such a way that they span the intervals of values of the reaction coordinates that correspond to the transition from

9. As the kinetic energy fluctuation is inversely proportional to the number of particles   , the optimum number of replicas is also size-dependent. As N increases, the sEkin =Ekin fp1ffiffiffi N kinetic energy distributions at every temperature will be narrower, and as no swapping occurs unless such distributions overlap, it will be necessary to use a smaller DT between consecutive replicas.

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reactants to products, we will ensure a good sampling in all relevant regions of the reaction path. The value of the spring constants in Eq. (20.45) should be selected carefully. On the one hand, too small of values could prevent an effective sampling of the system in the surroundings of sharp barriers. On the other hand, too large of values will produce very narrow distributions around sref i , which is a problematic issue because a good overlapping between adjacent windows is necessary to obtain reliable and sensitive free energy curves. Within a single window, it is straightforward to obtain the free energy curve of the system perturbed by the biased potential: if Pðs1 ; .; sn Þ is the probability of finding the system in a ðs1 ; .; sn Þ state pertaining to the window under consideration, the free energy for that configuration is given by this: Gðs1 ; .; sn Þ ¼ 

1 ln Pðs1 ; .; sn Þ  Vbias ðs1 ; .; sn Þ þ Cw kB T

(20.46)

where Cw is a constant whose value will only depend on the window we are sampling. If our process would just need a window to be properly described, the value of Cw would be irrelevant. However, usually we will need more than one window to describe our reaction, conformational change, etc. If that were the case, we would have to calculate the values of Cw for each window to be able to combine our results into a global free energy profile. The whole process is equivalent to shift the free energy curve for each window to make them overlap. Several methods have been devised to deal with this problem, such as the multiple histogram reweighting method (WHAM) (Kumar et al., 1992) or the dynamic histogram analysis method (Rosta and Hummer, 2015).

4.5.3 Metadynamics Metadynamics (Laio and Parrinello, 2002) differs from umbrella sampling in that it introduces memory into the sampling, and it has been described as a method that works by “filling the free energy wells with computational sand.” Throughout the simulation, the location of the system in terms of the reaction coordinates (collective variables) is determined, and the metadynamics procedure introduces an accumulated bias potential at that point aiming to discourage the system to return to the current conformation, then encouraging it to populate different conformations. Such a process is exemplified in Fig. 20.10. In the metadynamics approach, the biased potential is usually a multidimensional Gaussian function, one dimension per reaction coordinate, of a given width and height. At a certain time step (t), where the system’s position is described by the (s1 ðtÞ,.sn ðtÞ) vector (where n is the number of reaction coordinates), the added biased potential is given by the following: ! n Y ðsi  si ðtÞÞ2 Vbias ðs1 ; .; sn ; tÞ ¼ ℍ exp  (20.47) 2s2i i¼1

Free Energy

Computational Tools for the Study of Biomolecules Chapter j 20

(B)

(C)

(D)

Free Energy

(A)

δ

δ

FIGURE 20.10 Procedure of metadynamics method. The position of a system is represented as a blue point (dark gray in print versions) in an unknown free energy curve (in black) as a function of a reaction coordinate (d). (A) Initially the simulation is reaching a local minimum (left). (B) At the beginning of the simulation the system is only sampling the surroundings of that minimum, so a biased potential [in red (gray in print versions)] is being added to that part of the potential energy surface. (C) At some point, the biased potential is large enough to force the system to move to the global minimum (on the right). Note: as the system has spent most of the time around the left minimum, the biased potential is significantly smaller around the global minimum. (D) Finally, the biased potential is larger than the free energy barriers, and the system can easily move from one minimum to the other. At that point, the unknown black curve can be recovered just by reversing the biased potential.

where the product goes over the n reaction coordinates, si ðtÞ is the current value of the ith reaction coordinate, ℍ is the height of the gaussian functions, and the si parameters represent their width. The accumulated biased potential at a given time step is then given by X Vbias ðs1 ; :::sn Þ ¼ Vbias ðs1 ; :::sn ; tÞ (20.48) t

Once the simulation has converged, the value of the collective variables should change quickly, indicating that a flat potential is being sampled. At that point, it is possible to obtain the free energy profile as a function of the reaction coordinates by inverting the accumulated biased potential.

5. CONCLUSIONS The quick rise of computational facilities during the last 40 years has made possible that, nowadays, chemistry and biology are no longer purely experimental sciences. Actually, theoretical approaches are now able to complement cutting edge experimental results and to successfully predict chemical properties.

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However, the computational study of chemical and biochemical systems requires a huge amount of computational resources that quickly scales with the number of atoms, making “exact” treatments only feasible for systems involving no more than four atoms. Hence, different approximations are necessary to describe faithfully the chemistry of biosystems, giving rise to the myriad of computational methods that are currently used. The election of a suitable method to describe a given system is therefore a complicated choice, and a sensible election is driven by the number of particles of the system, its nature, and the property that we aim to compute. Throughout this chapter, we have described the main methods used to carry out atomistic simulations, and we have provided some hints about how a simulation should be set up. Mulliken’s vision became truth, and the era of the computational chemist has arrived; in a near future the distinction between computational practitioners and experimentalists will become blurrier, and understanding computational tools will be a must for every biochemist.

ACKNOWLEDGMENTS The authors acknowledge funding by the Spanish Ministry of Science and Innovation (grants CTQ2012-37404-C02, CTQ2015-65033-P, and Consolider Ingenio 2010 CSD2009-00038). PGJ acknowledges the Juan de La Cierva Incorporacio´n fellowship IJCI-2014-20615.

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Chapter 21

Walk-In Brain: Virtual Reality Environment for Immersive Exploration and Simulation of Brain Metabolism and Function G. Hartung, A. Alaraj and A. Linninger1 University of Illinois at Chicago, Chicago, IL, United States 1 Corresponding author: E-mail: [email protected]

1. SUMMARY In the 2013, w3.3 million deaths occurred from ischemic stroke (Feigin et al., 2015). Another estimated 10e12 million people in the United States alone have unruptured aneurysms (Wada et al., 2014). These cases involve problems with blood flow in the human brain. Medical professionals work to treat and understand these ailments, while the engineering research can offer assistance but lacks the medium to translate the medical knowledge and data into an engineering platform and translate back again for the medical professionals. To study these ailments, it is important to be able to accurately understand the unique vasculature in each patient. To view the brain in its entirety, noninvasive or minimally invasive brain imaging is used that relies on magnetic resonance (MR) techniques, including magnetic resonance imaging (MRI) and magnetic resonance angiography (MRA). MRI enables visualization of the brain’s macrostructure, including the scalp, skull, gray matter, white matter, and spaces filled with cerebrospinal fluid (CSF). MRA highlights the blood flow in the arteries and veins up to the resolution of the imaging machine. Below this resolution, the vessels are not distinguishable from the noise; thus they cannot be easily distinguished from the background. The raw output of MR techniques is presented as two-dimensional (2D) slices. Although these digital imaging sets of “slices” of the brain are originally collected in only one of the three orthogonal anatomical planes (axial, coronal, or sagittal), the data can be reconstructed to view the missing planes. This type of data is made for display and does not contain connectivity information that would allow for computational analysis, which in turn makes it difficult for Tools For Chemical Product Design. http://dx.doi.org/10.1016/B978-0-444-63683-6.00021-6 Copyright © 2016 Elsevier B.V. All rights reserved.

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engineers who are not trained in radiology to work with patient data. It is due to this that a new method will be described that is not only capable of visualizing data in a more intuitive manner but actually converts the raw images into a vectorized medium that can be utilized by computational analysis tools. The current state of the art will begin with the original image stack from the MRI machine. It will compose a three-dimensional (3D) representation of these images and filter the images in three dimensions. This filtration process will allow the structures to be more easily recognized by segmentation algorithms that will convert the information in the raw images into a 3D vectorized structure. The vectorized structure is different from the raw images as it is not defined by a grid location and pixel value but rather by 3D coordinates and connectivity information, namely that one point is connected to two neighboring points to form a triangulated face. The vectorized structures have many uses including 3D printing, visualization in 3D computer aided design (CAD) programs, and being meshed into volumes that can be used for simulations. The software needs to intuitively display the raw images as well as the vectorized structures either with or without simulation data. The solution is to utilize virtual reality immersion coupled with gesturing tools. The software is then capable of virtual patient simulation (computational flow dynamic, drug convection, etc.), vectorized structure modification (output of a virtual surgery), and of exploring and comparing additional simulations based on a modified structure. This creates an environment for exploration and manipulation of one or many patient reconstructions for measurements or medical device simulation. This software workflow can be seen in Fig. 21.1.

Medical Image Conversion

Using Computational Metrics

Immersive Virtual Reality Environment FIGURE 21.1 The flow diagram of the current software design. The software will have only the image stack as an input, and it will clean the image and produce a three-dimensional structure. This interface will allow simulation and modification of the structures. To efficiently explore and manipulate these complex structures, the use of virtual reality immersion in necessary. This would allow the comparison of multiple patients and medical device testing (such as stent placement).

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This software is robust and efficient, requiring only minutes to perform all operations (as opposed to days or weeks). This system facilitates collaborations between engineers and surgeons alike as complex data can now be explained in a manner of minutes, and patient diagnosis and surgical planning can include the information from simulations.

2. MEDICAL IMAGES 2.1 Overview Medical professionals treating patients with cerebral illness or trauma utilize imaging modalities like MRI to assist in understanding the unique ailments of the patient and plan the intervention. These techniques produce images in the format known as Digital Imaging and Communications in Medicine (DICOM). DICOM images are in grayscale and have an intensity value assigned to each voxel. In MRI, this value is based on the water density of tissue. The traditional method for visualizing DICOM images is as the series of 2D images one at a time. In the next sections a method will be described for the conversion of medical images into vectorized structures. The images will be combined into a 3D grid, filtered, and the structures extracted. These structures will then be converted to vectorized data. This process is summarized in Fig. 21.2.

FIGURE 21.2 The process of obtaining a vectorized data set from raw medical images. Left: the system input is the raw DICOM stack (or any set of medical image data). Middle: the filtration of the original data set is necessary to enhance desired anatomical features while simultaneously suppressing noise in the data. Right: the final product is extracted from the filtered image as an accurate representation of the anatomy being imaged. This structure can now be used for computational processes and simulations. The left and middle images are maximum intensity projection images, whereas the right image is a 3D structure in a virtual environment.

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FIGURE 21.3 Raw medical image data viewed in both two and three dimensions. Left: a representation of the raw DICOM image stack in two dimensions. Right: a representation of the raw DICOM image stack in three dimensions. The 3D representation allows an untrained audience, such as scientific researchers, to better understand the data.

2.2 Three-Dimensional Brain Imaging Modalities When information is represented in 2D space, it is called a pixel, the 3D equivalent is a voxel. The intensity values of the voxels can be extracted into a 3D voxel matrix. This 3D voxel matrix can be operated on algorithmically or can be visualized (Fig. 21.3, right). The traditional viewing techniques have been used in a single-plane form since the release of 3D Slicer in 1998 (Fedorov et al., 2012) and in multiple planes since the release of VMTK in 2003 (Fig. 21.3, left) (Antiga et al., 2008).

2.3 Extracting Vectorized Data This voxel matrix is a 3D grid of intensity values. Voxels that occupy space of the same anatomical structures have similar intensity values. The anatomical structures can be highlighted and a surface structure extracted. This raw voxel matrix has substantial background noise, so a filtering technique will be performed for optimal feature recognition. Because the 3D coordinates and volumes of the voxels are known, the anatomical structure of interest can be extracted as a series of points in 3D space, and an algorithm can be applied, such as the marching cubes algorithm, to create the connectivity information that completes the vectorized structure and outputs an stereolithography (STL) structure. This information can then be written into an STL file that can then be displayed in CAD or computational modeling software packages. This structure can also be 3D printed. Vectorizing voxels can be applied to a variety of cerebral structures including the arteries, veins, skull, scalp, white matter, gray matter, and CSF (Fig. 21.4). This functionality allows for the study of individual components independent of surrounding features. This is useful in the cases of an anomaly

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FIGURE 21.4 Different anatomical components reconstructed from the filtered medical image data stack. This function allows experts and non-experts to visualize and interrogate individual physiological components after noise is removed. Structures can be visualized individually or multiple entities can be overlaid simultaneously. If there is an anatomical inconsistency (an aneurysm, for example) the structure (arteries) can be isolated and examined in detail. CSF, cerebrospinal fluid.

that would normally be hidden or obscured by surrounding features, such as removing the gray matter to see the white matter or removing the skull to see the arteries.

2.4 Calculations of Physiological Metrics Medical professionals are continually trying to add metrics and numerical ranges to healthy and diseased patients (Wilmshurst, 2013; Mungas et al., 2002; Prins et al., 2004; Saunders et al., 1995). This allows easier diagnosis and consistency in the medical practice, such as having a volume range for healthy ventricles and a different range for hydrocephalic ventricles. This process of taking raw images and generating structures can be performed on multiple subjects to create a database. If structure recognition algorithms are employed, the process of measurement of a particular feature can become automated. Once the data has been converted to the vectorized form, it can provide quantitative measurements including total surface area and volume of the structure (Fig. 21.5). In this same manner, measurements can be taken at will such as measuring the diameter at a specific point in the Circle of Willis (CoW) or measuring the distance between an aneurysm and the skull.

3. VIRTUAL PATIENT SIMULATION 3.1 Overview Outcomes and treatment strategies of vascular trauma in the human brain (stroke, aneurysm, etc.) are difficult to understand because of the complex nature of the cerebral environment. Three-dimensional computational flow dynamics (CFD) simulations are a promising tool to show the effect of a surgical intervention, namely the flow pattern before and after an intervention

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FIGURE 21.5 Walk-in Brain virtual reality viewer platform showing reconstructed brain matter and subject-specific metrics identified from vectorized medical data. The metrics can identify global parameters as seen in the above display or be restricted to show any value of interest for corresponding regions of interest. This could include the diameter of an artery near an aneurysm or blood clot or the distance between gray matter and the skull. CSF, cerebrospinal fluid.

can be visualized during the surgical planning stages. In the next sections, the uses of this visualization tool to tie the complex nature of simulations back into the environment of the surgical planning room will be discussed.

3.2 Simulating Patient-Specific Structures in Three Dimensions Once the vectorized version of the vasculature has been created, as described in Section 21.3, the STL output files can be meshed into volumes using many commercial or open source mesh tools and then simulated on a computational fluid dynamic solver platform such as ANSYS (Canonsburg, PA). The wholebrain arterial tree is grouped by arterial territories (MCA, ICA, PCA) in Fig 21.6 (left). MRI machines can currently be used to measure blood flow in the CoW and give quantitative MRA data, such as a NOVA report (Nova Medical, Inc., Wilmington MA) that can be used to validate cerebro-arterial tree simulations. An example of the simulated pressure map of an arterial tree can be seen in Fig. 21.6 (center). Complex flow profiles and force parameters such as wall shear stress can be interrogated at any location along the computational model. An example of vorticity on an axial slice of a vessel shows the highly variable flow at a single region in Fig 21.6 (right). This simulation data is exhaustive and has a large number of states at each volume, with hundreds of thousands of volumes and complex 3D geometries. To interrogate this data in a short amount of time, a color map and a 2D image is insufficient. This is where the same visualization techniques that were

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FIGURE 21.6 Subject-specific simulation and vascular labeling of cerebral arterial tree. Left: a 3D lateral view of labeled vessels. Vessels are color coded based on their role in feeding a specific anatomical region. Middle: the computed pressure profile throughout a subject-specific arterial tree. A 3D CFD solver (ANSYS) predicts dynamic flow profiles through a full-brain vascular tree. Right: vorticity in the arteries shows the existence of rotational flow in the vessels. Red (dark gray in print versions) signifies regions of high pressure, and blue (gray in print versions) indicates low pressure.

applied to visualize the voxel matrix and the reconstructed anatomical structures in 3D can be applied yet again to visualize the simulation data. This allows the surgeons and medical professionals to interpret the data in a small amount of time, making it significantly more viable to include this kind of information in the surgical planning room.

3.3 Modification and Re-Simulation of Structures In cases where surgical intervention is required in the cerebral environment with extenuating complications, there can be significant debate on which surgical operation, if any, is the appropriate course of action. One way to assist in these predictions in the case of blood flow, for example, is to use CFD simulations to model specific interventions and compute the resulting blood flow changes that arise due to each methodology. This functionality begins with the simulation of the original vasculature. A surgical intervention can be thought of as an addition or a modification to the current vascular structure, like the addition of a stent, or the clipping of an aneurysm. The system will then be able to simulate on the new structure and the result of this simulation be visualized next to the original simulation and the results interrogated.

4. IMMERSIVE VIRTUAL REALITY ENVIRONMENT 4.1 Overview For the aforementioned software to be of use, it must have an interface that can be easily navigated. A software that can make these tools available for a wide variety of users would need to be intuitive. In the next sections the design of an

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FIGURE 21.7 The Walk-in Brain immersive medical suite allows for manipulation and interaction with raw, structural, and simulation data. Left: the user-interface for interacting with a structural data set depicts a subject-specific brain parenchyma and the cerebral vasculature. Right: a physician operates the software suite to explain a medical concept to a group of students. With an immersive software, as a physician works with a group of students, the students will feel as if they are visualizing a real brain in three dimensions without needing to be in an active operating room. CSF, cerebrospinal fluid.

immersive environment for the exploration of data and the use of these tools will be explained. We have a software that can take raw images and automatically generate vectorized reconstructions within an immersive environment.

4.2 Design of Virtual Reality Environment The first step to creating immersion is to establish a sense of the virtual reality environment. This can be achieved through the use of stereoscopic rendering that utilizes multiple viewpoints in the virtual scene and translates these viewpoints to the corresponding eyes of the observer. This creates a sense of realism in the size and distance of objects in the virtual space. The next step is to establish a sense of identity for the user within the virtual reality environment. This serves the purpose of increasing the sense of immersion while giving the user more intuitive control over the objects and tools within the environment. To accomplish this, we have added virtual hands that are linked to hand gestures in real life using the Leap Motion technology (San Francisco, CA). An example of what the software would look like can be seen in Fig. 21.7 (left). An example of an entire group engaging in the same virtual reality scene can be seen in Fig. 21.7 (right) as a physician explains how the CoW is incomplete in most patients to a group of engineers.

4.3 Subject-to-Subject Automated Recognition of Points of Interest Once the intuitive controls have been established, measurements can be easily taken by a user of the tool. Once this function has located the desired

Walk-In Brain: Virtual Reality Environment Chapter j 21

FIGURE 21.8 Interaction with subject-specific vectorized data allows the virtual implantation of a stent into an artery with an aneurysm in preparation for simulation of the modified vessel. Left: the simulation data representing the flow field inside of the vessel with the aneurysm. Right: the positioning of a virtual stent into the blood vessel prior to another simulation. This mechanism would allow any user to easily simulate the addition of a medical device on the fly on a specific patient.

measurement or operation and the user has executed this operation, the display of the measurement is displayed and logged in a file. Once the user has identified a location and an operation, the software will log the measurement and operation commands. This set of commands can be then performed successively on other patient data sets for comparison. The display of the measurement includes a small icon that opens a file browser and allows the user to select another patient to compare against the original patient. This feature can include automated systems to take the same measurement from both subjects based on feature recognition algorithms.

4.4 Manipulation of Original Structures with the Addition of Medical Devices Surgical tools such as clipping an aneurysm can be placed, and a modified anatomical structure (an arterial tree including the aneurysm clip, for example) can be exported for immediate simulation by CFD tools such as ANSYS. In the case of an occlusion, a surgeon could virtually place a stent. This action would involve simply the selection of the stent by the user, the positioning of the stent into the artery of interest, and the tuning of the length (Fig. 21.8). The user could then utilize the new volumetric structure with the previously computed boundary conditions for inlet flows and pressures at the carotid arteries to re-simulate the tree and note the changes in flow.

5. CONCLUSION Medical imaging technology has become an integrated part of the medical diagnostic and therapy planning methodology. We have proposed a platform

657

658

SECTION j V Biomedicine

for creating 3D reconstructions of the anatomical structures inside the image stacks. These structures can be measured to add a layer of quantitative analytics to the already obtained qualitative data. These structures also lend themselves to virtual device simulation that can assist surgical planning. The use of this tool must not require months to execute the tasks while the doctor is trying to treat a patient, but it must be immediate, as our tool is. We have proposed a fully automated pipeline to fit such a need in the modern medical facility.

REFERENCES Antiga, L., Piccinelli, M., Botti, L., Ene-Iordache, B., Remuzzi, A., Steinman, D.A., 2008. An image-based modeling framework for patient-specific computational hemodynamics. Medical and Biological Engineering and Computing 46, 1097e1112. Feigin, V.L., Krishnamurthi, R.V., Parmar, P., Norrving, B., Mensah, G.A., Bennett, D.A., BarkerCollo, S., Moran, A.E., Sacco, R.L., Truelsen, T., Davis, S., 2015. Update on the global burden of ischemic and hemorrhagic stroke in 1990e2013: the GBD 2013 study. Neuroepidemiology 45 (3), 161e176. Fedorov, A., Beichel, R., Kalpathy-Cramer, J., Finet, J., Fillion-Robin, J.-C., Pujol, S., Bauer, C., Jennings, D., Fennessy, F., Sonka, M., Buatti, J., Aylward, S.R., Miller, J.V., Pieper, S., Kikinis, R., 2012. 3D slicer as an image computing platform for the quantitative imaging network. Magnetic Resonance Imaging 1323e1341. Mungas, D., Reed, B.R., Jagust, W.J., DeCarli, C., Mack, W.J., Kramer, J.H., Weiner, M.W., Schuff, N., Chui, H.C., 2002. Volumetric MRI predicts rate of cognitive decline related to AD and cerebrovascular disease. Neurology 59 (6), 867e873. Prins, N.D., Van Straaten, E.C.W., Van Dijk, E.J., Simoni, M., Van Schijndel, R.A., Vrooman, H.A., Koudstaal, P.J., Scheltens, P., Breteler, M.M.B., Barkhof, F., 2004. Measuring progression of cerebral white matter lesions on MRI visual rating and volumetrics. Neurology 62 (9), 1533e1539. Saunders, D.E., Clifton, A.G., Brown, M.M., 1995. Measurement of infarct size using MRI predicts prognosis in middle cerebral artery infarction. Stroke 26 (12), 2272e2276. Wada, K., Makino, H., Shimada, K., Shikata, F., Kuwabara, A., Hashimoto, T., 2014. Translational research using a mouse model of intracranial aneurysm. Translational Stroke Research 5 (2), 248e251. Wilmshurst, J.M., 2013. Diagnosis and management of pediatric peripheral neuropathies in resource-poor settings. Future Neurology 8 (2), 133e148.

Index ‘Note: Page numbers followed by “f” indicate figures, “t” indicate tables and “b” indicate boxes.’

A Ab-initio methods, 587e597 Hartree-Fock approximation, 588e591 ABM. See Agent-based modeling (ABM) Absorption, distribution, metabolic, and excretion properties (ADME properties), 228 Acetic acid, 318 Active ingredients (AIs), 70, 89f, 153 Active pharmaceutical ingredient (API), 221, 223 design and development, 223e228 CAMD approach in drug discovery, 224f ligand screening, 225 ligand-based approaches, 226e228 receptor-based approaches, 226, 227f small molecule drug design tools, 223e225 structure-based drug design, 225e226 Activity coefficients, 251 prediction, 248e249 s profile of four common industrial solvents, 247f s profile of ionic liquid, 247f Additive(s) fuel, 495, 501e503 identification, 495e496, 495t Adjacency matrix, 157e158 ADME properties. See Absorption, distribution, metabolic, and excretion properties (ADME properties) ADs. See Applicability domains (ADs) Adsorption curves, 521e522 Advanced grid utilization, 294e306 CAPE challenges in deployment, 296e297 infrastructures in deployment, 296e297 motivation, 294 SaaS, 297, 298f workflows implementation, 301e306

for integrated molecular and process design, 298e300, 300f Aerodynamic shape design models, 113 AES. See Alkyl ethoxysulfate surfactant (AES) AFM. See Atomic force microscopes (AFM) Agent-based modeling (ABM), 113e114 Agent-based simulation, CVD modeling using, 120f agent-based modeling in NetLogo, 116 graphite film deposition on nickel, 119 mass of graphite film, 119f modeling, 113e114 assumptions, 114e116, 114f results and discussions, 116e119, 117fe118f Aggregation techniques, 385 AGGRESCAN algorithms, 232e233 AIs. See Active ingredients (AIs) Algae design, 386e390, 389f Algebraic modeling systems, 380 property clustering technique for molecular design, 140e145 algebraic property clustering method, 140e142, 143t problem statement, 140 proof of concept, 142e145, 144t, 146t Algorithmic workflow, 302f, 305f Alkyl ethoxysulfate surfactant (AES), 513e514 Alkyl groups, 253 Alkyl side chain groups, 239e240 AMBER. See Antechamber (AMBER) Amine-based solvent, 211 Analytic network process (ANP), 424 ANN. See Artificial neural network (ANN) Annual operating time (AOT), 365 ANP. See Analytic network process (ANP) Antechamber (AMBER), 615 AOT. See Annual operating time (AOT)

659

660

Index API. See Active pharmaceutical ingredient (API) Apolar amorphous solids, 515 Apolar crystalline solids, 515 Applicability domains (ADs), 321e322 Aqueous monoethanolamine (MEA), 211 Artificial neural network (ANN), 241e242 Atom connectivity matrix, 157e158 Atomic force microscopes (AFM), 543 Atomic Signature, 316e324, 317f, 326, 330, 337e338 Atomic topography documentation, 319e320 Attrition, 567 test, 567 Augmented PenaltyeOuter ApproximationeEquality Relaxation algorithm, 477 Augmented ε-constraint method (AUGMECON method), 33 Authentication system, 296

B Benefits, risks, opportunities, and costs (BROC), 424 Bernstein polynomials, 100 Bessel functions, 408 Best compromise solution, 104 Beyond atomistic simulations, 624e625 Bi-level optimization approach, 27e28 Bilinear programming problem, 374 Binary mixture, 479, 483t Binder distribution, 536e537 BinghameMaxwell model, 527e528 Biodiesel production, 386, 388t Biological software, 324 Biomass-based syngas, 386 BL. See Butyl levulinate (BL) Black-box approach, 393, 397 optimization, 361 Bleaches, 382 Blended product design, 475 Blending, 475 Blending-based product optimization. See also Tailor-made green diesel blend design algorithm designing liquid blended products, 475e476 gasoline blends, 478e485 solution approach, 477 Boiling points, 333e334, 333te334t, 527 Boltzmann constant, 635e636

Bolus viscosity, 411 Bond order, 616e617, 617f Bonmin approach, 250 Born-Oppenheimer approximation, 586 Bottom-up approaches, 5 Breakage propensity, 511 BROC. See Benefits, risks, opportunities, and costs (BROC) BU. See Butanol (BU) Bubble nucleation and inflation period, 548 Bulk density, 540, 560 Bulk flow properties, 562e565, 564f Butanol (BU), 499 Butyl levulinate (BL), 499 1-Butyl-3-methyl imidazolium (BMIM)+, 261e263 1-n-Butyl-3-methylimidazolium, 239f

C CAILD. See Computer-aided ionic liquid design (CAILD) CAMD. See Computer-aided molecular design (CAMD) Canonical orbitals, 589, 590f peptides, 223e225 representation of molecule, 320 Canonical molecular dynamics simulations, 634e637. See also Molecular design Langevin dynamics, 635e636 Monte Carlo methods, 636e637 CAPE. See Computer-aided process engineering (CAPE) Carbohydrates, 233e234 excipient design, 233e234 Carbon atoms, 316 Carbon capture and storage (CCS), 210e211 Carbon dioxide (CO2), 210e211, 503 CO2eamine solution, 210e211 Carbon monoxide (CO), 503 Carbon nanotubes, 96 Carreau model, 364 Casein protein, 514 CASSCF methodology. See Complete active space self-consistent field methodology (CASSCF methodology) Cation, 244e245 head groups, 244e245 side chain size, 244e245 size, 244e245

661

Index CC. See Coupled clusters (CC) CCD. See Coupled clusters doubles (CCD) CCS. See Carbon capture and storage (CCS) CCSD, 595e596 CEN. See European Committee for standardization (CEN) Cephalic phase, 396 Cerebrospinal fluid, 653 CFD simulations. See Computational flow dynamics simulations (CFD simulations) ChapmaneEnskog correlations, 107 “Charges on springs” methods, 614 CHARMM force field, 609e610, 610f Chemical absorptions, 210e211 bonds in QM/MM interface, 622e623, 622f chemical-based product design, 153 chemical-based products, 475 complexes, 373 graph theory, 12e13 ISI, 202 process design energy and water integration, 380 superstructure optimization, 377e380, 379t, 381fe382f products, 4, 61, 153e154 classification, 4t design, 4, 61 identification, 8 properties, 9t reaction, 95 reactivity, 202 Chemical product design, 62e76, 199, 348, 350, 350f architecture of property toolbox in VPPDLab, 65f architecture of VPPD-Lab software, 64f CAMD, 8e13 decomposition-based approaches, 24e25 DOE, 5e7 enumeration approach, 14e16 initial efforts, 5 mathematical programming approaches, 16e20 MDOE, 7e8 metaheuristic approaches, 20e24 modeling module, 66, 67f molecular signature descriptors, 13e14 multiobjective chemical product design, 25e33

new product template module, 76 prediction uncertainty, 34e35 product analysis, 75e76 product design module, 66e75, 68f device design, 73e75, 74fe75f emulsion design, 71e73, 72f formulation design, 70e71, 70f molecular design and blend design, 68e70, 69f template structure, 66f Chemical vapor deposition (CVD), 95. See also Zinc sulfide (ZnS)d deposition chemistry models, 98e100, 99f global optimization of substrate geometry, 100e113 kinetics, 96e97 modeling using agent-based simulation, 113e120 multiscale modeling, 97e100 operating conditions, 96 surface reactions in, 95 Chromosome, 21, 106 Chronic diseases. See Noncommunicable diseases (NCDs) Chronic-typed toxicity, 204e205 CI. See Configuration interaction (CI); Connectivity index (CI) Circle of Willis (CoW), 653e655 CISD. See Configuration interaction singles and doubles (CISD) Classical least squares (CLS), 7 Classical trajectories, 632e633 Clausius-Clapeyron equation, 545 Closed-loop SCs, 443e444 Closed-loop supply chain (CLSC), 443, 446f, 452 binary variables, 464 continuous variables, 464 conversion factor, 471t demand for each product from each first market, 465te467t emission costs, 472t grading levels, 470t literature review, 445e446 maximum and minimum rate of availability of raw materials, 470t multi-period, 444e445 parameters, 463e464 problem description, 446e447, 447f problem formulation, 447e452 results, 452e461, 454te456t

662

Index Closed-loop supply chain (CLSC) (Continued ) cases characteristics, 453t computational statistics, 460t network structures, 459t sensitivity analysis study, 456e461, 460f return of recycled product, 472t return of remanufacturable product, 469t, 472t revenue on sale of final product, 468t sets, 461e462 utilization factor, 470t Cloud computing resource utilization, 294e306 challenges in deployment of CAPE, 296e297 existing infrastructures in deployment of CAPE, 296e297 motivation, 294 SaaS, 297, 298f workflows implementation, 301e306 for integrated molecular and process design, 298e300, 300f Cloud point, 184 CLS. See Classical least squares (CLS) CLSC. See Closed-loop supply chain (CLSC) Cluster formation, 98 CNDO. See Complete neglect of differential overlap (CNDO) Coarse-grained methods, 624e625 Coefficient of performance (COP), 178e179 Cold extrusion, ice cream synthesis by, 429e438, 436f consumer wants and product function, 432e437 equipment selection and design, 438, 438f framing level, 429e432 inputeoutput level, 437, 437f task network, 437, 438f Collision with horizontal surface, 114 with vertical surface, 115 Collocation points (CP), 283 Colloidal systems, 358e359 Combinatorial contribution. See Mixing entropy effects Commodity supply chain, 45 Compaction curves, 565, 566f Compartmental approach, 394 Competitive markets, 56e57, 57f Complete active space self-consistent field methodology (CASSCF methodology), 596

Complete neglect of differential overlap (CNDO), 605e606 Computational approaches, 227e228 Computational chemistry, 632 Computational cloud, 294 Computational flow dynamics simulations (CFD simulations), 654 Computational grids, 294 Computational implementation, 361e362 Computational tools for study of biomolecules dynamics simulations, 631e641 energy calculations for molecules, 587e625 preparing molecular dynamics simulation, 625e630 quantum mechanical treatment, 584e587 Computer-aided algorithms, 319 Computer-aided design tools, 100 Computer-aided framework, 170e176, 171f CAMD constraint selection, 172e173 CAMD formulation, 173 solution strategy, 173e176, 174f problem definition, 170 Computer-aided ionic liquid design (CAILD), 241e242 implementation algorithm, 255e256 ionic liquid subgroups, 254te255t solution, 249e250 problem formulation and, 252e256, 259e261 thermodynamic modeling of ionic liquids for, 246e248 Computer-aided molecular design (CAMD), 8e13, 62, 125, 168, 199e200, 221, 241, 269, 277e279, 320, 325e338, 347e348, 358. See also Ionic liquid product design. See also Pharmaceutical formulation design. See also Structured particulate systems design algorithmic operations, 278f approaches to formulation design, 229e231 case studies, 177e185 fuzzy optimization, 213e216 problem formulation, 211e213 refrigerant design, 177e182 results, 214e216 six generated solvents, 215f, 215te216t solvent design for gas sweetening process, 210e216 surfactant design as emulsifier, 182e185

663

Index chemical product tree, 155f chemical-based products, 153, 154f constraint selection, 172e173 decision-making stage, 197 devices, 156 first-order groups, 186e188 formulation, 81, 173 of ionic liquid design problem, 242e245 ionic liquid structures, generation of, 243e245 inherent safety and health, 201e210 inherent occupational health indexes selection, 201e206 inherent safety indexes selection, 201e206 model development, 206e208 multiple-objective optimization, 209e210 problem formulation, 201 inherent safety design, 198 input parameters, 303t molecular design, 208e209 problem formulation, 156e167 solution methods, 167e169 molecules, 156 multiple-species products, 156 refrigerant design CAMD formulation, 188e192 signature case study ideal structure similarity searching, 334e338, 335te337t reactant, product, and reaction pathway design, 330e334 vHTS, 325e328 single-species products, 155e156 solution strategy, 173e176, 174f types of properties and estimation techniques, 8e13, 9t, 10f GC models, 11e12 group contribution+ method, 12e13 TIs, 12e13 Computer-aided process engineering (CAPE), 294 existing infrastructures and challenges in deployment of, 296e297 ontologies and agent-based approaches in, 295t Computer aided product design, 170e176 CAMD constraint selection, 172e173 CAMD formulation, 173 problem, 69, 170 solution strategy, 173e176

Computer-aided structure elucidation tool, 321e323 Computer-aided tools, 66 Conceptual model, 348e355, 352t decomposition of property function for, 351e353 formulation of product design problems, 353e355 Conditional value at risk (CVaR), 443e444, 450 Configuration interaction (CI), 593e594, 594f Configuration interaction singles and doubles (CISD), 593e594 Confocal optical microscopy, 518e519 Connectivity index (CI), 12e13, 241 Conservation rules for molecular property clusters, 131e132 Constant drying rate period, 547 Constitutive models, 351 Constitutive properties, 348e349 Constraint equations, 476 ε-Constraint methods, 32e33, 361, 384 Consumer preferences, 47, 52 products, 347, 420e421 properties, 48, 49t satisfaction score, 48e52, 51f wants, 432e437 Contact points, 555e556, 555fe556f COP. See Coefficient of performance (COP) Correlation energy, 591e592 Cosmetic emulsion, 363e367 optimal product/process design solutions, 366t predicted temporal profiles of drug concentration, 368f set of pareto optimal solutions of problem, 367f COSMO-RS methods, 248e249, 252 COSMO-SAC methods, 248e249 Coupled clusters (CC), 595e596 Coupled clusters doubles (CCD), 595e596 Coupled ordinary differential equations, 400e401 CoW. See Circle of Willis (CoW) Cox model, 8 CP. See Collocation points (CP) Crossover (genetic operator), 21 Crystal(s), 515 polymorphism modeling, 517 structures, 626e629, 628f

664

Index Crystalline and amorphous structure phase composition, 515e520 confocal photographs, 518f crystal size, 516e517 raman spectroscopy, 520 state diagram of WM, 517f supramolecular structure, 515, 516f TEM, 519e520 Crystallinity, 516 Crystallization, 626e629 Cubic equation, 179e180 CVaR. See Conditional value at risk (CVaR) CVD. See Chemical vapor deposition (CVD)

D Data mining, 279e280 Database, 63 approach, 174 Decision-maker (DM), 25e26 Decomposition-based approaches, 24e25, 274e283 CAMD, 277e279 classification using data mining, 279e280 decision-making stages of, 276f design philosophy, 277 for integrated molecular, 276e277 multiobjective formulation, 277e279 process design, 281e283 rigorous equipment models, 282e283 solvent-based CO2 capture process superstructure, 282f systematic flow sheet design methods, 281e282 Decomposition-based computer-aided optimization, 492e495 generation of feasible blends, 494 candidates, 492e494, 493t ranking and selecting, 495 DEG. See Diethylene glycol (DEG) Degeneracy, 320e321 Degree of regular molecular arrangement, 516 Delayed sigmoidal profile, 397 DEM. See Discrete element modeling (DEM) Demand for each product from each first market, 465te467t as function of price, 53 Density functional theory (DFT), 583e584, 597e603 general formulation, 597e600 GGA, 601

hybrid orbitals, 602e603 LDA, 600e601 time-dependent DFT, 603 Deposition rate, 116 Descriptor matrix, 319 Design for manufacture (DFM), 569 Design of experiments (DOE), 5e7 Desorption curves, 521e522 Device design, 73e75, 74fe75f DFM. See Design for manufacture (DFM) DFT. See Density functional theory (DFT) DFT-D. See Dispersion corrected DFT (DFT-D) DICOM. See Digital Imaging and Communications in Medicine format (DICOM) Diesel-biodiesel blends, 496e497 Diethylene glycol (DEG), 369e370 Differential scanning calorimetric (DSC), 517, 524, 524f Diffusion mass transfer phenomena, 75 2,2-Difluorobutane, 180 1,1-Difluoroethane, 180 Digestive system, 393e394, 395f Digital Imaging and Communications in Medicine format (DICOM), 651 Diophantine, 320e321 equations, 338 Direct methods, 527 Directed screening process, 225 Discrete element modeling (DEM), 559, 561 Disjunctive programming incorporates discontinuous functions, 207e208 Dispersed systems, 358e359 Dispersion corrected DFT (DFT-D), 603 Dispersion model, 406 Distribution costs, 52e53 DM. See Decision-maker (DM) Docking, 630 algorithms, 226 DOE. See Design of experiments (DOE) Domain’s size, 537 Dosing, 510, 562 Double hybrid, 602 Downstream chemical process, 348e349 Dried particle, 548 Drude method. See “Charges on springs”; methods Drug diffusion coefficient, 408e409 Dry milk particulate products, 514 DSC. See Differential scanning calorimetric (DSC)

665

Index Duality-based approach, 375 Duodenal brake, 398 Dynamic(s) emptying rate, 406 histogram analysis method, 640 simulations, 631e641 canonical molecular dynamics simulations, 634e637 classical trajectories, 632e633 enhanced sampling methods, 637e641 nonadiabatic processes, 633e634 purely quantum mechanical techniques, 631e632

E Effective diffusion models, 548 Efficient solution generation method, 104 EHM. See Extended Hu¨ckel method (EHM) 2EHN. See 2-Ethylhexyl nitrate (2EHN) Ehrenfest method, 634 EinsteineStokes relationship, 410 EL. See Ethyl levulinate (EL) Elastic and plastic deformation of particle systems, 565 Elastic region, 565 Electrical current, 537 Electron microscopy, 519e520 Electron-nuclear interaction, 598 Electronic Schro¨dinger equation, 585 Electronic structure methods, 587 p Electrons methods, 604e605 Electrostatic forces, 543 Electrostatic term, 610e612 emoGA. See evolutionary multiobjective GA (emoGA) Empirical force fields, 607e608 bonding terms for, 608e610 nonbonding terms for, 610e612 Empirical force fields, bonding terms for, 608e610 Emulsified UV sunscreen, surfactant design as emulsifier for, 182e185 consumer needs, 183t design problem, 185t target properties, 184t Emulsion design, 71e73, 72f Energy calculations for molecules, 587e625 ab-initio methods, 587e597 beyond atomistic simulations, 624e625 DFT, 597e603 force fields, 607e618 hybrid methods, 618e623

semiempirical methods, 603e607 Energy integration, 380 Engine lubricants, 79e80 Engineering properties, 48e52 Enhanced sampling methods, 637e641 metadynamics, 640e641 temperature replica exchange, 637e639 umbrella sampling, 639e640 Enumeration, 14e16, 126 Environmental assessment, 383, 384fe385f Enzymes, 382, 396 EO. See Evolutionary optimization (EO) EOC. See Expected operational cost (EOC) EQ process models. See Equilibrium process models (EQ process models) “Equalitarian” status, 596e597 Equilibrium process models (EQ process models), 273e274 Equilibrium-relative humidity, 521 Equipment selection and design, 438, 438f ER. See Expected revenues (ER) Ergun’s equation, 560e561 Ethanol, 386, 387f Ethyl levulinate (EL), 499 2-Ethylhexyl nitrate (2EHN), 503 European Committee for standardization (CEN), 488 Evolutionary modification, 420 evolutionary multiobjective GA (emoGA), 105e106 Evolutionary optimization (EO), 20 Exchange-correlation energy, 599 Excipients, 221, 232 Expected operational cost (EOC), 449 Expected revenues (ER), 448e449 Experimental validation, 496 fuel performance test, 496 property validation, 496 Extended Hu¨ckel method (EHM), 605 Extracting vectorized data, 652e653, 653f

F F.B. See Free bound (F.B) Factor XIa inhibitors, 326, 327f, 328te329t, 333te334t FAEE. See Fatty acid ethyl ester (FAEE) Falling rate period, 547e548 Fast-moving consumer goods companies (FMCG), 417e418 Fatty acid ethyl ester (FAEE), 373e374 Fatty acid methyl ester, 386

666

Index FDA. See Food and Drug Administration (FDA) FE. See Finite elements (FE) Feasible blends, 500, 500t candidates, 499, 499t generation, 492e494, 493t generation, 494 Feed availability, 376 Filtration process, 650 Finite elements (FE), 283 First order equations, 5e7 molecular groups, 12 groups, 186e188, 199e200 Fitness proportionate reproduction method, 22 Fitness value metric, 333e334 “Fluctuating charges” method, 613e614 Fluid phase processing, 358 FMCG. See Fast-moving consumer goods companies (FMCG) Food and Drug Administration (FDA), 229 Food(s) manufacturing PDPS, 422e429, 425t, 426f, 430te432t process synthesis in food industry, 420e422, 422f synthesis of ice cream by cold extrusion, 429e438, 436f products, 421, 538 Force fields, 607e618 empirical, 607e608 bonding terms for, 608e610 nonbonding terms for, 610e612, 613f Force Field Toolkit, 615 parametrization, 614e615 polarizable, 613e614 reactive force fields, 616e618 Formulated product design, 380e386 mathematical formulations, 374e380 raw materials, 373e374, 386e390 Formulation design, 70e71, 70f pooling problem, 376e377 product design problems, 353e355 three central design problems, 356t Forward networks, 443 Forward-stepping multiple linear regression approach, 337e338 Fracture point, 527e528 Fragments, 316, 318f Framing level, 429e432

Free bound (F. B), 500 Free energy methods. See Enhanced sampling methods Frontier, 275 Fuel additives, 495, 501e503 enhancement, 495e496 additives identification, 495e496, 495t performance test, 496 Full configuration interaction calculations (Full CI calculations), 593e594 Furey’s u coefficient, 326 Fuzzy optimization algorithm. See Fuzzy optimization approaches Fuzzy optimization approaches, 28e32, 30f, 209, 213e216. See also Metaheuristic approaches ε-constraint method, 32e33 maxemin aggregation approach, 29e31 two-phase approach, 31e32

G GAs. See Genetic algorithms (GAs) Gas(es), 515 adsorption, 542 gas sweetening process, solvent design for, 210e216 fuzzy optimization, 213e216 problem formulation, 211e213 results, 214e216 six generated solvents, 215f, 215te216t phase, 95 sorption isotherms, 541 Gasoline blends, 478e485, 485f. See also Tailor-made green diesel blends problem definition, 478e479, 479t problem formulation, 479e480 results and discussion, 482e485 solution strategy, 480e482 Gastric breakup, 401e404 emptying of liquid solutions, 397 rate, 397e399, 398f juices, 396, 396t secretions, 399e401, 401f Gastric phase, 396 Gaussian decay rate, 333e334 Gaussian orbitals (GTO orbitals), 590e591 GCM. See Group contribution method (GCM) GCs. See Group contributions (GCs)

667

Index Generalized gradient approximation (GGA), 601 Generate-and-search CAMD framework, 15f, 16 Genetic algorithms (GAs), 18e19, 21e23, 100, 102e103, 103f, 249e250, 330e331 implementation in shape design, 106e110 multiphysics model, 107e108, 108f parameterized substrate geometry model, 109e110, 109f Genetic operators, 331e332, 332f Geometrical models, 561 GGA. See Generalized gradient approximation (GGA) Ghost link atoms method, 623 Gibbs energy, 493, 494f Glass transition (Tg), 523e524 temperature, 526f Global optimization algorithms (GOP), 375 Globus, 296 Glucocorticoid receptor structures, 322e323 Glycaemic index, 393 GOP. See Global optimization algorithms (GOP) Gordon-Taylor equation, 523 Granular bond number, 550, 551f Granule fracture, 568e569 Graphite film deposition on nickel, 119 Group contribution method (GCM), 12e13, 127e129, 135e136, 135t, 139t, 199e200, 241, 248e249 Group contributions (GCs), 127 GCebased methods, 127e128, 161e167 functional properties, 166t mixture properties, 166t primary properties, 163te164t property models examples, 165e167 secondary properties, 165t models, 11e12, 269e273 Growing process, 373 GTO orbitals. See Gaussian orbitals (GTO orbitals)

H Hamilton formalism, 632 Hamiltonian operator, 584e585 Hammersley stochastic annealing algorithm, 35 Hard bounds, 377 Hartree-Fock approximation, 588e591 CC, 595e596

CI, 593e594, 594f correlation energy, 591e592 Hartree-Fock limit, 591e592, 592f Hartree-Fock wave function, 593 MCSCF, 596e597 MP perturbation theory, 594e595 HE. See Hexanol (HE) Health, safety, and environmental considerations (HS&E considerations), 222 Health assessment, 222e223 Heat of vaporization (Hv), 212 “Hedonic pricing”, 47 Helicobacter pylori (H. pylori), 322 Heuristic methods, 18e19, 168 heuristic-based approach, 232e233 Hexanol (HE), 499 1-Hexyl-3-methyl imidazolium (HMIM)+, 261e263 High-viscosity meals, 400 Hohenberg-Kohn theorems, 598 Homology modeling, 629e630 “House of quality”, 424 HS&E considerations. See Health, safety, and environmental considerations (HS&E considerations) Human anthropogenic activities, 210e211 Human brain, 654 Hybrid approaches, 232e233 Hybrid functionals, 601 Hybrid methods, 169, 618e623 additive and subtractive schemes, 619e622 chemical bonds in QM/MM interface, 622e623, 622f Hybrid orbitals, 602e603 Hydrogen, 627 Hydrophilic behavior, 503 Hydroxyl (OH), 208e209

I ICAM-1, 323 ICAS-ProCAMD software, 499 IFPRI. See International Fine Particle Research Institute (IFPRI) IGC, 542 Ileum, 406 Image analysis, 553 Immersive virtual reality environment, 655e657 design of virtual reality environment, 656, 656f

668

Index Immersive virtual reality environment (Continued ) original structures with addition of medical devices, 657, 657f subject-to-subject automated recognition, 656e657 Index for acute health hazard (IAH), 204e205, 207t Index for explosiveness (IEX), 203e204, 205t Index for exposure limit (IEL), 204e205, 207t Index for flammability (IFL), 203e204, 205t Index for Health Hazards (IHH), 202 Index for material phase (IMS), 204e205 Index for Physical and Process Hazards (IPPH), 202 Index for volatility (IV), 204e205, 206t Index score of molecule (ISHI), 205e206 Index-based approach, 201 INDO. See Intermediate neglect of differential overlap (INDO) Induced fit docking approach, 226 Induction period, 547 Industrial bioreaction pathway design, 324e325 Inherent Occupational Health Index (IOHI), 202 Inherent occupational health index selection, 201e206 parameters evaluation, 204t Inherent safety and health in CAMD framework, 201e210 inherent occupational health index selection, 201e206 inherent safety index selection, 201e206 model development, 206e208 molecular design, 208e209 multiple-objective optimization, 209e210 problem formulation, 201 Inherent safety design, 198 Inherent safety index approach (ISI approach), 201e202 selection, 201e206 parameters evaluation, 203t Inputeoutput level, 437, 437f Insect repellent lotion design, 86e90, 88f, 90fe91f Integrated approach, 569e572, 570f. See also Mesostructure. See also Particle structure. See also Supramolecular structure modeling approach, 570e572, 571f Integrated multiobjective molecular and process design. See also Molecular design

advanced grid utilization, 294e306 approaches for integrated solvent, 270te271t CAMD applications, 271te272t cloud computing resource utilization, 294e306 decomposition-based approach, 276e283 approach for integrated molecular, 276e277 CAMD, 277e279 classification using data mining, 279e280 decision-making stages of, 276f design philosophy, 277 multiobjective formulation, 277e279 process design, 281e283 with process operability decisions application to ORC, 287e293 consideration of operation under variability, 284f motivation, 283 proposed framework, 284e287 representation of sensitivity index, 287f Integrated product/process design, 360e361 Intensity of disintegration (ln), 404 Interactive methods, 26, 104 Intermediate neglect of differential overlap (INDO), 605e606 Intermolecular conservation rule, 131e132 International Fine Particle Research Institute (IFPRI), 509 International Union of Pure and Applied Chemistry (IUPAC), 325 Intestinal phase, 396 Intramolecular conservation rule, 131 IOHI. See Inherent Occupational Health Index (IOHI) Ionic liquid product design. See also Computer-aided molecular design (CAMD). See also Pharmaceutical formulation design CAILD, 241e242 solution, 249e250, 252e256 CAMD, 241 formulation of ionic liquid design problem, 242e245 Ionic liquid(s), 239e240 activity coefficients prediction in systems, 248e249 applications, 240b design for heat transfer applications, 257e263

669

Index CAILD problem formulation and solution, 259e261 constraints, 260e261 GC models for physical properties of heat transfer fluids, 257 melting point, 259 objective function, 260 results and analysis, 261e263 thermal conductivity, 257e258 design for polymer dissolution, 250e257 property prediction, 246e249 activity coefficients in system prediction, 248e249 thermodynamic modeling of ionic liquids, 246e248 structure generation, 243e245 Ischemic stroke, 649 ISI approach. See Inherent safety index approach (ISI approach) Iterative approaches, 5 IUPAC. See International Union of Pure and Applied Chemistry (IUPAC)

J Jejunum, 406 Jet fuel blend design, 83e86, 85t, 87t

K Kohn-Sham methodology (KS methodology), 599 orbitals, 599e600 KS methodology. See Kohn-Sham methodology (KS methodology)

L Lactose, 514 crystal, 516e517 crystallization, 516e517 Lag phase, 397 Lagrangian-based method, 375 Langevin dynamics, 635e636 LAS. See Linear alkylbenzene sulfonate (LAS) Laser diffraction (LD), 529e532, 553 Laundry detergents, 373e374, 380e386 LC. See Liquid crystals (LC) LCAO approximation. See Linear combination of atomic orbitals approximation (LCAO approximation)

LD. See Laser diffraction (LD) LDA. See Local density approximation (LDA) LELs. See Lower explosion limits (LELs) LennardeJones potential, 610e611 Ligand screening, 225 Ligand-based approaches, 226e228 Lignocellulosic biochemical, 496e497 Lignocellulosic biomass, 373 Linear alkylbenzene sulfonate (LAS), 513e514 Linear combination of atomic orbitals approximation (LCAO approximation), 589e590 Linear packing model, 561 Linear problem (LP), 375 Linear-response time-dependent density functional theory (LR-TDDFT), 603 Liquid crystals (LC), 516 Liquid molar volume (Vm), 212 Liquid(s), 515 blended product design, 475e476 bridges, 543 formulations, 354 liquideliquid extraction, 304e306, 360 input parameters required in, 303t meals, 398 perfumes, 362e363 spatial distribution, 559e560 Local density approximation (LDA), 600e601 Local spin density approximation (LSDA), 600e601 Localized orbitals method, 623 Lock and key approaches, 226 Lotions, 52e53 Lower explosion limits (LELs), 203e204 LP. See Linear problem (LP) LR-TDDFT. See Linear-response timedependent density functional theory (LR-TDDFT) LSDA. See Local spin density approximation (LSDA) Lubricant(s), 156 base oil design, 80 blend design, 79e83, 81t, 84t Luminal viscosity, 409 Lyophilization, 233e234 Lyophilized protein, 232 Lysinate (Lys), 258

670

Index

M Macroscale, 511 diffusion coefficient, 408e409 modeling, 559 Magnetic resonance angiography (MRA), 649 Magnetic resonance imaging (MRI), 649 Main ingredient (MI), 83e84 Manipulated properties, 50 Manufacturing costs, 52e53 foods PDPS, 422e429, 425t, 426f, 430te432t process synthesis in food industry, 420e422, 422f synthesis of ice cream by cold extrusion, 429e438, 436f process, 348e349, 349f product manufacturing process, 351e353 system, 417e418 Martini force field, 624e625, 625f Mass balance, 403 “Mass polarization term”, 584e585 Mass transfer, 404e411, 510 components, 548e549 solvent and discrete phase, 549 Material balance, 377 Material Phase Subindex (IMS), 206t Mathematica, 362, 369 Mathematical formulations chemical process design, 377e380 pooling problem, 374e377, 376f Mathematical programming approaches, 16e20, 69, 126, 168e169, 174, 175f Maxemin aggregation approach, 29e31 Maxemin operator method, 210 MCSCF. See Multiconfigurational selfconsistent field (MCSCF) MDOE. See Mixture design of experiments (MDOE) MEA. See Aqueous monoethanolamine (MEA) Medical images, 651e653, 651f calculations of physiological metrics, 653, 654f extracting vectorized data, 652e653, 653f three-dimensional brain imaging modalities, 652, 652f Medical trauma, 654 Mesoscale, 511 manipulation, 549e550 Mesostructure, 549e569. See also Integrated approach

bulk flow properties, 562e565, 564f compaction curves, 565, 566f contact points, 555e556, 555fe556f liquid spatial distribution, 559e560 particle attrition, 566e569, 568f packing, 560e561 spatial distribution, 557e559, 558f permeability, 561e562 size and shape distribution, 550e555, 552fe553f wetting, 561e562 Message passing interface model (MPI model), 107e108 Meta-generalized gradient approximation (MGGA), 601 Metadescriptor, 50e52 Metadynamics method, 640e641, 641f Metaheuristic approaches, 20e24. See also Fuzzy optimization approaches GA, 21e23 SA, 23e24 Methanol, 386 MeTHF. See Methyltetrahydrofuran (MeTHF) Methyl tertbutyl ether (MTBE), 482e485 Methyltetrahydrofuran (MeTHF), 482e485 Metropolis algorithm, 534, 636 MGGA. See Meta-generalized gradient approximation (MGGA) MI. See Main ingredient (MI) MichaeliseMenten kinetics, 406, 411 Micro-computed tomography (Micro-CT), 650 Micro-CT. See Micro-computed tomography (Micro-CT) Microbiological status, 426e429 Microcapsule, 74f, 75 Microelectronics, 95 Microstructure, 511e512, 560 Microstructured formulations, 347e348 Middleware, 294 MILP. See Mixed-integer linear programming (MILP) MINLP. See Mixed-integer nonlinear programming (MINLP) MIPSYN, 380 Miscible blends, 493e494, 500 Mixed-integer linear programming (MILP), 156e157 model, 447 problem, 17e19

671

Index Mixed-integer nonlinear programming (MINLP), 134, 156e157, 375 model, 242e243 problem, 17e20, 475e476, 479, 487 Mixing, 475 entropy effects, 251 mixture constraints, 475e476 mixture property model, 82 Mixture design of experiments (MDOE), 7e8 MNDO. See Modified neglect of diatomic overlap (MNDO) MO. See Molecular orbitals (MO) ModDev. See Model development (ModDev) Model development (ModDev), 66, 206e208 algorithms, 63 disjunctive programming, 207e208 Model reliability, 475 Model template algorithms (ModTem algorithms), 63 Modeling approach on structured particle product design, 570e572, 571f Modeling module, 66, 67f Modeling toolbox (MoT), 63, 66 Modified neglect of diatomic overlap (MNDO), 606 Modified octet rule, 244e245 ModTem algorithms. See Model template algorithms (ModTem algorithms) Moisture sorption techniques, 524 Molecular descriptors, 12e13, 16e17, 315e316 simulation, 226 structure representation, 157e158 synthesis, 137e140, 138fe139f, 139t systems engineerings, 3e4 vector, 277e278 Molecular design, 6f, 200, 208e209, 322e323, 358 and blend design, 68e70, 69f CAMD, 325e338 molecular descriptors, 315e316 problem formulation, 156e167 GCebased methods, 161e167 process model and other constraints, 167 property constraints, 159e167 structural constraints, 157e159 problem graphical representation, 132e134, 132f algebraic property clustering method, 140e142, 143t problem statement, 140 proof of concept, 142e145, 144t, 146t

signature advantages, 319e321 applications, 321e325 case studies, 325e338 molecular descriptor, 316e318 solution methods, 167e169 heuristic techniques, 168 hybrid techniques, 169 mathematical programming techniques, 168e169 rule-based techniques, 168 Molecular dynamics methods. See Empirical force fields simulation preparation, 625e630 docking, 630 experimental structures, 626e629, 628f homology modeling, 629e630 Molecular orbitals (MO), 588 Molecular property clustering techniques algebraic property clustering technique for molecular design, 140e145 chemical processing industry, 125 GCMs, 127e129 molecular design, 125e126, 127f property clusters, 129 property integration, 128e129 property prediction, 127e128 visual molecular clustering design approach, 129e140 conservation rules for clusters, 131e132 operator, 130 Molecular signatures (MS), 157e158, 316e317 descriptors, 13e14 models, 246 Molecular weight (Mw), 212 Møller-Plesset perturbation theory (MP perturbation theory), 594e595 Monoelectronic operator, 588e589 Monoethanolamine properties, 217t subindex scores, 217t Monte Carlo methods, 636e637 MOO. See Multiobjective optimization (MOO) MoT. See Modeling toolbox (MoT) MP perturbation theory. See Møller-Plesset perturbation theory (MP perturbation theory) MPI model. See Message passing interface model (MPI model)

672

Index mPW2-PLYP, 602 MRA. See Magnetic resonance angiography (MRA) MRCI methods. See Multireference configuration interaction methods (MRCI methods) MRI. See Magnetic resonance imaging (MRI) MS. See Molecular signatures (MS) MTBE. See Methyl tertbutyl ether (MTBE) Multiagent systems, 294 Multiconfigurational second-order perturbation method, 596e597 Multiconfigurational self-consistent field (MCSCF), 596e597 MultiConfigurational Time-Dependent Hartree, 632 Multicriteria decision-making approach, 424 Multiobjective chemical product design, 25e33 bi-level optimization approach, 27e28 fuzzy optimization approaches, 28e32 weighted sum method, 26e27 formulation, 277e279 algorithmic operations of CAMD, 278f function, 448 GAs, 105e106 molecular design technique, 26e27 Multiobjective optimization (MOO), 25e26, 103e105, 209e210, 274e275 simple weighting method, 105 technology, 276e277, 298e300 Multiphysics model, 107e108, 108f “Multiple electrostatic moments” method, 614 Multiple histogram reweighting method (WHAM), 640 Multiple-species products, 156 Multipoints arbitrary shape design model, 100e102, 101f Multireference configuration interaction methods (MRCI methods), 596e597 Multiscale modeling, 97e100, 113 of CVD, 97e100 chemistry models, 98e100, 99f transport phenomena models, 97e98 Mutation, 21

N n-electron system, 593 National Fire Protection Association (NFPA), 203e204 Natural selection process, 249e250

NCDs. See Noncommunicable diseases (NCDs) NDDO. See Neglect of diatomic differential overlap (NDDO) Neglect of diatomic differential overlap (NDDO), 605e606 Nelder-Mead method, 362 Net present worth (NPW), 55, 56fe57f NetLogo, agent-based modeling in, 116 New product template module, 76 NFPA. See National Fire Protection Association (NFPA) NLP. See Nonlinear programming (NLP) NLP-BB. See Nonlinear programmingebased branch and bound (NLP-BB) NMR imaging, 537 No-preference methods, 26 Non-Pareto optimization, 105e106 Noncoupled ordinary differential equations, 400 Nonadiabatic processes, 633e634 Nonbonding terms for empirical force fields, 610e612, 613f Noncommunicable diseases (NCDs), 198e199 Noncompartmental models, 393 Nondominated solutions, 103e104 Nonlinear constraints, 481 Nonlinear programming (NLP), 361e362, 375 Nonlinear programmingebased branch and bound (NLP-BB), 250 Nonnegative weighted factor, 448 NPT. See Particles, temperature, and pressure (NPT) NPW. See Net present worth (NPW) Nuclear dynamics, 586 NVT. See Particles, temperature, and volume (NVT)

O OA approach. See Outer approximation approach (OA approach) Occupational Health Hazard Index (OHHI), 202 OCFE. See Orthogonal collocation on finite elements (OCFE) Octet rule, 158, 188e192, 208e209 modified, 244e245 ODEs. See Ordinary differential equations (ODEs) Odor value (OV), 362e363

673

Index OHHI. See Occupational Health Hazard Index (OHHI) Oil-in-water emulsions, 52e53, 363e364 Ointment layer, 351 One-dimension (1D) chain of amino acids, 223e225 descriptors, 315e316 Operating system, 294 Operational properties, 348e349 Operational windows, 423e424 Optical devices, 96 Optical microscopy, 517e518 Optimal ionic liquid structure, 256e257, 256f, 262f Optimal manufacturing process, 357 Optimization, 47, 477. See also Multiobjective optimization (MOO) enzymatic hydrolysis, 396 formulations for product/process design, 357e362 computational implementation, 361e362 integrated product/process design, 360e361 two-stage approach to invert property function, 359e360 methods, 385 optimization-based CAMD, 273 Optimum green diesel blends, 487e488, 495, 501, 502f, 502t Optoelectronic devices, 95 ORCs. See Organic Rankine cycles (ORCs) Ordinary differential equations (ODEs), 394e395, 406 Organic Rankine cycles (ORCs), 274, 287e288 application description and variability issues, 287e288 implementation details, 289e291 investigated working fluid mixtures, 290t ORC system, 289f results and discussion, 291e293 solar ORC system investigation, 290t selected mixtures in, 293t Orthogonal collocation on finite elements (OCFE), 282 Outer approximation approach (OA approach), 249e250 OV. See Odor value (OV) Oxidation stability, 503

Oxides of nitrogen (NOx), 503 Oxygenated green diesel fuel blend, 501

P Paramchem, 615 Parametrization, 614e615 parameterized substrate geometry model, 109e110, 109f Pareto optimal fluids, 274 Pareto-based optimization method, 105e106 set, 279 solutions, 103e104 Pariser, Parr, and Pople method (PPP method), 604e605 Partial miscible blends, 493e494, 497, 499e500 Particle attrition, 566e569, 568f composition, 558 interactions, 543 morphology, 546 packing, 560e561 porosity, 540e541 process designer, 569 roughness, 544 spatial distribution, 557e559, 558f surface forces, 543 properties, 545 systems, 551e552 wetting, 540e541 Particle size distribution (PSD), 529e532 Particle structure, 532e549, 533fe534f. See also Integrated approach. See also Mesostructure. See also Supramolecular structure formation during drying, 544e546, 547f modeling, 546e549, 549f mass transfer of volatile components, 548e549 mass transfer of volatile solvent and discrete phase, 549 porosity and pore size distribution, 540e541 spatial distribution of domains, 538e540, 539f specific surface area, 541e542 surface energy, 542 surface forces, 542e543 surface roughness, 543e544

674

Index Particle structure (Continued ) volume fraction and size distribution of domains, 535e538, 536f Particle-mesh ewald method (PME method), 611e612 Particles, temperature, and pressure (NPT), 635e636 Particles, temperature, and volume (NVT), 635e636 Particulate matter (PM), 503 Particulate structure, 537e538 PBCs. See Periodic boundary conditions (PBCs) PBM. See Population balance modeling (PBM) PC-SAFT equation, 162 PCR. See Principal component regression (PCR) PDPS approach. See Product-driven process synthesis approach (PDPS approach) Pentanol (PEN), 499 Peptides, 223e225 Performance metrics, 363e364 Perfumes, 362e363 Periodic boundary conditions (PBCs), 612 Permeability, 561e562 Pharmaceutical agents, 221 Pharmaceutical drugs, 4 Pharmaceutical formulation design, 228e234. See also Ionic liquid product design CAMD approaches to formulation design, 229e231 drug molecule, 228 formulation design to minimize aggregation of protein drugs, 231e234 selection and design of API, 229 Pharmaceutical industries, molecular design in active pharmaceutical ingredient, design and development of, 223e228 API, 223 CAMD approach in drug discovery, 224f ligand screening, 225 ligand-based approaches, 226e228 receptor-based approaches, 226, 227f small molecule drug design tools, 223e225 structure-based drug design, 225e226 pharmaceutical formulation design, 228e234

CAMD approaches to formulation design, 229e231 drug molecule, 228 formulation design to minimize aggregation of protein drugs, 231e234 selection and design of API, 229 pharmaceutical product design concepts, 222e223 Pharmaceutical ointment formulation, 367e370 drug solvent and oily aqueous excipient, 370t Pharmaceutical product design concepts, 222e223 Pharmacokinetics, 393, 394f, 404 Pharmacophore, 226e227 Physiological metrics calculations, 653, 654f PIIS. See Prototype Index for Inherent Safety (PIIS) Plasma drug concentration, 393 Plug flow reactor, 407 PM. See Particulate matter (PM) PME method. See Particle-mesh ewald method (PME method) Polar amorphous solids, 515 Polar crystalline solids, 515 Polarizable force fields, 613e614 Polarized optical microscopy (POM), 517e518 Polyfunctional groups, 12 Polymers, 231, 382 POM. See Polarized optical microscopy (POM) Pool capacity, 376 Pooling problem, 376f formulation, 376e377 state of the art, 374e376 Pople-Nesbet-Berthier equations, 589e590 Population balance modeling (PBM), 553e554 Porosity distribution, 540e541 Posteriori methods, 26 Potential energy, 607 PPP method. See Pariser, Parr, and Pople method (PPP method) Predictive thermodynamic models, 246 PRHI. See Process Route Healthiness Index (PRHI) Priceedemand consumer model, 53e55, 54f Principal component regression (PCR), 7 Priori methods, 26

675

Index ProCAMD approach, 174, 182f Process design, 281e283, 420e421, 421t property integration, 128e129 rigorous equipment models, 282e283 solvent-based CO2 capture process superstructure, 282f systematic flow sheet design methods, 281e282 function, 357, 361 ISI, 202 models, 69, 167 simulator, 76 synthesis, 417e418, 419f in food industry, 420e422, 422f Process Route Healthiness Index (PRHI), 202 Process systems engineering (PSE), 3e4, 417e418 Processability, 383 Prodrg, 615 Product analysis, 75e76 module, 78 attribute identification, 47 demand, 377 function, 432e437 identification, 46e47 manufacturing process, 351e353 performance, 383 product operational properties, decomposition of property function for, 351e353 quality, 377 Product design, 45, 221e222, 421, 421t, 443 and development, 61 integrated model, 46e47, 48f module, 66e75, 68f device design, 73e75, 74fe75f emulsion design, 71e73, 72f formulation design, 70e71, 70f molecular design and blend design, 68e70, 69f procedures, 46 simulator, 62e63 Product-driven process synthesis approach (PDPS approach), 423e424, 425t, 426f, 430te432t classes of tasks, fundamental tasks, and mechanisms, 433te435t generalities, 422e424 structure of methodology, 424e429 Product-oriented process synthesis, 422e423

Product/process design, 347 conceptual model, 348e355, 352t examples, 362e370 cosmetic emulsion, 363e367 formulation of pharmaceutical ointment, 367e370 perfumes, 362e363 interactions, 420e421 optimization formulations for, 357e362 problem, 69 Profit model and optimization, 55 Property clustering, 129 methods, 129 molecular, 130e131 visual molecular, 134 clusters, 128e129 constraints, 159e167 GCebased methods, 161e167 estimation methods, 135e136, 135te136t function, 350, 353, 353f, 357, 363 decomposition for product operational properties, 351e353 function, 426e429, 428f integration for process design, 128e129 models, 10, 11f, 34, 63, 165e167, 172, 497e499 identification, 488e491 operators, 129 prediction, 63, 126e128, 153, 199e200, 221e222 toolbox, 63, 66 types, 160t validation, 496 Property prediction uncertainty, 34e35 Protein drug aggregation carbohydrate excipient design, 233e234 formulation design to minimizing, 231e234 prediction, 232e233 Protein stability, 231e232 Protein-based drug formulations, 231e232 Proteineprotein interactions, 322 Prototype Index for Inherent Safety (PIIS), 201e202 PSD. See Particle size distribution (PSD) PSE. See Process systems engineering (PSE) PubChem bioassay database, 326 Compound database, 327e328 Pure compound property models, 81e82

676

Index Purely quantum mechanical techniques, 631e632 Pyloric sphincter, 396e397, 401e402

Q QCQP. See Quadratic program with quadratic constraints (QCQP) QFD. See Quality function deployment (QFD) QM/MM methods. See Quantum mechanical/ molecular mechanics methods (QM/MM methods) QSAR/QSPR methods, 321e324 QSARs. See Quantitative structure activity relationships (QSARs) QSPRs. See Quantitative structure property relationships (QSPRs) Quadratic program with quadratic constraints (QCQP), 374 Qualitative formulation rules, 358e359 Qualitative predictive algorithms, 232e233 Quality balance, 377 Quality factors, 349, 354e355 Quality function, 363 Quality function deployment (QFD), 424, 427f Quantitative property functions, 358 Quantitative structure activity relationships (QSARs), 12e13, 226, 319e320 Quantitative structure property relationships (QSPRs), 12e13, 223, 241, 316 Quantum mechanical treatment, 584e587 Quantum mechanical/molecular mechanics methods (QM/MM methods), 583e584, 587, 618e623 additive and subtractive schemes, 619e622 chemical bonds, 622e623 Quasi-Monte Carlo sampling, 385

R R-152a, 180 RAA. See Risk-averse approaches (RAA) Raman spectroscopy, 520 Rapid granular flow, 562 Ratio of solid mass, 402e403 Rational product design, 221e222 Raw voxel matrix, 652e653 Reaction pathway design, 330e334 Reactive force fields, 616e618 ReaxFF, 616 Receptor-based approach, 225e226, 227f

Reference methods, 10 Reformulation-linearization technique (RLT), 375 Refrigerant design, 177e182 CAMD formulation, 188e192 molecular design results, 181t ProCAMD screenshot, 182f process specifications, 179t R-134a properties, 178t target product properties, 179t vapor compression cycle, 177f Regimes, 562, 563f Response surface methodology, 229e230 Reverse networks, 443 Reverse problem formation (RPF), 322e323, 330fe331f Rheology, 527e529, 528f Rigorous equipment models, 282e283 Risk measure (RM), 448, 450 Risk-averse approaches (RAA), 443e444 Risk-neutral approaches (RNA), 443e444 RLT. See Reformulation-linearization technique (RLT) RM. See Risk measure (RM) RNA. See Risk-neutral approaches (RNA) Robust programming, 35 RPF. See Reverse problem formation (RPF) “Rule-based generate-and-test” synthesisedesign methods, 168 Rule-based techniques, 168

S SA. See Simulated annealing (SA) SaaS. See Software-as-a-service (SaaS) SAXS. See Small-angle x-ray scattering (SAXS) SC. See Stratum corneum (SC) Scenario cost, 449 SCF. See Self-consistent field (SCF) Scheffe´ models, 8 Schro¨dinger equation, 584e585 SCs. See Supply chains (SCs) SCSC. See Supply chain structure cost (SCSC) Second order equations, 5e7 Second order molecular groups, 12 SEE. See South Eastern European (SEE) Segregation mechanisms, 558e559, 558f Self-consistent field (SCF), 588 SEM. See Surface electron microscopy (SEM)

677

Index Semiempirical methods, 603e607 p electrons methods, 604e605 all valence electrons methods, 605e607 Sensitivity analysis, 298e300, 456e461, 460f index, 291, 291f Pareto fronts, 292f metric, 285e286 SGPDP. See Stage-Gate TM Product Development Process (SGPDP) Shape distribution, 537 SHM. See Simple Hu¨ckel method (SHM) Shrinkage reducing admixtures (SRAs), 334 Shrinking core models, 548 Sieve analysis, 552 Signature, 318 advantages, 319e321 canonical representation of molecule, 320 combining atomic Signatures, 320e321 degeneracy, 320 documentation of atomic topography, 319e320 tunable specificity, 320 applications, 321e325 experimental validation, 323 inclusion in biological software, 324 industrial bioreaction pathway design, 324e325 molecular design, 322e323 QSARs, 321e324 QSPR, 322e324 signature as 3D molecular descriptor, 325 case studies, 325e338 molecular descriptor, 316e318, 317f Simple Hu¨ckel method (SHM), 604 Simple weighting method, 105 Simulated annealing (SA), 18e19, 23e24 Simulating patient-specific structures in three dimensions, 654e655, 655f Simulation-based food process design small intestine, 404e411 stomach, 396e404 Simulation-based methods, 232e233 Single-objective optimization (SOO), 298e300 Single-species products, 155e156 Six generated solvents, 215f, 215te216t Skin feeling, 363e364 lipids, 351

Slater orbitals (SO), 590e591 Slip and stick regime, 562 Slow frictional regime, 562 Small intestine, 404e411 Small-angle x-ray scattering (SAXS), 520 SO. See Slater orbitals (SO) SoaveeRedlicheKwon equation, 178e179 Softeners, 382 Software implementation, VPPD-Lab, 76e78, 77f Software-as-a-service (SaaS), 297, 298f services layer of proposed, 299f Solar ORC systems, 289 investigation of, 290t Solid(s), 401e402 amorphous materials, 515 phase chemistry, 98 true amorphous materials, 516 Solution approach, 477 of groups concept, 246 strategy, 480e482 Solvent design, 134e140 GCM, 135e136, 135te136t molecular synthesis, 137e140, 138fe139f, 139t problem statement, 135, 135t problem visualization, 136e137, 137f property estimation methods, 135e136, 135te136t visualization of solvent design problem, 136e137, 137f Solvent mixture design, 89f stability check, 78, 80f SOO. See Single-objective optimization (SOO) South Eastern European (SEE), 301 Spatial distribution, 561 Spatial distribution of domains, 538e540, 539f Specific surface area, 541e542 Spray-dried detergent particles, 512e514, 512fe513f Spray-dried milk powder, 514 SRAs. See Shrinkage reducing admixtures (SRAs) SSCs. See Sustainable SCs (SSCs) Stability check of solvent mixtures, 78, 80f Stage-gate procedures competitive markets, 56e57, 57f consumer preference model, 52

678

Index Stage-gate procedures (Continued ) consumer satisfaction score, 48e52, 51f manufacturing and distribution costs, 52e53 priceedemand consumer model, 53e55, 54f product design integrated model, 46e47, 48f profit model and optimization, 55 Stage-Gate TM Product Development Process (SGPDP), 46 Standard deviation, 35 State-of-the-art optimization algorithms, 361e362 pooling problem, 374e376 Static regime, 562 “Static” correlation energy, 596e597 Sticky point temperature (Ts), 524e525 Stochastic approach, 319 design method, 534 optimization, 126, 386 Stomach, 396e404 gastric breakup, 401e404 gastric emptying rate, 397e399, 398f gastric secretions, 399e401, 401f small intestine, 404e411 Strain hardening, 528 Stratum corneum (SC), 369 Structural constraints, 157e159, 243e244 Structural groups, 12 Structure property models, 246 Structure-based drug design, 225e226 Structured methodology, 418 Structured particle product challenges, 569e572 modeling approach, 570e572, 571f relevance in industry, 509e511 scales, 511e514 classification of structure in particulate systems, 511f spray-dried detergent particles, 512e514, 512fe513f spray-dried milk powder, 514 Structured particulate systems design. See also Computer-aided molecular design (CAMD) integrated approach, 569e572 mesostructure, 549e569 particle structure, 532e549 relevance of structured particle products, 509e511

scales of structured particle product, 511e514 supramolecular structure, 515e532 Structured products, 421e422 Structureeproperty relationship, 333e334 Substrate geometry global optimization in ZnS deposition, 100e113 aerodynamic shape design models, 113 GAs, 102e103 implementation in shape design, 106e110 multiobjective, 105e106 multiobjective optimization, 103e105 multipoints arbitrary shape design model, 100e102, 101f multiscale modeling, 113 results and discussion, 110e112, 111fe113f Superstructures, 281e282 optimization, 377e380, 379t, 381fe382f, 420 Supply chain structure cost (SCSC), 450 Supply chains (SCs), 443 Supramolecular scale, 511 Supramolecular structure, 512, 515e532, 550. See also Integrated approach. See also Mesostructure. See also Particle structure crystalline and amorphous structure phase composition, 515e520, 516f mechanical properties, viscoplasticity, and rheology, 527e529, 528f PSD, 529e532 thermal phase transitions, 523e527, 523f, 525f water activity, 521e522 Surface energy, 542 forces, 542e543 reactions, 95 roughness, 543e544 Surface electron microscopy (SEM), 519e520 Surfactants, 382 design as emulsifier, 182e185 consumer needs, 183t target properties, 184t UV sunscreen design problem, 185t Surgical tools, 657e658 Sustainability, 200 Sustainable SCs (SSCs), 443

679

Index Systematic flow sheet design methods, 281e282 Systematic generation, 420

T Tabu search (TS), 20 Taguchi loss functions, 354e355 Tailor-made fuels, 156 Tailor-made green diesel blend design algorithm, 488e496, 489f. See also Blending-based product optimization decomposition-based computer-aided optimization, 492e495 generation of feasible blend candidates, 492e494, 493t generation of feasible blends, 494 ranking and selecting, 495 experimental validation, 496 fuel performance test, 496 property validation, 496 fuel enhancement, 495e496 additives identification, 495e496, 495t problem formulation, 488e491 problem definition, 488, 492t property model identification, 488e491 Tailor-made green diesel blends, 487. See also Gasoline blends application, 496e503 feasible blends, 499e500, 499te500t fuel additives, 501e503 optimum green diesel blends, 501, 502f, 502t problem definition, 496e497 property models, 497e499 results and discussions, 503 Target product profile (TPP), 222 Task network, 437, 438f TDDFT. See Time-dependent density functional theory (TDDFT) TEM. See Transmission electron microscopy (TEM) Temperature replica exchange, 637e639 Template generator, 76 Ternary mixture, 479, 484t TGA. See Thermogravimetric analysis (TGA) Theophylline, 229e230 Thermal conductivity, 257 Thermal phase transitions, 523e527, 523f, 525f Thermodynamic model parameter (TML parameter), 63

Thermodynamic modeling of ionic liquids, 246e248 Thermodynamic principles, 377e378 Thermogravimetric analysis (TGA), 524 Three-dimension (3D) brain imaging modalities, 652, 652f descriptors, 315e316 signature as 3D molecular descriptor, 325 volumetric grid, 651 Time-dependent density functional theory (TDDFT), 603 Time-dependent wave packet approach, 631e632 Time-independent methods (TIQM methods), 631e632 TIs. See Topological indices (TIs) TML parameter. See Thermodynamic model parameter (TML parameter) Topological indices (TIs), 12e13, 230e231, 316 Toxicity, 222e223 TPP. See Target product profile (TPP) Trajectory surface hopping methods (TSH methods), 634 Transesterification reactor, 386e388 Translate product quality factors, 355 Transmission electron microscopy (TEM), 519e520 Transport phenomena models of CVD, 97e98 Trauma, 651 TS. See Tabu search (TS) TSH methods. See Trajectory surface hopping methods (TSH methods) Tunable specificity, 320 Two-dimension (2D) descriptors, 315e316 elastic collision, 115 molecular descriptors, 316 Two-phase approach, 31e32 Two-stage approach to invert property function, 359e360 stochastic approach, 444e445, 447

U UELs. See Upper explosion limits (UELs) UF. See Uncertainty factor (UF) UHC. See Unburned hydrocarbon (UHC) UHF calculations. See Unrestricted HartreeFock calculations (UHF calculations) Ultraviolet sunscreen (UV sunscreen), 182 Umbrella sampling method, 639e640

680

Index Unburned hydrocarbon (UHC), 503 Uncertainty, 33 property prediction, 34e35 Uncertainty factor (UF), 34e35 Unconfined compression tests, 528e529 UNIFAC model, 246e247 GC method, 241 Unrestricted Hartree-Fock calculations (UHF calculations), 589e590 Upper explosion limits (UELs), 203e204 UV sunscreen. See Ultraviolet sunscreen (UV sunscreen)

V Value at risk (VaR), 443e444 Van der Waals forces, 543 interaction, 610e611 Vapor pressure (VP), 135e136, 211 Vaporeliquid equilibrium model, 363 VaR. See Value at risk (VaR) Vector-evaluated GA. See non-Pareto optimization Virtual high-throughput screening (vHTS), 325e328 Virtual orbitals, 590e591 Virtual patient simulation, 653e655 modification and re-simulation of structures, 655 simulating patient-specific structures in three dimensions, 654e655, 655f Virtual producteprocess design laboratory software (Virtual PPD-lab software), 24e25 application examples, 78e90, 79t design of insect repellent lotion, 86e90, 88f, 90fe91f design of jet fuel blend, 83e86, 85t, 87t design of lubricant blend, 79e83, 81t, 84t stability check of solvent mixtures, 78, 80f implementation, 76e78, 77f systematic framework for chemical product design, 62e76 Virtual reality environment design, 656, 656f Viscoplasticity, 527e529, 528f Viscosity, 212, 364, 399, 406 model, 364e365 subindex, 206t, 208f Visual molecular clustering design approach, 129e140 conservation rules for molecular property clusters, 131e132 GC properties, 130

graphical representation of molecular design problem, 132e134, 132f molecular property clustering method, 130e131 solvent design, 134e140 GCM, 135e136, 135te136t molecular synthesis, 137e140, 138fe139f, 139t problem statement, 135, 135t property estimation methods, 135e136, 135te136t visualization of solvent design problem, 136e137, 137f Visualization techniques, 229 Vitrification, 233e234 Volatile fragrances, 362e363 Volume fraction and size distribution of domains, 535e538, 536f Voxel matrix, 652e653 VP. See Vapor pressure (VP)

W Walk-in brain flow diagram of proposed software design, 650f immersive virtual reality environment, 655e657 medical images, 651e653, 651f virtual patient simulation, 653e655 Washburn equation, 559e560 Wastewater treatment operations, 380 Water activity, 519f, 521e522, 522f integration, 380 sorption isotherms, 521e522, 527 WAXS. See Wide-angle x-ray scattering (WAXS) Weighted sum method, 26e27 Wetting, 561e562 WHAM. See Multiple histogram reweighting method (WHAM) WHO. See World Health Organization (WHO) Wide-angle x-ray scattering (WAXS), 520 William-Landel-Ferry equation, 525 Workflow(s), 294 implementation, 301e306 parameterization of tools, 301e304 results and discussion, 304e306 for integrated molecular and process design, 298e300, 300f tool parameterization, 301e304, 302f, 305f World Health Organization (WHO), 198e199 Wrappers, 326

681

Index

X X-ray diffraction (XRD), 517, 520 X-ray microtomography, 520 X-ray tomography, 537e538

Y Young-Laplace equation, 542 Young’s modulus, 527e528

Z Zero differential overlap (ZDO), 605e606 Zero-dimension (0D), descriptors, 315e316 Zinc sulfide (ZnS), 96 deposition. See also Chemical vapor deposition (CVD)

aerodynamic shape design models, 113 GAs, 102e103 implementation of GA in shape design, 106e110 multiobjective GAs, 105e106 multiobjective optimization, 103e105 multipoints arbitrary shape design model, 100e102, 101f multiscale modeling, 113 results and discussion, 110e112, 111fe113f substrate geometry global optimization in, 100e113 molar mass, 114