Chemistry of Functional Materials Surfaces and Interfaces: Fundamentals and Applications 0128210591, 9780128210598

Table of contents :
Front-Matter_2021_Chemistry-of-Functional-Materials-Surfaces-and-Interfaces
Front Matter
Copyright_2021_Chemistry-of-Functional-Materials-Surfaces-and-Interfaces
Copyright
Preface_2021_Chemistry-of-Functional-Materials-Surfaces-and-Interfaces
Preface
Chapter-1---Introduct_2021_Chemistry-of-Functional-Materials-Surfaces-and-In
Introduction
Reference
Chapter-2---Thermal-energy-_2021_Chemistry-of-Functional-Materials-Surfaces-
Thermal energy scale kT
Reference
Chapter-3---Surfaces-and-in_2021_Chemistry-of-Functional-Materials-Surfaces-
Surfaces and interfaces
Surface tension of liquids
Predictive models for calculating the surface tension of liquids
Interfacial tension between liquids
Relating surface tension to surface energy
Surface and interfacial energy of solids
Solid-liquid interfaces
Scaling effects: When surface tension dominates gravity
Case study: How surface tension of liquids affects life at small scale and in outer space?
Capillary rise
Capillary number
Curved liquid surfaces, Laplace pressure, Young-Laplace equation
Case study: Emulsions and foams
Kelvin equation
Case study: Surface tension of liquids at the nanoscale and in nanopores
Methods for measuring the surface and interfacial tensions of liquids
Case study: Aerosol spray coatings and the importance of the dynamic surface tension
Measuring ultralow interfacial tension-The spinning drop tensiometer
Case study: Role of interfacial tension in enhanced oil recovery
Surface and interfacial tensions with temperature
References
Chapter-4---Surfactants-and-a_2021_Chemistry-of-Functional-Materials-Surface
Surfactants and amphiphiles
Introduction
Brief historical account of surfactants
Major classes of surfactants
Anionic surfactants
Cationic surfactants
Zwitterionic and amphoteric
Nonionic surfactants
Other important classes of surfactants
Specialty surfactants
Gemini surfactants
Biosurfactants
Self-assembly of surfactants
Self-assembly in ternary systems, foams, and emulsions
Attempting to quantify amphiphilicity with HLB
Case study: An intuitive understanding of the structure-activity relationship in surfactants
Amphiphilicity beyond the molecular scale-Janus particles
Supra-amphiphiles
Surfactants and the environment
References
Chapter-5---Wettability-of-surfaces--nanopa_2021_Chemistry-of-Functional-Mat
Wettability of surfaces, nanoparticles, and biomimetic functional surfaces
Contact angle of liquids on macroscopic surfaces
From macroscopic to microscopic sessile droplets
Classification of surface hydrophobicity vs. the magnitude of the contact angle with water
Dynamic, advancing, and receding contact angle
Contact angle hysteresis
Wettability of liquids on rough and nanostructured surfaces-Wenzel model
Wettability of liquids on heterogeneously flat surfaces-Cassie-Baxter model
Transition from Cassie-Baxter to Wenzel state
Case study: Wettability of antifogging surfaces-From mirrors to solar panels
Roll-off and sliding angles of a sessile droplet
Case study: Waterproof clothing
Measurement of the contact angle with the captive bubble method
Natural and biomimetic functional surfaces
Case study: Water collecting surfaces and surface directional transport of droplets
Marangoni flow
Case study: Nonstick ``omniphobic´´ surfaces-From mobile phone screens to car interior surfaces
Case study: Research in ``icephobic´´ surfaces for the aircraft industry, biomimicry inspired by penguins, and ca ...
Adhesion of cells on rough and nanostructured surfaces
Spreading and superspreading in the presence of surfactants
The autophobic and autophilic effects
Case study: Superwetting agents in agriculture and surface cleaning
Surface cleaning mechanism
Contact angle of micro- and nanoparticles
Wettability of (nano-)powders, nanofibers, and porous materials-Washburn method
Case study: Ore separation by flotation
References
Chapter-6---The-fundamental-equati_2021_Chemistry-of-Functional-Materials-Su
The fundamental equations of interfaces
The thermodynamic perspective-Energy of adhesion
Fowkes model for the energy of adhesion
Owens, Wendt, Rabel, and Kaelble (OWRK) method
Girifalco-Good equation of state
Neumann's equation of state
Van Oss, Choudhury, and Good (OCG) model
Fox-Zisman model
Case study: Usefulness of interfacial models in applications
Case study: Wetting envelope
Case study: Pickering emulsions and energy of adhesion of nanoparticles to immiscible phases
References
Chapter-7---Elements-of-thermodyna_2021_Chemistry-of-Functional-Materials-Su
Elements of thermodynamics of interfaces
Gibbs-Duhem equation for interfaces
Gibbs adsorption isotherm
Choice of the boundary thickness, Gibbs dividing line, and excess function
Interfacial adsorption isotherms and surface tension
References
Chapter-8---Populated-interfaces-a_2021_Chemistry-of-Functional-Materials-Su
Populated interfaces and their reactivity
Partitioning of solute between immiscible phases
Partitioning and adsorption at liquid interfaces
Soluble films-Gibbs monolayers
Insoluble films-Langmuir monolayers
Langmuir-Blodgett monolayers-Manipulation of a monolayer of molecules
Self-assembled monolayers
References
Chapter-9---Metal-organic-interfaces-in-_2021_Chemistry-of-Functional-Materi
Metal-organic interfaces in organic and unimolecular electronics
Energy levels at metal-organic interfaces
Electron transport across metal-organic interface
Basic organic electronic devices and their metal-organic interfaces
Role of interfacial tension in organic electronic devices
Unimolecular electronics
Making electrical contacts to single molecules vs monolayers of oriented molecules
Metal-organic interfaces: Weak vs strong coupling
Transport mechanism through MOMs
Archetypal unimolecular device-The unimolecular rectifier and rectification mechanism
References
Chapter-10---Main-interaction-forces-be_2021_Chemistry-of-Functional-Materia
Main interaction forces between molecules and interfaces
van der Waals interactions between molecules and between interfaces
Attractive and repulsive van der Waals interactions
Combining laws applied to van der Waals interactions
Surface tension and surface energies from intermolecular forces
Hydrogen bonding
Dipole-dipole interactions
Hydrophobic interaction
Repulsive hydration force
Hildebrand and Hansen solubility parameters
Flory-Huggins interaction parameter
References
Chapter-11---Interactions-between-elec_2021_Chemistry-of-Functional-Material
Interactions between electrically charged interfaces
Electric double layer
Distribution of counterions in the absence of electrolyte
Distribution of counterions around a charged surface in the presence of electrolyte
Grahame equation and Debye length
Double-layer interaction forces and energies
DLVO theory
Zeta potential
Case study: Constructing the interaction potentials between nanoparticles with DLVO and non-DLVO forces
References
Chapter-12---Colloids-and-nan_2021_Chemistry-of-Functional-Materials-Surface
Colloids and nanoparticles
Lyophobic colloids
Preparation of the lyophobic colloids
Preparation of colloids by solvent replacement and physical condensation
Chemical synthesis of lyophobic colloids
Interfacial forces and stability of lyophobic colloids
Lyophilic colloids
References
Chapter-13---Role-of-interfaces-in-the-synthes_2021_Chemistry-of-Functional-
Role of interfaces in the synthesis of polymeric nanoparticles and nanostructured materials
Case study: Synthesis of polymeric nanoparticles via emulsion polymerization
Emulsion polymerization in the presence of surfactants
Surfactant-free emulsion polymerization
Emulsion polymerization with polymerizable surfactants-Synthesis of surfactant-free nanoparticles
Miniemulsion polymerization
Microemulsion polymerization
Ultrasonic-assisted surfactant-free emulsion polymerization
Seeded emulsion polymerization for preparation of core-shell and asymmetric Janus nanoparticles
Case study: Synthesis of nanostructured materials from Pickering emulsions
Bulk polymerization of Pickering emulsion droplets
Interfacial polymerization of Pickering emulsion droplets
References
Chapter-14---Adsorption-and-interactio_2021_Chemistry-of-Functional-Material
Adsorption and interaction of particles at interfaces
Adsorption of nanoparticles at interfaces
Interfacial adsorption dynamics and mechanism
Interaction between nanoparticles at interfaces
Langmuir-Blodgett assembly of nanoparticles into 2D crystals
Templated self-assembly of nanoparticles at interfaces
References
Chapter-15---A-short-account-of-the-role-of-_2021_Chemistry-of-Functional-Ma
A short account of the role of interfaces in Integrated Circuits manufacturing
Introduction of photolithography and Integrated Circuits manufacturing
Role of interfaces in photolithography
Surface tension and pattern collapse of nanometer scale structures
Particle removal in IC manufacturing
References
Index_2021_Chemistry-of-Functional-Materials-Surfaces-and-Interfaces
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Pp
Q
R
S
T
U
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W
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Z

Citation preview

CHEMISTRY OF FUNCTIONAL MATERIALS SURFACES AND INTERFACES

CHEMISTRY OF FUNCTIONAL MATERIALS SURFACES AND INTERFACES Fundamentals and Applications ANDREI HONCIUC

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2021 Elsevier Inc. 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: 978-0-12-821059-8 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

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Preface

even less so acquire a relevant practical experience. Navigating through the maze of scientific literature and information hard to decipher can be extremely intimidating for the future chemists. The same is true in industry; working in industry one realizes that time is of the essence. Chemists and laboratory technicians are expected by the company to be innovative and thrive in interdisciplinary fields, learn on the go, and become experts in the shortest amount of time, on the job. Therefore, I feel that this book would be useful as a textbook for students, chemists working in industry, and laboratory technicians first encountering the chemistry of interfaces, interfacial phenomena, colloids, nanotechnology, polymer nanoparticle synthesis, etc. I have used myself part of this material in my teachings both in academia and training of technicians from industry. While this material used as a coursework material at master’s level has initially included much more theory and formula, I could feel the students had difficulties grasping these, due to the pressure, lack of time, and an extremely burdening curriculum. I thus preferred to make the hard choice of reducing the material only to essential theories and adopt a more descriptive and intuitive presentation. One of the leitmotifs of the book is the emphasis on practical applications of such theories. After several years in refining this material I believe it came to a format well received by the students. In addition, to make it more useful for chemists performing interfacial experiments, in industry or academia, I have tried to add experimental details or hints on data interpretation from my own experience.

In these times it is undeniable that most industries deal increasingly more often than ever with surface and interfacial phenomena. Chemists, physicists, and material scientists, with background and training in materials, surfaces, and interfaces are in great demand. From my experience in both industry and academia, I have observed that students attending courses of a general chemistry degree program encounter rather late in their curriculum courses dealing with interfacial phenomena and chemistry of interfaces. Some curricula have included the chemistry of interfaces under different formats, at the undergraduate level, some only at master’s level, in specialized modules. This can in part be explained by the fact that Chemistry has become an enormously vast array of scientific domains, branching into biochemistry, organic chemistry, physical chemistry, catalysis, industrial chemistry, inorganic chemistry, analytical chemistry, materials chemistry, nanotechnology, polymer chemistry, petroleum chemistry, etc. Due to fecund research in the past two decades Chemistry of functional materials and interfaces covers a multitude of intertwined interdisciplinary subjects from the nanoscale, such as synthesis of polymeric and inorganic nanoparticles, to macroscopic phenomena such as manufacturing of functional surfaces, food, and consumer products such as cosmetics, detergents, heterogeneous catalysts, etc. The amplitude and the amount of information in each of these fields put pressure on students, more so than several decades ago; it is now harder for the students to keep track of the newest advances,

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C H A P T E R

1 Introduction Interfaces are the boundaries separating two phases and define all objects in the three-dimensional world. Depending on the strength of cohesion forces and binding energies between atoms and molecules, the phases can be gases, liquids, and solids, defining the physical states of matter. When the cohesion energies between the constituting atoms and molecules are stronger than randomizing effects of the thermal energy, the physical state changes from gas to a condensed phase of matter, liquid, or solid. The Boltzmann distribution gives the probability P that a system will be in a certain state as a function of the state’s energy and temperature: P
eE=kT kT factor is often used as a scale energy factor in the molecular interactions. The cohesive energies per atom or molecule at 298 K can vary from several kT between gas atoms, between
9 and
23 kT in liquid Hg (the liquid with the strongest cohesive energy, 57.9 kJ/mol [1]), and >50 kT in solids up to 342 kT in W (1 kT  4.05  1021 J), the metal with the highest melting point. The kT energy scale factor is introduced and discussed in detail in Chapter 2. Because the most important interactions between material interfaces take place in the liquid, or between material interfaces and liquids, the solid-liquid, liquid-liquid, and liquid-air interfaces deserve special attention. The overall balance between the repulsive and attractive forces between solutes and colloidal objects in liquids must be comparatively equal or larger than 9–23 kT to have aggregation, adsorption, self-assembly, etc., and below 9 kT to obtain stable dispersions and colloids. As mentioned, liquids form at T ¼ 298 K, when the cohesive energy between the constituting atoms and molecules is larger than 9 kT. While in the bulk of a liquid the interaction forces of a molecule or atom are fully symmetric at interfaces, in contrast, in the topmost layer of molecules or atoms the interaction forces are asymmetric. Due to this asymmetry, a certain tension/force arises in the plane of the interface. The stronger the interfacial tension, the stronger the asymmetry. At contact between two phases, the topmost layer of molecules at the phase boundary also interacts with the molecules from the other phase, this is called adhesion. The adhesion forces and energies counterbalance the asymmetry of the forces acting on the topmost molecular layer, i.e., the stronger the adhesion force, the smaller the interfacial tension. If the adhesion force is stronger than the cohesion force, then the interfacial tension disappears, the interface disappears, and the phases become fully miscible, as discussed in Chapter 3. This interfacial tension has also the character of an energy density, and for pristine interfaces this is causally related to the cohesion energy in the bulk material; interfacial energy density is about half the cohesion energy in bulk. Surface and interfacial tension of liquid-gas and liquid interfaces, as well as interfacial and surface energy of solids-liquid and solid-gas interfaces, are thoroughly discussed in Chapter 3. The effects of the interface tension can be seen in small liquid droplets or molten metals, as the shape of the droplet itself is modeled by this interfacial tension. The small world of insects and bugs are particularly affected by the interfacial tension. Because their size is comparable to the capillary length, when the shape of the liquids is fully determined by interfacial tension, not by gravitation, they have a different perception of the surrounding world than humans do. Interfacial tension can have a devastating effect on insects; some drown as they cannot escape the surface tension, but some have adapted to take full advantage of it. For example, small water droplets can be manipulated and transported by ants without any need for bottles or glasses, and some mosquitos have adapted on water to straddle along the smooth water surface, etc. (Fig. 1). Intuitively, the interfacial tension is the 2D equivalent of the cohesion energy in 3D. Interfacial tension is discussed in detail in Chapter 3. However, when the surface and the interface are chemically modified, e.g., with surfactant adsorbates, the interfacial tension and energy density of interfaces do not reflect anymore the cohesive energy between the molecules in the bulk phase. Thus, the interface itself can be treated as a thermodynamic system on its own, as discussed in Chapter 7. The interfacial tension and interfacial energy density between phases are now an exclusive reflection of Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00004-1

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1. Introduction

FIG. 1

(A) Ant drinking water (https://www.shutterstock.com/image-photo/ant-drinking-water-505718482); (B) mosquito striding on the surface of water (https://www.shutterstock.com/image-photo/water-bug-standing-on-surface-calm-1732352752).

the lateral interactions between surfactant molecules, polymers, or particles adsorbed at the interface. In fact, understanding how to change the interfacial tension and energy density between phases was one of the key enabling elements in the development of most technological advances in the 20th and 21st centuries, ranging from detergency, oil, and ore extraction to the advanced manufacturing of processors and advanced electronic devices (see Chapter 15). Surfactants and amphiphiles are molecules, polymers, and other building blocks of matter that adsorb spontaneously at interfaces. Surfactants lower the interfacial tension and energy density between phases (water-oil, water-gas, solid-water) independently of their cohesion energy. This enables the formation of emulsions and foams and increase in surface wettability. Earlier, it was mentioned that when the adhesion forces are stronger than the cohesion forces between two liquids, the interfacial tension vanishes, and the liquids become miscible. The fact that, in the presence of a surfactant at interfaces, the interfacial tension is not anymore a true reflection of the bulk cohesion energy of the phases can be understood from the following example. If the interfacial tension between two water and oil phases becomes vanishingly small due to the addition of a surfactant, then the two phases do not mix, but this time they form emulsions consisting of very fine oil droplets dispersed into water. Chapter 4 gives an introduction into the vast field of surfactant chemistry. Emphasis is given on surfactant classification, surfactant design, and structure activity relationship. In simple words, what makes a surfactant effective and how is this reflected in different physicochemical parameters? Chapter 4 also introduces other amphiphiles, such as Janus nanoparticles and supra-amphiphiles, noting that amphiphilicity is a scalable property, being active well beyond the molecular scale, well into the nano- and microscales. Amphiphiles and surfactants have an important property, which is to self-assemble into suprastructures. This enables the creation of smart, reconfigurable, or “environmentally aware” materials, bottom up, via self-assembly processes. Most of the surfaces we interact with on a daily basis are solid, such as the screen of the smartphone, the cup of coffee, the wheel of the car, etc. The tactile feel, the adhesion, is determined by the interfacial energy between our skin and these surfaces. In the modern world, the concept of functional surfaces is gaining more popularity and it becomes a requirement in the consumer products. Functional surfaces can be defined as surfaces that perform a function, such as self-cleaning windows, or have a superior property, such as antiadherent, omniphobic antifingerprint in smartphone screens, for example, while others are icephobic, or antifogging, etc. The key concepts in understanding the phenomena behind functional surfaces and interfaces are adhesion and wetting. Surface wetting refers mainly to the interaction of a liquid with a solid surface. Earlier, it was mentioned that when the adhesion forces are stronger than the cohesion forces between two liquids, the interfacial tension vanishes, and the liquids become miscible. The interfacial tension or energy between a solid and a liquid can also be altered, for example, with surfactants; however, when the interfacial energy between a solid and a liquid becomes vanishingly small, the solid surface becomes fully wetted by the liquid. The converse is true: when the interfacial energy is large, the surface becomes nonwetted, and the liquid pearls up on the surface of the solid. Scientists have learned that, in addition to interfacial energy between the solid and liquid, the geometry of the interface is key to designing functional surfaces. Finding inspiration in nature, scientists found out that hierarchical structuring of the surface of the solid can lead to a variety of functional surfaces, such as superhydrophobic, superhydrophilic, icephobic, omniphobic, self-cleaning, etc. Chapter 5 gives an overview of the phenomena of

Reference

3

wetting, wettability, and contact angle as the main measurement methods for macroscopic and nanoscale surfaces. Chapter 5 also introduces the several functional surfaces. In Chapter 6, a series of equations permitting the calculation of unknown surface tension, energy, work of adhesion, etc. from known measurable macroscopic parameters have been grouped under the name “fundamental equation of interfaces.” Their versatility in predicting the values of many interfacial parameters, for example, interfacial tension, wettability, polarity of the surface, etc. from contact angle makes them extremely useful in practice. In Chapter 7, the surface and interfacial tension are introduced via thermodynamic treatment of the interfacial layer. Although this treatment has no direct practical implications, it gives the theoretical background necessary for the interpretation of interfacial adsorption isotherms and interfacial tension vs concentration curves for surfactants and amphiphiles. Chapter 8 treats surface functionalization that can be achieved in different ways, by physical methods such as roughening of the surface, or photolithographic nanopatterning, and by chemical methods, by adsorption of surfactant molecules. The adsorption of surfactant molecules on solid surfaces involves either chemical or physical bonding, resulting in the formation of a self-assembled monolayer. Several types of chemical bonding and substrates are reviewed. In addition, a surfactant monolayer can be prepared first at the water-air interface and then transferred onto the surface of the solid via the Langmuir-Blodgett and dip-coating methods. Solid-solid interfaces also have practical relevance, especially in layered electronic devices. Solid-solid interface, in particular the metal-organic interface, is the locus of another type of phenomena of practical importance, namely the electron transfer. In the previous chapters, the interfaces were the place where different forces met. In Chapter 9, the metal-organic interfaces are treated as the contact point between electron energy levels of a metal, material with delocalized electron energy levels called bands, and the organic molecules and polymers whose energy levels are discrete and localized. Understanding electron transfer between metal electrodes and organic conductors is of practical importance, especially for the manufacturing of organic photovoltaics, organic light emitting diodes, and other organic electronic devices. Any of these devices requires at least several layers of electroactive organic materials, and knowledge of adhesion, wettability, and interfaces is required for their development and manufacturing. Chapters 10 and 11 deal with the interaction forces and energies between interfaces in different media. These interaction forces can be repulsive or attractive and they are the same forces governing the molecular interactions. The balance between the attractive and repulsive interaction forces is of practical importance, controlling the phenomena of particle aggregation, colloid stability, particle adsorption on surfaces, self-assembly of nanoparticles, etc. Chapter 12 introduces colloids, which are the oldest type of nanomaterials known and are today encountered in the food industry, pharma, and many other consumer products. Colloids are constituted from finely divided particles, nanoparticles, or liquid droplets dispersed into a continuous medium. Because their surface-to-volume ratio is very high, their behavior is governed almost exclusively by their surface and interfacial properties. Synthesis of colloids as well as stability criteria is discussed. As a continuation on the topic of colloids, but deserving special attention, Chapter 13 introduces the synthesis of polymeric nanoparticles and polymeric nanostructured interfaces via emulsion polymerizations. As expected, the interfacial aspects determine the types of emulsions and nature of the nanomaterials that can be synthesized. The types of emulsions and conditions of formation are briefly reviewed. A case study covers some examples of synthesis of nanostructured interfaces, polymerization of the emulsions stabilized by amphiphilic particles. Some nanoparticles, depending on their surface properties, can also spontaneously adsorb at interfaces; they can form monolayers and stabilize emulsions. The factors responsible for why some particles can adsorb at liquid-liquid, liquid-gas, and solid-liquid interfaces are discussed in Chapter 14. Once adsorbed at the interfaces the particle-particle interactions leads to the decrease in the interfacial tension. Responsible for this is their lateral interaction, which is governed by the same types of forces as in case surfactants, and in addition by particle specific interactions, capillary floatation, or immersion forces. In fact, in recent times, nanoparticles have been used in the synthesis of photonic crystals via the Langmuir-Blodgett method and other self-assembly structures. The last chapter of this book discusses the role of interfaces in integrated circuit manufacturing via photolithography. Photolithography is the only top-down preparation method of nanomaterials and nanostructured surfaces. In the past few years, it evolved into the most precise technique to prepare with large machines, structures as small as 7 nm (the gate of the field-effect transistor). In practice, the photolithographic manufacturing process of chips and processors requires in-depth knowledge and control of interfacial phenomena such as adhesion, wetting, capillary forces, and interfaces.

Reference [1] G. Kaptay, G. Csicsovszki, M.S. Yaghmaee, An absolute scale for the cohesion energy of pure metals, Mater. Sci. Forum. 414–415 (2003) 235–240. https://doi.org/10.4028/www.scientific.net/MSF.414-415.235.

C H A P T E R

2 Thermal energy scale kT At the nanoscale, the interaction energies are generally expressed in multiples of kT, also referred to as the thermal energy scale. The average kinetic energy of a gas atom with three degrees of freedom is 3/2 kT, is roughly the energy of thermal fluctuations at a given temperature
1 kT. The thermal energy has a randomizing effect contributing to an increase in the entropy of the thermodynamic system. By expressing the energy of intermolecular interactions or nanoparticle interactions as multiples of kT, the interaction strength can be compared with the randomizing effect of temperature. Next, it is instructive to follow the kT in several different contexts as well as its origin. A thermodynamic system will tend to move toward a lower energy state when available. When applied to chemical systems, for example, a solute in a solution or a gas has a chemical potential defined as the rate of change of the Gibbs free energy with the number of species in the system, at constant temperature and pressure:
 δG (2.1) μi ¼ δNi T, P Therefore, the change in chemical potential of a gas or a solute in a solution changes with the change in concentration. Chemical potentials are important in describing the equilibrium in physicochemical processes such as evaporation, melting, boiling, solubility, interfacial adsorption, liquid-liquid extraction, etc. The reason why the chemical potentials are so important in the equilibrium chemistry is that when the two chemical systems are open and can exchange molecules or atoms, the rate of change of their free energy would be equal when equilibrium is established. Take, for example, the molecules in the vapor and the liquid phase at equilibrium; by equating the chemical potentials of the molecule of type i in two phases at equilibrium, or two regions 1 and 2, we obtain μ1i + kT ln Xi1 ¼ μ2i + kT ln Xi2

(2.2)

At equilibrium between n different phases, the above equality must be satisfied for all phases: μni + kT ln Xin ¼ constant

(2.3)

Xni

is the molecular fraction, volume fraction, or concentration of solute in phase n. For pure solution, this is where usually taken as unity. The factor k ln X is known under different names, such as the entropy of mixing, configuration entropy, entropy of confining the molecules, etc. Eq. (2.2) gives us the possibility to calculate the distribution of molecules between two phases, or two regions of space at equilibrium, for example, a liquid in equilibrium with its vapors, or the distribution of the molecules of gas in the atmosphere due to changes in the gravitational potential with altitude. For example, the number density ρz of the molecules of gas in the Earth’s atmosphere changes with the altitude z and the mathematical function that gives us the possibility to predict this change is μzi + kT ln ρzi ¼ μ0i + kT ln ρ0i

(2.4)

where ρzi is the number density of molecule i at altitude z and ρ0i is the number density of molecules of gas i at the surface of the Earth z ¼ 0. Rearranging the above formula gives us the barometric formula or barometric law that gives the density at the altitude z as a function of the number density of air molecules at the sea level ρ0i :

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00015-6

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2. Thermal energy scale kT

ρzi

¼ ρ0i exp



 z  μi  μ0i ðmgzÞ 0 ¼ ρi exp kT kT

(2.5)

where m is the molecular mass and g is the gravitational acceleration. Note that the potential energy of the air molecules mgz is “compared” to the kT at any height above the Earth’s surface. With the increase in the potential energy of the molecules compared to kT, less molecules are found at higher altitudes (Fig. 2.1). In other words, if mgz is small compared to kT, then the thermal energy would uniformize the distribution of molecules with the altitude such that little variation in the number density of air molecules would be registered. The same distribution applies to ions that, for example, carry a charge e between two different regions that have different potentials ψ 1 and ψ 2:
 eðψ 2  ψ 1 Þ (2.6) ρ2i ¼ ρ1i exp kT and this is known as the Nernst equation. It is nonetheless important to note that interactions are additive; for example, if the difference in energy between two regions is given by potential, potential energy, and chemical potential, then the exponent will be the sum of all these contributions. The above equations also give us the possibility to gauge the strength of interaction between molecules. For example, if a liquid is in equilibrium with its vapors at standard conditions of pressure 1 atm and temperature 298 K, then 1 mol of gas will occupy approximately 22.4 m3 and a mole of liquid approximately 0.02 m3. Then the difference in energy between the liquid and gas states will be [1]: 0 gas

μi

gas

0 liquid

 μi


kT ln

Xi

liq Xi


kT ln

22:4
7kT 0:02

(2.7)

where 1 kT is approximately the energy of the thermal fluctuations. Therefore, it can be said that if the interaction strength between molecules in a gas phase at temperature T is larger than 7 kT, then it condenses into liquid. Conversely, if the cohesion strength between the molecules of a liquid become smaller than 7 kT, then it transforms into gas as the cohesion energy is simply too low to hold the molecules together. This alludes to what is known as the Trouton rule, which states that the entropy of vaporization is roughly the same for different kinds of liquids, about 85 J K1 mol1, which is roughly 9.5 kT.

FIG. 2.1

The bottle was capped (left) in the mountain and brought to the ground level (right).

2. Thermal energy scale kT

FIG. 2.2

7

Various interaction energies on the kT scale.

The kT criterion can be generalized to gauge the interaction strength between molecules; as stated above, if the interaction between molecules in a medium is larger than 9.5 kT at a given temperature, then this interaction will dominate over the thermal fluctuations and form a condensed phase, due to aggregation, adsorption, or self-assembly. For interaction energies, the use of the kT energy scale is convenient, as 1 kT equals the thermally induced 3D Brownian motion energy of a molecule (surfactant, or solute, or particle), which provides a reference value of interaction energies for molecules sticking together vs fly apart, binding vs unbinding, etc. (Fig. 2.2). Fig. 2.2 provides a variety of interaction energies represented on the kT energy scale. Similarly, the kT factor is also met in kinetics. For example, the Arrhenius equation per molecule is Ea

k ¼ Ae kT

(2.8)

where Ea is the activation energy barrier and k is the rate constant of the reaction. If, for example, Ea is much larger than kT, then the reaction rate is also very small. On the other hand, if the energy barrier is comparable to kT, then the reaction rate is high, and the reaction can be activated by the thermal energy. The kT factor is also encountered in the Boltzmann distribution, which is a probability distribution that gives the probability of a state to exist function of the state’s energy and temperature and it is given by
 Ei exp  kT (2.9) P¼ n
 X Ej exp  kT j where P is the probability of state i, of the energy Ei, and n is the total number of accessible states of corresponding energies Ej (j¼1 n). The Boltzmann distribution describes the distribution of particles, such as atoms or molecules, over all accessible energy states. In a system consisting of many particles, the probability of picking a random particle with the energy Ei is equal to the number of particles in state i divided by the total number of particles in the system, that is, the fraction of particles occupying the state i:
 Ei exp  Ni kT (2.10) ¼ n Pi ¼
 Ntotal X Ej exp  kT j

8

2. Thermal energy scale kT

The denominator in the above equation is the partition function 1/Z: 1 ¼ n Z X j

1
 Ej exp  kT

Reference [1] J. Israelachvili, Intermolecular and Surface Forces, third ed., Academic Press, San Diego, CA, 2011.

(2.11)

C H A P T E R

3 Surfaces and interfaces An interface is the boundary between two immiscible phases in contact, such as liquid-liquid, liquid-solid, liquidair, etc. Immiscibility arises when the constituent molecules interact stronger with the molecules from the same phase than with the molecules from the other phase, i.e., the “cohesion forces” are stronger than the “adhesion forces.” The force of cohesion is defined as the sum of the forces that act between the molecules of the superficial layer and the bulk, while the forces of adhesion are defined as the forces that act between the superficial layer and the molecules of the next phase. The interface is characterized by a certain thickness, which is intuitively taken as the thickness of the last layer of molecules at the surface of the phase that enter in “contact” or “feel” the influence of the molecules in the other phase. It has been the subject of intense research where exactly lies the borderlines defining the interface between two phases in contact. This can be simplistically defined as two monolayers thick, one monolayer at the interface belonging to one phase and the other monolayer to the next phase (Fig. 3.1). This is probably the most satisfactory way to intuitively understand the interface thickness. However, this not very rigorous, because the molecules from subsequent layers also feel the presence of molecules from the other phase via “longer ranged” forces that operate and whose intensity decays with the distance from the interface. Michael C. Petty stated that “if the molecules are electrically neutral, then the forces between them will be short-range and the surfaces layer will be no more than one or two molecular diameters; in contrast, the Coulombic forces associated with the charged species can extend the transition region over considerable distances” [1]. The experimental studies of the neat liquid-liquid interfacial thickness revealed that the hexadecane-water thickness is about
6 Å by X-ray reflectivity and
15 Å by neutron reflectivity [2]. The apparent discrepancy comes from the limitation of the both methods which include two contributions, namely the intrinsic width of the interface “that characterizes the crossover from one bulk composition to the other and a statistical width due to thermally induced capillary wave fluctuations (ripples) of the interface” [2]. This also reflects the difficulty of the experimental methods to probe the interfaces at molecular length scales. The X-ray reflectivity studies of the thickness of the mercury-water interface was
5 Å, which is comparable to that of mercury-vapor interface of
5 Å and that of pure water-vapor interface
3 Å [3]. These and other studies have revealed that the liquid-liquid and liquid-vapor interfaces are at least two monolayers of molecules or atoms. Recently, combined surface vibrational spectroscopy and molecular dynamics revealed an even more complex aspect of interfaces; in addition to interfacial thickness variation, molecular structuring by ordering and layering of molecules near interface were observed [4]. The characteristic molecular vibrations were probed at the waterchloroform and water-dichloromethane interfaces as a function of interfacial depth. From the concentration profiles of both water and organic solvent molecules it was observed that both the dichloromethane and water extended deeper into the opposite phase forming a thicker interface, while the water-chloroform interface was sharper. Near the water-chloroform interface water monomers were detected, not associated via H-bonds and the concentration profile of chloroform deeper into the bulk organic phase is oscillatory suggesting the CCl4 molecules are layered near the interface, not observed for dichloromethane. Numerous examples of ordering and structuring of molecules near the interface were reported, as well as the consequences, for example, surface freezing of the top molecular layer of alkane at alkane-vapor interface is 2–3°C higher than the freezing temperature, while this was not observed at an alkane-water interface, which suggests an increased ordering of alkane molecules in the former case [2].

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00009-0

9

Copyright © 2021 Elsevier Inc. All rights reserved.

10

3. Surfaces and interfaces

Molecular modeling also helped in gaining insight into the interfacial boundaries. It was found that the waterhexane interface is very sharp and is about two monolayers thick [5]; the water molecules near the hydrophobic interface are oriented such that the molecular plane and the dipole moment are parallel to the plane of the interface and the long axis of the hexane molecules is also parallel to the interface [5, 6]. In addition, some of the water molecules at the hydrophobic interfaces are incapable of hydrogen bonding, about one in four molecules exhibit dangling hydrogen bonds, which gives rise to a large interfacial energy [7]. On the other hand, water molecules near strongly polar interfaces such as quartz are capable of hydrogen bonding and are oriented in an ice-like structure and no dangling bonds were observed in surface vibrational studies with vibrational sum-frequency spectroscopy [7]. The consequence of the molecular orientational ordering, layering, reduced capability of molecular bonding, and interfacial mixing lead to a change in the solvent properties near the interface. For example, second-harmonic generation in combination with solvatochromic surfactants of different lengths known as “molecular rulers” were able to probe solvent polarity with depth near the weakly and strongly associating water-organic solvent interfaces. For example, the solvent polarity near the weakly associating water-cyclohexane interface quickly converges from the aqueous to the organic limit in less than 9 Å, while the strongly associating water-1-octanol interface revealed a transition region of ordered octanol molecules at the interface giving rise to a hydrophobic barrier [8]. The chemical structure and the molecular dimensions greatly affect the thickness of the interface. Further systematic studies performed with “molecular rulers” revealed that at the water-organic solvent interfaces the interface thickness and polarity strongly depend on the molecular structure [9, 10]. The conclusion that can be drawn from experimental evidence is that the interface can be visualized as a sheet or as a thin “membrane” with certain thickness. The thickness of the interface depends on the ability of the phases to interact given by the balance between the adhesion and cohesion forces. For weakly interacting phases the interface thickness is nearly two monolayers thick (Fig. 3.1A), while for strongly interacting phases the interface will be thicker than two molecular monolayers (Fig. 3.1B). In addition, the polarity gradient across the interface can change due to molecular ordering at the interface, which propagates to a certain depth in bulk, depicted as a color gradient in Fig. 3.1B. The membrane separating two immiscible phases has therefore boundaries and is an open thermodynamic system because it can exchange matter and energy with the neighboring phases. Molecules move continuously to and from interface to bulk. A thermodynamic system is everything that has boundaries, an object constitutes a thermodynamic system, be that a car, a grain of salt, or an interface, and all possess a certain internal energy, U. The energy of the interface between the phases, also most commonly referred to as “interfacial energy,” is highest when the cohesion energy is much larger than the adhesion energy. Interfacial energy decreases to negligible values when the adhesion forces become comparable to cohesion forces and the phases begin to mix. Water-hexane interface is an example of a high interfacial energy interface while water-ethanol interface has a zero interfacial energy, i.e., completely miscible. FIG. 3.1 (A) The ideal sharp interface between two weakly interacting phases α and β can be imagined as a thin membrane, two monolayers thick with a sharp molecular density profile that separates two phases. (B) The thicker interface between two phases that are strongly interacting with diffuse density profile, thicker than two monolayers. The oscillation in the β phase indicate ordering. The solvent polarity near this interface changes due to ordering and loss or gain in bonding capability.

3.1 Surface tension of liquids

11

The molecules at the interface have energy higher than those in the bulk because they are not symmetrically surrounded by other “alike” molecules in a perfectly balanced sphere. This imbalance of attraction forces and suppression in the ability of the molecules to bond lead to more energetic molecules at the interface.

3.1 Surface tension of liquids In the bulk, a molecule or an atom can be surrounded by a maximum 12 neighboring molecules (6 in the same plane and 3 on each side of the neighboring planes) and experience a symmetric attraction from all sides in the 3D space. On the other hand, at the surface of a liquid the molecules are about only half-way surrounded by molecules, thus experience an asymmetric attraction toward the bulk of the liquid (see Fig. 3.2A). The forces of cohesion act asymmetrically on the interfacial layer and the topmost layers of molecules of a phase are compressed (Fig. 3.2B). In addition to the cohesion forces that act perpendicularly on the surface plane, the surface tension forces act in the plane of the surface and oppose any action to increase the surface area. Surface tension can be intuitively understood as a unit vector force. To visualize this, an imaginary line can be drawn, of length l, on the surface of the liquid; this imaginary line splits the row of two molecules (Fig. 3.3) If it were possible, by pulling apart the two rows of molecules on the surface of the liquid, a resisting tension force would arise because the molecules from each row attract each other generating a tension opposing the split (Fig. 3.3A). If the length of this dividing line is l, then the force with which the pair of molecules in the two rows attracts each other is. F¼γl

(3.1)

where γ is the unit tension force (N/m), i.e., the surface tension. Therefore, the surface tension γ is the unit force acting on the surface plane to minimize the surface area. To better understand the origin of the surface tension, we imagine a cross section through the surface of a liquid (Fig. 3.3). At equilibrium no net force is acting on this horizontal line (plane) of molecules. If it were possible, the pull of only one molecule out of this line (plane) would be countered by an opposing tension force trying to minimize the area of the surface layer. The unit surface tension forces act left and right on the molecule being pulled out of the line and the sum of these is the cohesion unit force (Fig. 3.3C). It costs energy to bring new molecules from the bulk to surface. When surface is expanded, more “bonds” from the bulk are “broken” as new molecules are brought to occupy the “holes” in the newly created surface, represented by the dotted circles in Fig. 3.3B. The energy of the molecules in bulk of the liquid with maximum of 12 neighbors is lower than the energy of the molecules at the surface with the maximum 6 neighbors. The energy required to bring a molecule from the bulk to increase the area of the surface is the energy of uncompensated bonds; at the surface, a molecule has about half of the neighbors of a molecule in the bulk, half of its “physical bonds” remain uncompensated (Fig. 3.3B). Therefore, the surface energy is only a fraction of the cohesion energy as explained later in more detail.

FIG. 3.2

(A) Molecular interactions in a liquid; (B) compression of the topmost surface layer of molecules due to the force of cohesion.

12

3. Surfaces and interfaces

FIG. 3.3

(A) Surface of a liquid on which an imaginary line of length l divides two parallel rows of molecules; when trying to pull sideways the two rows of molecules by applying a force F on each side, the surface tension forces oppose the distancing of molecules; the surface tension unit vectors are oriented perpendicular to the imaginary line. (B) Deformation of the liquid-gas interface by pulling only one molecule out of the surface; in this case two new empty “holes” (dotted circles) are created by the expansion of the liquid-gas interface. Two new molecules must be brought in from the bulk liquid to occupy the empty holes, depicted by the green curved arrows. The total energy of the interface will increase by an amount equal to the energy of uncompensated bonds of the new molecules occupying the holes. (C) Same situation as in (B) with the depiction of the opposing surface tension forces resisting the deformation. The vectorial sum of the surface tension vectors acting on the molecule being pulled out of the interface is the cohesion force acting on the molecule.

FIG. 3.4

Forces acting on a steel needle, with a hydrophobic surface, floating on the surface of water without penetration.

Numerical example 3.1 Draw the surface tension force vectors acting on a steel needle with a hydrophobic surface floating on the surface of water depicted in Fig. 3.4. The needle does not penetrate the surface. Calculate the maximum radius of a steel needle r, of length l ¼ 1 cm that can be held on the surface of the water without sinking. The density of steel is 8000 kg/m3, ρwater ¼ 1 kg/dm3, γ water ¼ 73 mN/m.

13

3.1 Surface tension of liquids

Solution When the steel needle does not penetrate the surface, it means that the water does not wet the surface of the needle, in which case the water contact angle with the surface of the needle is θ ¼ 180 degrees. In addition, the water surface will suffer a certain deformation such that the resultant of the forces acting at the three-phase line will be oriented vertically, against the pulling gravitational force acting on the needle. At equilibrium the surface tension force balances the gravitational force:

2Lγ L ¼ mg Therefore, R can be directly calculated:


R¼

2γ L πρg

1=2


;R¼

2  0:0728 π  8000  9:81

1=2 ¼ 0:77 mm:

Numerical example 3.2 A wooden stick of the length l floats on the surface of pure water. If we lower the surface tension of water by adding a droplet of soap on the right side of the stick, in which direction will the wooden stick move? Under the action of which force? Write down the equation for this force.

TABLE 3.1 Surface tension of several liquids and molten metals to compare the surface tension to the strength of intermolecular interactions. Liquid

Surface tension (mN/m)

Temperature (°C)

Neon

5.2

247

Oxygen

15.7

193

Ethyl alcohol

22.3

20

Olive oil

32.0

20

Water

58.9

100

66.2

60

72.8

20

75.6

0

Mercury

465

20

Silver

800

970

Gold

1000

1070

Copper

1100

1130

14

3. Surfaces and interfaces

The surface tension of various liquids changes with temperature. The magnitude of the surface tension reflects the strength of interaction forces between the composing molecules and atoms, i.e., the cohesion forces (Table 3.1). For neon the strength of the interaction forces between atoms are very weak and the surface tension reaches 5.2 mN/m at 247°C. The cohesion forces are comparatively stronger for oxygen molecules than for neon atoms. Metallic bonds between mercury atoms are considerably stronger than the van der Waals forces between neon atoms, therefore even at room temperature the surface tension value is comparatively large.

3.2 Predictive models for calculating the surface tension of liquids There were attempts to apply theoretical models to calculate the surface tension from the energy of cohesion or enthalpy of vaporization. For example, Stefan’s equation has been often used to do this [11]: 2 3 2 ZS 4ΔHvap ρ =3 5 (3.2) γL ¼ 1 2 Z = M =3 N A 3 where Δ Hvap is the enthalpy of vaporization of the liquid (kJ/mol) in standard conditions of pressure and temperature of 105 Pa and 273.15 K, respectively, M is the molecular weight (g/mol), NA is the Avogadro number, and ρ is the density of the liquid (g/cm3). ZZS is the ratio between the coordination number of molecules at the surface with respect to bulk; this cannot be determined directly by experiment but can be calculated [12]. The ratio of the coordination numbers for the compounds ranges from 0.0559 to 0.1784, whereas a value 0.25 for the ratio ZZS has been obtained for many organic substances [12].

Numerical example 3.3 Calculate the surface tension of water using Eq. (3.2) knowing that ΔHvap ¼ 41 kJ/mol, M ¼ 18 g/mol, ρ ¼ 1g/cm3, and ZZS ¼ 0:13 is the average value of all the determined values by Strechan et al. [12].

Solution 

41  104 γ water ¼ 0:13 6:86  8:44  107





1=3 ! KJ mol 2=3  g 2=3 mol mJ    ¼ 76 2 mol g m3 molecules m

(3.3)

The obtained value slightly overestimates the experimentally determined value of water surface tension 72.4 mJ/m2 at room temperature. Therefore, the correct calculation of ZZS is important for obtaining accurate values of the surface tension.

Significant effort has been dedicated to modeling the coordination number ratio ZZS . Another extendedly used empirical model, especially for determining the surface tension of molten metals, is called the bond-broken model or the bond-cutting model where the surface energy is calculated based on the energy of cohesion Ecohesion [13]: γL ¼

Z  ZS Ecohesion Z

(3.4)

3.3 Interfacial tension between liquids Surface tension is only a particularization of interfacial tension and it is used only when referring to liquid-gas (vapor) interface. Interfacial tension refers to liquid-liquid or solid-liquid interfaces, but because it is a more general concept than the surface tension it can be used throughout, also for liquid-gas interfaces. For liquid-liquid interfaces, the topmost layers of molecules from each phase are in contact (Fig. 3.5). In contrast to the liquid-gas case, the topmost layer at the liquid-liquid interface will now be under the action of two forces, forces of cohesion with the molecules from the bulk of the same phase and forces of adhesion with the molecules from the other phase. Consequently, the topmost layer of liquid is not as strongly compressed as at the liquid-gas interface. The stronger the forces of adhesion, the stronger the attraction of the topmost layer to the second liquid phase.

15

3.3 Interfacial tension between liquids

FIG. 3.5

Balance of the forces of cohesion with the force of adhesion at the liquid-liquid interfaces.

FIG. 3.6 (A) The surface tension vectors corresponding to liquid 1 and liquid 2 oppose the deformation of the liquid 1-liquid 2 interface. Interfacial tension vector is depicted here as the sum of the surface tension vectors of the pure liquids, but does not sufficiently describe the real situation. (B) The force needed to deform or expand the interface is lower because the opposing force due to the surface tension is now minimized by the adhesion forces with the molecules in the second phase. In other words, to promote a molecule from bulk to interface it costs much less energy at the liquid-liquid interface because the intermolecular bonds in bulk are now partially compensated at the liquid-liquid interface by the adhesion bonds with the molecules from the surface of the second phase. (C) The balance of forces at equilibrium, the surface tension force is compensated by the adhesion force.

Opposing deformation of the interface between two liquids, as depicted in Fig. 3.6A, is the interfacial tension unit vector γ 12. It can be imagined that γ 12 is exactly the sum of the surface tensions of the two liquids, γ 1 and γ2. In fact, the force of adhesion between the two liquids makes γ12 smaller than the sum of the surface tension corresponding to each liquid. It costs less energy to bring a molecule from the bulk to the liquid-liquid interface than to the liquid-gas interface. This is because breaking of the “bonds” of cohesion of the bulk molecules to come at the interface will be partially compensated by the adhesion “bonds.” Therefore, γ12 is the sum of two surface tension minus twice the force of adhesion (Fig. 3.6B and C): γ 12 ¼ γ 1 + γ 2  2Fa

(3.5)

16

3. Surfaces and interfaces

FIG. 3.7 (A) U-shaped wire frame holding a thin liquid film membrane which has a mobile side of length l that can slide under the action of an external force; (B) the cross section of the liquid membrane film having two surface tension forces, corresponding to each interface of the liquid membrane, opposing the expansion of the surface area under the action of the pulling force F.

Two extreme situations can be distinguished, if Fa is very high and comparable to the cohesion forces, then γ 12 ! 0 and the two liquids can easily mix and will not form an interface. If, however, the molecules between the two phases are incapable of “bonding” or Fa is extremely low, then γ12 ! γ 1 + γ 2, consequently it is more difficult to expand or deform this interface.

3.4 Relating surface tension to surface energy The surface tension is a force per unit length. However, the surface tension can also be related to energy per surface area, or energy density. Consider a wire frame with one mobile side, which can slide on the U-shaped frame without friction (Fig. 3.7). The mobile side has a length l. On this frame we have a membrane of water, a thin film. If we try to pull the mobile side to increase the area of the membrane by Δx, then the work done will be W ¼ F  Δx

(3.6)

but F is 2γl, the factor 2 comes from the fact that there are two sides of the surface. Therefore, surface tension is also the energy per unit area: γ¼

W Energy  ≡ J=m2 2l  Δx Area

(3.7)

The surface tension can thus be redefined as the energy required to increase the surface area with one unit.

3.5 Surface and interfacial energy of solids Surface and interfacial tensions have units of force per unit length N/m or energy per unit area J/m2 and the two forms are perfectly equivalent. For the solid-gas interfaces instead of interfacial tension one uses the concept of “surface energy.” Similarly, for the solid-liquid interfaces “interfacial energy” is used instead of “interfacial tension.” The surface energy of solids arises because of all unsaturated or dangling bonds per unit area of surface of a solid. Surfaces of metals, for example, have high energy associated with them because the atoms in the first surface layer have fewer of neighbors than in bulk and therefore unsatisfied capacity to metallic bonding. The cohesive energy of metals is given by the enthalpy of atomization ΔHa (equivalent to its bond strength), which is 418 kJ/mol for Fe, 844 kJ/mol for W, 368 kJ/mol for Au, and 327 kJ/mol for Al [14]. A great amount of work is needed to form and shape metals of high cohesive energy. The surface energy is taken as a fraction of the cohesion energy, γ ¼ f  cohesion energy, 0 < f < 1. In calculations of the surface energy from energy of cohesion, f could arbitrarily be chosen as 0.5 (see Fig. 3.3). There are roughly 1.6  1019 atoms/m2 on the surface of an Fe and the surface energy can be estimated from the cohesion energy:
 kJ atoms mJ  1:6  1019  5535 2 (3.8) SE  0:5  418 m2 m 6  1023 atoms The surface density of metal atoms Nd was calculated from the density of the metal: Fe (ρ ¼ 7850 kg/m3, Nd ¼ 1.6  1019), W (ρ ¼ 19,600 kg/m3, Nd ¼ 1.32  1019), Au (ρ ¼ 19,320 kg/m3, Nd ¼ 1.25  1019), and Al (ρ ¼ 2712 kg/m3,

3.5 Surface and interfacial energy of solids

17

Nd ¼ 1.27  1019). The calculated surface energy using the above equation is 5535 mJ/m2 for Fe, 9294 mJ/m2 for W, 3833 mJ/m2 for Au, and 3462 mJ/m2 for Al. These calculated values give the expected trend but the magnitude differs significantly from the experimental and calculated values of the surface energies of the corresponding metals, listed in Tables 3.3 and 3.4. The source of this difference is found in the value of the factor f used in the calculations of the above formula, under the initial assumption that the surface energy is about half of the cohesion energy. This factor plays a similar role with the coordination number seen in Stefan’s Eq. (3.2). If value of the factor is taken as 0.16 instead of 0.5, which is close to that used for calculating the surface tension of water, see Eq. (3.3), the recalculated value for the surface energy of metals is 1772 for Fe, 2974 mJ/m2 for W, 1226 mJ/m2 for Au, and 1108 mJ/m2 for Al, which are very close in magnitude to the experimental data and those calculated by more advance models, Tables 3.3 and 3.4 [22]. This shows that the magnitude of the surface energy originates in the cohesion energy of the condensed phase. It is, however, difficult to predict a priori the value of the factor f used in such calculations, it can be done empirically just as in the case of the coordination number of Stefan’s equation or the use of more complex theories could provide a deeper explanation and a method for calculating such factors from fundamentals. Unlike liquids where the action of surface tension force is visible, especially in small droplets that acquire spherical shape under its action, in the case of solids the action of surface energy has no visible mechanical action. For example, if a solid is cut into smaller pieces then they will not suddenly change their shape due to the action of surface tensions. However, the action of surface energy/tension becomes visible if the solid can be melted at high temperatures. For example, a molten metal, when in liquid state at high temperatures above the melting point, behaves just as any liquid, will occupy the smallest volume so it will squeeze in spherical droplets, upon cooling the metal is shaped, formed, extruded, or pulled, so its surface remains “frozen” in a metastable state, therefore its surface possesses a high energy. A metastable state is a state in which a system can spend an extended time in a configuration other than the system’s state of least energy. Surface energy of materials is of great technological importance, as, for example, in material fatigue and stress analysis. The cracks in materials can propagate and produce failures, whose detection is critical in aircraft construction and safe operation. The crack produces in a material to relax the elastic stress in the vicinity of the crack. The crack equilibrium length depends on the balance of forces between the elastic stress and increase in the surface energy of the material. Yet another area in which knowledge of the surface energy plays an important role is the wettability of “reservoir rocks” for the oil extraction and recovery. The natural oil reservoirs were usually classified as oil-wet, water-wet, or intermediate based on the affinity of the rock’s surface to oil or toward water. Wettability of the rock to water affects the reservoir production and the performance of enhanced oil recovery processes [23]. Another relevant field is that of sealants and adhesives. For optimum adhesion, an adhesive must completely wet and cover out the surface to be bonded. Wetting is necessary for an adhesive to cover a surface to maximize the contact area and the attractive forces between the adhesive and bonding surface. For a good performance, the surface energy of the adhesive must be substantially lower than the surface energy of the substrate to be bonded, as, for example, regular adhesives bond very poorly on the low surface energy Teflon, or polyethylene but bond very well on higher surface energy glass or metal surfaces. This is on the other hand also the principles behind nonstick coatings of the pans, such as Teflon. Surface energy of several polymer surfaces is presented in Table 3.2. To improve the adhesion of paints and coatings the surface must be thoroughly washed and degreased. Grease and wax have a low surface energy material and prevent a good adhesion when present on surfaces. To improve adhesion on low energy surface, different methods can be applied, which include plasma treatment, UV-light exposure, chemical oxidation with piranha solution, etc. Exposure of a surface to UV light will generate ozone and singlet oxygen that oxidizes the surface. It has been proposed that UV-generated ozone or singlet oxygen will insert in the CdH bonds of a hydrocarbon surface and create polar functional groups such as dCOOH, dCO, dCOH, etc. For example, polyethylene (PE) surface energy is roughly
31 mN/m, and increases after the treatment with various methods: after exposure to UV
33 mN/m, after flame treatment
39 mN/m, and after etching with chromic acid
40 mN/m [24]. On the other hand, surface treatment for lowering the surface energy is also possible by surface modification with hydrophobic compounds. For example, a very popular hydrophobizing agent used often to lower the surface energy of glass, or silicon wafers in semiconductor manufacturing technology is the 1,1,1,3,3,3-hexamethyldisilazane (HMDS); upon reaction with the fused silica or silicone surface and HMDS the surface is fully covered by a monolayer of hydrophobic trimethylsilyl groups (TMS-FS). The TMS-FS monolayer can be degraded by exposure to UV light to fine-tune the surface hydrophobicity. The photodegradation kinetics of the TMS-FS was characterized by measuring the water contact angle as function of UV irradiation time (Fig. 3.8) [25]. Most of the experimental data of surface energies of metals come from surface tension measurements in molten state extrapolated to zero temperature [26]. The surface energy of metals can also be computed from the first principles. Computational and experimental work have also shown that the surface energy of metals depends on the orientation

18 TABLE 3.2

3. Surfaces and interfaces

Solid surface energy data (SFE) for common polymers.

Name

CAS Ref.No.

Surface energy at 20°C (mJ/m2)

Dispersive component (mJ/m2)

Polar component (mJ/m22)

Polystyrene PS

9003-53-6

40.7

34.5

6.1

Polytrifluoroethylene P3FEt/PTrFE

24980-67-4

23.9

19.8

4.1

Polytetrafluoroethylene PTFE

9002-84-0

20

18.4

1.6

(Teflon)

24980-67-4

23.9

19.8

4.1

Polyvinylchloride PVC

9002-86-2 9002-85-1

41.5 45

39.5 40.5

2 4.5

Polyvinylacetate PVA

9003-20-7 25087-26-7

36.5 41

25.1 29.7

11.4 10.3

Polymethylacrylate (polymethacrylic acid) PMAA

9002-86-2 9002-85-1

41.5 45

39.5 40.5

2 4.5

Polyethylacrylate PEA

9003-32-1 87210-32-0

37 41.1

30.7 29.6

6.3 11.5

Polyethylmethacrylate PEMA

9003-42-3

35.9

26.9

9

Polybutylmethacrylate PBMA

25608-33-7

31.2

26.2

5

Polyisobutylmethacrylate PIBMA

9011-15-8

30.9

26.6

4.3

Poly(t-butylmethacrylate) PtBMA

–

30.4

26.7

3.7

Polyhexylmethacrylate PHMA

25087-17-6

30

27

3

Polyethyleneoxide PEO

25322-68-3

42.9

30.9

12

Polyethyleneterephthalate PET

25038-59-9

44.6

35.6

9

Polyamide-6,6 PA-66

32131-17-2

46.5

32.5

14

Polyamide-12 PA-12

24937-16-4

40.7

35.9

4.9

Polydimethylsiloxane PDMS

9016-00-6

19.8

19

0.8

Polycarbonate PC

24936-68-3

34.2

27.7

6.5

Polyetheretherketone PEEK

31694-16-13

42.1

36.2

5.9

Polymethylmethacrylate PMMA

Data from Solid surface energy data (SFE) for common polymers, (n.d.). http://www.surface-tension.de/solid-surface-energy.htm (Accessed 18 September 2019).

FIG. 3.8 Water contact angle of hydrophobized glass surface with hexamethyldisilazane (HMDS) after exposure to the UV light for different periods of time. From A. Honciuc, D.J. Baptiste, D.K. Schwartz, Hydrophobic interaction microscopy: mapping the solid/liquid interface using amphiphilic probe molecules, Langmuir. 25 (2009) 4339–4342. Copyright 2009 American Chemical Society.

19

3.5 Surface and interfacial energy of solids

TABLE 3.3 Surface energies (SE) of some 3d transitional metals calculated by the full charge density (FCD) method in generalized gradient approximation (GGA). Metal

Surface plane

SE-FCD (J/m2)

SE-experiment (J/m2)

Li

(110) (100) (111)

0.556 0.522 0.590

0.522

Fe

(110) (100) (111)

2.430 2.222 2.733

2.417

Al

(111) (100) (110)

1.199 1.347 1.271

1.143

Ni

(111) (100) (110)

2.011 2.426 2.368

2.380

Cu

(111) (100) (110)

1.952 2.166 2.237

1.790

Au

(111) (100) (110)

1.283 1.627 1.700

1.500

W

(110) (100) (111)

4.0 4.635 4.452

3.265

For comparison the experimental data are included. Adapted from L. Vitos, A.V. Ruban, H.L. Skriver, J. Kollar, The surface energy of metals, Surf. Sci. 411 (1998) 186–202.

of the surface facets, see Table 3.3. For a polycrystalline metal surface, it can be expected that its surface energy is somewhat an average of these. Depending on the material type, the type of interactions between the constituting atoms or molecules in the material and the surface energy varies wildly, as highlighted in Table 3.4. As already mentioned, the materials with strong cohesion have a high surface energy, which is a fraction of the energy of cohesion. This is also the basis for the calculation of surface energies directly from the number of uncompensated or broken bonds, the “broken bonds” concept [19, 20]. Rough tendencies for surface energies of solids can be sketched: polymers 0, the contour of the droplet where all three phases, liquid, solid, and gas meet is called “three-phase” line. The forces acting at this three-phase line are illustrated in Fig. 3.11 and correspond to all the interfacial tension vectors: γ SG, γ SL, and γ LG. The orientation of these vectors is such that they minimize the interfacial area they represent. By convention the interface is indicated by capital letters in the subscript and the denser phase is mentioned first. In addition, the letter “G” in the subscript indicating the solid-gas interface or liquid-gas interface can be dropped, e.g., γ S and γ L. Based on the representation in the cartoon one can predict if the droplet will spread on the surface function of the relative magnitude of each interfacial tension vectors. It is intuitively clear that if the γ SG vector is very large in comparison to γ SL then the surface will be wetted by the liquids because, γ SG is pulling stronger on the three-phase line. The forces acting against γ SG are γ SL and the projection of the γ LG vector on the horizontal axis. On the other hand, if the force of the adhesion Fa between liquid and solid is very large then γ SL will be extremely small, according to Eq. (3.5), and the expansion of the liquid droplet takes place and surface is fully wetted. Oppositely, if Fa is rather very small then γ SL > γ SG, compression or de-wetting of the surface will take place. The three interfacial tension vectors acting at the three-phase line are related through Young’s equation: γSG ¼ γSL + γLG cos θ

(3.10)

The above equation was first described in words by the American scientist Young and later put in this form by Bangham and Razouk [31]. The vertical components due to vertical projection of the γ SL sin θ vector cancels out with the surface strain vector created in the solid under the three-phase line, for an interesting discussion of this aspect consult the critical review by Good [32]. It is important to note that Eq. (3.10) is only valid for the “dry” wetting, which is the ideal case of a wetting liquid with zero vapor pressure. However, this situation is not realistic, and in most cases, the wetting liquid will evaporate ahead of the three-phase line creating a situation of “wet” wetting, due to adsorption of a

3.7 Scaling effects: When surface tension dominates gravity

23

monolayer or submonolayer of molecules on the solid substrate ahead of the three-phase line. But the “wet” wetting can be also caused by other factors, for example, by the humidity in the atmosphere or adsorption of other volatile components in the environment on the surface of the solid, effectively lowering the surface energy of the solid and even that of the liquid. In normal atmospheric conditions, we deal with the “wet” wetting situation. In Young’s equation, we have used the interfacial tension of the pure solid and the liquid with the gas. Thus in order to account for the case of the liquid evaporation ahead of the three-phase line, or adsorption from atmosphere, the “effective” surface energy of the solid and surface tension of the liquid can be related to the energy and tension of the pure solid and liquid in “vacuum,” γ S and γ L by the following relations first proposed by Bangham and Razouk [31]: γ S  γ SG ≡ π eSG

(3.11)

γ L  γ LG ≡ π eLG

(3.12)

where the pressures π eSG and π eLG are the equilibrium film pressures of the adsorbate, which is a monolayer or less, whose contact angle on the surface is zero. π eLG is analog to the surface pressure in the Langmuir-Blodgett monolayer, discussed in the later chapters. Including the above corrections, Young’s equation becomes γ S  π eSG ¼ γ SL + ðγ L  π eLG Þ cos θ

(3.13)

3.7 Scaling effects: When surface tension dominates gravity At the surface of the Earth, the gravity deforms the liquid droplets when their diameters exceed a certain threshold value lc. This value is called the capillary length, which depends on the nature of the liquid and the gravitational constant. P¼

G mg ρ  V  g ρ  l3c  g ¼ ¼
¼ ρ  lc  g A A A l2c

(3.14)

Very often we can visualize water droplets smaller than 1 mm in diameter that have perfectly round shape, when sitting, for example, on a leaf of a plant. The bigger droplets are deformed and flattened by the gravitation. The reason the spherical droplets can be seen when the water droplets are small is that below a certain size the surface tension dominates gravity (Fig. 3.12). The capillary length below which surface tension dominates gravity can be calculated, from the balance of surface tension and gravitational forces acting on a liquid droplet. The Laplace pressure acts to keep the liquid droplet spherical: γ (3.15) P¼ lc When the two pressures are balanced: γ ¼ ρ  lc  g lc rffiffiffiffiffiffiffiffiffiffi γ lc ¼ ρg

(3.16)

where lc is known as the capillary length or capillary constant.

3.7.1 Case study: How surface tension of liquids affects life at small scale and in outer space? The capillary length scale is the crossover point between the hydrostatic pressure and the Laplace pressure, below which the surface tension dominates the gravity, depicted in Fig. 3.13. In addition, the change in the capillary length on Earth (g ¼ 9.81 m/s2) and on Mars (g ¼ 3.7207 m/s2) is significant so if there were water and vegetation on Mars the landscape would look different, pearls of water on the plant leaves will be twice as large as on the Earth surface (Fig. 3.12), ensuring an more unusual landscape. On the other hand, on Jupiter (g ¼ 25.85 m/s2), where the gravitation is significantly stronger than on Earth, the droplet of liquid would probably be less visible with the eye. Interestingly, the size of the water droplets seems to be significantly larger than a few centimeters and appear to be floating in imponderability on the international space station (ISS) which orbits only around 450 km away from the

24

3. Surfaces and interfaces

FIG. 3.12

(Top) Water droplets on a leaf of a plant. (Bottom) Water droplets on a plant leaf with different sizes. The larger droplets are deformed by the gravitation, while the smaller droplets remain spherical.

FIG. 3.13

The crossover point between the Laplace pressure of a liquid and the hydrostatic pressure as a function of the characteristic scale on the surface of Jupiter, Earth, International space station (ISS), and Mars.

Earth’s surface and the gravitational acceleration is still about 90% of the value from the Earth (g ¼ 8.6 m/s2). For this value of the gravitational acceleration the capillary length is only slightly larger than that on the Earth. By the size of the water droplet generated one would have expected that the capillary length is much larger. However, the reason for observing such centimeter large water droplet is that the ISS and all the objects in it orbit the Earth and experience a free fall which creates the imponderability. In fact, the large water droplets generated are due to this imponderability and free fall (Fig. 3.14).

25

3.8 Capillary rise

FIG. 3.14 NASA astronaut watches a water bubble float on the International Space Station (ISS). From NASA astronaut Chris Cassidy, Expedition 36 flight engineer, watches a water bubble float freely between him and the camera, showing his image refracted, in the Unity node of the International Space Station., NASA Image Video Libr. (2013). https://images. nasa.gov/details-iss036e018302.html (Accessed 18 September 2019).

Small creatures, such as insects, comparable in size to the capillary length have learned to adapt and smartly use the surface tension of water for locomotion or to acquire special abilities such as ability to collect water in desert or dive in and breathe under water. Due to the surface tension dominating the gravity below the capillary length, the small creatures can manipulate liquid or air droplets similarly to the way we manipulate solid objects. For example, ants and similar size insects can carry water droplets as we carry cups or balloons filled with water. Some aquatic insects such as diving beetles can carry bubbles of air with them when diving into water, this air bubble is held in place by special hairs that are attached to the body; the role of the attached air bubble is to provide the insect with oxygen for breathing in this way without the need for gills [33, 34]. Some insects have more advanced adaptations called “plastron” that aids breathing, which is a special array of grids that create an air cushion around the body [34]; when the insect breathes it consumes the oxygen from the air cushion which lowers the partial pressure of oxygen which is then replenished by the dissolved oxygen from the surrounding water [33]. Their life on other habitable planets of the size of Jupiter or Mars would require new adaptation due to this critical capillary length. Water striders, insects living on the surface of the water, use surface tension for locomotion. They can move very quickly on the surface of water and do not get wet due to the hydrophobic hairs covering their entire legs and body surface; the insects’ weight is supported by the surface tension force and they propel themselves by moving their legs in a sculling motion [35]. Recent studies of the biomechanics of water surface locomotion [36] revealed that the propulsion mechanism involves momentum transfer through surface-generated hemispherical vortices (drag) generated by their leg stroke on the water surface and not by capillary waves as initially believed [37]. The striking force of the water surface by the insects’ leg ranges between 0.1 and 2 mN/cm when walking and jumping and depends on the size and type of the insect [38, 39]. Other insects such as Microvelia use a different propulsion mechanism on the surface of the water, it uses the surface tension gradients for propulsion, the Marangoni effect, by releasing the surfactant-like body fluids [36]. For larger creatures, compared to capillary length with large Baudin number Ba ¼ Mg/γP ≫ 1, where M is mass, P is the wetted perimeter, like iguanas that are able to walk short distances on the surface of water to escape predators [36], the surface tension cannot keep them afloat, so to walk on the water surface they commonly use high driving power and speed to generate inertial forces [39]. Other creatures such as the “pistol shrimp” are able to hunt and communicate by releasing jet streams of bubbles that travel as fast as 6.5 m/s [40]. Plants have developed natural strategies for water repellency, and this will be mentioned throughout the current work, this constitutes a source of inspiration for creating new material surfaces through biomimetics [41].

3.8 Capillary rise Capillary rise phenomenon can be observed on immersing a glass capillary of radius r in a water container, water will rise in the capillary. Capillary action is the process used by plants to take water and minerals from the ground. Between water and the clean glass walls of the capillary there is strong adhesion. If the force of the adhesion Fa between liquid and solid is very large, then according to Eq. (3.5), γ SL will be extremely small, γ SL ≪ γ SG, and the liquid is pulled

26

3. Surfaces and interfaces

FIG. 3.15 (A) Before equilibrium, water rises in the capillary due to the interfacial tension forces acting at the three-phase line. When Fa is large, γ SL

will be small and γ SL ≪ γ SG. (B) At equilibrium, the surface tension of water opposes the gravitation. Note that the horizontal component of the surface tension force cancels out. Here R is the radius of the capillary.

up into the capillary under the action of γ SG (Fig. 3.15A). Therefore, the total force acting to raise the liquid in the capillary is the resultant of the surface tensions multiplied by the circular perimeter of the capillary: F ¼ 2πrðγ SG  γ SL Þ ¼ 2πrγ LG cos θ

(3.17)

The second relationship is Young’s equation and is valid at equilibrium. At the molecular level the expansion of the solid-liquid interface is driven by the adhesion of more water molecules to the walls of the capillary (Fig. 3.15A). The maximum height (h) at which the liquid rises in the capillary is achieved when the resultant of the interfacial forces are balanced by the weight of the liquid in the capillary (Fig. 3.15B): ρ  g  h  π  r2 ¼ γ  2π  r  cos θ

(3.18)

2  γ  cos θ h¼ rρg

(3.19)

Eq. (3.19) is also known as Jurin’s law. Eq. (3.19) can be deduced from the difference in pressure above (on the concave side) and below the meniscus (on the convex side). For the case when Fa is very small, according to Eq. (3.5), γ SL will be large, γ SL ≫ γ SG, and the liquid is pulled down from the capillary under the action of γ SL (Fig. 3.16A). Opposing the resultant of the surface tension forces 2πr(γ SG  γ SL) is the volume of water displaced (Fig. 3.16B). Liquid rise in fine capillaries is among others responsible for the water uptake by plants, wicking action of textiles, functioning of fountain pens, chromatography, and many other liquid and water transport phenomena.

3.9 Capillary number The capillary number is a dimensionless quantity that results from the balance between drag forces in a fluid that tend to deform a moving bubble or a droplet and the interfacial tension forces that oppose this deformation. Ca ¼

μV viscous drag forces ¼ γ surface tension forces

where μ is the dynamic viscosity of the fluid, V is the velocity of the fluid, and γ is the interfacial tension of the fluid. The capillary numbers should not be confused with the capillary length or constant, lc.

3.9 Capillary number

27

FIG. 3.16 The case when Fa ≪ Fc leading to an expansion of the surface area of the liquid due to the stronger cohesion forces, leading to the lowering the level of the liquid in the capillary due to the action of the surface tension.

3.9.1 Curved liquid surfaces, Laplace pressure, Young-Laplace equation If the interface dividing two phases is planar then the pressure experienced in each phase will be equal on both sides of the plane. Laplace pressure ΔP is the pressure difference that arises between two phases separated by a curved interface under the action of interfacial tension. The relationship between ΔP and γ is given by Young-Laplace equation that will be derived next in its simplest form. The curvature is defined as the deviation from planarity, 1/R, where R is the radius of the circle describing the bend. In a perfectly spherical soap bubble the pressure is greater inside the bubble because the surface tension acts at the surface of the soap bubble to decrease its surface area, thus compressing the gas inside. Similarly, the pressure is greater inside a gas bubble flowing in the sparkling water, or in an oil droplet in emulsion due to the action of surface tension. Therefore, the pressure is larger on the concave side of the interface (Fig. 3.17). To derive the Young-Laplace equation in its simplest form we consider a gas bubble at equilibrium in a liquid. The force acting from the interior of the bubble is Finterior ¼ Abubble Pinterior ¼ 4πR2sphere Pinterior

(3.20)

The force acting from the exterior of the bubble is Fexterior ¼ Abubble Pexterior + FIFT ¼ 4πR2sphere Pexterior + FIFT

FIG. 3.17

Depiction of concave and convex sides of a surface.

(3.21)

28

3. Surfaces and interfaces

The last term on the right-hand side of Eq. (3.21) is the force due to the surface tension and can be calculated, as described in Section 3.4, from the work needed to increase the area and the radius of the bubble by an infinitesimal amount, dR and dA: !
 dR2sphere dA ¼ 4πγ (3.22) FIFT ¼ γ ¼ 8πγRsphere dR dR The balance of forces is 4πR2sphere Pinterior ¼ 4πR2sphere Pexterior + 8πγRsphere

(3.23)

4πR2sphere ΔP ¼ 8πγRsphere

(3.24)

The final form of the Young-Laplace equation in a cylindrical capillary is ΔP ¼

2γ Rsphere

(3.25)

In the above equation the curvature was taken positive 1/Rsphere > 0, but if the meniscus has a negative curvature then 1/Rsphere < 0 and Δ P < 0. A simpler derivation is to equate the force on the meniscus’s surface due to the atmospheric pressure and the surface tension force acting on the three-phase line perimeter: πR2sphere  ΔP ¼ 2πRsphere  γ

(3.26)

The Young-Laplace equation shows that the difference in pressure between the bubble decreases with the increase in the radius of the sphere, that is, if R is infinitely large, the surface has no curvature and the difference in pressure vanishes. A more general form of the Young-Laplace equation includes curved interfaces that are not spheres because the example considered above, a sphere, is only a particular case of more complex shapes. For example, the curved surface may have different curvature along direction x direction, which is described by the radius R1; in y direction, this curvature could be described by the radius R2 (see Fig. 3.18). For such case the Young-Laplace becomes ΔP ¼

FIG. 3.18

(Left) A curved surface whose curvature is described by R1 in the x direction and R2 in the y direction. In this case both curvatures are positive. Such situations can be met in liquids contained in rectangular cuvettes or trays (Middle). (Right) An example of a liquid bridging between the tips of two pipettes showing one positive and one negative curvature.

2γ R1 + R2

(3.27)

29

3.9 Capillary number

Note that if one of the radii is very large or infinity this reduces to the previous form of the equation. Also, menisci can have one curvature positive 1/R1 > 0 and one negative 1/R2 < 0, in which case the above equation must be correctly modified. The Young-Laplace equation could also be easily deduced from the capillary rise, that is, the difference of pressure pushing from the concave side of the meniscus must be equilibrated by the surface tension: ΔPπR2meniscus ¼ γ2πRmeniscus

(3.28)

Oppositely, it can also be used to calculate the height of the liquid column in a capillary and obtain Jurin’s law, Eq. (3.19).

Numerical example 3.5 What are the consequences of Laplace pressure? If one connects balloons with different radii through a tube, what will be the radii of the balloons at the end, after the balloons have freely exchanged the gas? (see Fig. 3.19). Explain why?

FIG. 3.19

Effect of the Laplace pressure on the balloon of different radii connected through a tube which allows for free flow of gas.

3.9.2 Case study: Emulsions and foams Emulsions are typically produced from two immiscible liquids, such as oil and water, by shaking or shear. One of the phases will become the dispersed phase spreading in the form of droplets in the bulk of the other liquid. There are two main types of emulsions: oil-in-water (o/w) and water-in-oil (w/o) [42]. The emulsion type in pure immiscible phases is mainly determined by the volumetric fraction, where typically the phase with the lower volumetric fraction tends to be the dispersed phase. For example, upon shaking of the biphasic system of water and heptane, where heptane has a low volumetric fraction, an instantaneous emulsion is produced where large heptane droplets are observed for a short time, but the phases quickly separate. When high shear stress is applied, by ultrasonication or high-speed homogenization, to the same biphasic system one can observe that the heptane droplets become slightly smaller and it takes a longer time for the phase separation to occur. In other words, in emulsion formation it takes external energy input to break the droplets and opposing this is the Laplace pressure which is directly proportional to the interfacial energy. The interfacial energy between heptane and water is around 40 mN/m. To break the droplets with less energy and obtain a better stability for the emulsions, surfactants are used. Surfactants play a dual role, firstly, they lower the interfacial tension which helps with obtaining smaller droplets and secondly, they stabilize the emulsion and prevent coalescence. When surfactants are present, the emulsion type is determined mainly by the nature of surfactant, according to Bancroft’s rule [43], which states that o/w emulsions are obtained if the surfactants have a higher affinity for the water phase and w/o emulsions are obtained are obtained if surfactants have a higher affinity for the oil phase. The Bancroft rule applies also to Pickering emulsions and other type of amphiphiles such as Janus nanoparticles or

30

3. Surfaces and interfaces

pseudo-amphiphilic nanoparticles which stabilize emulsions [44–47]. Emulsions are thermodynamically unstable systems as they carry a nonzero interfacial energy. Emulsions have only kinetic stability, meaning that they will phase separate. Emulsions are found in many food products [48], cosmetics, paint and coating formulations, drugs, syrups, and also find uses in agriculture and in high-tech fields [49]. The droplet characteristic size is typically above 100 nm. A special type of emulsion is microemulsion, when the dispersed phase is well below 100 nm, typically between 10 and 50 nm. Unlike emulsions the microemulsions are thermodynamically stable, the interfacial energy (Gibbs free energy) between the immiscible phases with the addition of surfactant (often with a co-surfactant) is almost zero [50]. Although regular emulsions have surfactants, only in special cases with special types of surfactants microemulsions are obtained. Arguably, it is believed that due to surfactant adsorption and structuring at the interface, the interfacial energy is virtually zero [50–52]. Unlike regular emulsions, microemulsions form spontaneously or by very light shaking. Due to the small size of the dispersed phase they appear clear and transparent, the dispersed phase is so small that it does not scatter light, while regular emulsions appear milky and white. Surfactant micellar solutions are examples of pseudo-microemulsions. Microemulsions are of interest for their use in enhanced oil recovery, due to their good oil solubilization efficiency [53]. Similarly, with emulsion formation, the liquid foam formation is the dispersion of air bubbles in the water phase. In this case the magnitude of the interfacial tension plays a role in bubble breaking and foam formation. Surfactants are added to lower the surface tension of the liquid and they play a crucial role in foam stabilization [54].

3.10 Kelvin equation From the Young-Laplace equation we have learned that the pressure inside a droplet of liquid is higher than that outside, due to the action of the surface tension. In 1870 Lord Kelvin showed how the vapor pressure of a liquid is affected by curvature of the interface. Due to Laplace pressure ΔP in a liquid droplet the evaporation of molecules is faster than those from a liquid in a large container with a flat surface. In other words, the vapor pressure is greater in the former case. Oppositely, the vapor pressure inside a gas bubble formed in a liquid is lower than that above flat surface liquid, due to the negative Laplace pressure ΔP on the liquid side, convex side. Therefore, liquid may condense inside the gas bubble leading to bubble collapse. To summarize, if the curvature is concave on the liquid side, then Pcurved >Pflat. If the curvature is convex on the liquid side, then Pcurved < Pflat (where Pflat is the vapor pressure when the surface has zero curvature). The derivation of the Kelvin equation can be done by applying the hydrostatic principles or the more abstract thermodynamic ones [55]. The thermodynamic approach follows the change in the free energy Δ G upon curving the surface. Considering the vapor pressure from a flat surface Pflat as the initial state and the vapor pressure from a spherical liquid bubble Pcurved we obtain ΔG ¼ RT ln

Pcurved Pflat

(3.29)

The change in the free energy can also be determined from the equation: dG ¼ VdP  SdT at the constant temperature, the change of the free energy per mole of liquid becomes ð ΔP 2γVm ΔG ¼ Vm dP ¼ Vm ΔP ¼  Rcurved 0

(3.30)

(3.31)

where 1/Rcurved is the curvature of the surface and is positive on the convex side and negative on the concave side. Vm is the molecular volume that is constant regardless of the curvature. Bringing the two equations together we obtain Kelvin’s equation: Pcurved 2γVm ¼ Pflat rcurved
 2γVm Pcurved ¼ Pflat exp  RTrcurved RT ln

(3.32)

31

3.11 Case study: Surface tension of liquids at the nanoscale and in nanopores

TABLE 3.5 Calculated equilibrium pressure ratios for droplets and bubbles as a function of their radius. Radius (nm)

Pcurved Pflat

1000

1.001

0.999

100

1.011

0.989

10

1.114

0.898

1

2.950

0.338

for droplets

Pcurved Pflat

for bubbles

The above equation has important consequences. It shows that the vapor pressure from a bubble liquid is larger than that from a flat surface: this phenomenon is responsible for cloud stabilization—condensation and reevaporation of the water from tiny liquid droplets. A liquid aerosol consists of tiny droplets of different sizes and different Laplace pressures. In smaller aerosol droplets of a cloud, the evaporation of liquid is faster than that in the larger ones. Therefore, in proper conditions of pressure and temperature the larger droplets in clouds continue to grow due to condensation at the expense of smaller ones (Ostwald ripening) eventually falling as rain. Eq. (3.1) shows that the size of the droplet has a significant effect on the vapor pressure of the liquid below  10 nm, Table 3.5. For these calculations, it was assumed that the surface tension of liquid remains constant with the change in the radius of the droplet, but it has been shown that the surface tension of water in pores as tiny as 10 nm, when there are so few liquid molecules, decreases from 72.8 mN/m, the known value in bulk, to 55 mN/m at 20°C.

3.11 Case study: Surface tension of liquids at the nanoscale and in nanopores At a given temperature, surface and interfacial tensions of a planar interface is a constant characteristic of the liquids. However, as the characteristic sizes of the liquids, in the form of droplet, bubbles, etc., decrease below 10 nm, significant differences in the value of the surface/interfacial tension can be observed. Experimentally, it was found that the surface tension of liquids in nanopores deviates from that of a flat surface [56]. Surface tension changes only when the liquid meniscus of a liquid achieves very large curvatures. Theoretically, the relationship between surface tension and the curvature of the liquid was derived by Richard C. Tolman using arguments from Gibb’s thermodynamic theory of the interfaces [57]. Others calculated, using models different from that of Tolman, the change in the surface tension of water and other liquids (cyclohexane, benzene, etc.) with the curvature and noted that the surface tension increases with concavity (bubbles) and decreases with convexity (droplets) [58]. For example, in the case of a spherical water droplet with a radius of (radius of the curvature in this case) 5 nm, the surface tension dropped to 67 mN/m and for a radius of the curvature of 2 nm the surface tension was 58 mN/m. It therefore follows that when using Kelvin’s equations to calculate the vapor pressure around a liquid droplet smaller than 10 nm corrections to surface tension must be made. The relationship between the surface tension and the droplet curvature can be given by the following expression: 
1 γ 2δ ¼ 1+ γ∞ r where γ ∞ is the surface tension of a planar surface (with an infinite curvature), γ is the surface tension of the liquid, δ is Tolman’s length on the order of the molecular diameter [59], and r is the radius of the curvature. It is generally assumed that δ > 0 for spherical droplets and δ < 0 for bubbles in a liquid. It is worth noting that the expressions obtained by Tolman and later by Ahn et al. [57, 58] are essentially the same using different arguments. Such experiments on droplets and bubbles that are below 10 nm are, however, very difficult to carry out. Therefore, measurements were done on liquids contained in nanopores, for example. Due to the very few liquid molecules contained in the nanopore, the nanopore walls strongly influence the surface tension. The density and the surface tension of the water in pores of a mesoporous silica, with a pore radius between 1.55 and 3.90 nm, were determined to be lower than those of bulk liquid water. This anomalous change in the density and surface tension of the water was attributed to the hydrogen bond interaction between liquid water molecules and the surface hydroxyl groups on silica surface, which led to some level of molecular ordering and structuring in the fluid [56]. The surface energy of other materials, such as metals, crystals,

32

3. Surfaces and interfaces

alloys, was also shown to be size-dependent. Establishing rigorous models to calculate and predict interfacial energy values for materials in the nanoscale is of vital importance [59]. Jiang and Lu have recently attempted to model the evolution of surface energy of different materials and found that solid-vapor interface energy, liquid-vapor interface energy, solid-liquid interface energy, and solid-solid interface energy of nanoparticles and thin films decrease with the decrease in their dimensions to several nanometers, while the solid-vapor interface is size-independent and equals the corresponding bulk value [59].

3.12 Methods for measuring the surface and interfacial tensions of liquids Capillary rise is arguably the oldest method for the measuring the surface tension of liquids. A thin capillary of known radius is immersed in a liquid and due to the interaction of forces of the liquid with the capillary walls, the liquid rises in the capillary. By measuring the height of the capillary and using Jurin’s equation, Eq. (3.13), one can determine the surface tension of the liquid. Stalagmometer method or the drop volume method is based on the weighing of one or several drops of liquid formed at the end of a capillary and allowed to drop in a weighing pan. The pendant drops formed at the tip of the capillary start to detach when its weight reaches the magnitude balancing the surface tension. Therefore mg ¼ 2πrγ

(3.33)

where r is the radius of the capillary and m is the mass of the single droplet. The measurement of several droplets can make the method more accurate. The limitations of the method come from the fact that not the entire droplet at the end of the capillary falls, and this depends on the liquid properties; large errors can be produced this way unless correction factors are introduced. Wilhelmy plate method was initially proposed by Ludwig Wilhelmy in the 19th century and it is based on immersion of a Pt plate of known dimension with a roughened surface into a liquid to determine its surface tension. The Pt plate is suspended from a balance so that the total weight can be measured. The total weight is the contribution of the surface tension and the weight of the plate given by Ftotal ¼ Weight ¼ mg + Pγ cos θ

(3.34)

where P is the wetted perimeter of the Pt plate (width  length) and θ is the contact angle of the liquid with the Pt surface. The depth of the immersion must be adjusted so that the effect of buoyancy is eliminated. If the contact angle is zero the determination of the surface tension can be very accurate by this method. Du No€ uy ring method is similar to the plate method but instead a Pt ring is submersed in the liquid. Upon submersion the ring is pulled out slowly until completely detached from the liquid surface. The maximum force needed to detach the ring is measured and it is equal to Ftotal ¼ Wring + 2  2πrγ

(3.35)

where Wring is the weight of the ring and r is its inner and outer radius which are considered equal because the ring is very thin, made from a very thin wire and thus multiplied by factor 2 as the surface tension acts on both sides. With this method liquid-liquid interfacial tension can also be measured. Drop shape analysis of a pendant drop is a new method where the surface tension of a liquid and the interfacial tension between two liquids can be determined with an optical system that captures the shape of a pendant drop and analyzes the contour. The setup of such a system is depicted in Fig. 3.20 and can be done with a modern contact angle goniometer system and the contour of the droplet can be automatically extracted and analyzed with the software. The shape of a pendant drop or hanging droplet of fluid in air or in another liquid are determined by the action of two forces, the gravitation and the surface tension. While the surface tension acts to minimize the surface area of the droplet the gravitation tends to pull it down and thus stretch/elongate the droplet. The Young-Laplace Eq. (3.27) tell us that there is a pressure difference between the exterior and the interior of a curved interface, the higher pressure is always higher at the interior of the droplet. We note this pressure difference as ΔP. If the drop is perfectly spherical then the pressure difference will be constant everywhere in the droplet. For a pendant drop, however, the gravitation causes an elongation along the z coordinate, which can be arbitrarily chosen in a plane cutting the long axis of the drop in the middle in the vertical direction (Fig. 3.20B). The elongation of the droplet causes variation in the Laplace pressure along the z axis, causing ΔP(z) to change, from that at the apex ΔP0, and this can be written as

3.12 Methods for measuring the surface and interfacial tensions of liquids

33

FIG. 3.20 (A) Typical setup for measuring the surface and interfacial tensions of a liquid with optical methods. (B) The drop shape contour analysis in cylindrical coordinates and the parameters with the reference point at the apex of the pendent droplet.

ΔPðzÞ ¼ ΔP0  Δρgz

(3.36)

which at the apex takes the following expression: ΔPð0Þ ¼

2γ ¼ 2κ0 R0

where R0 is the radius of the droplet at the apex and κ 0 ¼ 1/R0 is the curvature at the apex. The meridional κs and the 1 circumferential κΦ curvatures (where κ 1 s and κ Φ are the corresponding radii sweeping in the plane of the paper and perpendicular to the plane of the paper, respectively, see Fig. 3.20B) of the droplet will change at any point away from the apex [60]. The Laplace-Young equation further away from the apex becomes ΔPðzÞ ¼ γ ðκs + κΦ Þ ¼ ΔPð0Þ  Δρgz

(3.37)

where Δ ρ is the density difference between fluids inside and outside of the droplet; when the fluid outside of the droplet is air, the density can be taken as
1.18 kg/m3, which is the density of air at sea level and 23°C. The above equation can be reparametrized by introducing the arc length ds. Based on geometric arguments it can be found that dx dz ¼ cos Φ and ¼ sin Φ ds ds

34

3. Surfaces and interfaces

with the boundary conditions at the apex s ¼ 0, x(s ¼ 0) ¼ z(s ¼ 0) ¼ Φ(s ¼ 0) ¼ 0, and x(s ¼ L) ¼ D/2, where L is the full arc length and D is the diameter of the needle from which the droplet is hanging. From this it results that the circumferential curvature kΦ ¼ sinΦ/x and the meridional curvature ks ¼ dΦ/ds. Inserting these curvatures in the Young-Laplace Eq. (3.37) we obtain
 dΦ sin Φ 2γ + ¼  Δρgz γ ds x R0 which yields the final form of the shape equation of a pendant droplet at any point along the z axis: dΦ 2 sin Φ Δρgz ¼   ds R0 x γ

(3.38)

The above differential equation can be solved by numerical procedures. The above equation can be rewritten in dimensionless form by replacing the dimensions x with dimensionless reduced variables X. One way to do that is to multiply the above equation by a length-scale factor equal to the capillary length lc ¼ (γ/Δ ρg)1/2, or the capillary constant. Thus, all the variables of length will become dimensionless X ¼ x/lc, ¼ z/lc, S ¼ lsc , and B ¼ R0/lc Thus, the above set of equations can be rewritten such that it contains the new dimensionless variables:
 dΦ 2 sin Φ ¼  Z (3.39) dS B X The shape of the pendant drop is therefore dependent on a dimensionless quantity, namely the Bond number ¼ B2, after the English physicist Wilfrid Noel Bond. The shape of an axisymmetric droplet depends only on parameter β. The bond number can be best interpreted as a measure of the relative magnitude of gravitational force to surface tension force for determining the shape of the drop. Gravitational force will elongate the pendent droplet (maximizing the surface area) while the surface tension forces will make the pendent droplet more spherical (minimize the surface area). For example, when the bond number β ≪ 1, the surface tension force dominates, and the drop is nearly spherical, and for β > 1, the gravitational force dominates and the pendant drop becomes elongated [61]. When β for a particular pendant drop geometry can be determined as well as the drop radius R0 at the apex, the interfacial tension γ can be calculated with the relationship [61]: β ¼ B2 ¼ R20

Δρg γ

(3.40)

Historically, Bashforth and Adams [62] were the first to solve Eq. (3.42) numerically and that the same authors also tabulated the solutions calculated by hand for the bond numbers β that show the deviation of the drop from the ideal profile of a sphere and researchers used this tables to identify the profile of the drop and obtain the surface tension values this way. However, in modern computerized systems the integration is performed automatically for any value of β and after extraction of the contour of the droplet in the digital image it finds the best solution for the Young-Laplace equation. An automated contour shape analysis software can search the best match of the experimental drop profiles, with the theoretically calculated profiles using the surface tension as one of the adjustable parameters. The numerical solution of the Young-Laplace equation yield additional data, such as drop volume V and droplet surface area A: ð V ¼ π X2 sin Φ dS ð A ¼ 2π XdS This procedure is called the axisymmetric drop shape analysis method (ADSA) and is one of the possible algorithms that can be used. The advantages of this method over all other techniques is the rapidity and accuracy. Also it is a great to study time dependence evolution of the surface and interfacial tensions as well as “aging effects.” Maximum bubble pressure method for measuring dynamic surface tension In this method gas bubbles are produced at a constant rate in a fluid through a capillary of precisely known radius. The pressure inside the bubble continues to increase and the maximum value is achieved when the bubble has a hemispherical shape and thus its radius coincides with the radius of the capillary. As the bubble continues to grow the pressure inside the drop decreases again.

3.12 Methods for measuring the surface and interfacial tensions of liquids

35

Numerical example 3.6 Can you explain why the pressure inside an air bubble decreases after the bubble increases in size beyond the hemispherical shape? The pressure changes in the bubble are monitored and plotted over time. The evolution of the bubble at the end of the capillary is depicted in the cartoon of Fig. 3.21.

FIG. 3.21 Evolution of the pressure in an air bubble produced in a liquid with surface tension to be determined. The maximum pressure inside the air bubble is achieved when it achieves a perfectly hemispherical shape of radius equal to that of the capillary.

At the point of the maximum bubble pressure, the bubble has a hemispherical shape of radius equal to the radius of the capillary, R, the surface tension can be determined using the Laplace equation: γ¼

R  ΔPmax 2

(3.41)

As we will see later, this method is most commonly used in determining the dynamic surface tension of a formulation containing surfactants and thus their adsorption dynamics at interfaces. A pure liquid has a negligible change in surface tension over time. Other methods used to determine the dynamic surface tension is the oscillating liquid jet method, which will be discussed later. As with any other methods for the surface tension measurements the capillaries must be kept absolutely clean. The advantage of this method is the accuracy, speed, and it can be applied to a variety of fluids, even biological fluids as it requires rather small amounts of the liquid sample. Spinning drop method is yet another way to measure the interfacial tension between two immiscible liquids. A small droplet of the lighter phase liquid is suspended in a heavier phase liquid and then placed in a horizontal rotating capillary. The shape of the drop is deformed by rotating the capillary at a certain rotational velocity. The shape of the drop will be deformed, elongate with the long axis perpendicular to the axis of rotation, and its long axis radius r will depend on the interfacial tension, the angular frequency of the rotation ω, and the density difference between phases Δ ρ. Thus, the interfacial tension can be calculated from Vonnegut’s equation: γ¼

r3 ω2 Δρ 4

The advantage of this method is that it can determine accurately very low interfacial tensions as it is the case in microemulsions, or design of surfactants formulations for the enhanced oil recovery. Enhanced or tertiary oil recovery is applied after almost 40% of the oil has been extracted from the well in the primary and secondary recovery processes. The enhanced oil recovery can be achieved by adding surfactants and detergent-like polymers in the aqueous liquid pumped into the well so that the wettability of rock improves and consequently the oil can be displaced from the pores of the rock and instantly emulsified due to the very low interfacial tension.

36

3. Surfaces and interfaces

FIG. 3.22 (A) Principle of the oscillating method and general measurement setup. (B) Photograph of the oscillating jet of an aqueous solution containing surfactants, which emerges from an oval orifice, the actual jet and its shadow with clearly separated waves and a reference ruler can be observed. Waves of different wavelengths can be clearly seen. At shorter times, closer to the orifice (A) the wavelength is short, because the surfactants did not have time to fully adsorb on the surface. At later times, from the sixth wave the difference in wavelength become less obvious.

The vibrating jet method for measuring the dynamic surface tension is a very creative yet very cost effective to implement, although more challenging for the user. Its theory was already worked out by Lord Rayleigh. The method is based on the measurement of the wavelength of an oscillatory jet of liquid emerging through an elliptical orifice as it progresses in time and space (Fig. 3.22) [63]. The wavelength of the oscillating jet as it departs from the orifice becomes longer and longer until it disappears (Fig. 3.22). The setup consists of a liquid reservoir, a set of flow regulators, and most importantly an oval orifice, which can be made simply by deforming a Pasteur pipette (Fig. 3.22). The exact dimensions of the orifice, the long and short axis must be precisely known for accurate calculations of the surface tension. The surface tension values are calculated from the wavelength using the following expression:
2 V γ ¼ Ca  ρ λ where Ca is the capillary number and can be determined with pure water, ρ is the density of the solution, V is the flow rate in mL/s, and λ is the wavelength of the wave. The time of corresponding to a certain wave can be calculated from the distance d of the midpoint of the wave from the orifice (Fig. 3.22), and the velocity of the jet v, with the equation: tðsÞ ¼

d v

where the velocity of the jet can be calculated with the equation: v¼

V a

where a is the area of the cross section of the elliptical orifice. This method is suitable for measuring the instantaneous dynamic surface tension for times in the range of 10–400 ms. Variants of the oscillating jet methods where waves in the jet are produced by excitation can probe the instantaneous interfacial tension to time intervals as short as 0.1 ms [64]. Note that the stalagmometer method can also be used to determine the dynamic surface tension where the droplet formation rate can be increased by a peristaltic pump. In this case the droplet size at lower surface tension will be smaller.

3.12.1 Case study: Aerosol spray coatings and the importance of the dynamic surface tension Measuring the dynamic surface tension is particularly useful in dynamic processes. For example, formulations of aerosol paint contain surfactants or surface-active agents which play the role of wetting agents and ensure an even

3.13 Measuring ultralow interfacial tension—The spinning drop tensiometer

37

FIG. 3.23 (Left) Long time of flight for aerosol droplets and the finish of the painted coat surface. (Right) Short time of flight and pitted surface of paint coat.

spread of the coated paint on a surface. In industrial coatings the quality of the paint must meet particularly tight requirements, the surface finish must be smooth and free of cratering or pits. Pits are created on the surface when, for example, the distance of the spray nozzle is too close to the surface to be painted. In such situation, the time of flight for the droplet from the nozzle to surface is much shorter than the time it takes for the surfactant to saturate and reach the surface of the aerosol droplet and when it lands on the surface it will not properly coat the surface (Fig. 3.23). Zhang and Basaran [65] have studied the role of surfactant in spray coating and concluded that the surfactant dynamics and the dynamic surface tension play a major role, firstly with respect to the ability of the aerosol droplet landing on the surface to wet and spread on the surface and secondly due to gradients in surface tension of the paint that induce a Marangoni flow causing local stress. In inkjet printing surfactants are added to improve the wetting properties of the ink. The time the ink droplets take from the moment they exit the printing nozzle and to the moment they reach the printed surface is about 1 ms [66]. Therefore, very fast dynamic surface tensions are needed that can be achieved at high surfactant concentrations and special design for the surfactant structures. Dynamic surface tension is an important parameter in wastewater treatment, flotation of minerals, and other industrial processes [67].

3.13 Measuring ultralow interfacial tension—The spinning drop tensiometer The spinning drop tensiometer is an instrument used to accurately measure ultralow interfacial tension values, typically 4. All droplets acquire eventually a fully cylindrical shape if the spinning speed is sufficiently large, however, this puts a limit to the instrument’s ability to measure very high values of the interfacial tension. Recent software algorithms developed based on the drop shape analysis using the Young-Laplace equation lift these restrictions, so larger values for the interfacial tension can be measured.

3.13.1 Case study: Role of interfacial tension in enhanced oil recovery Primary, secondary, and tertiary oil recovery phases refer to the method applied for the oil extraction from the reservoir. For primary extraction recovery, the oil is extracted from the natural pressure built up over time in the reservoir, where the oil is naturally pushed out of the reservoir, therefore a set of valves and pipes are enough. For the secondary oil recovery, pressure is built up in the reservoir by adding water, waterflooding, or gases. After first and second recovery phases have taken most of the oil, there are still significant oil reserves left in the reservoir and if economically justified the tertiary (or enhanced) oil recovery can proceed. In the tertiary oil recovery, chemicals or gases are used to displace oil that is trapped in the pores of the rock, due to viscous, gravity, and capillary forces. The tertiary oil recovery is especially used for heavy oil and tar sand extraction. Heavy oils and tar sands can have a significant percentage in oil reservoirs but are poorly displaced in primary and secondary recovery. Therefore, the bulk production of these comes from the tertiary oil recovery [68]. Chemical flooding is among the methods used to enhance oil recovery, in which different chemicals such as surfactants, polymers, alkalis, biopolymers, and combinations thereof are used to improve the oil displacement from the rock (microscopic efficiency) and to improve the volumetric sweep efficiency (macroscopic efficiency) [69]. The macroscopic efficiency refers to the increase in the volume of oil brought to the surface. Because of the large viscosity difference between the oil and water the mobility of the water phase is much larger than that of the oil phase, therefore the pumped water may flow around the oil, leaving the oil phase behind. To increase the viscosity of the water phase, polymers and biopolymers are used and a polymer flood is also performed to increase the mobility of the oil phase. Mathematically the mobility is expressed as M¼

λdisplacing krw =μw ¼ λdisplaced kro =μo

where kro and krw are the effective permeability of oil and water, respectively, and μo and μw are the viscosities of oil and water phases, respectively. A mobility value of 1 is considered ideal because the displaced phase moves at the same speed as the displacing phase, but for a mobility of 10 the water moves 10 times faster than the oil. Chemical flooding into the oil well is performed to improve the oil displacement from the rock (microscopic efficiency). The principle is to reduce the interfacial tension between the water phase and the oil phase to as low as possible to increase the capillary number Ca ¼ ηU/γ where U is the linear velocity of the injected phase (m/s) and η is the viscosity of the injected phase. Ca correlates closely to oil recovery and residual oil saturation Sr0 (S0 oil saturation is the volume fraction of oil within the pore volume) [69]. Ca is in the range of 107 to 106 for typical water flooding and by increasing the capillary number to 104 and 103 the oil saturation can be reduced to 90% [70] and residual oil saturation approaches zero if capillary number reaches 102 [71]. This can be achieved by decreasing the oil/water interfacial tension (IFT) from 10–40 mN/m to 102 to 103. Such low interfacial tensions can be achieved in formulations using surfactants, alkali surfactants, and polymer/alkali/surfactants [69, 72, 73]. The alkali is used for the saponification of potential product in oil and to achieve in this way ultralow interfacial tension values. Both ionic and nonionic surfactants have been used since 1970s [73]. Petroleum-derived sulfonate surfactants are the most economical surfactants used to lower the interfacial tension between the water and the oil and to alter the wettability of the porous rock from oil-wet to water-wet.

Numerical example 3.7 What is the capillary number for a brine oil interfacial tension γ ¼ 10 mN/m, injected phase velocity U ¼ 3.5  106 m/s, and viscosity η ¼1 mPa s? Calculate the value of the oil/water interfacial tension needed to achieve a capillary number of 102, for a full oil recovery from the well, for the same conditions?

As already mentioned, surfactants also influence the amount of residual oil recovered via other mechanisms, such as emulsification of oil and changing the wettability of rock [69]. However, the adsorption of surfactant on the rock creates losses that reduces the concentration of surfactants, reducing the chemical flooding to water flooding, losing

References

39

therefore oil recovery efficiency. Surfactant formulations in chemical flooding are done with the spinning drop tensiometer to measure the minimum concentration of surfactants needed to achieve IFT values of 103 mN/m.

3.14 Surface and interfacial tensions with temperature The surface or interfacial tension with increase in temperature always decreases. This has been observed experimentally and the meaning of it can be understood from the Gibbs-Duhem equation treated in the next chapters. Essentially it can be easily demonstrated that the surface entropy for a 1 m2 surface area and constant pressure is
 dγ (3.42) Ssurface ¼  dT This means that the surface excess entropy increases with the increase in temperature since dγ/dT is always negative. Because the surface excess is positive it indicates that the molecules at the interface have more entropy, are more disordered than in bulk. As we will see the surface excess thermodynamic functions is generally the amount of energy, concentration, or in this case entropy possessed by the surface as compared to bulk. There have been attempts over the years to predict the surface tension of the liquids at different temperatures. Eo˝tvo˝s’ empirical equation relates molecular volume Vm, temperature T, surface tension γ, and critical temperature, Tc (the temperature at which the phase boundaries vanish and the liquid coexists with its vapors and the γ ¼ 0): γ ðVm Þ2=3 ¼ kðTc  T Þ

(3.43)

where k is a constant, Vm ¼Mw/ρL, ρL is the density of the liquid, and Mw is the molecular weight. The Eo˝tvo˝s constant k is a measure of the entropy of formation of surface, in other words the entropy change induced by bringing the liquid molecules from the bulk to the surface [74]. The constant k takes a value of 2.12 for nonpolar liquids. For H-bonding, liquids have a lower value for k, for example, it ranges 0.7–1.5 for alcohols; 0.9–1.7 for organic acids; and for water, k varies between 0.9 and 1.2, according to the measurement temperature range. There are other empirical relationships proposed but they are not discussed in this chapter.

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[55] K.P. Galvin, A conceptually simple derivation of the kelvin equation, Chem. Eng. Sci. 60 (2005) 4659–4660, https://doi.org/10.1016/j. ces.2005.03.030. [56] T. Takei, K. Mukasa, M. Kofuji, M. Fuji, T. Watanabe, M. Chikazawa, T. Kanazawa, Changes in density and surface tension of water in silica pores, Colloid Polym. Sci. 278 (2000) 475–480, https://doi.org/10.1007/s003960050542. [57] R.C. Tolman, The effect of droplet size on surface tension, J. Chem. Phys. 17 (1949) 333–337, https://doi.org/10.1063/1.1747247. [58] W.S. Ahn, M.S. Jhon, H. Pak, S. Chang, Surface tension of curved surfaces, J. Colloid Interface Sci. 38 (1972) 605–608, https://doi.org/ 10.1016/0021-9797(72)90395-5. [59] H.M. Lu, Q. Jiang, Size-dependent surface tension and Tolman’s length of droplets, Langmuir 21 (2005) 779–781, https://doi.org/10.1021/ la0489817. [60] F.S. Kratz, J. Kierfeld, Pendant drop tensiometry: a machine learning approach, J. Chem. Phys. 153 (2020) 094102, https://doi.org/ 10.1063/5.0018814. [61] G.O. Berim, E. Ruckenstein, Bond number revisited: two-dimensional macroscopic pendant drop, J. Phys. Chem. B 123 (2019) 10294–10300, https://doi.org/10.1021/acs.jpcb.9b08851. [62] F. Bashforth, J.C. Adams, An Attempt to Test the Theories of Capillary Action: By Comparing the Theoretical and Measured Forms of Drops of Fluid, University Press, 1883. [63] E.V. Srisankar, J.P. Shah, K.S. Narayan, A simple apparatus for measuring dynamic surface tension, J. Chem. Educ. 64 (1987) 378. [64] M. Ronay, Determination of the dynamic surface tension of inks from the capillary instability of jets, J. Colloid Interface Sci. 66 (1978) 55–67, https://doi.org/10.1016/0021-9797(78)90183-2. [65] X. Zhang, O.A. Basaran, Dynamic surface tension effects in impact of a drop with a solid surface, J. Colloid Interface Sci. 187 (1997) 166–178, https://doi.org/10.1006/jcis.1996.4668. [66] R.C. Daniel, J.C. Berg, A simplified method for predicting the dynamic surface tension of concentrated surfactant solutions, J. Colloid Interface Sci. 260 (2003) 244–249, https://doi.org/10.1016/S0021-9797(02)00148-0. [67] R.J. Pugh, Dynamic surface tension measurements in mineral flotation and de-inking flotation systems and the development of the on line dynamic surface tension detector (DSTD), Miner. Eng. 14 (2001) 1019–1031, https://doi.org/10.1016/S0892-6875(01)00088-7. [68] T. Ahmed, D.N. Meehan, Introduction to enhanced oil recovery, in: Advanced Reservoir Management and Engineering, Elsevier, 2012, pp. 541–585, https://doi.org/10.1016/B978-0-12-385548-0.00006-3. [69] M.S. Kamal, I.A. Hussein, A.S. Sultan, Review on surfactant flooding: phase behavior, retention, IFT, and field applications, Energy Fuel 31 (2017) 7701–7720, https://doi.org/10.1021/acs.energyfuels.7b00353. [70] A.M. Howe, A. Clarke, J. Mitchell, J. Staniland, L. Hawkes, C. Whalan, Visualising surfactant enhanced oil recovery, Colloids Surf. Physicochem. Eng. Asp. 480 (2015) 449–461, https://doi.org/10.1016/j.colsurfa.2014.08.032. [71] J. Hou, Z. Liu, S. Zhang, X. Yue, J. Yang, The role of viscoelasticity of alkali/surfactant/polymer solutions in enhanced oil recovery, J. Pet. Sci. Eng. 47 (2005) 219–235, https://doi.org/10.1016/j.petrol.2005.04.001. [72] B. Song, X. Hu, X. Shui, Z. Cui, Z. Wang, A new type of renewable surfactants for enhanced oil recovery: Dialkylpolyoxyethylene ether methyl carboxyl betaines, Colloids Surf. Physicochem. Eng. Asp. 489 (2016) 433–440, https://doi.org/10.1016/j.colsurfa.2015.11.018. [73] S. Kumar, A. Mandal, Studies on interfacial behavior and wettability change phenomena by ionic and nonionic surfactants in presence of alkalis and salt for enhanced oil recovery, Appl. Surf. Sci. 372 (2016) 42–51, https://doi.org/10.1016/j.apsusc.2016.03.024. [74] S.R. Palit, Thermodynamic interpretation of the Eotvos constant, Nature 177 (1956) 1180, https://doi.org/10.1038/1771180a0.

C H A P T E R

4 Surfactants and amphiphiles 4.1 Introduction Amphiphilicity shows a property that can be shared by surfactant molecules, macromolecules, molecular assemblies, and nanoscopic objects, such as Janus nanoparticles [1, 2] that, inter alia, partition spontaneously at the boundary between two phases, such as liquid-liquid, liquid-gas, or solid-liquid interfaces. In doing so, the amphiphiles lower the interfacial tension and interfacial energy between phases. Amphiphiles can self-assemble into monolayers and suprastructures of different shapes and forms dictated by the geometry and orientation of the building blocks. Amphiphilicity implies the existence of chemical functional groups that in water are hydrophilic and hydrophobic (lipophilic) connected by chemical or physical bonds and form distinct and spatially segregated regions in space with contrasting surface polarity (Fig. 4.1), such as in surfactants, block copolymers, and Janus particles. Pseudo-amphiphiles are surfaces, homogeneous particles, or copolymers that are constituted by both hydrophilic and hydrophobic groups mixed at the molecular scale (Fig. 4.1), without spatial segregation and which are wetted by both water and oil. Due to the lack of well-defined spatial segregation between polar (hydrophilic) and nonpolar (hydrophobic) functional groups, pseudo-amphiphiles do not self-assemble into well-defined structures and are not as effective as the amphiphiles at lowering the interfacial energy between phases. Amphiphilicity is a scalable property, being active at the molecular level, at the nanoscale and could presumably be extended into the microscale. The scalability of the amphiphilic property is however fundamentally an open question and it is a subject of interest in fundamental research [1–3]. Surfactants are the best-known class of amphiphiles and consist of a hydrophilic (polar) and hydrophobic (nonpolar) chemical functional group connected by chemical bonds, usually represented as in Fig. 4.2A. The hydrophobic part is usually a hydrocarbon chain and the hydrophilic part can be an anionic, cationic, or nonionic functional group. Surfactants can self-assemble into a variety of structures, such as micelles, bilayers, monolayers, vesicles, etc. (Fig. 4.2B).

4.2 Brief historical account of surfactants Soaps were made and used from immemorial times, with the first records traced back to antiquity, in Mesopotamia [4]. Soaps are fatty acids surfactants, and in the past were obtained with rudimentary synthetic methods from basic materials available in nature such as tallow fat, olive, argan, or palm oils, and alkali-rich ashes, remnant residue from wood burning. The soap-making activities spread later on throughout the European continent (Fig. 4.3). The soap may have contributed to an improved quality of life, eliminated, or reduced the diseases in the densely populated regions, and enabled urban life. The reaching of new standards of living was marked by the appearance and mass production of personal care products, i.e., toiletries and cosmetics. Many Mediterranean regions prospered from the soap and cosmetics manufacturing activity because of their rich natural olive oil resources, such as the case of Provence in the south of France, or Castile in Spain, Florence in Italy [5]. Olive oil is rich in saturated palmitic, stearic and unsaturated oleic, linoleic, and linolenic acids (Fig. 4.3), which leads to good quality soaps. Sulfated oils were the first synthetic surfactants prepared after soaps, in 1834 by Runge, by mixing olive oil and sulfuric acid and in 1875 sulfated castor oil also known as “Turkey red” was prepared and used as dyeing additives, mordants, in textile industry [6]. A sulfated oil is not a pure surfactant but a mixture of sulfate esters, water, and fatty acid surfactants. In 1935, Colgate-Palmolive introduced the first soap-free shampoo, using sulfated mono- and di-glyceride surfactants (Fig. 4.3) [6].

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00011-9

43

Copyright © 2021 Elsevier Inc. All rights reserved.

44

4. Surfactants and amphiphiles

FIG. 4.1 Cartoon depicting amphiphiles and pseudo-amphiphiles.

A

Hydrophobic tail Hydrophilic head

B

Bilayer & fragments, 80%, from food waste, paper, plastic, wood, and fiber [76]. There is a great diversity of microorganisms that are capable of biodegrading carbon-based pollutants such as oil and plastics to produce biosurfactants, but they are not well known. Another important carbon source could be the landfill garbage feedstock where the nonbiodegradable component, such as plastics, amount to 5%–14% in landfills [76]. These can be polymers such as PVC, PET, PE, PPE, Teflon, etc. It is worth perhaps investigating pathways to rapidly decompose such lowbiodegradable materials and transforming them in valuable chemicals. Purely chemical methods for processing landfill discarded PET and transformation in water-soluble surfactants were also reported [77], but these are even more expensive and energy intensive. It is therefore fundamentally interesting to understand whether these materials could be presensitized to make them digestible feedstock to bacteria. One possible presensitization method is the surface pretreatment, or exposure to UV light to produce polar groups on the surface, dCOOH, dCOO, dC]O, via active oxygen insertion, to make these plastics more “palatable” to the aerobic microorganisms. The second major bottleneck is surfactant separation and purification that can be the most expensive part of the production. Among the classical surfactant separation techniques used today, we can quote precipitation, solvent extraction, selective crystallization, ion-exchange, membrane filtration, foam fractionation, chromatographic separation [78]. Faster and more efficient separation techniques are needed. For faster and improved separation techniques, fundamental properties of surfactants must be considered.

4.5 Self-assembly of surfactants Surfactants start to form aggregates in water and aqueous solutions at the CMC value. The first aggregates that formed are spherical micelles. For practical uses, the CMC value is among the most important technical parameter of surfactants, as it is the deciding factor for choosing the appropriate concentration in formulations. CMC is unique to a surfactant molecule. The CMC value can be determined by several different method. The easiest method to measure CMC is from the surface tension vs concentration curve. Fig. 4.19 shows the typical evolution of the water surface tension with surfactant concentration. Three main stages can be identified on this curve: (I) at low concentrations 107–106 M of surfactants, the surface tension of water remains unchained at 72.4 mN/m at room temperature, the surfactant molecule adsorb on a pristine water surface, and the adsorbed surfactant are in the so-called 2D gas; (II) at intermediate concentrations 106–104 M of surfactant, the surface of the water is only partially saturated but 2D networks of surfactant molecules form and the surfactant-surfactant lateral interaction in the plane of the interface leads to a progressive and linear decrease in surface tension; (III) at high surfactant concentrations, the surface of the water is fully occupied by surfactants, and no further interfacial adsorption takes place. Further increase in the concentration of surfactants leads to the association of surfactants present in the bulk into spherical micelles. The surface tension remains unchanged for further increase in surfactant. The breakpoint between stage II and III of the curve in Fig. 4.19 can be identified as the CMC value. The surface tension can be measured with the ring method, Wilhelmy plate method, or the pendent drop method. Some commercial instruments are fully automatized to determine the CMC value. Other methods used to determine the CMC, conductivity for ionic surfactants, fluorescence, turbidity, etc. [39, 41]. The evolution of the surface tension (Fig. 4.19), with the surfactant concentration adsorbed at the interface Γ is given by the following state equation [79]:

59

4.5 Self-assembly of surfactants

FIG. 4.19

Typical evolution of the water surface tension with concentration for a surfactant.


γ ¼ γ 0  RTΓ ∞ ln

Γ∞ Γ∞  Γ



where Γ ∞ is the saturation surface concentration of surfactant, T is the temperature (K), and γ 0 is the surface tension of pristine interface. On the other hand, the surface tension changes with the surface available area, e.g., an expanding pendant drop of liquid, and in this case, the evolution of the surface tension with the creating of a fresh surface ΔA is given by [79]:   
 ΔA kt γ ¼ γ 0  RTΓ ∞ ln Γ ∞  ln Γ ∞  Γ 1  e A0  ΔA where A0 is the beginning surface fully saturated with surfactants, Γ ∞, k is the rate of adsorption constant, and t is time. When starting with a fresh interface A0 ¼ 0, the above equation reduces to [79]  γ ¼ γ 0  RTΓ 1  ekt The micelles formed by surfactants are believed to be mostly spherically shaped, or prolate, rod, cylindrical, or worm like. The interior of the micelles is hydrophobic while the exterior is hydrophilic. The interior of the micelle contains no water even though it is swimming into the bulk aqueous system. This is also the driving force of the micelle formation, the dehydration of the nonpolar hydrophobic chains, which is entropically favorable. Intuitively, water molecules surrounding an alkyl chain are ordered forming a relatively rigid clathrate structure, upon removal of the hydrophobic chain from water, the hydration layer of the molecule are released; breaking the clathrate structure and regaining their all degrees of freedom contribute to increasing the entropy. Organic solutes can be solubilized into the hydrophobic

60

4. Surfactants and amphiphiles

micelles, which is also the reason for their detergency, but also as important vehicles for delivery of water-insoluble actives in cosmetics, pharmaceuticals, and other applications. Of practical importance for technicians measuring the CMC is the appearance of the dip around the CMC instead of a clear break between the segments II and III, as shown in Fig. 4.19; most of the time this is due to organic impurities present in impure surfactants or due to decomposition, for example, alkanes due to decomposition of alkyl sulfates. The organic impurities adsorb at the water surface and lower the surface tension of water, but around CMC are being solubilized by the surfactant micelles and are transported back into the bulk solution, indicated in Fig. 4.19, and the surface tension recovers. An important parameter characterizing the micelles is the aggregation number, which is the average number of surfactants present in a micelle. For sodium dodecyl sulfonate (SDS), this is around 60–70 [39]. The radius of the micelle cannot exceed the full extended length of the alkyl chain of the surfactant. In fact, experimental studies suggest that the diameter of the micelle is close to the full extended length of the alkyl chain, which means that the interior of the micelle is very compact, water free, and liquid like. The aggregation number can be expressed in two ways: as the ratio between the volume of the micelle to the volume of a single surfactant molecule: N¼

4πR3micelle Vmicelle ¼ vsurfactant 3vsurfactant

(4.1)

and as the ratio between the micelle area and the area of the surfactant: N¼

Amicelle 4πR2micelle ¼ asurfactant asurfactant

(4.2)

The above two expressions are equal and lead to the following equality: vsurfactant 1 ¼ Rmicelle asurfactant 3

(4.3)

While in a typical surfactant structure, the alkyl chain contributes most to the volume of the molecule vsurfactant and the micelle dimensions Rmicelle, the area of hydrophilic group contributes exclusively to the micelle-water interfacial area of the surfactant asurfactant. Therefore, the above equation can be interpreted as the volume of the alkyl chains divided by the area of the hydrophilic group at the interface times the length of the alkyl chain. In a cone V/(Abase  h) ¼ 1/3, where h is the height of the cone, in a truncated cone, 1/3 < V/(Abase  h) < 1, in a cylinder V/(Abase  h) ¼ 1. Therefore, the above equation led to the development of the critical packing parameter CPP [80, 81]: CPP ¼

v l c a0

where v is the volume of the hydrophobic chain, lc is the length of the hydrophobic chain, and a0 is the area occupied by the hydrophilic group at the micelle-water interface. For P  1/3, the surfactant should form spherical micelles, for 1/3 < P < 1 surfactants should form micelles with prolate shapes, cylinders, and worm like, while for CPP 1 should form planar monolayers and bilayers. The value of CPP should is responsible for the curvature of the self-assembled structure given by surfactant geometry. It should also be emphasized that for charged ionic groups, the a0 is not the physical area occupied by the hydrophilic group but the area of double-layer interaction, best given by the Debye length. For example, multivalent ions, an increase in salt concentration of the aqueous solution, use of voluminous organic counterions, will contribute to the compression of the electric double layer (see Chapter 11). The volume of the hydrophobic part is mainly influenced by branching and length of the alkyl chain. The main weakness of the critical packing parameter theory is the post hoc rationalization which limits its actual practical use, in other words, one must first determine the type of self-assembled structures generated by a surfactant then packing parameters can be calculated. For 1/3 < CPP < 1, the spontaneous curvature of the self-assembled structure should in fact also be spherical (Fig. 4.20), but with a smaller curvature, however, this is not the case, because there should be no water inside of the hydrophobic micelle core and a void space would be under enormous hydrostatic pressure, the spherical structure is “clamped” into a cylindrical structure so that the alkyl chains are in contact. This gives rise to packing stress at the ends of the cylinder-, rod-, or worm-like micelles (Fig. 4.20), as well as domain boundaries so the curvature constraints can be relaxed. The existence of the packing stress is the reason for the rod-like and worm-like micelle grow with an increase in surfactant concentrations, eventually evolving into surfactant mesophases [80]. An actual visualization of the micelles formed can be provided via electron microscopy studies [82, 83]. The geometry of the surfactant can be tuned not only by chemical design but also by tuning the effective area a0 occupied by the hydrophilic group, described

4.5 Self-assembly of surfactants

FIG. 4.20

61

Surfactant packing parameters and their self-assembly structures.

by a radius equivalent to the Debye length. As already mentioned, the Debye length is affected by the salt concentration, counterion valence, charge of the ionic group, etc. In this way, an effective tuning of the surfactant geometry can be tuned by salt addition. With the help of fluorescence microscopy, Guan et al. [84] have visualized the transition from spherical micelles to rod like and finally to cylinder like of an anionic surfactant, with the increase in the NaCl concentration, that effectively compressed the Debye length of the anionic sulfone group. The transition from spherical to wormlike micelles was also visualized with electron microscopy in binary cationic/anionic surfactant mixtures induced by the increase in salt concentration in solution [85]. For CPP > 1, the structure generated has negative curvature, e.g., inverse micelles, which have the hydrophilic part at the core of the structure while the hydrophobic part at the exterior structure. However, such negative curvature self-assemblies are formed mainly in the ternary system, e.g., water-oil-surfactant. Thermodynamics of the micelle formation has been treated extensively in the literature. The structural complexity of the micelles can be affected by using surfactants with “exotic” functional groups. Polymeric surfactants, mostly derived from PEO, form micelles with a corona. By employing co-assembly of chemically,

62

4. Surfactants and amphiphiles

unlike molecules that can undergo phase separation and organization within the micelles giving rise to compartmentalized Janus micelles [86]. The surfactant solution reaching the CMC value is associated with some important changes in the macroscopic physical properties of the surfactant solution. By increasing the surfactant concentration well above the surface saturation and CMC value, several phenomena are observed. For short-chain surfactants C8-C10, the viscosity of the solution increases linearly, while for longer chain surfactants >C14 the viscosity of the solution viscosity appears to increase nonlinearly with concentration. The former was explained by the fact that micelles are spherical and small and their number increases, while in the second case the volume and the micelles change, the addition of surfactant leads to a transformation from spherical micelles to long worm-like micelles that continue to grow like filaments reaching hundreds of nanometer. The assembly of surfactants at high concentrations gives rise to structural phases that can be either discrete or infinite. The discrete assemblies with spherical, prolate, cylindrical, monolayer and bilayer rafts, vesicles, liposomes, etc. while infinite assemblies which are interconnected structures forming 2D or 3D structures, such as fibers, sponges, layer stacks, liquid crystals, etc. At high enough concentrations, the discrete structures such as micelles and bilayers can in turn self-assemble into suprastructures, forming different surfactant mesophases and liquid crystals, a phenomenon also called sometimes hierarchical self-assembly. These organized structures can have a variety of fascinating macroscopic properties, ranging from iridescent colors, viscoelasticity, gel-like behavior, vivid colors between crossed polarizers, etc. [87]. These bottom-up formations of nanostructures represent a wellspring for inspiring ideas to create new materials at the nanoscale. To have a complete overview of all the self-assembly structures and phases produced by a surfactant, one must construct a phase diagram, which requires significant amount of work and skill in different techniques to obtain unambiguous results. Binary phase diagrams are represented typically as a 2D graph with a concentration on the abscissa and temperature on the ordinate. To construct this, solutions of different concentrations of surfactants are prepared and their phases are established by specific methods. A borderline is drawn between phases. Finding this borderline is complicated by the coexistence of different phases, which must be first separated and then identified. Direct observation of surfactant assemblies is extremely challenging for the sample preparation, as these are dynamic and fragile structures, the surfactant molecules come in and out of the structure, with energy comparable to 1–2 kT. The electron microscopy studies of surfactant phases by Vinson et al. [83] show the existing experimental challenges to resolve these to an unprecedented resolution, alas the single-molecule observation still remains a great challenge. Other techniques employed in the characterization of surfactant phases are, X-ray, neutron scattering techniques, cross polarizers, conductivity, etc. The cartoon in Fig. 4.21 depicts the typical lyotropic phases encountered in binary water-surfactant solutions. Most of the surfactants form lyotropic phases meaning that they are determined by surfactant-surfactant interactions, but sometimes these are thermotropic phases, meaning that some of the interactions are enhanced by an increase in temperature. In all these self-assembly structures, surfactant molecules are oriented. The surfactant phases can be categorized into two classes by the way they scatter light, isotropic phases, micellar solutions, cubic phases, are clear and transparent, and anisotropic liquid crystalline phases, hexagonal, lamellar, etc. scatter light and appear cloudy. Between the cross polarizers, the former gives black images while the latter gives bright images. In addition, the patterns appearing between the cross polarizers can be used to identify the phases, e.g., between hexagonal and lamellar phases. Depending on surfactant structure (geometry) and polarity contrast some of the phases dominate, while some others do not form. The desire to predict which type of self-assembled structure is formed has led to the development of the packing parameter, discussed above. The surfactant mesophases are useful for templating and synthesis of nanostructured materials such as mesoporous silica [88], assembly of organic cages by micelles [89], and many others [90–92]. Surfactant liquid crystal phases form between the Krafft point and the surfactant melting point. The liquid crystal lyotropic phases [93] have been used for decades in liquid crystal displays (LCDs) until their slow replacement by light-emitting diodes (LEDs) and quantum dot light-emitting diodes (QLEDs). Other important parameters characteristic of a surfactant are the Krafft point and the cloud point. Krafft point refers to the temperature at which the CMC value is equal to the solubility of the surfactant. Krafft point increases for a given hydrophilic group with increase in the number of carbons in the hydrophobic group and decreases with branching. For a given hydrophobic group, the Krafft point decreases with increase in the number of hydrophilic groups and decreases for ionic surfactants with the level of hydration of the counter ion [94]. For formulation stability at low temperature, identification of surfactants with a low Krafft point is vital. Cloud point refers to the temperature at which the nonionic surfactants become insoluble in water and thus the solution turns into a cloudy suspension. Typically, at this temperature, the PEO and PPO chains become dehydrated and the chains change conformation from initially extended to globular coils that scatter light [94]. For nonionic ethoxylated surfactant, the cloud point increases with the increase in the length of the PEO chain [95].

4.5 Self-assembly of surfactants

FIG. 4.21

63

Typical surfactant phases encountered in binary water-surfactant systems.

4.5.1 Self-assembly in ternary systems, foams, and emulsions In ternary systems, water-oil (emulsions) and water-gas (foams, mist, and fog) surfactants adsorb at the water-oil and water-gas interfaces self-assembling into monolayers. Due to surfactant action, the interface can acquire a spontaneous curvature such that it becomes strongly negative (concave) or positive (convex) toward one phase or the other. When this happens the phase on the concave side becomes the dispersed phase (gas bubbles or oil droplets) and the phase on the convex side becomes the continuous medium. When the interface curvature approaches zero, the dispersion can become bi-continuous. When gas bubbles or liquid droplets are forced into contact, the interfacial monolayers also come into contact and form different self-assembly structures. Many different types of self-assemblies can form in ternary systems, such as reverse micellar phases, inverse cubic, hexagonal, and bi-continuous or lamellar phases. Foams can be produced in the laboratory for studying and testing by sparging, introducing the gas through small orifices into water containing surfactant. The adsorption of surfactant at the water-gas interface depends on the surfactant dynamics. For very dynamic surfactants that quickly adsorb at the interface of the gas bubble, the probability of foam formation is high. The bubbles are pushed up through the liquid and agglomerate at the surface forming a layer of foam. The lifetime and probability of producing this foam layer depend on surfactant concentration, liquid drainage rate, surface tension gradients, etc. The liquid drainage, the main factor leading to foam destruction, depends largely on the polarity of the hydrophilic group. Typically, the ionic surfactant with highly polar groups forms excellent and stable foams, due to better retention of water layers in the foam lamella. A foam column has two main distinguishable layers, starting from the surface of the water: (i) the sphere foams, approximately spherical gas bubbles separated by thick viscous water film with surfactants, followed by (ii) an aged layer of polyhedral (almost perfect dodecahedra) gas bubbles separated by the thin liquid film. Layer (ii) forms due to water drainage that leads to the thinning of the separating liquid film to several hundred of nanometers, while the Laplace pressure is minimized due to flat wall formation, giving a polyhedral aspect of this layer. Foam lamella is believed to be composed of self-assembled surfactant planar multilayers, which form by approaching and compressing the liquid between the gas bubbles, having each a monolayer of surfactant on their surface. A great bod of literature on foams formation, stability, measurement, and applications is available [96–98]. Foam and froth are used interchangeably, noting that froth may also contain trapped particles. In particle removal from surfaces, cleaning applications, the ability of surfactant to foam is essential, as many of these particles are trapped at the gas-bubble water interface and lifted in foam. This is important for flotation in the separation of minerals, foam in shampoo for dandruff removal, etc. Qualitatively, a good foaming agent generates small foam bubbles. Emulsions depending on the fraction of oil and water can be formed by discrete droplets or bi-continuous phases. The surfactant structure and affinity to the oil or water phase has a profound effect on the emulsion type obtained. Finkle and Bancroft [99, 100] rules give an insight into the spontaneous curvature attained by the water-oil interface due to surfactants’ chemical structure and amphiphilic balance, which determines the affinity for one phase or the

64

4. Surfactants and amphiphiles

TABLE 4.1 A range of HLB values and the approximate indication for their application and appearance of surfactant solutions. Appearance of the solution

HLB

Property/application

Insoluble

0

–

Poorly dispersible

3–6

Antifoaming agent Emulsifier w/o emulsions

Turbid

7–9

Wetting agent

Translucent to clear

10–15

o/w Emulsifier detergent

Very soluble, clear solution

15–18

Hydrotrope solubilizing agent

other. When surfactants have a high affinity toward the oil phase, the water-oil interface becomes concave on the waterside forming w/o emulsions, and vice versa when the surfactants have a higher affinity toward water phase, the water-oil interface becomes concave on the oil side forming o/w emulsions. Recently, Wu and Honciuc [101] found that Finkle and Bancroft rules apply to larger amphiphiles, such as Janus nanoparticles. Janus nanoparticles adsorb irreversibly at the water-oil interface and pack into rigid monolayers the phase determining both the emulsion phase and the curvature of the emulsion droplets. Qualitatively, a good emulsifying agent generates small liquid droplets.

4.5.2 Attempting to quantify amphiphilicity with HLB Amphiphilicity implies the existence of the opposing forces of attraction and repulsion and spatial segregation of hydrophilic and hydrophobic groups. The amphiphilic balance is the balance between the strength of attraction forces vs. repulsion forces, which gives each surfactant its own characteristic. For example, the attraction forces (hydrophobic and van der Waals) can by slightly stronger than the repulsion forces (electrostatic or steric) in which case the surfactant is less soluble in water, it is more attracted to the hydrophobic oil phase. For this reason, such a surfactant is more appropriate for using as w/o emulsifier (see Bancroft rule) or antifoaming agent. If the repulsion forces dominate, then the opposite is truth, surfactant has a higher affinity to water, can work as o/w emulsifier, it is a better foaming agent. For practical purposes, the qualitative explanation is not sufficient, a more quantitative measurement for the amphiphilic balance associated with a particular surfactant is necessary. Therefore, early efforts were dedicated to developing a scale for surfactant. Currently, the accepted parameter is the HLB. The calculation of the HLB is not unique, and in the mid-1950s, two different methods were proposed by Griffin’s method and Davies’ method. The generalized equation derived from Griffins’ method is [39, 41, 102, 103] HLB ¼ 20 

Mhydrophile M

where Mhydrophile is the molecular weight of the hydrophilic group and M is the molecular weight of the whole molecule. The Griffins’ HLB scale ranks a surfactant from 0 to 20. The value on the HLB scale should roughly correlate with the surfactant property and solubility (Table 4.1) judged by the appearance of the surfactant solution. Because Griffins’ equation does not take into account the “degree” of the polarity of the hydrophilic group and can be difficult to apply to surfactants whose molecular structure of the hydrophile is complex, zwitterionic, sugars, ethoxylated chains, etc. The resulting HLB values may not reflect the true amphiphilic balance of the surfactant. Davies’ proposed a different approach [104]: HLB ¼ 7 +

m X n¼1

Hn 

k X

Li

i¼1

where Hn is an arbitrary number (also called group number) assigned to reflect the polarity ranking of the hydrophilic group (arbitrary), and Li is the group number arbitrarily assigned to reflect the polarity ranking of the hydrophobic/ lipophilic group. The last term of the right-hand side of the above equation is typically n  0.457 or n  0.87, where n is the number of dCH2d (dCH3, dCHd, ]CHd) or dCF2d groups, respectively. The Hn group values range from a maximum of 38.7 for most polar hydrophilic group sodium sulfate SO4  Na + to 1.9 for hydroxyl dOH [104, 105]. It is unfortunately directly evident that the Davies’ formula also has limitations, in the sense that if the group number is not known it cannot be calculated, it also fails to reflect the emulsification behavior for the polyethoxylated surfactants. Attempts to improve Davies’ model were done by Lin et al. [106] who tried to relate the HLB to CMC, by Kunieda and

4.6 Case study: An intuitive understanding of the structure-activity relationship in surfactants

65

Shinoda [107] to the emulsion phase inversion temperature, others sought correlations between HLB to cloud point [95], the solubility of surfactant, heat of dissolution, dielectric permittivity, interfacial tension, Hildebrand parameters, etc. [105].

Numerical example 4.1 Find the HLB number of a mixture of surfactants A and B, with A:B ¼ 3:1, knowing that A has HLB ¼ 8 and B has HLB ¼ 16.

Answer HLB is believed to be an additive function; therefore, the HLB of the mixture is

HLBmixture ¼ HLBA  XA + HLBB  XB ¼ 10 The method for mixing surfactants is common for obtaining the surfactant mixture for emulsification with the desired HLB.

Most of the commercially available surfactants have an accompanying technical sheet, with important parameters, including CMC value, solubility, cloud point, Krafft point, HLB, etc. Given that the HLB value is scientifically still an ambiguous definition, should one from the practical perspective, believe the values provided by the manufacturer for the HLB values? The answer is yes, because no matter how these were calculated, by which method, the manufacturer will provide an experimentally verified HLB value that reflects the surfactant properties as an emulsifier. While the HLB concept is very crude and ambiguous it can be extremely useful to formulators as a rough guide to choose among the different surfactants. In the emulsification of oils for example, the HLB concept is the most useful. Formulators used the HLB matching concept for producing an emulsion and the HLB value of the surfactant must match the HLB value of the oil. The oils are not the same, in fact their polarity changes wildly with their molecular structure, so required-HLB (RHLB) value is assigned to a particular oil. The RHLB is the value required by an oil to produce stable o/w or w/o emulsions. The RHLB for oil is first determined with a homologous series of surfactants with known HLBs; sometimes there are HLB kits that can be purchased for this purpose, consisting of a series of surfactant and a mixture of surfactants (mostly Span and Tween surfactant mixtures) with incremental HLB value from 2 to 18 (see Table 4.2). Some RHLB values of o/w emulsion are given in Table 4.3. RHLB values for w/o emulsions can be determined in the same way. In oil mixtures, the RHLB values can be calculated as in Numerical example 4.1.

4.6 Case study: An intuitive understanding of the structure-activity relationship in surfactants For a fresh chemistry graduate or technician starting to work in the industry to design surfactants and surfactant formulations, it can be particularly challenging meandering through all the variety of molecular structures and TABLE 4.2

Homologous series of surfactants with varying HLB values [105].

Surfactant

HLB

Span 85

1.8

Span 80

4.3

Span 60

4.7

Span 40

6.7

Span 20

8.6

Tween 81

10

Tween 85

11

Tween 80

15

Tween 60

14.9

Tween 40

15.6

Tween 20

16.7

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4. Surfactants and amphiphiles

TABLE 4.3 Required HLB (RHLB) for o/w formation of several oils [103,105,108,109]. The values in parenthesis are from [108]. Oil

RHLB for o/w

Argan oil

11

Beeswax

12

Benzene

15

Cetyl alcohol

15

Cyclohexane

15

Calendula oil

6

Coconut oil

8

Dimethicone

5

Grape seed oil

7

Lanolin

10

Olive oil

7

Vitamin E

6

Paraffin wax

10(12)

Xylene

14

RHLB of w/o

5

–

18

4

General trends Oil

RHLB of o/w

Vegetable oil

5–7

Silicone oil

8–12

Petroleum oil

9–11

Fatty acid esters (emollients)

10–12

Fatty acids and alcohols

14–15

choosing the right surfactant for a certain application. This problem is aggravated by the fact that commercially available surfactants have proprietary structures and can be found only under the trademark name, such as Surfynol, Pluriol, Lutensol, Tvida, Dynol, etc. Often a set of technical properties are indeed given by the manufacturer, such as CMC, foaming, HLB value, etc. perhaps even a set of recommendations for applications. One way to alleviate this problem is to consult specialized books, which often hold a directory of surfactant brand names, some basic information on the structure as well as applications for which they are suitable. One such reference book is the “Handbook of Industrial Surfactants” by Michael and Irene Ash [110], which organizes commercially available surfactants function, application, HLB, CAS number, chemical composition, or class to the extent possible and in addition, it provides an alphabetic list of tradenames. This book has been last updated to the fifth edition of 2010. Another valuable resource with a general character for a technician formulator is that of Rosen and Dahanayake [111] which may clarify some basic application principles of surfactants and contains a useful directory of surfactants manufacturers and surfactant tradenames. Application-specific surfactant reference books are also available [112], although these paper format reference books remain valuable resources, are somewhat outdated, most of the resources have moved online, but alas not in a centralized database. Apart from this, some basic knowledge of the structure-activity relationship is a must for the formulator and technicians as well as students designing an experiment. This case-study section is an attempt to give a basic and intuitive overview of the structure-activity relationship to a certain property of the surfactants. I have purposely used the word “intuitive” because a strictly universal scientific theory able to predict from the chemical structure, the precise activity, and behavior of any surfactant does not yet exist. Some chemical structure design rules are known by most experienced surfactant scientists and are used to develop new surfactant structure and classes and are subjected to intense scientific research. Beginning with a list, should hopefully be useful to form the underlying foundation for the life-long learning process.

4.6 Case study: An intuitive understanding of the structure-activity relationship in surfactants

67

Structural elements affecting: (1) Minimum water surface tension (ST): for a fully saturated surface, is determined by the strength of attraction between the hydrophobic chains and the strength of repulsion between the polar hydrophilic groups. For example, for fluoroalkyl chains, the cohesive energy is about 30% less than the cohesive energy between the alkyl chains of the same length, so the surface tension is consequently lower for surfactants containing fluoroalkyl tails than that of the surfactants with alkyl tails of same length. A rough rule of thumb is that the minimum value of the ST achieved by a surfactant is set and approach asymptotically the surface tension of the fluoroalkane or alkane with the same number of carbon and chemical structure as the fluoroalkyl and alky of the surfactant in question. The lowest interfacial tension is typically achieved for surfactants with the highest polarity contrast between the polar and nonpolar functional groups. (2) Dynamic of adsorption and dynamic surface tension: Molecules having chains with the same number of C, but branched have a faster adsorption dynamics, decrease the surface tension faster but the minimum surface tensions are higher than the linear ones [79] (3) Self-assembly formation: Micelle formation and self-assembly the ability is determined by both the amphiphilicity, polarity contrast between molecules, spatial segregation between the polar and nonpolar groups. The opposing forces must be such that equilibrium is not pushed to the unimeric state (too high repulsion) or to complete phase separation (too strong attraction). The main attraction forces are hydrophobic and van der Waals, which both scales with the carbon chain length, and the repulsion forces are electrostatic. The polar groups that are too weak to lead to a good amphiphilic contrast are hydroxyl, aldehyde, ketone, and amine. The fatty alcohols will completely phase separate [39] (4) Critical micelle concentration (CMC) value: it is important for formulations. For example, a small CMC value is beneficial for use of less valuable material and can minimize the environmental and the negative impact of surfactant interaction with materials, swelling of monomers, skin irritation, etc. CMC value is determined by several factors such as the surfactant solubility in water, the volume of the molecule, and the area that is able to occupy at the interface, packing ability, and packing density of the molecules into a monolayer at the interface, etc. An increase in water solubility of surfactants also decreases the CMC. Influence of the hydrophilic head for a given hydrophobic tail: CMC of nonionic is lower than that of the ionics; cationics have only slightly higher CMC than anionics, a moderate increase in the CMC as the polar head becomes larger [39], the valency of the counterion decreases the CMC, changing the counterions from inorganic to organic decrease the CMC (the counterion can also be an anionic or cationic surfactant, whose structure and bulkiness can be used to tune the surfactant solubility and CMC to an extreme range). Influence of the hydrophobic tail for a given polar/hydrophilic group: branching of the alkyl chain such that the overall carbon atoms remain constant leads to an increase in water solubility of the surfactant and an increase in the CMC value. Extreme branching and shortening of the alkyl chains will lead to exceedingly high CMC values. At the same time, the CMC is extremely sensitive to the length of the alkyl chain, increasing the linear alkyl chain will lower the CMC value by several orders of magnitude [39]. A counter effect of branching is the molecular volume, larger molecules saturate the interface much faster than smaller molecules, and it can push the CMC value to lower values. Insertion of aromatic and double bonds also increases the CMC value. Gemini surfactants occupy a larger area of the surface due to their volume and exhibit a lower CMC value than that of the unimers. Perfluoroalkyls have a considerably lower CMC than alkyls. The above list is obviously insufficient and should be further consolidated. Some reference books of [39–41, 96, 111] provide a multitude of invaluable in-depth structure-activity relationship rules.

4.6.1 Amphiphilicity beyond the molecular scale—Janus particles Amphiphilicity was previously defined as a polarity contrast between two regions which gives rise to contrasting forces of attraction and repulsion between the hydrophobic and hydrophilic groups, respectively. If the repulsion forces are too strong, then unimeric states are preferred, if the attraction forces are stronger, then phase separation occurs. Self-assembly formation is the equilibrium state existing between unimeric and phase separation. Previously, it was also noted that spatial segregation of hydrophobic and hydrophilic groups is necessary for these forces to operate. Spatial segregation and geometry of the amphiphile are important to the type of self-assembly structure it can generate. Along these lines, the amphiphilic property operates at different scales. At molecular scale, it has been demonstrated. The amphiphilic property is scalable if the influence of other competing forces, such as capillary, gravitational, buoyancy is not stronger than the amphiphilic forces of repulsion and attraction. Amphiphilicity also operates at the nano and microscales and this has been demonstrated by the use of amphiphilic Janus particles (JPs), in the range

68

4. Surfactants and amphiphiles

FIG. 4.22 SEM images of AIBN-JNPs with progressively enlarged P(3-TSPM) lobe (light-gray/white) from the same seed PS NPs (dark-gray). (A–E) AIBN-JNPs with progressively larger lobes obtained for a volume of 3-TSPM monomer (A) 0.5 mL, (B) 1 mL, (C) 2 mL, (D) 3 mL, and (E) 4 mL added to 1 g of PS seed NPs; (F) EDX spectra, normalized with respect to the reference carbon peak of the PS seed NPs. (G) EDX mapping of “2 mL—TSPM” JNPs obtained from larger seed PS NPs, 320  5 nm diameter, showing the asymmetric distribution of oxygen, silicon elements, namely a higher concentration in the P(3-TSPM) lobe in contrast to a symmetric distribution of carbon in both Janus lobes. Reproduced from D. Wu, J.W. Chew, A. Honciuc, Polarity reversal in homologous series of surfactant-free Janus nanoparticles: toward the next generation of amphiphiles, Langmuir 32 (2016) 6376–6386. Copyright 2016 The American Chemical Society.

of 100–500 nm. The structure of the self-assembled structures is difficult to resolve at the molecular level and some structures are implied. Amphiphilic Janus particles, due to their size and rigid self-assembly structures that can be seen with the electron microscopy, serve as a model to systematically study the self-assembly processes and formation of suprastructures via self-assembly. Wu et al. [1, 101] have observed a polarity reversal in a homologous series of poly(styrene-co-3-(triethoxysilyl)propyl-methacrylate) (PS-P(3-TSPM)) JNPs with varying lobe ratio (Fig. 4.22A–E). The authors obtained direct

69

4.7 Supra-amphiphiles

experimental evidence that the chemical composition of the two lobes is different (Fig. 4.22G). In this way tuning of the polarity contrast between the polar P(3-TSPM) and nonpolar PS, Janus lobes was achieved, i.e., HLB or Janus balance. The direct consequence of the polarity switch was the phase emulsion inversion condition from w/o to o/w. In addition, the authors investigated the role of the hydrophobic AIBN or hydrophilic APS used in the polymerization of the second lobe. The two initiators had no influence on the particle geometry and the size of the grown lobes in the same reaction conditions but had a profound effect on the surface energy of the obtained JNPs such that the AIBN was more hydrophobic than the JNPs obtained with APS, which could be generally valid for any system of monomer/polymer seed particle. The polarity contrast between the Janus lobes was termed Janus balance [113], which is a quantifiable parameter comparable to the hydrophilic-lyophilic balance (HLB) used for surfactants as proposed by Griffin [102, 114]. Wu et al. proposed the following equation for calculating the HLB value of the JNPs: HLB ¼ 20 

APð3TSPMÞ  F1 APð3TSPMÞ  F1 + APS  F2

(4.4)

where the AP(3TSPM)is the area of the polar lobe, APS the area of the nonpolar PS lobe and in addition, we have introduced Fi, (i¼1,2)—weighing factors accounting for the “degree” of polarity of the lobes. Admitting that there cannot be a purely polar or nonpolar surface for a polymer particle, the value of F can be calculated from the ratio between the polar and nonpolar dispersive surface energy components for each of the Janus lobes: p

F1 ¼

γ Pð3TSPMÞ p γ Pð3TSPMÞ

+ γ dPð3TSPMÞ

, and F2 ¼

γ dPS + γ dPS

p γ PS

(4.5)

where the small Greek gammas are the surface energies and the subscripts “p” and “d” indicate the polar and dispersive surface energy components of the corresponding Janus lobe. However, determining the surface energy of each Janus lobes is technically challenging. Recently, Kang and Honciuc [2, 3] have synthesized two-lobe snowman-type JPs consisting of a hydrophilic and hydrophobic lobe. By tuning the relative size-ratio between the lobes, the amphiphilicity, and the geometry of the particles was changed (see Fig. 4.23). We have previously mentioned the post hoc rationalization of the packing parameter of surfactant, the defining element deciding the geometry of the self-assembled structure [80]. In the case of JPs, the packing parameters can be determined from actual particle dimensions, assuming that the interaction range is smaller than the particle itself. Indeed, the packing parameter determined the curvature of the self-assembled structures, with the CPP roughly following the same values as in surfactant, thus confirming the theory of Israelachvili [80]. Due to their structural rigidity, these self-assembled structures can be observed (see Fig. 4.24). In addition to their self-assembly capabilities, the JPs are also able to adsorb at water-oil and water-air interfaces producing a significant lowering of the surface tension [28, 101].

4.7 Supra-amphiphiles Supra-amphiphiles (SAs) are a combination of puzzle pieces that can be molecules, macromolecules, surfactants, amphiphiles particles, etc. arranged together such that spatial segregation of hydrophobic and hydrophilic group is achieved. The distinguishing feat in supra-amphiphiles is that the hydrophilic and hydrophobic groups are connected via noncovalent bonds, or cleavable and reversible dynamic covalent bonding. These types of bonds can be p-p interaction, hydrophobic interaction, charge transfer interaction, electrostatic interactions, host-guest inclusion, etc. The weak bonding between the hydrophobic and hydrophilic parts makes these supra-amphiphiles and their self-assembled suprastructures responsive to external stimuli. The stimuli-responsiveness, and “environmental awareness” makes the supra-amphiphiles especially interesting for their use as building blocks for intelligent materials, in drug-delivery applications, cosmetics, etc. The field of SAs is currently growing at a fast pace and it is difficult to give a comprehensive account of the myriads of engineered molecules. One of the most comprehensive reviews on SAs was recently published by Chang et al. [115], which classifies them by construction and topology, in classes and subclasses: linear polymeric SAs, branched and hyperbranched polymeric SAs, and cross-linked SAs. A triblock SAs with dual stimuli responsiveness to temperature and CO2 have been synthesized by Liu et al. [116] from three segments: (a) b-cyclodextrin modified with poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA);

70

4. Surfactants and amphiphiles

FIG. 4.23

Synthesis of PtBA-PTPM JNPs with different geometries. (A) Synthesis of JNPs by seed emulsion polymerization. (B) Summary of JNPs used in the present study, these JNPs vary in the PTPM lobe size, phase separation degree, and overall dimension. (C) SEM images of JNPs in (B). Scale bars 150 nm. PtBA-tert-butyl methacrylate, PTPM-poly(3-(triethoxysilyl)propyl-methacrylate) [3].

(b) poly-e-caprolactone (PCL) capped with adamantane at one end and an alkenyl group at the other end; (c) poly(N-isopropylacrylamide) (PNIPAM) capped with the thiol group at one end. The PDMAEMA-b-PCL-bPNIPAM linear supra-amphiphile was prepared by mixing the three individual blocks in one pot following the host-guest interaction between PCL-adamantane and PDMAEMA-cyclodextrin and thiol-ene Michael addition between the PDMAEMA-alkenyl and the PNIPAM-thiol (see Fig. 4.25). From the same group another example of a hyperbranched SAs, is given in Fig. 4.26, which was synthesized from hyperbranched poly(3-ethyl-3-oxetanemethanol) modified trans-azobenzene (AZO) as the hydrophobic part and polyglycerol-modified β-CD as the hydrophilic part interacting via trans-AZO-β-CD host-guest interaction [117]. The hyperbranched SA could self-assemble into mono-walled vesicles, which were to light. Under illumination to 365 nm light, the trans-AZO will convert to cisAZO, and the host-guest complex is destroyed, the vesicle will disintegrate, which makes it interesting for drugdelivery applications. Examples of supra-amphiphiles are numerous with ingenious designs and architectures [20, 118–121]. The field of supra-amphiphiles is less than a decade old. A significant amount of work lies ahead and soon interesting physicochemical phenomena for these amphiphiles will be uncovered, as well as applications.

4.8 Surfactants and the environment Surfactants for household cleaning and industrial applications are produced in significant volumes each year [122]. It is predicted that by 2040, the world population will reach 10 billion [123]. This coupled with the industrialization and increase in the standard of living in the developing countries, and the demand for surfactants will greatly increase. The extensive use of these chemicals generates environmental concerns with respect to their toxicity to mammals, aquatic life, and their accumulation in soils [124]. Based on toxicological studies, severe governmental regulations were made. Foam floating on the rivers in the 1950s, due to extensive use of alkylbenzene sulfate surfactants (poorly processed by the wastewater treatment stations) [125] was an early warning to the public consciousness that progress, if not sustainable, would have harmful and irreversible impact on the environment. Detergents containing phosphate builder were also banned in the 1970s and have today restricted use in most countries; the phosphate is a nutrient for algae, the rivers turned green, phenomena called eutrophication, causing depletion of oxygen in rivers and death of the aquatic

4.8 Surfactants and the environment

71 FIG. 4.24 (I.) Self-assembled structures obtained from the PtBA-PTPM JNPs with different PTPM lobe sizes. (a–c) Capsules formed by the JNP-1JNP-3. (d–e) A monolayer (d) and double layer (e) JNPs sheets formed by the JNP-3. (f and g) Capsule (f ) and broken capsule (g) assembled by the JNP-4. (h) JNPs with larger PTPM lobes (top) enjoy less rotation freedom as compared to the JNPs with smaller PTPM lobes (bottom). (II.) Comparison between surfactants and JNPs: (a) the critical packing parameter Cpp ¼ lcva0 with the idealized surfactant shapes for different self-assembled suprastructures. (b) Representation of the Janus critical packing parameters JCpp ¼ lVa . The angle α is measured from the actual dimensions of the particles. From C. Kang, A. Honciuc, Influence of geometries on the assembly of snowman-shaped Janus nanoparticles, ACS Nano 12 (2018) 3741–3750. https://doi.org/10.1021/acsnano. 8b00960.

life [126]. Another notorious example is the banning of the nonylphenol ethoxylate due to its endocrine disruption activity, structural similarity to the estrogen hormones [127]. Even if not banned, the risk to the environment and aquatic life is still very high, even for the biodegradable surfactant if present in sufficiently large quantities. Many classes of surfactants are known to be toxic to fish because they destroy their external mucus layer that normally protects

72

4. Surfactants and amphiphiles

FIG. 4.25 Preparation of the PDMAEMA-bPCL-b-PNIPAM supra-amphiphile, self-assembly, and responsive reaction to temperature and gas. Reproduced with permission from B. Liu, H. Zhou, S. Zhou, H. Zhang, A.-C. Feng, C. Jian, J. Hu, W. Gao, J. Yuan, Synthesis and selfassembly of CO2–temperature dual stimuliresponsive triblock copolymers, Macromolecules 47 (2014) 2938–2946. https://doi.org/10.1021/ ma5001404. Copyright© 2014 American Chemical Society.

FIG. 4.26 Synthesis of the hyperbranched supra-amphiphile, self-assembly, and responsiveness to light. Reproduced with permission from Y. Liu, C. Yu, H. Jin, B. Jiang, X. Zhu, Y. Zhou, Z. Lu, D. Yan, A supramolecular Janus hyperbranched polymer and its photoresponsive self-assembly of vesicles with narrow size distribution, J. Am. Chem. Soc. 135 (2013) 4765–4770. https://doi.org/10.1021/ja3122608. Copyright© 2013, American Chemical Society.

References

73

them from parasites and bacteria (most fish will die at a detergent concentration of 15 and 5 ppm concentration will destroy their eggs) [128]. Yet another class, the long-chain fluorinated surfactants, such as perfluorooctane sulfonates (PFOS) and perfluorooctanoic acid (PFOA) are persistent, bioaccumulative, and toxic to mammals and are cancer suspects [129]; they have restricted use in the EU, US, and other locations. Albeit slow to implement, regulations put pressure on the producers. DuPont chemical company followed by Chemours, a subsidiary company, offered for example the well-known Zonyl fluorinated surfactant family consisting of long fluoroalkyl tails (C8-C16) and alkoxy chains. The PFOS, PFOA ban in the United States and Europe determined the company to switch to the shorter chain linear and branched 0 then the liquid spontaneously wets the surface, total wetting; in the case, S  0 partial wetting can be expected, 0 degrees < θ  180 degrees and the dropqwill ffiffiffiffiffiffi have a finite contact angle to the substrate (Antonov’s rule). γ the gravity can be neglected, the hydrostatic pressure rapidly If the drop is smaller than the capillary length lc ¼ ρg equilibrates inside the drop; the drop then adopts the shape of a spherical cap in order to obey Laplace’s law. Wetting is a thermodynamic process, and it is exclusively determined by the difference between the free energy of the final system (droplet of liquid touching the surface and formation of the solid-liquid interface) and the free energy of the initial system (droplet of the water not touching the surface). The kinetics and the time evolution dynamics of the pure liquid droplet spreading on the substrate until the equilibrium is reached is given by Tanner’s law [1]:  1=10 3=10 γ LG t (5.3) RðtÞ  V η  3=10 1=10 γ LG θ ðtÞ  V t (5.4) η where V is the volume of the liquid droplet (assumed constant during spreading), n is the viscosity of the liquid, R is the radius of the base of the liquid droplet, and t is the time. The time evolution of the liquid droplet is influenced by different factors, such as the topography of the substrate, diffusion phenomena in case of liquids containing surfactants, the volatility of the liquid, etc., which lead to deviations from Tanner’s law.

5.1 Contact angle of liquids on macroscopic surfaces The measurement of the contact angle can be performed with any liquid, such as pure liquids, solvents, colloids, and even emulsions, whose shape is determined by its surface tension and curvature is defined by the Young-Laplace equation. Liquids that are too viscous cannot be used in contact angle measurements. If the liquid is too viscous, in the form of a paste or non-Newtonian emulsion fluid, the contact angle cannot be measured by the sessile drop method, simply because its shape is not determined by the surface tension. A paste or thick cream finds itself in a metastable fluid-like

5.1 Contact angle of liquids on macroscopic surfaces

81

FIG. 5.2

(A) The diagram of a contact angle goniometer consisting of a light source (yellow), dosing unit, and precision syringe (blue), a telescopic lens (green), a camera or an eyepiece (red). (B) The typical view through the eyepiece of a classic contact angle goniometer, where the measurement is done manually by adjusting the wires to match the baseline and tangent to the droplet at the three-phase line. (C) In modern goniometers, the contact angles are calculated live from a snapshot image or from the frames of a live video by fitting the Young-Laplace equation to the contour profile of the sessile droplet. In this last case, the baseline is detected automatically.

state due to the very high strength of the intermolecular forces and could acquire very irregular shapes when handled, and only after relatively long relaxation times, it will tend to acquire a shape of a minimum area. Such challenges are met frequently in the cosmetic industry where attempts are made to correlate the ability of creams and lotions to wet the human skin with the sensory feel that it produces. The measurement of the contact angle is typically done with the already mentioned contact angle goniometer (Fig. 5.2A). Most modern goniometers are equipped with a digital camera which allows for real-time observation of the liquid droplet resting on a flat surface, also called the sessile drop. In the past, the measurements of the contact angle were done visually with the goniometer (Fig. 5.2B) (an instrument for measuring angles), but today, the procedure is highly automatized. A snapshot of the fluid droplet is digitized, the contour of the droplet fitted to the YoungLaplace equation, and a baseline is detected; the software automatically calculates the contact angle at two points, left and right side (Fig. 5.2C). The contour of the droplet can be fitted to outer equations, such as an ellipse and a circle, and all depends on which shape is the most appropriate.

5.1.1 From macroscopic to microscopic sessile droplets Sessile drop is a droplet of liquid resting on a surface and not free to move is the leitmotif in measuring the contact angle (Fig. 5.1). The static contact angle measurements are those performed at equilibrium, that is, the contact angle between the liquid droplet and the substrate is quickly established (Fig. 5.3A) and remains stable over time. Even so,

FIG. 5.3 Evolution of the contact angle of a sessile water droplet with time. (A) The ideal case, the equilibrium contact angle showing constant values with time. (B) The contact angle value drops initially and it settles around a plateau value, which can be taken as the equilibrium contact angle. (C) The contact angle value decreases until the liquid droplet wetted completely the surface. In such case, no contact angle value can be reached and the few initial values are taken as the nonequilibrium contact angle.

82

5. Wettability of surfaces

the equilibrium contact angle is not the thermodynamic equilibrium because a droplet may not be in equilibrium with its vapors, if the atmosphere is not rigorously controlled, the liquid continuously evaporates. This can be observed when the equilibrium (mechanical equilibrium) contact angle is being monitored with time, the decrease in the volume of the liquid droplet due to evaporation has a net effect of decreasing the contact angle values from the initial values as the three-phase line remains pinned. However, very often there are situations when an equilibrium (mechanical) contact angle is not achieved and the liquid droplet continues to spread with time, e.g., initially large contact angles and very slowly this decreases with time. In this situation, the contact angle is rather difficult to interpret. If the contact angle initially decreases but reaches a plateau then the value of the plateau contact angle can be taken as equilibrium contact angle (Fig. 5.3B). The contact angle determination by the sessile method with the optical goniometer (Fig. 5.2) is normally performed with liquid volumes between 1 and 10 μL. The upper limit for the size of the sessile droplet is set by the capillary length, in order to neglect the influence of the gravitational effects. Despite the heated debate whether there is strong relationship between the static contact angle of the liquid and the volume of the droplet, it has been concluded that the measurements with sessile droplet volumes in this range are rather independent of the size of the droplet [2]. At significantly lower droplet volumes in the nL and pL ranges the contact angles show some size dependence due to the contribution of the contact line tension. If the contact angle continues to decrease at a rate faster than that due to liquid evaporation then the choice of the contact angle is very subjective (Fig. 5.3C). In practice one can monitor the contact angle values of sessile drops over a time range of 60 s and then decide which value of the contact angle is more valuable for the particular application, the beginning value, e.g., first 10 s, or the average value. In real application, the surface scientist is often confronted with such situations. The reason for the continuous expansion of the liquid droplet on the surface could be the liquid evaporation and recondensation on the solid surface ahead of the three-phase line, which leads to an increase in the γ SG and thus continues to expand. Another reason could be the chemical heterogeneity of the surface, or chemical changes of the solid substrate in contact with the liquid, either due to the adsorption of surfactants or dissolution of the substrate and changing of the properties of the material, or swelling. The explanations can be diverse, and the cause must be analyzed in the context of the liquid and solid substrate to be measured. Smaller sessile droplets with volumes in the nanoliter and picoliter range can be sometimes needed for measuring surfaces with irregular shapes. Measurement of the contact angles of nL and pL liquid droplets are possible with today’s technology due to high-performance optics and dosing systems; for example, droplets as a small 30 pL volume can be generated reproducibly [3]. The small droplet volumes are necessary for miniaturized mechanical devices, printed circuit boards, and various mechanical parts of irregular shapes, the microstructured exoskeleton of insects [4], nanopatterned surfaces [5], medical implants, or single fibers. Biocompatibility of biomaterials used in medical, biomedical, optometric, dental, and pharmaceutical industries is often associated with hydrophilicity and good water wettability [6]. For example, dental implants that must be hydrophilic in order to bond to the bone tissue, the contact angle with water must be as low as possible [7]. However, determining the contact angle on such irregular shapes represents a challenge but can be made possible with nL dosing system; the cartoon in Fig. 5.4 shows a tiny droplet generated on the surface of threads of a dental implant. More advanced instrumentation, such as environmental scanning electron microscopy (ESEM) or atomic force microscopy (AFM) can be utilized in measuring the contact angle of irregular shape samples; these methods have been extensively reviewed [8] and offer interesting and viable alternatives to the existing macroscopic methods. The imaging with ESEM is not trivial but enables imaging of microdroplets on flat and nanopatterned surfaces (Fig. 5.5). The generation of droplets in the ESEM chamber is achieved by the condensation of the water vapor on the substrate, by controlling the relative humidity (RH) in the sample chamber by adjusting the pressure and the temperature of the sample such that nucleation and growth of water droplets appear (Fig. 5.6). The imaging of the droplets can be

FIG. 5.4 Cartoon of a tiny liquid droplet fitting between the screw threads of a dental implant. Such nL volume water droplets can be produced with today’s technology and monitored with high power magnifying optics.

5.1 Contact angle of liquids on macroscopic surfaces

83

FIG. 5.5 Microdroplets on patterned Si wafer surfaces hydrophobized after coating with 1,1,-2,2,-tetrahydroperfluorodecyltrichlorosilane using ESEM. Reproduced with permission from M. Nosonovsky, B. Bhushan, Patterned nonadhesive surfaces: superhydrophobicity and wetting regime transitions, Langmuir 24 (2008) 1525–1533. https://doi.org/10.1021/la702239w. Copyright 2008, American Chemical Society.

performed during growth, giving the advancing contact angle, (e.g., keeping P ¼ 10 mbar and lowering T to 10°C), or during droplet evaporation (P ¼ 10 mbar and increasing T above 10°C) giving the receding contact angles, or static contact angles if both P and T are kept constant so that the droplet is in equilibrium. Electron microscopes equipped with environmental capability enable imaging in relatively high-pressure modes up to c. 15 mbar thanks to the pressure limiting apertures (PLA) and cooling stages. The PLAs are conical nozzles with aperture radii on the order of several hundreds of nanometers permitting in this way a large pressure difference between beam column under ultrahigh vacuum (UHV) and the low vacuum (or 15 mbar pressures) in the sample chamber under differential pumping, while allowing the electron beam to reach closer the sample. If the angle of observation is not perfectly parallel to the surface but deviated with an angle α, then it produces a distortion in the projection of the droplet profile. Therefore, the real contact angle θ must be geometrically derived from the apparent measured contact angle, ζ from the images, which is relatively simple and was thoroughly discussed by Brugnara et al. [10] However, determination of the contact angle is also possible when the electron beam is perpendicular to the sample surface only that the contact angle must be extracted from the beam intensity profile as described by Stelmashenko et al. [11] This later imaging technique has the advantage of the ease of measurement of a large number of droplets throughout the substrate surface. On the other hand, AFM is the ideal tool to measure the profile of a micro-/nanodroplet with very high accuracy, but with some caveats. The typical measurements are done in tapping mode and this method is more suitable for measuring droplets at the solid-liquid interfaces than at the solid-vapor interface because of the longer time required for the tip preparation and acquisition of the first image, typically 10–15 min, during which the liquid may have evaporated. In contact mode, the AFM tip/cantilever will penetrate through the interface and droplet profiling is not possible. In AFM tapping mode, the height and the contact angle decrease with greater imaging force (Fig. 5.7A and B), under a high imaging force, the droplet flattens out. A high force can also be used to rupture an interfacial droplet and move it. Such applications are however nontrivial and require extensive optimization effort of the imaging parameters.

FIG. 5.6

Saturated vapor pressure of water as a function of temperature [9] in the relevant environmental SEM (ESEM) working conditions.

84

5. Wettability of surfaces

FIG. 5.7 (left) Profiles of a single interfacial decane nanodroplet at different AFM tapping-mode set points in 25% ethanol in water solution on OTS modified glass substrate. (A) high setpoints, low imaging force; (B) low set-points, high imaging force. (right) AFM image of the dodecane water. Reproduced with permission from X.H. Zhang, W. Ducker, Interfacial oil droplets, Langmuir 24 (2008) 110–115. https://doi.org/10.1021/la701921z. Copyright 2008, American Chemical Society.

For example, care must be taken that the force applied to the tip is not causing the penetration of the droplet and consequently the formation of liquid bridges between the tip and the liquid droplet. Therefore, in tapping mode AFM the contact between the tip and the droplet must be kept as short as possible to reduce the probability of bridge formation and liquid droplet profile distortion (Fig. 5.7), on the order of microseconds, which can be achieved with cantilevers that have high resonance frequencies. Experiments have shown a variation of the contact angle as the droplet size decreases in the nL and pL range, i.e., diameters of the droplet baseline in the micrometer range. The analysis of the contact angle dependence with the size has thus required the introduction of a contact line tension. If the influence of the contact line tension becomes significant then it should be accounted for. Intuitively, the line tension can be understood as the tension that arises in a line, such as an elastic line or a cord. The three-phase line in the case of a droplet is the perimeter line that can have a positive or a negative tension. There have been efforts to include the effects of the line tension γ SLG, defined as the excess free energy at the threephase line (J/m), which directly correlates with the size of the droplets and Yong’s equation [2]: γ (5.5) γ SL ¼ γ SG + γ LG cos θ + SLG r which reduces to Young’s equation for r ! ∞ and r is the radius of the base of the droplet. The above equation can be rewritten into a different form such that: γ (5.6) cos θ ¼ cos θ∞  SLG rγ LG where cos θ∞ ¼

γ SL  γ SG γ LG

(5.7)

The line tension values can be calculated plotting cos θ vs. 1/r. Typical values range between 109 and 108 J/m for small r (below 1 mm to several μm) and 106 to 105 J/m for r larger than 2 mm. For very small volumes of liquid in the pL range, this becomes significantly influenced by the local heterogeneity of the surface or roughness and porosity [12]. The contact line tension can also be negative or positive, unlike surface tension that is always positive.

5.2 Classification of surface hydrophobicity vs. the magnitude of the contact angle with water Hydrophilic surfaces for which the contact angle is less than 30 degrees can be of great practical importance. For example, the contact lenses are hydrophilic and adhere to the tears, thus a thin tear film can be formed between

5.2 Classification of surface hydrophobicity vs. the magnitude of the contact angle with water

85

the cornea and the lens. PMMA polymer was used for such applications, however in the early days it was untreated, the contact angle with water was about 60 degrees, but in modern contact lens technology, this is hydrophilized and the contact angles have become more comfortable for the wearer. One way for surface hydrophilization is to expose the surface to UV light, plasma, and arc discharge. In this way even, the surface of Teflon can be made hydrophilic, which allows for adhesive, such as epoxy, to bind the surface of Teflon. Also, the dental implants or bone implants, typically TiO2, must be made hydrophilic prior to implantation for a better osteoblast adhesion and bone growth. Hydrophilic surfaces: those surfaces have a high affinity to water. One can imagine a simple experiment, immersing a material in water then pulling it out. If the surface remains wet, and water has difficulty running of the substrate, then the material has a high affinity to water and is hydrophilic. In other words, the surface of the material is hydrated. In fact, most of the superhydrophilic materials tend to adsorb water from the atmosphere. For example, NaCl or CaCl2 are hygroscopic materials and adsorb water from the atmosphere. Van Oss [13] proposed that the degree of hydrophilicity can be estimated by the hydration energy and concluded that the hydrophilic molecules have a hydration free energy below ΔG <  113 mJ/m2, and above this threshold they are hydrophobic. His results come from analyzing the free energy of hydration of molecules. Note that we have used here and throughout this book, as it is also customary in the community, some concepts interchangeably namely the hydration energy of a molecule and the hydration energy of a surface, or the surface energy of a solid and the surface energy of a molecule, polar and dispersive energy components of a surface and molecules. While there are some fundamental differences, one could easily imagine that a molecular entity also has an interface with its surrounding, meaning that the concepts that apply to the surface of a molecule such as hydration, surface energy, polarity, can be easily extrapolated to macroscopic surfaces. Therefore, Van Oss’s threshold for the free energy of hydration can be applied to surfaces as well. Using this threshold value for the hydration energy, one can use it in the equation relating the energy of adhesion to contact angle Wadh ¼ γ LG(1 + cos θ) from which it comes out that the threshold contact angle for water on the hydrophilic surface is 58 degrees. Above this value, substrates can be considered partially hydrophobic and hydrophobic, 58 degrees < θ < 110 degrees, where 110 degrees is the maximum achievable contact angle. Drelich et al. [14] proposed that surfaces with 0 degrees < θ < 58 degrees are partially hydrophilic, and surfaces with θ ¼ 0 degrees are hydrophilic. For example, water spreads completely, θ ¼ 0 degrees, on freshly cleaned very flat uniform glass (also referred to as float glass that is prepared by pouring a sheet of molten glass on a bed of molten metal, typically Sn or Pb). Water also spreads completely on high energy surfaces such as noble metals, Au, Pt, etc. Interestingly, water on ice has a nonzero contact angle. Even though these perfectly flat surfaces have a very low contact angle with water, they are not considered superhydrophilic. Superhydrophilic surfaces: those surfaces have some degree of roughness such that the Wenzel factor r > 1 (see Eq. 5.10). For these surfaces, the water spreads completely with θ ¼ 0 degrees. But then why are they superhydrophilic? Because by introducing roughness and nanostructuring on any surface whose θ < 60 degrees for the Wenzel factor r ¼ 1, will be completely wetted by water for r > 1. Why is then superhydrophilicity important if clean glass can also be completed wetted by water? The answer is that the surface cleanliness of glass and other high energy surfaces such as those of metals is hard to maintain; for example, glass or gold left in the air for a longer time acquire nonzero contact angles with water due to adsorption mercaptans normally exhaled from the respiration of humans, oxidation processes, etc., in other words, these surfaces will become unclean very easily. Following the surface adsorption from the atmosphere of different agents, the contact angle of water on nonclean glass can easily increase to several tens of degrees. By surface roughening or nanostructuring on the other hand, it is achieved that these surfaces maintain their full water wettability and contact angle zero even if they become slightly dirty in the atmosphere. The superhydrophilic surfaces have important application in, adhesion, antifogging, cleaning, nanotechnology, high-tech applications for high-performance lenses and telescope mirrors, or antibiofouling surfaces of great importance in household and health sectors. Hydrophobic surfaces: as already mentioned contact angles with water between, 58 degrees < θ < 110 degrees, indicate a hydrophobic surface. A θ ¼ 110 degrees, is the maximum achievable contact angle with water of a surface according to theoretical calculations on idealized flat surfaces, but in reality, this is not so strict, and slightly larger contact angles up to 120 degrees can be measured. Superhydrophobic surfaces: those surfaces have an advancing water contact angle θ > 150 degrees. The term of superhydrophobicity, or super water repellency was introduced in 1996 by Onda et al. [15, 16] to describe unusually high water contact angles, 170 degrees, observed on the surface of the wax-like solidified mixture of alkyl ketene dimer (AKD) and di-alkyl ketone (DAK) during cooling produced a fractal-like structuring of the surface. Such large contact angles have not been observed on flat and smooth hydrophobic materials, where the typical hydrophobization agents used to increase the contact angle were the perfluorinated compounds. Superhydrophobicity requires roughness or patterning of the surface and can be achieved in principles on substrates whose θ > 60 degrees by a one- or two-level surface topographical structuring/nanostructuring (see Fig. 5.8). The parameters indicating a superhydrophobic surface advancing water contact angle θ > 150 degrees, and the contact angle hysteresis as well as the sliding (or roll off ) angle does not exceed 5–10 degrees. Superhydrophobic surfaces

86

5. Wettability of surfaces

FIG. 5.8 Two levels of topographical surface structuring for achieving superhydrophobic surfaces.

were inspired by nature, in lotus leaves or petals of roses. Interestingly, touching of the superhydrophobic surfaces triggers an unpleasant tactile feeling. Switchable surfaces: they are stimuli-responsive surfaces capable of reversibly switching their surface properties between superhydrophobicity and superhydrophilicity. These can be fabricated by chemical modification of rough surfaces with stimuli-responsive polymers and molecules. The externally applied stimuli can be light, electrical potential, temperature, pH, etc. Such surfaces with switchable wettability are significant for both fundamental research and practical applications.

5.3 Dynamic, advancing, and receding contact angle By dynamic contact angle, one understands the contact angle of a liquid droplet during the advancing or receding of the three-phase line perimeter. Advancing and the receding contact angle can be measured in different ways, either by expanding and contracting the volume of the sessile drop by pumping in or out liquid, or by tilting it. In addition, the advancing and receding contact angle can be measured with a tensiometer by measuring the force during immersion and withdrawing of a sample from a liquid. Often there is a difference between the values of the receding and the advancing contact angles, and this is called hysteresis. It is believed that a large hysteresis is an indication of large surface heterogeneity at the micro- and nanoscale, in terms of roughness or surface chemical patchiness that eventually pin the three-phase contact line and prevent it from receding. Expansion and contraction of a sessile drop: the “static” advancing-receding contact angle can be performed by leaving the syringe needle into the sessile droplet and pumping liquid and withdrawing it from the droplet according to the cartoon in Fig. 5.9. The difference between advancing and receding contact angles is called hysteresis and it is an important parameter in surface characterization. The dynamic advancing-receding contact angles can be measured with a tensiometer by suspending a sample from a sensitive balance and lower it into the liquid of known surface tension, depicted in Fig. 5.10. The dynamic advancing

FIG. 5.9 Measurement of the advancing and receding contact angles by pumping or withdrawing liquid from a sessile drop (left). Advancing and receding contact angle by tilting stage measurement, where the sample surface is tilted at various angles. The roll-off angle can also be measured by this method, meaning the value of the angle at which the droplet detaches from the surface and rolls off the surface (right).

5.3 Dynamic, advancing, and receding contact angle

87

FIG. 5.10 (A) Measurement of the dynamic contact angle with the tensiometer. The sample hangs from a sensitive balance that measures the dipping (advancing) and withdrawal (receding) forces of the plate from and into a liquid with known surface tension. (B) Tensiometer data, showing the change in weight during dipping and withdrawing of a tooth implant from water, from which the advancing and receding contact angles are calculated in C. The effects of threads of the implant as they go in and out of liquid are clearly visible. Modeling the complex shape of the tooth implant is crucial for the accuracy of the method, because the wetted perimeter constantly changes as the water front goes around the threads. (C) The advancing and receding contact angle values of the tooth implant calculated from the data in B. A hysteresis is clearly visible between the average value of the advancing contact angle of 102.5 degrees and receding contact angle of 83.5 degrees. The presence of threads contributes to increase in the uncertainty of the measurements but does not impede the actual measurement. (D) Preparation of the powder films glued on a glass slide by agitating/shaking the glass slide with fresh glue into a sample tube containing powders. The coated glass slide can be used for the dynamic contact angle measurement with the tensiometer.

and receding contact angle can be measured by slowly lowering or retracting the sample in the plate form into or from the liquid, respectively. The contact angles are then calculated by measuring the forces F during the plate immersion or withdrawal with the following equation: cos θ ¼

Ftotal Pγ

(5.8)

as described before P is the wetted perimeter, which is the cross-section of the sample that must be precisely known. The wetted perimeter of a plate of a certain thickness is a rectangle and that of a cylinder is a circle. Samples with different geometries can be measured, such as rods, tubes, hollow tubes, if the surface has the same properties in the inner as in the outer surface, needles, wires, and even more complex shapes such as a bone and teeth implants. If the wetted perimeter varies during the dipping of the sample, for example, a conically shaped piece upon dipping will have an increasing perimeter due to changing circular radius of the cone’s cross-section this has to be modeled and taken into account to obtain the real value of the contact angle. Very complex shapes such as a screw with fine threads (Fig. 5.10B and C), has obviously a very complex surface geometry that would be difficult to model, or may even trap air bubbles between the threads, but even so, if all aspects are considered one could apply this method to measure an effective contact angle, depending on the application, although different methods might be more appropriate for it. It is also important to note that the tensiometer method can be used extensively for determining the contact angle of powders. A powder can be any solid, molecular solid, take for example caffeine, naphthalene, etc., or constituted of particles, such as zeolites, metallic nanoparticles or polymeric micro- and nanoparticles. This is a powerful aspect

88

5. Wettability of surfaces

TABLE 5.1 Table containing the total surface energy components of the theophylline and caffeine using the contact angle data from three polar liquids, water, ethylene glycol and formamide, measured on powders immobilized with glue on a glass slide with the tensiometer method. γtotal LV

γ LW S

γ AB S

γ +S

γ2 S

Theophylline

44.4

43.8

0.7

0.0

6.7

Caffeine

47.9

44.5

3.4

0.5

5.9

%Caffeine coverage

0

25

50

75

100

Contact angle (degrees)

89.7  1.1

84.5  1.6

81.4  3.2

78.7  1.2

73.2  3

Data from J.W. Dove, G. Buckton, C. Doherty, A comparison of two contact angle measurement methods and inverse gas chromatography to assess the surface energies of theophylline and caffeine, Int. J. Pharm. 138 (1996) 199–206.

of these surface science methods, as the polarity of a certain molecular compound can be measured applying the entire arsenal of tools and theories, such as the estimation of the surface energy and its polar, disperse, and hydrogen components, or even acid and base components, which can be extremely useful. These methods have been successfully applied [17] to pharmaceutical actives; the surface energy components of two important drugs, such as theophylline (used in the therapy of respiratory diseases) and caffeine (nerve stimulant) both from xanthine class, see, showing slightly more acidic and hydrophobic nature of caffeine (Table 5.1). In order to fix the powder on the surface of the plate hydrophobic or very low surface energy glue can be used, namely, a thin sheet of glue is applied on a microscope glass plate, ensuring that the glue relaxes in a flat and smooth surface free of ridges, pores, or microstructures. Before the glue cures the plate is immersed in a powder container and by agitating the container a cloud of dust settles on the surface of the glue as in Fig. 5.10D. It is important that the deposition on the surface of the glue is as homogeneous as possible. The sample is then blown with compressed nitrogen to remove the loose particles. Ideally, a monolayer of particle is now on the surface of the glue, tightly packed and the surface has no patches exposing bear glue surface. This can be verified with the help of AFM or SEM. Even in ideal packing conditions, there might be some space in between the particles exposing the glue surface, which may come into contact with the contacting liquid. This is especially critical with the increasing the size of the particles to the micro range and less so for molecular powders. Experiments performed have shown that the determined contact angles on powders fixed on the glue surface have a linear dependence on the surface coverage, between that measured on powder-free glue surface and 100% powder coverage (Table 5.1). Of significant importance in measuring powder is the roughness of the surface. If the surface is rough due to the porosity of the substrate or size of the powder grains then the wetted perimeter must be determined before with a liquid with a known contact angle and surface tension, typically hexane, whose contact angle is typically taken as zero. If the perimeter cannot be determined this way, then it is expected that the measured contact angles are in fact deviating from the real ones. The minimum size of roughness estimated as the average height between peaks and plateau that is thought to affect the contact angle data for water is regarded to be around 0.1 μm [18]. The dynamic advancingreceding contact angles of a sessile droplet can be measured by tilting a substrate. The advancing-receding contact angle values depend on the tilting stage angle, α. The critical tilting stage angle is the value for which the sessile droplet begins to roll on the surface. The measured value of the contact angles measured is called roll-off advancing-receding contact angles.

5.4 Contact angle hysteresis The contact angle hysteresis is the difference between the advancing and receding contact angle θA/θR and is mostly attributed to the existence of heterogeneity on the surface which causes the pinning of the three-phase contact line. Understanding the contact angle hysteresis is relevant for the development of functional surfaces, among which those with ultrahigh liquid-repellant properties, termed superliquiphobic surfaces [19]. While it may seem trivial, finding a rigorous and unified treatment of the contact angle hysteresis has been historically a very debated problematic and for further reading the work of McCarthy and coworkers give a good summary of these issues [20–22], and by many others [23–27]. If we imagine a sessile droplet on a horizontal substrate with partial wetting of the substrate, upon tilting, it may slide or roll to a new position. During tilting, the sessile droplets deform such that at the advancing front it acquires a higher contact angle and at the receding front the contact angle becomes lower than that measured when the substrate is horizontal. If both contact angles are sufficiently large the droplet may slide or roll on the substrate. The

5.4 Contact angle hysteresis

89

mechanics of movement of a sessile droplet from one metastable state to the other requires activation energy. For the advancing front, the activation energy is lower than for the receding front. The reason for this is because only the receding front requires the unpinning of the three-phase contact line, while the advancing front does not. At the advancing front even though the contact line is pinned the droplet can advance with the liquid-vapor interface falling on to the substrate, much like of a tank treads, as depicted in the cartoon of Fig. 5.12B. The main issues debated were the origin of contact line pinning, see the comparative discussion between McCarthy’s group [28] and Morra’s group [27] and the introduction of the concepts of shear and tensile induced hydrophobicity. The common understanding is that chemical or topological heterogeneity leads to contact line pinning. The shape of the nanopillar tops and their edge sharpness is € critical for liquid pinning, as evidenced in a classical experiment by Oner and McCarthy [22] in which they varied the nanopillar shape. Hysteresis, however, has been observed even on atomically smooth and chemically homogeneous substrate, that molecular (bond length scale) heterogeneities in solids as well as the molecular volume and structure of liquids can contribute to hysteresis [20], meaning the contact angle hysteresis is a nonvanishing quantity. The common knowledge from existing theories suggests that a shorter contact line at the receding front should lead to lower activation energy and for the detachment and low hysteresis of the receding line, such as in the Cassie-Baxter situation (sessile droplet sitting at the top of nanopillars). The lengthening and increasing the tortuosity of the contact line at the receding front such as in the Wenzel or any intermediate situation between the Cassie-Baxter and Wenzel cases (sessile droplet completely or partially wetting the nanopillars) leads to an increase in the detachment energy and a high hysteresis. The surfaces in the former case are called “slippery” superhydrophobic surfaces and in the latter case “sticky” superhydrophobic surfaces [24]. Contact angle hysteresis on smooth chemically heterogeneous surfaces: several types of surfaces exhibit very low contact angle hysteresis, 1, than that for the ideally atomically flat surface (left), for which r ¼ 1. Note that the droplet touches the bottom of the wells.

smooth interface. When the contact area of the liquid (L) to the surface (S) is smaller than that for the ideally flat surfaces, r < 1, and this reduces the energy of adhesion. Oppositely when the contact area between L and S is larger than that for an ideally flat surface, r > 1, as depicted in Fig. 5.13, it means that the liquid is able to penetrate the crevices rugosities of the surface, which increases the energy of adhesion. The parameter r is calculated by dividing the actual, roughness-enhanced surface area by its projection. Therefore, the observed contact angle must be related to r and the previous equation becomes: ð1 + cos θÞ ¼ rð1 + cos θ0 Þ

(5.10)

where θ0 is the ideal contact angle of the liquid on an ideally flat surface. The last equation differs somewhat from the classical equation proposed by Wenzel in 1936: cos θ ¼ rcos θ0

(5.11)

However, Israelachvili [32] pointed out that the most serious shortcoming of the last expression is the fact that it predicts no effect of the roughness when θ0 ¼ 90 degrees [32]. Based on experimental evidence, area some researchers argued that the wetting perimeter is the most important factor, rather than the contact area [33]. Why is this equation useful? This equation is useful to predict the effects of the surface roughness and structuring on the observed contact angle. The way roughness affects the wettability of a surface by a liquid can be dramatic, for example, it can enhance it if the wettability of the liquid is good. For example, for a liquid with a good wettability of θ0 < 10 degrees for r only slightly larger than unity (when the liquid penetrates the hills and valleys of a rough surface as in Fig. 5.13), it becomes a perfectly wetting liquid with θ ¼ 0 degrees. Oppositely, for a poor wetting liquid with θ0 > 70 degrees for the case of r < 1, the contact angle greatly increases such that Lotus leaf effect is observed, θ0 ¼ 70 degrees. Lotus effect and this is due to the nanostructured surface of the Lotus leaf that has micron-sized pillars [34] on which water makes a large contact angle and cannot wet in between these pillars. Such surface structuring serves different purposes, for example, the Lotus leaves never become dirty. Several such situations are summarized in Table 5.2, for values calculated with Eq. (5.10), the Israelachvili’s modified form of Wenzel’s Eq. (5.11). Although both formula allow for r < 1 when the liquid does not follow the surface topography, sits on top of the roughness hills, in literature, the Wenzel situation is typically referred only to the situation depicted Fig. 5.13 when the liquid follows the topography of the surface, for r > 1 [23].

5.6 Wettability of liquids on heterogeneously flat surfaces—Cassie-Baxter model Smooth flat surface with two chemically different regions reflected in the difference in the contact angles of a liquid θ1 and θ2. What is the value of the contact angle that a liquid L makes on such surface? For this we choose a point P situated at a boundary between the two chemically different surface regions 1 and 2, depicted in Fig. 5.14A and B. The chemical composition near P varies continuously from 1 to 2 such as the surface fraction of each surface component, e.g., functional group, is f1 and f2, where f1 + f2 ¼ 1. The Young-Dupr
e equation for the liquid L on surface S is Wadh LS ¼ γ LG ð1 + cos θÞ

(5.12)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi But the work of adhesion is also given by Wadh ¼ Wcoh SS  Wcoh LL . By combining the two expressions, we obtain the resulting energy of adhesion of the liquid L on a flat surface:

92

5. Wettability of surfaces

TABLE 5.2 Evolution of wettability and surface contact angle due to surface roughness for poor, average and good wetting liquids calculated with Israelachvili’s equation and original Wenzel’s equation. r

θ0 θ (degrees) θ (degrees) (degrees) θ0 (rad) Israelachvili’s equation Original Wenzel’s equation Comments

1

10

0.17

10.0

10.0

Flat surface

1.0076464 10

0.17

0.0

7.1

For all r > 1.0076464, θ0 ¼ 0 Liquid penetrating

0.5

10

0.17

90.5

60.5

Liquid not penetrating

1 40 Average wetting liquid 10 degrees  θ0  70 degrees 1.0310589 20

0.70

40.0

40.0

Flat surface

0.35

0.0

14.3

For all r > 1.031059, θ0 ¼ 0 Liquid penetrating

1.1323283 40

0.70

0.0

29.8

For all r > 1.1323283, θ0 ¼ 0 Liquid penetrating

0.5

40

0.70

96.8

67.5

Liquid not penetrating

1

70

1.22

70.0

70.0

Flat surface

1.4896446 70

1.22

0.0

59.3

For all r > 1.489645, θ0 ¼ 0 Liquid penetrating

0.5

70

1.22

109.2

80.2

Liquid not penetrating

0.2

90

1.57

143.2

90.0

Liquid not penetrating Lotus effect

Good wetting liquid θ0  10 degrees

Poor wetting liquid θ0 > 70 degrees

FIG. 5.14

(A) In Cassie-Baxter model the liquid droplet sits on a chemically heterogeneous but flat surface consisting of patches of different chemical compositions, i.e., different functional groups. (B) The microscopic picture of the three-phase line at point P; in Israelachvili’s interpretation at point P, the three-phase line experiences on average a surface whose properties vary continuously between the patches S1 and S2 of pure chemical composition. In the region S12 the overall chemical composition of the surface varies continuously between the properties of the pure surface S1 and S2 with the corresponding fractions f1 and f2. (C) The position of a liquid droplet in the original Cassie-Baxter model sits on top of the pillars of a nanostructured surface, such that the liquid experiences a flat surface but heterogeneous between air and top of the pillars, in contrast to the Wenzel model where the droplet penetrates the nanopillar structure.

γ L ð1 + cos θÞ ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Wcoh SS  Wcoh LL

(5.13)

For a chemically heterogeneous surface, the above equation can be rewritten as γ L ð1 + cos θÞ ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f1 Wcoh S1 S1 + f2 Wcoh S2 S2  Wcoh LL

(5.14)

where S index is the surfaces, and this gives the general relation for the contact angle at a chemically heterogeneous surface, the Israelachvili’s modified form of Cassie-Baxter’s equation [32]: ð1 + cos θÞ2 ¼ f1 ð1 + cos θ1 Þ2 + f2 ð1 + cos θ2 Þ2 The original Cassie-Baxter equation is [35]

(5.15)

93

5.7 Transition from Cassie-Baxter to Wenzel state

cos θ ¼ f1 cos θ1 + f2 cos θ2

(5.16)

which was initially derived for a surface with pores. According to Israelachvili [32], the difference between the above equations is that the Cassie-Baxter’s equation is more appropriate for the surfaces with microscopic patches than nanoscopic ones. If the surface region S2 consists of pores that contain air and because air is considered an ideally hydrophobic medium with a corresponding contact angle θ2 ¼ 180 degrees, Eqs. (5.15), (5.16) become cos θ ¼ f1 cos θ1  1 + f1 ¼ f1 ð cos θ1 + 1Þ  1

(5.17)

This last equation implies that when f1 ≪ 1 and θ1 large then it is possible to observe very large contact angles on a surface containing pores. For example, if f1 ¼ 0.2 and θ1 ¼ 90 degrees then the apparent contact angle θ  143 degrees. Several situations are summarized in Table 5.3, for values calculated with Eq. (5.15), the Israelachvili’s modified form of Cassie-Baxter’s equation (5.16). In literature, the Cassie-Baxter wetting state is that of liquid droplet sitting on the peaks of pillars of a patterned surface [23], as shown in Fig. 5.14C.

Numerical example 5.1 If the contact angle of water on a purely hydrophobic surface is θ ¼ 110 degrees and that on a purely hydrophilic surface is θ ¼ 0 degrees, find using Cassie-Baxter equation the contact angle when the hydrophobic fraction f1 and hydrophilic f2 fraction are: (a) f1 ¼ 0.5, (b) f2 ¼ 0.1, and (c) f1 ¼ 0.1

Answer (a) cosθ ¼ 0.5  (0.34) + 0.5  (1) ¼ 0.33, θ ¼ arccos(0.33) ¼ 70.8 degrees, 1 rad ¼ 360 2π ¼ 57:3 degrees. (b) cosθ ¼ 0.9  (0.34) + 0.1  (1) ¼  0.206, θ ¼ arccos(0.206) ¼ 101.9 degrees. (c) cosθ ¼ 0.1  (0.34) + 0.9  (1) ¼ 0.866, θ ¼ arccos(0.866) ¼ 30 degrees. Thus, according to Cassie equation, a surface may be said to be fully hydrophobic when θ > 90 degrees partially hydrophobic when θ between 45 and 90 degrees and weakly hydrophobic below 45 degrees.

5.7 Transition from Cassie-Baxter to Wenzel state Usually, liquids exhibit either the Cassie-Baxter wetting state or the Wenzel wetting state on a patterned/rough surface. In the Cassie-Baxter state, air trapped in the grooves between surface features forms a patchy or marbled (solid/air) superhydrophobic surface, resulting in a larger contact angle θ than those compared to the contact angle θ with a flat surface (see Fig. 5.15) [36]. The Cassie-Baxter wetting state is considered a metastable state, as the liquid sits on top of the pores or pillars and could eventually penetrate in between the pores via different mechanisms, such as TABLE 5.3 Evolution of wettability and surface contact angle due to surface chemical heterogeneity or pores for poor, average and good wetting liquids calculated with Israelachvili’s and original Cassie-Baxter’s equation.

Good wetting liquid θ0  10 degrees

Average wetting liquid 10 degrees  θ0  70 degrees

Poor wetting liquid θ0 > 70 degrees

θ2 (degrees)

θ (degrees) Israelachvili’s equation

θ (degrees) Cassie-Baxter equation

Comments Chemically heterogeneous surface

f1

f2

θ1 (degrees)

0.1

0.9

10

5

5.7

5.7

0.5

0.5

10

5

7.9

7.9

0.9

0.1

10

5

9.6

9.6

0.1

0.9

20

40

38.4

38.4

0.5

0.5

20

40

31.3

31.5

0.9

0.1

20

40

22.6

22.7

0.2

0.8

90

180

123.6

143.2

0.3

0.7

90

180

116.9

134.5

0.2

0.8

75

180

116.0

138.5

Chemically heterogeneous surface

Lotus effect for f1 < 0.2 Surface with pores or pillars for which θ2 ¼ 180 degrees

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5. Wettability of surfaces

FIG. 5.15 Transition from Cassie-Baxter to Wenzel states on a structured surface composed of pillars. The Cassie-Baxter situation assumes that the water does not penetrate the grooves of the surface and consequently experiences a mixt air/solid surface. Transition to the Wenzel state takes place when water penetrates the grooves of the surface, either by unpinning of the three-phase line or evaporation due to the Laplace pressure and filling up the pores, resulting in higher surface wettability due to increase in the contact area.

unpinning of the three-phase line or evaporation and filling up the pores due to increasing Laplace pressure (Fig. 5.15). Murakami et al. [36] discuss the activation energy barrier that exists at the transition between the Cassie-Baxter to Wenzel state and also succeeded to measure it by making nanopillars of different aspect ratio and distance, prepared by photolithography from a perfluorinated photoresist. This activation energy of transition could be overcome either by mechanical, electric, heat or light, or increase in Laplace pressure due to sagging of the liquid droplet between the pillar. The fluid dynamics on such surfaces is very different, for example, the liquid droplets are very mobile and dynamic in the Cassie-Baxter state and immobile in the Wenzel state due to fully wetting of the surface and pinning of the threephase line. It turns out that to control the liquid dynamics on such surfaces design of the textured surface that possess low activation energy between both states is necessary. Unfortunately, due to relatively large activation energies, this is not possible without the help of external stimuli. This triggered the active research of stimuli-responsive surfaces that switch between superhydrophobicity, water contact angles larger than 150 degrees, to superhydrophilicity that is complete wetting, under different external stimuli, e.g., electric, pH, temperature, etc. For example, one class of photosensitive materials, inorganic semiconducting oxides such as TiO2, ZnO, SnO2, WO3, V2O5, and Ga2O3 can switch the surface chemical environment between two states (oxygen vacancies and hydroxyl groups). Therefore, it is possible to obtain a surface capable of reversibly changing its wettability properties from superhydrophobic (in the dark) to superhydrophilic (under UV light exposure) upon creating nanopatterns or simply roughening the surface of such materials [37]. Electro-responsive surfaces that can switch between the two states have also been created. For example, using nanolithographic processes, Krupenkin et al. [38] have created “nanograss” and “nanobrick” substrates that switch their wettability by water upon application of electric potential; the underlying principle, in this case, is either the evolution of gas at the solid-liquid interface which is effectively able to produce de-wetting or the rapid changes in the temperature of the solid-liquid interface which provides the extra energy to switch between the two states. A chemical example is given by Xu et al. [39] which report an electrochemical process for making superhydrophobic surfaces from semiconducting polypyrrole (PPy) polymer, the underlying principle of switching under electric potential is that when the PPy is electrochemically doped (oxidized state the N acquires partial positive charges), it becomes hydrophilic and this can be reversibly changed by electrochemically to an undoped or neutral state which is hydrophobic. Thermoresponsive wettability switching surfaces have also been created from anodized alumina pores surface grafted with the temperature-responsive polymer PNIPAM (polyisopropylacrylamide) by Fu et al. [40] There are many examples of smart stimuli-responsive switchable surfaces that have been designed in the last decades, and extensively reviewed by different authors [41, 42].

5.7.1 Case study: Wettability of antifogging surfaces—From mirrors to solar panels The fog is the result of the water vapor condensation from the surrounding air in tiny droplets on a surface when its temperature is less or at the dew point. Similarly, when breathing on a surface “breath figures” [43] appear due to

5.8 Roll-off and sliding angles of a sessile droplet

95

condensation of the exhaled water vapor into many tiny droplets; when the diameters are greater than half of the shortest wavelength of violet light (380 nm), the fog/breath figures become visible as a whitish-cloudy layer. The whitishcloudy appearance of the fog on a transparent material surface causes a blurred view because due to the scattering of the incident light. Condensation of water vapor and fogging on transparent material surfaces such as safety goggles, eyeglasses, windows, helmets, skiing helmets, car windshields, etc. can pose a serious threat to the safety of humans as it hinders good visibility. Other products with antifogging properties can be sold as premium products such as specially treated bathroom mirrors, eyeglasses, camera lenses, etc. Briscoe et al. [44] measured the reflectance and transmittance of normal incident light on different transparent polymer and glass slides covered by fog and found that the intensity of the transmitted light is unaffected by fogged surfaces for which the water contact angle is below 48.8 degrees. For substrates with the contact angle between 48.8 and 90 degrees, the transmitted light intensity decreased significantly, due to the total internal reflection at the water/air interface when the droplets have a water contact angle greater than the critical value of 48.8 degrees according to the Snell’s law [44]. In addition to the shape, the size of the droplets is the second factor which affects the intensity of the transmitted light, namely the smaller the size, the larger the number of water droplets per unit area, which contributes to a stronger light scattering. Upon increasing the size of the water droplets coalesce and the fog converts into larger droplets, that scatter less light, and eventually can coalesce into a thin continuous film that regains transparency. Freshly cleaned glass or quart substrates exhibit low or zero water contact angles with water. On these the water condensation immediately produces a thin and continuous water layer that does not impede the visibility. However, the glass surfaces immediately become dirty by the adsorption of dust and organic molecules, from the environmental air or exhaled breath air, such that typical water contact angles for these glass substrates lie commonly between 40 and 60 degrees. Therefore, fogging of the glass mirrors, windows, and windshields is mostly observed. Special treatment must be then performed to treat these surfaces and make them hydrophilic again. Antifogging coatings, such as polymers bearing polar groups hydroxyl (OH), amino (NH2), or carboxyl (COOH), and inorganic materials such as SiO2, TiO2, or ZrO2 are typically applied on transparent substrates to improve the affinity with water and lower the water contact angle. Different such strategies have been extensively reviewed and discussed in the literature [45, 46]. Superhydrophilic surfaces are particularly interesting in applications for their antifogging properties. To reiterate, “superhydrophilicity” refers to solid surfaces on which water exhibits zero water contact angles and exhibits the same property after long exposure to a normal atmosphere (unlike glass surfaces). A typical superhydrophilic surface is that of a nanostructured/rough hydrophilic surface (Wenzel factor r > 1) over which water spreads completely factor. In theory, surfaces with water-repellent properties (superhydrophobic with low contact angle hysteresis) may also exhibit antifogging properties. The requirement, in this case, is that the substrates must be tilted so that the water droplets condensed surface can easily roll off. This is particularly interesting for the surface of photovoltaic panels, which can have multiple properties, antiicing, antifogging, and self-cleaning.

5.8 Roll-off and sliding angles of a sessile droplet Roll-off angle can be measured by tilting a stage/substrate and it is the tilt angle α at which the droplet detaches from the substrate (Fig. 5.16). This is very important in applications dealing with the design of self-cleaning surfaces, or water-repellent textiles such as ski clothing or sailing equipment. For example, in aviation, it is particularly desired to have the surface of the wings such that water rolls as fast as possible to reduce friction forces. This is typically applied on the hydrophobic surface with very high contact angles, on the more hydrophilic surfaces with low contact angles is also possible but the droplet of liquid deforms and slides rather than rolling off as a sphere. Tilting speed of the stage is also a factor that can influence the roll off angle. The equation predicts the minimum angle of tilt α at which a sessile droplet with surface tension γ LV will spontaneously move [28, 47]: mg  sin α ¼ w  γ LV  ð cos θR  cos θA Þ

(5.18)

where g is the gravitational constant, m is the mass, and w is the width perpendicular to the direction of drop movement of the sessile droplet. The roll-off or sliding angle of a sessile droplet should decrease with both decreasing liquid surface tension and decreasing of the contact angle hysteresis.

96

5. Wettability of surfaces

FIG. 5.16 The roll-off advancing and receding contact angle of a sessile drop by tilting stage method.

5.8.1 Case study: Waterproof clothing Waterproof and windproof clothing and garments are of great interest and in great demand especially for sports or activities performed in extreme weather conditions, at sea or in winter. Manufacturing clothing with waterproof quality may seem at first glance easy and can be achieved by continuously coating garments’ surface with a polymer, such as PVC, Neoprene rubber, polyurethane, silicones, fluorocarbons, etc. These hydrophobic polymers can increase the contact angle for water and greatly reduce the roll-off angles. However, designing of waterproof and windproof clothing constitutes a challenge for the comfort of the wearer. The main factor determining the comfort is the breathability of the clothing and their ability to transmit the water vapor resulting from body perspiration and sweat. In the absence of breathability, wearing impermeable clothing can create significant discomfort as the accumulated water can lead to severe risks of injuries in extreme weather conditions. In hot weather, the accumulated water may lead to overheating of the body and in extreme cold weather, the perspiration-soaked clothing loses their insulating properties and increased the risk of chill and hypothermia. According to Lomax [48], water vapor is transmitted through noncoated textiles through three main mechanisms: (i) Simple diffusion through the interyarn spaces, mainly governed by garment construction, such as size and concentration of interyarn pores, and the fabric thickness. (ii) Capillary transfer when the liquid is drawn off—“wicked”— through the yarn and evaporated at the outer surface. This depends on the wettability and the contact angle of the fibers, and the size and number of capillary spaces. (iii) Diffusion through individual fibers, when the water penetrates and soak the individual fibers and desorbs at the outer surface. This depends on the hydrophilicity and hydrophobicity of the fiber itself. For open-weave fabrics, the first diffusion mechanism is dominant and does not depend on the type of yarn used. As the size of interyarn spaces decreases in tightly knitted fabrics, as is the case in winter clothing, the secondary mechanisms (ii) and (iii) become more important. The tightly woven fabrics constructed from hydrophilic fibers such as wool, cotton, viscose, etc., are more transmissive to water than the similar synthetic hydrophobic fibers from polyester, polyethylene, nylon, etc., because of their ability to diffuse water into the fiber structure. The surface of a textile can be imagined as a thin sheet with pore sizes (several microns) several orders of magnitude smaller than the rainwater droplets (several millimeters). To assess the waterproofness of textiles, assuming the capillarity and wicking are the dominant mechanisms, the pressure required for the water to penetrate the pores is given by the Laplace pressure: ΔP ¼

2γ cos θ R

where γ is the surface tension of water, θ is the contact angle of the water, and R is the pore radius. From the above equation, it can be deduced that by reducing the size of the interyarn pores and increasing the contact angle θ, the textile becomes water repellent. To increase the contact angle θ a variety of coating can be applied to make the fiber hydrophobic, with care not to close the pores. Amphiphilic molecules that attach to the fiber and expose hydrophobic parts are suitable for this purpose, however, their main drawback is that they can be washed out in several washing cycles with regular detergent and the hydrophobization treatment must be reapplied. Further, increasing the surface roughness of the textile can lead to a superhydrophobic Cassie-Baxter regime. If the textile sheet has the same properties on the inside in contact with the body as on the outside, it will compromise and diminish the breathability of the fabric from inside out. Therefore, it is essential to design clothing with a high density of small interyarn spaces that are hydrophobic or superhydrophobic on the outside and hydrophilic and water

5.9 Measurement of the contact angle with the captive bubble method

97

absorbent on the inside. For this purpose, either only the outer side of the textile sheet is hydrophobized or multilayer sheets are used. The first textiles engineered waterproof and water-vapor permeable properties were designed during the World War II at the Shirley Institute, a research center in the United Kingdom dedicated to developing novel cotton textiles and their production technologies. These are available under the Ventile trading name. They were first worn by the Royal Airforce (RAF) in wartime in 1943 by pilots flying over the Atlantic, keeping warm and comfortable in the cockpit but remained waterproof in contact with water increasing pilot’s survivability. These garments were later used in the first summit of Everest in 1953 and by Sir Ranulph Fiennes when he crossed the Arctic from 1979 to 1982 [49]. In the dry state, Ventile garments are interwoven in a special pattern from natural cotton to impart a low-level of air permeability (windproof ) and an exterior hydrophobic finish is typically applied. The hydrophilic nature of the fiber, the weaving pattern combined with the exterior hydrophobic treatment ensures a good level of water vapor permeability in dry conditions. When the fabric is wetted by rain, or contact with water, the cotton yarns swell rapidly which reduces the interyarn pores from approximately 10 μm down to 3–4 μm across. The reduction in pore size, together with the applied exterior hydrophobic finish prevents any further penetration by water [48]. The modern understanding in the design of waterproof and breathable clothing involves the construction of garments in a multilayer approach, a water-absorbent inner liner, a hydrophilic textile layer, or membrane capable of water transport through pores or hydrophilic fibers and an outer coating or a porous hydrophobic layer. GORETEX, Sympatex, Barricade, DryVent, HyVent are modern multilayer textiles and are used in a variety of waterproof, windproof breathable textiles from ski suits, outdoor shoes, winter and working gloves, and other protective equipment. GORE is an expanded microporous polytetrafluoroethylene (ePTFE) membrane used in the construction of waterproof breathable textiles, GORE-TEX. Sympatex textiles instead of pores use hydrophilic polyether channels to transport water, and hydrophobic polyester repels water.

5.9 Measurement of the contact angle with the captive bubble method In certain situations, in which a liquid droplet is not stable on the surface, the contact angle of a liquid on a substrate cannot be measured directly with the sessile droplet method. A different approach to measure the contact is to immerse the solid substrate until is fully wetted and then slowly displace the liquid from the interface with a gas bubble. Typically, an air bubble is produced in situ with a hook type needle and is carefully deposited on the substrate surface from underneath as depicted in Fig. 5.17. When the substrate is perfectly horizontal, the air bubble remains captive underneath the substrate, hence the name of the method. This measurement method is essentially measuring a contact angle value that is close to a receding contact angle because the surface is essentially prewetted, and the air bubble displaces the liquid. This method was used in the surface analysis to evaluate the hydrophilicity of reverse osmosis [50] and ultrafiltration membranes [51] with the purpose to predict the membrane performance and fouling potential. Measurement of the contact angle by sessile drop poses a challenge first because the adsorption of the droplet within the pores of the membrane leads to altered results and poor reproducibility and secondly the sessile droplet method requires the drying of the reverse osmosis polymer membrane which is far from its real operating conditions and can dramatically change its surface wettability [50]. Similarly, for the silicone hydrogel contact lenses, the contact angle determination by the sessile drop method is not possible as it requires first the dehydration of the polymer hydrogel [52]. Because the

FIG. 5.17

Captive air bubble method.

98

5. Wettability of surfaces

hydrophobic groups within the polymer chains may reorient themselves at the surface if left in a dry environment, it can render the surface of these materials less “wettable.” Because the surface tension liquid air interface can be determined from the height and width of the captive air bubble [53, 54], it has been found useful in the analysis of the interfacial mechanics and interfacial activity of lung surfactants and is applicable in a broad range from ultralow to very large surface tension values [55]. Surface analysis of lung surface active materials for which the sessile droplet method is not appropriate.

5.10 Natural and biomimetic functional surfaces Nature’s ability to generate surface wettability by generating functional surfaces remains a source of inspiration for materials scientists and chemists; petal roses and Lotus leaves exhibit a large contact angle with water and can selfclean and never become dirty. This inspired the creation of self-cleaning nanostructured surfaces, for example for windows in the skyscrapers that cannot be easily cleaned, or textiles for ski-clothing or rain-repellent that do not get wet even in extreme conditions. Dirt particles sitting on a rough or patterned surface, exhibiting an extremely low interfacial contact area with the substrate, are picked up by the running water droplets and thus the surface is easily cleaned (Fig. 5.18). Thus, the principle behind self-cleaning surfaces is to design surfaces that produce an extremely low interfacial contact area between dirt particle and the substrate that contributes to exceptionally low adhesion energy, while the adhesion between the dirt particle and the water droplet is larger due to a larger interfacial area. The self-cleaning effect works best with water and it does not work with low surface tension organic solvents. There are many examples of functional nanostructured surfaces where the interplay between nanostructuring and the interfacial phenomena are masterfully combined by nature to serve the living organisms. Several examples are worth mentioning. The Stenocara desert beetle wings—“elytra” are well known for their peculiar capability of water collection in the desert from the morning fog. Water condenses on the back of the beetle and will roll automatically toward its mouth [56]. The compound eye of a mosquito that even in a very humid environment can keep dry and clean, due to micro-sized hemispheres with an average diameter of 26 μm, rendering its surface superhydrophobic. This has inspired the creating of antifogging surfaces. Geckos are able to climb on both smooth glass windows as well as on rough tree barks; thanks to about half a million keratinous “seta” of 30–130 μm in length and 1–2 μm in diameter that equip the toes and the feet of this lizard. Each micro-seta is further branched into a few hundreds of

FIG. 5.18 (Left) no cleaning effect of a sliding droplet of water on a normal surface; dust or salt particles do not detach from the surface. (Right) cleaning of the surface by a rolling water droplet with a high contact angle on a structured/rough surface; the droplet carries increasingly more dust particles as it rolls down the surface.

5.10 Natural and biomimetic functional surfaces

99

spatula-shaped nano-hairs of 100–200 nm diameter making the Gecko feet highly adhesive and superhydrophobic [57]. And the examples are numerous: duck feather, mosquito eyes, and legs for water straddling, crane wings are superhydrophobic, Chinese watermelon, etc. The fascinating examples found in nature have triggered and continued to inspire scientists in creating new functional surfaces, often called biomimetic functional surfaces for different applications, industrial, or consumer goods.

5.10.1 Case study: Water collecting surfaces and surface directional transport of droplets In the Earth’s regions suffering from the absence of precipitation, fog can serve as a safe freshwater resource for entire populations and thus represents a strong motivation for developing technologies for fog water collection [58]. Several lifeforms have adapted to survive in extreme drought conditions. In the morning wet breeze of the arid Namib desert, the beetle Stenocara can collect water droplets on its back, by tilting its body forwards at roughly 45-degree angle; due to the special surface structure the water droplet grows and at when it reaches a certain volume it rolls down into the beetle’s mouth for drinking [56]. Detailed microscopic surface investigations revealed that the wings (elytra) of Stenocara consist of hydrophobic (valleys) and hydrophilic (bumps) regions. Water droplets condense from the fog on the hydrophilic patchy bumps of the Stenocara; the water droplets continue to grow eventually reaching the boundary of the hydrophilic/hydrophobic patchy bump, with the three-phase line becoming pinned at this boundary. The pinned sessile water droplet continues to grow on the wings of Stenocara wings until the weight of the drop overcomes capillary adhesion, and it rolls off. The natural surface of the desert beetle fulfills two functions, water collection, and directional transport. The key is the alternating hydrophilic and hydrophobic/superhydrophobic patches. While water easily condenses on hydrophilic surfaces, transport is hindered on such surfaces due to the pinning of the droplet’s three-phase line. Oppositely water condensation is somewhat hindered on hydrophobic/superhydrophobic patches, but the pinning of the droplet is minimized and thus it can more easily roll off [56, 59]. In the absence of the hydrophobic/superhydrophobic patches, the control over the water collection and its transport toward the mouth of the beetle for drinking would be poor and the droplet would be lost by reevaporation. This has inspired intensive biomimicry efforts to create a self-filling bottle and containers. Cactus species are extremely tolerant of drought and can survive arid regions thanks to a very efficient fog water collecting system [60]. The fog-water collection mechanism consists of conical spines and trichomes distributed on the cactus stem; the surface grooves and barbs help contribute to the condensation of water droplets. The droplet transport from the tip of the spine to the base when to be capture by trichome filaments is achieved due the spine’s conical geometry which causes a gradient of the Laplace pressure that stimulates capillary propulsion [60]. Spider silk, which is composed of hydrophilic fibrous proteins with a unique structure consisting of periodic spindle-knots made of random nanofibrils and separated by joints made of aligned nanofibrils. Being hydrophilic the spider silk has the good water-collecting ability from the atmosphere. The water droplets condensed on the silk fibers are directionally transported from the joints to the nearest spindle knots. It is believed that a surface energy gradient between the spindle-knots and the joints and a difference in Laplace pressure tow driving forces for droplet transport from the joints to the spindle knots. As pointed by Butt et al. [59], three important aspects contribute to efficient fog harvesting: enhanced condensation, control of lateral adhesion, and guided transport. Enhanced condensation occurs on highly hydrophilic surfaces. Fog water droplets can also be collected by a simple impaction process; in practice in high mountainous areas polymer woven nets are placed in the path of traveling fog cloud [61]. When fog water collection is done by impaction, hydrophobic polypropylene, PTFE, etc. Woven meshes are used to increase the efficiency of collection by the rapid detachment of the droplet from the surface. The second important parameter is the guided transport of the surface droplet to a capture point to avoid its loss by reevaporation. Guided transport or directional droplet movement on a surface can be achieved either by a gradient in surface wettability (gradient in surface energy [62]) and/or by geometric means such as conical shape [63] that leads to a gradient in the Laplace pressure between the advancing and receding front (Fig. 5.19) [64]. The gradient in surface energy is equivalent to the gradient in surface tension in fluids, responsible for directional motion, Marangoni flow. The driving force FChem due to surface chemical gradient of wettability is proportional to the gradient of the surface wettability [64]: FChem  πR0 γ ð cos θB  cos θA Þ where R0 is the radius of the droplet (Fig. 5.19A), γ is the surface tension, θA and θB are the contact angles at less wettable and more wettable side of the droplet, respectively. The driving force FLaplace for a droplet on a conical structure can be expressed as [64]:

100

5. Wettability of surfaces

FIG. 5.19 Driving forces for directional movement of liquid droplets. (A) Driving force arising from surface wettability gradient caused by surface chemistry (FChem) propels liquid droplets toward more wettable region. (B) Driving force arising from shape gradient (FLaplace) propels liquid droplet toward region with a larger curvature radius (smaller curvature 1/R). Reproduced with permission from J. Ju, Y. Zheng, L. Jiang, Bioinspired onedimensional materials for directional liquid transport, Acc. Chem. Res. 47 (2014) 2342–2352. https://doi.org/10.1021/ar5000693. Copyright © 2014 American Chemical Society.

FLaplace  

ð RL

2γ

R S ðR + R 0 Þ

2

sin α dz

where R is the local radius of the cone-structured object (Fig. 5.19B), RS and RL are the local radii of the object at the two opposite sides of the droplet, α is the half apex angle of the cone, and dz is the minute incremental radius along the cone. Simple surface wettability gradients can be prepared in different ways, for example by exposing a clean glass microscope slides to the diffusing front of the vapor of decyltrichlorosilane; after the gradient is formed the glass substrate is heated at 75°C for 15 min to complete the bonding on the substrate [65, 66].

5.10.2 Marangoni flow The Marangoni effect is the mass transfer along with the interface between two fluids under the action of a surface tension gradient. For example, if a droplet of liquid of low surface tension such as ethyl alcohol is left falling in the middle of a puddle of a larger surface tension liquid such as water, due to the surface tension gradient formed, the water liquid pulls away from the alcohol droplet. This phenomenon was also observed in wine, near the meniscus of the wine the liquid wets the glass, and its meniscus is bent upward. As the ethanol evaporates from this region and its concentration decreases a surface tension gradient is created and thus the water with a larger surface tension breaks away from the rest of the liquid and crawls up the wine glass, with time the so-called “tears of wine” are formed (Fig. 5.20). This phenomenon was first observed by James Thomson, the brother of Lord Kelvin but is named after Carlo Marangoni an Italian physicist that wrote his dissertation on this phenomenon in 1865. The Marangoni effect is exploited in various applications, for example in the semiconductor industry in wafer cleaning. In wafer cleaning spotting must be avoided as this causes local heterogeneities, which are disastrous for the subsequent lithographic steps. To avoid spotting as the silicon wafer is pulled out of the water bath the surface is immediately sprayed with alcohol which due to its lower surface tension repels water which is then easier pulled down by gravitation leaving the surface of the wafer spot free [67].

5.10.3 Case study: Nonstick “omniphobic” surfaces—From mobile phone screens to car interior surfaces Superhydrophobic surfaces repel water and can lose their liquid repelling properties when a transition from the Cassie-Baxter to Wenzel regime occurs (Fig. 5.15), by liquid condensation in the pores, by unpinning of the three-phase line, and by submerging under water to high hydrostatic pressures, or when they contact organic solvents with low

5.10 Natural and biomimetic functional surfaces

FIG. 5.20

101

Marangoni effect was observed on the walls of a wine glass.

surface tensions (γ LV < 30 mN/m). Omniphobic and superomniphobic surfaces are those surfaces that repel any kind of liquid such as low surface tension organic solvents. These surfaces may find use in many applications self-cleaning surfaces for windows, car interiors, and photovoltaics, corrosion-resistant and antifouling ship hulls, etc. There are very few naturally occurring surfaces that exhibit contact angles larger than 90 degrees for organic solvents with low surface tensions such as gasoline, pentane, octane, ethanol, methanol, etc. Interestingly, some biofilm colonies and pellicles of Bacillus subtilis are nonwetting even up to 80% ethanol and are thus resistant to biocides [68]. The cuticle of Springtails (Collembola) animals exhibits omniphobicity which are not wetted upon immersion into many low-surface-tension liquids such as alkanes or polar and nonpolar solvents [68]. Their omniphobicity is attributed strictly to their hierarchical surface structure that mechanically prevents its penetration by the solvent rather than the chemistry of the surface. According to Marmur [69], the approach used by many researchers to achieve superhydrophobicity/omniphobicity is the use of multivalued topography (reentrant or self-affine, surfaces), which means that a line drawn perpendicularly to the surface may meet the interface more than once, such as the case with the mushroom-shaped pillars (Fig. 5.21). In the reentrant surface structures, the central idea is that the meniscus of a liquid droplet has a convex curvature, and the three-phase line remains pinned to the entrance part of the mushroom hat. Then, the meniscus exerts a net force upward, competing with the collapse of the droplet by the hydrostatic pressure or gravity [70]. Mushroom pillars can be achieved by photolithography, the building of nanopillars followed by etching of the understructure of the pillar. The strategies for developing surfaces are not restricted to multivalent patterned surfaces, and new and more efficient methods are being constantly developed [71]. For example, slippery liquid-infused porous surface (SLIPS) inspired by Nepenthes pitcher plants are also omniphobic because their structure is impenetrable. The motivation for developing such omniphobic surface is driven by the continuous development of technology such as smartphone screens or an increase in demand for comfort such as car interiors.

5.10.4 Case study: Research in “icephobic” surfaces for the aircraft industry, biomimicry inspired by penguins, and carnivorous plants Ice buildup on surfaces poses a serious threat to the transportation infrastructure especially for air transport [72], but it can be damaging to the energy infrastructure powerplants, wind turbines, and solar panels and can adversely affect telecommunication infrastructure. The deicing or defrosting technologies such as infrared and thermal deicing panels,

FIG. 5.21

Multivalued topography or reentrant surface achieved by designing of mushroom-shaped nanopillars.

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5. Wettability of surfaces

or chemical deicing by treatment with freeze point depressants such as salts, propylene, and ethylene glycols can be costly and in the latter case can have a negative environmental impact. Therefore, in many of these industries, the design of materials surfaces with icephobic properties comes as a viable alternative to prevent ice formation, which in addition to reducing the risk of accidents, damage to infrastructure can also contribute energy saving. Many such functional surfaces have been demonstrated and were created as a result of several decades of intense research [73]. The current understanding of icephobic surfaces suggests that a superhydrophobic surface with low or negligible contact angle hysteresis is the key to preventing the ice formation and buildup on the surface [74]. While, it was initially believed that all superhydrophobic surfaces have icephobic properties, and many such surfaces have been developed, and it was proven that this is not sufficient and a low contact angle hysteresis is necessary [74–76]. In practice, a nanostructured surface can be made superhydrophobic and exhibit a contact angle with water larger than 143 degrees. This can be achieved by different means that lead to hierarchical structuring of the surface, such as coating, patterning, anodization, coating with nanoparticles, roughening, etc. However, the surfaces that fulfill the icephobic characteristics, especially of those in high humidity and ultralow temperature, are those for which water does not penetrate the hierarchical structure and the transition between Cassie-Baxter wetting to Wenzel wetting does not occur. Such a transition from Cassie-Baxter to Wenzel wetting regime is possible due to condensation and evaporation in the pores of the surface (Fig. 5.15). When water droplets are in the Cassie-Baxter regime of wetting the droplets fall of quickly from the surface and any formed ice has poor adhesion and can be easily removed. In addition, air trapped between the pores acts as insulating pockets and slow down the heat transfer. In some conditions, when water does penetrate the pores of the surface, as in the Wenzel regime of wetting (Fig. 5.15), the icephobic properties are lost, and in fact the surface promotes ice formation, which is very hard to remove due to very high adhesion. Scientists first looked for inspiration at the solutions found by nature to prevent ice buildup on the surfaces. In nature, the feathers of the penguin do not show buildup of ice even though the penguins live in the coldest places on Earth. As shown by Wang et al. [77], the penguin feathers exhibit a contact angle of 147 degrees (Fig. 5.22), and the reason for penguin’s feather icephobicity is the three-level structuring of the feather surface consisting of barbs branched from the main rachis, which in turn are themselves branched into barbules which again are branched into hamuli. In addition to this level of structuring, hydrophobic coating by fatty acid, such as arachidic acid, of the feathers and 100 nm grooves present on the surface of the barbules, help trap air, and enhance their icephobic properties.

FIG. 5.22 (I) Penguin feather structure consisting of feather main axis—rachis, which branches out into barbes, brabules, and hamuli, constituting in a hierarchical multilevel structuring of the feathers. (II) Hierarchical micro- and nanostructures (b, c) and water contact angle (d) on body feathers of penguins Spheniscus humboldti. (a) Photograph of the body feather; environmental scanning electron micrographs of (b1) the rachis and barb; (b2) the barbules with the hamuli; (b3) elaborate wrinkles on the barbules and hamuli; (c1) the tips of barbules without hamuli; and (c2) oriented nanoscaled grooves on the barbules (100 nm deep). (II) From S. Wang, Z. Yang, G. Gong, J. Wang, J. Wu, S. Yang, L. Jiang, Icephobicity of penguins Spheniscus humboldti and an artificial replica of penguin feather with air-infused hierarchical rough structures, J. Phys. Chem. C 120 (2016) 15923–15929. https://doi.org/10.1021/acs.jpcc.5b12298 with permission. Copyright © 2016, American Chemical Society.

5.11 Adhesion of cells on rough and nanostructured surfaces

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Inspired by this Wang et al. [77] developed a polyimide nanofiber membrane with a microstructure resembling the penguin feather. The ice-phobic surfaces can be obtained by using the lotus leaf-inspired superhydrophobic surfaces. However, these surfaces may enhance ice adhesion in high humidity conditions due to the transition of wetting regimes from CassieBaxter to Wenzel. Different strategies had to be sought to prevent the water penetration into the grooves, in extreme conditions. Therefore, new types of icephobic surfaces were developed, namely the slippery liquid-infused porous surface (SLIPS). The tropical carnivorous pitcher plants such as Nepenthes were identified to have icephobic properties. In addition to a surface nanostructure, the nepenthes family of plants secrete lubricant on the surface of the pitcher that traps insects and small animals, which makes it a nonadhesive and extremely slippery surface. This strategic adaptation helps the plant capture the insect landing on the surface of the pitcher, which essentially slip down into the pitcher where they are being devoured. The pitcher plant is a lubricant-infused “slippery” surface which can be useful to repel ice from surface. Inspired by this, Wong and coworkers [78] pioneered SLIPS with excellent icephobic properties from two types of porous surfaces, a random network of Teflon nanofibrous membrane (average pore size 200 nm) and a periodically ordered epoxy resin nanostructured surface (300 nm, height, 500 nm–2 mm, pitch, 900 nm) which was rendered hydrophobic by treating the surface with heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane. The starting surfaces already show excellent superhydrophobicity and omniphobicity. However, by infusing the porous structure with perfluorinated fluids, such as 3 M Fluorinert FC-70, DuPont Krytox 100 and 103, the hysteresis contact angle becomes extremely low, 0, then the liquid will spontaneously spread on the substrate. It has been found experimentally that the radius of the droplet of a pure liquid increases with time due to spreading according to Tanner’s law R(t) α ktn [91, 92], where

5.12 Spreading and superspreading in the presence of surfactants

105

the power n was empirically determined for the viscous spreading of small droplets to be n ¼ 0.1 [93], and the k is a prefactor. Surfactants can lower the surface tension of liquids and therefore change their wetting ability. The surfactants can lower the surface tension of water such that the spreading coefficient S becomes positive. The spreading dynamics is linearly dependent on the surfactant concentration. However, unlike pure liquids the value of the prefactor was found to be about 25% lower than for the case of pure liquids with the same viscosity and surface tension, meaning that the droplet dynamics during spreading is slower [93]. This can be explained by the fact that during the spreading of a droplet the surface area increases, the new interface is continuously created, which must be then saturated with surfactants. Surfactants, depending on their structure, have a finite dynamic and it takes time to adsorb from bulk to interface, this lag time will lower the spreading dynamics of the droplet [94]. There is however an exception, and this comes from organosilicone surfactants, for which n ¼ 1, one order of magnitude larger than that determined in Tanner’s equation [93, 94]. This is known as superspreading behavior, which means a rapid spreading of a droplet on a hydrophobic surface such as PE or Teflon to a final contact angle of zero. The ability of the low-molecularweight siloxane surfactants to promote spreading in aqueous solutions on hydrophobic surfaces such as polyethylene was discovered in the 1960s and the capability of the trisiloxane surfactants to promote spreading on waxy weed leaf surfaces such as Velvetleaf and Lambsquarters is the basis for their use as herbicide wetting agents [95]. This superspreading behavior suggests that other delivery mechanisms of the surfactants from bulk to the interface are responsible. The mechanism of spreading in the case of the superspreaders has not been fully elucidated and remains elusive [96]. Three different mechanisms were hypothesized to play a role in the superspreading effect. First, the Marangoni flow—during the initial stage of droplet spreading the interfacial concentration of the surfactant should be higher at the apex of the droplet and then at the edge, due to this radial gradient of surface tension, the liquid droplet will spread radially outward. However, this does not explain why the superspreading phenomenon is mostly specific to organosilanes. Secondly, it has been proposed that the existence of a precursor water film ahead of the three-phase line may be crucial for the superspreading to occur. The origin of the thin water layer ahead of the three-phase line originates in the water condensation due to humidity, and in the absence of humidity, the superspreading phenomenon is not observed. Vice versa in the presence of humidity, not all organosilane surfactants show superspreading ability, this depends exclusively on the surfactant structure. Thirdly, numerous experiments indicate that the phase behavior of the organosilane surfactants, especially of surfactants with the trisiloxane hydrophobe, is responsible for superspreading behavior. The surfactants that can form bilayer aggregates, such as vesicles or lamellar phases such as L3-phase also known as a sponge phase are capable of superspreading. These phases are believed to play an extremely efficient role in delivering surfactants from bulk to interface or even participate in the spreading mechanism itself via an “unzipping” process of a bilayer [96]. Examples of superspreaders are the organosilicone surfactants, known as trisiloxane surfactants. Superspreading has attracted much attention especially for agrochemical formulations. For example, Silwet L-77 (originally from Union Carbide now Momentive) (Fig. 5.23) is a well-known superspreading agent used in agrochemical formulations. Initially, it was speculated that the superwetting ability of the trisiloxane surfactants come from their ability to lower the surface tension values to exceptionally low values. Perfluorinated surfactants have however the ability to lower the surface tension of water to significantly lower values than trisiloxane yet do not exhibit superspreading ability as discussed recently [97]. Although numerous investigations have been done and this subject continues to capture interest of researchers, the exact mechanism of superspreading remains an open topic for debate.

5.12.1 The autophobic and autophilic effects In the case of pure liquids, there is a strong correlation between the surface tension and the wettability of surfaces. In the presence of surfactants, this is not always the case, mainly because the surfactants can be carried over ahead the three-phase line, adsorb and change the properties of the substrates giving rise to the phenomena of autophobicity and autophilicity [98, 99]. Autophobicity is a rarely observed phenomenon which is encountered mostly in formulations containing surfactant molecules, such as CTAB that is able to adsorb ahead of the three-phase line and lead to the increase in the contact angle of a hydrophilic surface such as clean glass surface or silica. In this case, the liquid droplet starts to contract after a short expansion. This is in contrast to the ever-expanding liquid droplet due to hydrophilization of the substrate ahead of the three-phase line. The exact details of how this phenomenon of autophobization occurs are not fully resolved. The diffusion of some solute molecules could happen in 2D after adsorbing first at the SL interface and due to microscopic oscillations of the three-phase line back and forth to lead eventually to de-wetting of the substrates and contraction of the droplet as depicted in Fig. 5.24. Another hypothesis deals with the possibility of evaporation and re-adsorption of the liquid on the solid surface ahead of three-phase line. Both scenarios are plausible, but a microscopic mechanistic proof is pending. This phenomenon is sometimes confused with the Marangoni but the two

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FIG. 5.23 General structure of Silwet-type organosilicone surfactants [95].

FIG. 5.24

Contraction of a droplet after short expansion due to hydrophobization of the surface in front of the three-phase line.

have a different origin. Similarly, the autophilic effect takes place when a liquid droplet expands on a hydrophobic surface due to hydrophilization upon adsorption of surfactants ahead of the three-phase line.

5.12.2 Case study: Superwetting agents in agriculture and surface cleaning Already done

5.12.3 Surface cleaning mechanism The wetting phenomena are very important in cleaning applications. For example, detergent formulations always contain surfactants that are good wetting agents. Through the fact that detergent solutions wet the surface to be cleaned much better than the dirt, leads to the displacement and eventually a detachment of the dirt from the surface. Ethanol or isopropanol due to their low surface tension and good solvation abilities can also be used additionally to improve the cleaner’s effectivity, such as removal of adhesive labels from glass surfaces, or as window cleaners. The mechanism of dirt removal can be well understood in terms of the contact angle, for example, the “roll-back” mechanism for liquid-like dirt removal (Fig. 5.9). The roll-back mechanism can be understood based on Young’s equation of the balance of forces and Dupre’s formalism for the energy of adhesion. Consider the stain of the oil attached on the surface, which is immersed in water, Young’s equation is γ SW ¼ γ SO + γ OW cos θ

(5.19)

where SW is the solid-water interface, SO is the solid-oil interface, and OW the oil-water interface. Inserting the above expression for the γ SW into the expression of the energy of adhesion between the oil (dirt) and the solid surface we obtain Wadh SO ¼ γ SW + γ OW  γ SO ¼ γ SO + γ OW cos θ + γ OW  γ SO γ  γ SO cos θ ¼ SW γ OW

(5.20) (5.21)

From Eq. (5.21), we see that a decrease of the γ SW interfacial energy between solid-water will lead to a decrease in the cos θ, i.e., an increase in the contact angle θ, in which case the oil dirt will begin to spontaneously de-wet the stained surface. If the interfacial energy becomes very low, with the use of surfactants and detergents, much lower than the γ SO,

5.13 Contact angle of micro- and nanoparticles

FIG. 5.25

107

The depiction of the “roll-back” mechanism.

then the cos θ will become negative and the contact angle of the oil dirt with the surface will become larger than 90 degrees up to 180 degrees and the oil will detach from the surface (Fig. 5.25). That is the “roll-back” mechanism of dirt removal. The function of the contact angle can be distinguished into three situations: (i) if the contact angle is 180 degrees the detergent bath will spontaneously completely displace the liquid soil from the substrate; (ii) if the contact angle is less than 180 degrees but more than 90 degrees then the soil will not be displaced spontaneously but can be removed by hydrodynamic currents (agitation); (iii) if the contact angle is less than 90degrees at least a part of the oil will remain attached to the substrate, even when subjected to hydraulic currents of the bath and mechanical work is then required to remove the residual soil from the substrate.

5.13 Contact angle of micro- and nanoparticles Existence of nanoparticles in water and air because of industrial activity calls for additional understanding of their interaction with the environment and living organisms. Currently, there is a great need for understanding of how nanoparticles behave in bulk form, as fine powders to develop proper safety and handling protocols. For example, some fine nanoparticle powders may more easily disperse into air or water than others, posing a more immediate threat to the environment. The same need exists across many industries, to understand and predict the collective behavior of nanoparticles in powders for production, processing, mixing, or tableting into consumer products. Therefore, wettability and contact angle can serve as one of the essential parameters to describe the surface state of the nanoparticles and predict their collective behavior. The contact angle of particles in different size ranges, from the nanoscale to microscale particles cannot be measured with the sessile drop. In fact, developing methods for measuring the wettability of particles is of real interest to researchers in the interfacial science community. The ability to measure the wettability and surface energy of nanoparticles can have a significant impact on many practical and industrial implications. The behavior of nanoparticles in a liquid medium is largely dictated by their surface energy and wettability, which first impacts their dispersibility in water [100], partition at interfaces and flotation [101], aggregation, drying, colloidal stability, and their usefulness in applications such as vehicles for drug delivery [102], oil recovery, heterogeneous catalysis [103], manufacturing of nanoparticle reinforced composites [104], emulsification of oil [105], pharma [106], cosmetics and food [107], etc. The physicochemical state of a surface of nanoparticles also determines their collective behavior in powders, such as compressibility, granulation [108], pelleting ability, fluidization, flowability, and compactibility [108, 109], etc. [110, 111]. Last but not least the lung toxicity of nanoparticles is also critically determined by the particles’ surface energy [112]. Therefore, knowledge of the surface wettability and surface energy of nanoparticles can greatly improve the ability to predict their behavior in a liquid or gas medium and their collective behavior in powders. There have been attempts to conclude the wettability of nanoparticles from indirect measurements of the contact angles on macroscopic surfaces composed of the materials with the same chemical composition. Clearly, the validity of such measurements can be challenged, because the measured macroscopic surface may chemically differ considerably and the surface properties of nanoparticles are largely affected by the synthetic methods and adsorbed stabilizers. Even if both the nanoparticle surface and the macroscopic surface are ideally clean, simulations studies clearly show a strong dependence of the surface energy with the size [113]. Most of the methods dedicated to particles rarely dare to approach the measurement of the contact angle on nanoparticles with diameter ≪ 1 μm. Therefore, currently the wettability and surface energy of nanoparticles is an ambiguous subject, because it is very difficult to measure and there are very few reports on this topic of increasing importance. Even though many attempts have been made to implement a method to reliably measure the contact angle and surface energy with relative success, it appears to be a lost cause, because still there is no universal method to perform this optimally on a wide range of nanoparticles.

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FIG. 5.26 Spherical particle adsorbed at the air-water interface. The contact angle with water β can be determined in two equivalent ways: (left) between the position of the air-water interface with the surface of the particle or (right) from the angle formed between the radius pointing at the three-phase line. The parameters a and d0 are the immersion depth of the particle in water measured from the center and apex of the particle, respectively, and d is the immersion of the particle in the second phase, air or oil. From A. Honciuc, Amphiphilic Janus particles at interfaces, in: F. Toschi, M. Sega (Eds.), Flowing Matter, Springer International Publishing, Cham, 2019, pp. 95–136. https://doi.org/10.1007/978-3-030-23370-9_4.

The typical methods developed for the measurement of the contact angle rely on measuring the interfacial immersion depth of nanoparticles. For example, in order to measure the contact angle of water on a nanoparticle then the nanoparticle must first adsorb at the water-air interface (Fig. 5.26). From simple geometrical calculations, the contact angle β can be easily calculated from the interfacial immersion depth [114]. Most nanoparticles can be trapped at liquid-liquid or liquid-vapor interfaces [114] which is therefore an advantage for the mentioned method with regards to its applicability. The key step and most challenging one is however finding experimental means to determine this interfacial immersion depth at any interface. Macroscopic methods such as Washburn capillary rise methods fail on nano-powders, the measured contact angle, if at all can be measured, are overestimated, which leads to extremely low values for surface energies [115]. The wicking method consists of essentially preparing a plate, such as a glass slide, with a layer of particles which can be immersed in a fluid and the rising height and speed of the fluid are monitored, the 2D equivalent of the Washburn method. Alternatively, the contact angle can be measured directly by the contact angle goniometry on the plate covered with nanoparticles. Alas, these methods are plagued by the influence of the supporting plate and additional measurements must be performed to measure the influence of the supporting material in the results. Another method is that of contact angle goniometry pelleted nano-powder, which was also used in our group [116]; this worked well for the case when the nanoparticles are sufficiently hydrophobic and the liquid is very polar. The main limitation of the method is that the sessile liquid droplet is sucked into the pellet by capillary forces. To circumvent this, we have used high-speed video acquisition to determine the contact angle from the first microseconds the sessile droplet touched the surface before being sucked into the substrate. However, the contact angle determined is a nonequilibrium contact angle and the measurements are rather difficult to make and not very reliable. Direct measurement of the contact angle on single particles via colloidal probe atomic force microscopy (AFM) [117] or interferometry is limited to microparticles. State of the art single-particle contact angle measurements involve electron microscopy to monitor the contact angle of single particles, such as gel-trapping technique (GTT) [118] and freezefracture shadow casting (FreSCA), developed at ETH in Switzerland [119]. The key in these experiments is the sample handling and preparation. Despite their success, these methods present some limitations. In the GTT method, the choice of the liquid is limited, due to the high temperatures involved in the gelation process, which is critical for low boiling point liquids such as short-chain alkanes. Isa et al. [119] also pointed out that the length scale of the gelation agent is on the same length scale as the particle size thus creating inhomogeneities in the trapping and measurement. Also, the polarity of the gel is different from that of water. Variants such as AFM-GTT because of tip convolution is not able to measure simultaneously the height and the radius of the particles. The FreSCA method utilizes a special design for water vitrification, which is technically challenging for determining the surface energy of nanoparticles by measuring the contact angles at different solvent/water interfaces. The gelification GTT method was developed by Paunov [118] for determining the contact angle of solid colloid particles adsorbed at the air-water or oil-water interfaces. Once trapped at the interface the gelling of the water phase is induced by the addition of a nonadsorbing polysaccharide. The particle monolayer trapped at the interface decanewater interface, with the water being a 2% gellan solution at 50°C (gellan gum is a gel-forming polysaccharide secreted

5.13 Contact angle of micro- and nanoparticles

109

FIG. 5.27

Scanning electron micrographs of monodisperse polystyrene latex particles of an average diameter of 9.6 μm on the surface of PDMS obtained by the gel trapping technique for the air-water interface. (For A1, the observation angle ζ ¼ 60 degrees; for A2, ζ ¼ 85 degrees). Reproduced with permission from V.N. Paunov, Novel method for determining the three-phase contact angle of colloid particles adsorbed at air water and oilwater interfaces, Langmuir 19 (2003) 7970–7976. https://doi.org/10.1021/la0347509. Copyright © 2003, American Chemical Society.

by the microbe Sphingomonas elodea and consists of monosaccharides β-D-glucose, β-D-glucuronic acid, and α-L-rhamnose). After cooling the system to room temperature and gelation, decane is removed and on the gel surface, poly(dimethylsiloxane) (PDMS) elastomer is spread and then cured, which allows the particles embedded within the PDMS surface to be imaged with SEM (Fig. 5.27). Alternatively, the Pickering emulsions to easily measure the contact angle of nanoparticles for a wide range of solvents. The production of Pickering emulsions stabilized by particles has been around for several decades. Solid-state colloidosomes can also be produced by emulsification of molten wax in water at high temperature, 90 degrees. Therefore, the attachment energy depends on both the contact angle and it scales with the square of the radius of the particle. The theory is that the particle attachment force must strong enough not to detach during the uplift, opposing the inertial forces (gravity) and friction forces, from which the critical contact angle applying different mathematical and physical models, as reviewed by Varbanov et al. [126]. Because of the existing challenges to measure the contact angles locally at the lowest scale, a large amount of experimental work was conducted to measure the contact angle on flat mineral surfaces to understand the effects that modifiers such as xanthane, cyanide, surfactants, and various ions have on mineral flotation. However, the precise measurement and prediction of contact angles for real mineral surfaces remains extremely difficult.

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C H A P T E R

6 The fundamental equations of interfaces 6.1 The thermodynamic perspective—Energy of adhesion In thermodynamics, the change of internal energy of a system ΔU depends only on the initial and the final states of the system and not on the path connecting those states, even though Q and W depend on the path. ΔU ¼ Q + W

(6.1) 2

The adhesion energy between two immiscible phases, Wadh (J/m ), can be expressed as the work done to detach the two phases initially in contact, for example, a solid (S) and a liquid (L) in the gas-phase (G) and create two new ones solid-gas (SG) and liquid gas (LG) (Fig. 6.1). The adhesion energy must be then equal to the difference in the energy of the system in the final state consisting of the two new interfaces LG, SG minus the energy of the initial system consisting of only SL interface summarized by the following equation named after the French scientist Athanase M. Dupr
e [1]: Wadh ¼ γ SG + γ LG  γ SL

(6.2)

Note that the force and consequently the work needed to detach the two phases depends on the path followed; the force needed to pull the two interfaces apart is different from the force needed to separate two phases by first sliding the solid phase and then pulling, for example, the path 2 in Fig. 6.1. Even though the paths followed for the separation process are clearly different the energy of adhesion must be the same. A soft adhesive tape can be removed with a small force from a surface by peeling (detaching small surface segments one after the other), while a rigid glass slide bonded to the same surface with the same type of adhesive requires a greater force (pulling apart two large surface segments at once) because it cannot be removed by peeling. Although in each case the magnitude of the forces and the paths are very different, the work of detaching the surfaces is obtained by integrating the measured force function over the distance, the energy of adhesion is the same. In the interfacial science the energy of adhesion Wadh (J/m2) and the work of adhesion, are sometimes used interchangeably if the heat exchange during detachment is negligible or the same regardless of the detachment method employed. However, noting the above fundamental differences the energy and the work of adhesion can be used interchangeably noting above the phenomenological difference between these notions. The Dupr
e equation can be combined with Young’s equation (3.10) to obtain a very valuable result, the YoungDupr
e equation, which relates the energy of adhesion (work of adhesion) only to the surface tension of the liquid and its contact angle with the solid surface: Wadh ¼ γLG ð1 + cos θÞ

(6.3)

Thus, the energy of adhesion between the two phases can be readily determined with the above equation if the surface tension of a liquid is known and the contact angle measured. The energy of adhesion is minimum when θ is 90 degrees or larger, for example, the water on wax then the adhesion is very low. Teflon coating is used in nonstick pans as it is both hydrophobic and oleophobic, that is the energy of adhesion of both oil and water are low, the contact angles are very large. The energy of adhesion is maximum when the contact angle θ is 0 or γ j and γ i < γ j or when γ i < γ j and γ i > γ j . The consequences of AB ¼ γ LW this fact are very interesting: the three scientists argue that a total low or negative interfacial tension γ total ij ij + γ ij  0 AB LW can exist especially between water and polar liquids or solids, for example, ethanol and water, when jγ ij j > γ ij and γ AB ij < 0. But such systems exist for only a very short time as they are completely miscible at equilibrium. In some cases, the negative surface tension persists for a very long time, such as water and dextran, which is only very slowly soluble in water, or agarose and water, etc. Other polymers, such as polymethylmethacrylates, polyvinyl alcohols, proteins, polysaccharides, phospholipids, nonionic surfactants, etc. are regarded as monopolar surfaces, see above, and interact strongly with polar liquids such as water, the acid-base interaction, in this case, exceeds by far the LW component and thus negative interfacial tensions appears between these compounds and water [20]. In this situation, water will penetrate between these molecules and will lead to their dispersibility in water, which is sometimes referred to as hydration pressure [18]. The implications are that the system lowers its energy by increasing the surface area. Such an effect is desired in designing good adhesive surfaces or glues. For immiscible liquids, such as oil and water negative energy of the interfacial tension γ total ow can be obtained by adding a surfactant, in which case the system will spontaneously form stable microemulsions [18]. The result of the van Oss, Choudhury, and Good expressed in Eqs. (6.25), (6.32) can be combined with the Young-Dupr
e equation (6.3) and we obtain for a liquid L in contact with solid S: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi total LW AB LW γL+ γ ¼ Wadh + Wadh ¼ 2 γLW γS+ γ (6.36) ð1 + cos θÞγ L ¼ Wadh L γS + 2 L S +

From this equation, it becomes obvious that by contact angle measurement with three different liquids, at least two +  LW +  polar, with known γ LW L , γ L , and γ L of the surface tension, by using the above equation three times the γ S , γ S , γ S of any solid can be determined. Similarly, we can determine this way the components of the surface tension of any unknown liquid by measuring their contact angle on substrates with known surface energy components. The system of three LW equations can be simplified if γ LW S or γ S is first determined with an apolar liquid (e.g., alkanes) or solid (e.g., Teflon or PE), respectively: ð1 + cos θÞ2 γ LW L ¼ γ LW S 4

(6.37)

After the γ LW S the system of equations from Eq. (6.35) can be simplified to the system of two equations (from the other two more polar liquids): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi LW + γ + γ L1 ð1 + cos θÞγL1 ¼ 2 γ LW γ S+ γ  L1 γ S + 2 L1 S ð1 + cos θÞγL2 ¼ 2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi LW + γ + γ L2 γ LW γ S+ γ  L2 γ S + 2 L2 S

Again, care must be taken when solving the system of the equation such that meaningful nonzero values are found for the square root solutions [21]. +  + In Table 6.2, γ LW L , γ L , and γ L are contributions to the total surface tension of the liquid. Notice that for water, the γ L  and γ L are equal which is expected, while for dimethylsulfoxide DMSO we observe that it is a monopolar (electron donor) liquid, the O atom is a hard Lewis base with a strength similar or greater than that of the O atom in water and is capable of bonding with metal cations.

126

6. The fundamental equations of interfaces

TABLE 6.2 Surface tension of several liquids with the γ LW L , γ +L , and γ  L contributions contributions [19,21]. Substance

γ total (mN/ m)

γLW

γ AB

γ+

γ2

Water

72.8

21.8

51

25.5

25.5

Glycerol

64

34

30

3.92

57.4

Ethylene glycol

48

29

19

1.92

47

Formamide

58

39

19

2.28

39.6

Dimethyl sulfoxide

44

36

8

0.5

32

Chloroform

27.15

27.15

0

3.8

0

Diiodomethane

50.8

50.8

0

0

0

6.7 Fox-Zisman model By measuring the contact angle of different pure organic liquids on a given surface and plotting it with the surface tension of the liquid (cos θ vs γ L). Zisman and Fox proposed the following empirical equation and stated that by extrapolating the obtained linear portion of the cosθ vs γ L curve, the interpolated value on the surface tension axis, called the critical surface tension γ c below which θ is zero, will give “a measure of the solid’s surface energy”: cos θ ¼ 1  bðγ L  γ c Þ

(6.38)

Fox and Zisman based their interpretation of critical surface tension γ c, on the premise that, as γ LV decreases toward γ SG, γ SL will approach zero; when γ SL, reaches zero, γ LV will be equal to γ SG as deduced from Young’s equation. In Fig. 6.6, it can be observed that there is an almost linear decrease in the contact angle with the decrease in the surface tension of the liquid on two different substrates. A strict linear dependence is obtained only for the cosθ of the linear alkanes with PTFE; as the polarity of the solvent increases the curve becomes concave. Therefore, by extrapolating the linear portion of the curve of the cosθ vs γ L, the curves cross the x-axis at the γ c  18 mN/m for PTFE, Fig. 6.6a, and at the γ c  20 mN/m for the more polar TFE-E (Fig. 6.6b). The γ c would have been unrealistically low if obtained by the extrapolation of the cos θ vs γ L curve of the more polar solvents, γ c  11 mN/m. The γ c increases with the decrease in the fluorine content of the polymer. Another conclusion that can be drawn from Zisman-Fox plot is that the solvents whose γ L < γ c completely wet the substrate; only pentane can completely wet PTFE while pentane through tetradecane can completely wet the surface of the TFE-E. The Fox-Zisman method will only give an estimate of the total surface energy but no information about the polar and dispersive contributions. The Fox-Zisman plot only holds for pure liquids and not for binary mixtures such as water and ethanol, probably for the same reasons as the simple relationships between the mixture and pure components do not hold. The Zisman plot works relatively well only for low-energy surfaces such as polymers but not on highly polar surfaces such as metals or metal oxides. Similarly, for surfactant solutions the ability of the surfactant solution to spread on low-energy surfaces is determined by the critical surface tension, γ c, and the surfactant concentration must be so chosen as to lower the surface tension of water below γ c..

6.8 Case study: Usefulness of interfacial models in applications Knowledge of the relative magnitude of the components of the interfacial and surface energy is useful in elucidating the mechanisms of surface processes in a variety of practical applications, adhesion, flotation, material properties, flocculation, coatings, corrosion, etc. In the absence of any another method for classification of macroscopic surfaces and interfaces function of their polarity, acidity, hydrogen bond capability, etc., measuring the relative contribution of the various terms to the total surface and interfacial energy seems very appealing. However, because the surface energy components cannot be measured directly, the use of the models strongly depend on the measurement of the contact angles, which are methodology dependent. This limits the practicality and widespread use of these models in applications.

6.8 Case study: Usefulness of interfacial models in applications

127

FIG. 6.6 Zisman-Fox plot of cos θ vs surface tension for pure solvents for determining the total surface energy of a solid as γ c. (a) the contact angles of solvents on PTFE, the dotted line represent a linear fit for the top portion, linear alkanes and a polynomial fit of second order for the more polar solvents; (b) the contact angle on a more polar substrate TFE-E, a 50:50 copolymer of tetrafluoroethylene and ethylene, the dotted line represents a second order polynomial fit as a guide to the eye. Data from H.W. Fox, W.A. Zisman, The spreading of liquids on low energy surfaces. I. Polytetrafluoroethylene, J. Colloid Sci. 5 (1950) 514–531. doi:10.1016/0095-8522(50)90044-4; H.W. Fox, W.A. Zisman, The spreading of liquids on low-energy surfaces. II. Modified tetrafluoroethylene polymers, J. Colloid Sci. 7 (1952) 109–121. doi:10.1016/0095-8522(52)90054-8.

Separation of minerals by ore flotation is extensively used in mining, as discussed in Chapter 5. The condition for the floatability of mineral particles is their attachment to an air bubble so that it can be transported to the surfaces where it is collected by skimming. Most of the research in the flotation is done to characterize the surface of minerals in terms of wettability and contact angle. Chemicals such as collectors are used for making minerals floatable and depressants are used to achieve selective floatability of minerals that have initially the same floatability. For this, measurement of the relative contribution of the surface energy components of mineral surfaces can help understanding the behavior of floatable minerals in the presence of depressants, collectors to achieve selective flotation and separation of the ore from gangue and other minerals. Karag€ uzel et al. [22] used the OCG model to determine the LW, acid and base components to the total surface energy of the albite (Na-feldspar, NaAlSi3O8) and orthoclase (K-feldspar, KAlSi3O8), which are used in glassmaking, ceramics manufacturing, and are usually found together. The separation of two types of feldspar minerals by selective flotation is challenging due to their identical crystalline structures. The contact angles of varying polarity solvents were measured using the thin layer wicking sample preparation technique and applying the Washburn method. With the OCG model, they have determined the LW, acid-base components. When treated with the alkyl propylene diamine collector (G-TAP from Clariant, typical reagent used in flotation as hydrophobizing agent to improve attachment to the air bubble), both minerals had a decrease in the total surface energy and of the acid γ + and base γ  components due to the replacement of surface polar groups by nonpolar groups. Addition of NaCl into the flotation system at constant amine concentration improved the relative selectivity of the two minerals because the surface Lewis basicity γ  component of the albeit is increased relative to orthoclase, hence the adsorption of the collector on the former is inhibited and its floatability decreased. Numerous other studies investigated the change in the relative surface energy components of relevant minerals in the presence of flotation reagents using the OVG model to elucidate the surface interactions [23–25].

128

6. The fundamental equations of interfaces

Surface biofouling and microbial adhesion are another areas in which determining the surface energy and its component can help elucidate the bacterial attachment mechanisms. Prokopovich and Perni [26] investigated the bacterial attachment of Escherichia coli and Staphylococcus aureus (responsible for food poisoning and hospital infections) on polysaccharide-based films. The surface energy parameters were determined with the OVG model. Their study revealed that γ LW had a very little contribution to the attachment of the bacteria. On the other hand, the γ  electron donor properties of the polysaccharide films were associated with the attachment of the S. aureus (a Gram-positive bacterium, electron acceptor characteristics of this bacterium) but not with E. coli (a Gram-negative bacterium). Determination the surface acidity of different types of woods affects their interaction with adhesives and coatings. Gindl and Tschegg [27] used the OVG model and concluded that the Lewis acid component γ + of the total surface energy of different wood species is small as compared to γ LW but correlates well with the classical acidity determined by pH between different wood species. Cohesion of powders is particularly relevant for the pharmaceutical industry. It is assumed that interparticle interactions are determined mostly by the surface properties of the powder, which govern the physical-chemical interactions, such as pelletability, flowing ability, in addition to mechanical processes such as interlocking. An extensive discussion on the role of the different surface energy component in powder cohesion was presented recently by Shah et al. [28], in which methyl, dodecyl, phenyl, and vinyl functional groups were grafted on powders grains of mefenamic acid (using the silanization method) surface to investigate the role of γ LW, whereas a series of haloalkane functional groups were grafted to study the role of γ AB on powder cohesion. In their study, Shah et al. [28] found that powder cohesion increases linearly with surface energy. To determine which components to the surface energy contributed most to powder cohesion, contributions from γ LW and γ AB were first decoupled and it was found that increase in cohesion due to contribution from γ AB was about 11.7 times higher than that from γ LW. The γ LW and γ AB components of liquids can also be determined by measuring the contact angles against substrates with known surface energy components. In some applications, it is important to determine the Lewis acidity or basicity and acceptor vs donor capability for solvents not only in aqueous but also in a nonaqueous environment. For example, in a solution containing different mass fractions of urea in water are expected to vary linearly and reflect the concentration of the solute [29]. The aqueous solutions of urea become less polar with increasing urea mass fraction while the overall surface tension also increases, due to a significant growth of the γ LW ij component. In addition, aqueous solutions of urea are characterized by an enhanced electron donor γ  capacity and a diminished electron acceptor γ + capacity compared to pure water. Consequently, γ +/γ  was continuously reduced with increasing urea concentration. The enhancement of electron-donating property was also reflected in the pH of the solutions. The adhesion between liquids and surfaces is of practical relevance not only in classical ink printing but also on printing conductive circuits on insulating polymer substrates [30]. The resolution in ink printing depends on the smallest radius of individual droplets that can be deposited on the substrate [31]. The relationship between the contact angle and the radius of the droplet is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 Vd sin 3 θ 3 (6.39) r¼ πð2  3 cos θ + cos 3 θÞ where Vd is the volume of the droplet. A small reduction in contact angle from 30 to 10 degrees increases the radius of the printed drop by 50%. Small contact angles of the ink droplets with the substrate result in “over-spilling” of the ink and limit the pattern resolution, while large contact angles result in instabilities that prevent the stable coalescence of droplets [31]. Therefore, precise control of the wetting of the substrate by ink is essential in printing applications.

6.9 Case study: Wetting envelope Construction of wetting envelope graphs is important for predicting the wettability of a surface by different liquids based on their disperse and polar components of the surface tension. The wetting envelope for a given surface is a contour plot of γ pL vs γ dL for which the cos θ in the OWRK equation remains constant. In Fig. 6.7 the contour graph for polymethylmethacrylate was calculated by solving the OWRK equation for three different contact angles 0, 45, and 60 degrees, knowing that for PMMA the surface energy components γ dS ¼ 29.6 mN/m and γ pS ¼ 11.5 mN/m. Therefore, each data point of the contour plot represents a solution of the OWRK equation in terms of γdL, γpL for the corresponding contact angle: qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi p p 2 γ S γL + 2 γ dS γdL 1 (6.40) cos θ ¼ γL

6.10 Case study: Pickering emulsions and energy of adhesion of nanoparticles to immiscible phases

129

FIG. 6.7 Wetting envelopes of polymethylmethacrylate

(PMMA) surface with surface energy components γ dS ¼ 29.6 mN/m and γ pS ¼ 11.5 mN/m, calculated for three contact angles, 0, 45, and 60 degrees. In addition, the surface tension disperses and polar components for water, glycerol, and methanol are represented with respect to the curves. The continuous lines are guide to the eye.

The wetting envelope graphs have a typical bow-shaped form. Any liquid for which surface tension components are known can be represented on this graph together with the wetting envelope curves. Depending on where the solvent coordinates fall on the graph γ pL vs γ dL the magnitude of its contact angle with the substrate can easily be predicted. For example, the contact angle of the glycerol with PMMA should be between 60 and 45 degrees, while the contact angle of methanol on PMMA is zero, and that of water is exactly 60 degrees (Fig. 6.7).

6.10 Case study: Pickering emulsions and energy of adhesion of nanoparticles to immiscible phases Nanoparticles adsorb at oil-water interfaces and can stabilize emulsions. The emulsions stabilized by nanoparticles are called Pickering emulsions, named after the British chemist, Spencer Umfreville Pickering. Depending on the nanoparticle surface polarity with respect to the polarity of the oil and water, the Pickering emulsions can be oil-in-water (o/w) with the oil being the dispersed phase or water-in-oil (w/o) with the water being the dispersed phase. For the preparation of Pickering emulsions homogeneous nanoparticles (NPs) or two-lobe Janus nanoparticles are used (JNPs). The determining factor for the formation of o/w or w/o emulsion phases is the preferential adhesion of the nanoparticles for one of the phases. The Dupr
e’s formalism for the work of adhesion for a nanoparticle to oil, Eq. (6.10), as depicted in Fig. 6.8A, can be written as follows: NP=oil

Wadh

¼ γ oil=water + γ JNP=water  γ NP=oil

(6.41)

and the work of adhesion of the nanoparticles to water (Fig. 6.8B) can be written as NP=water

Wadh

¼ γ oil=water + γ JNP=oil  γ NP=water

(6.42)

where γ oil/water is the IFT of the oil-water interface (mN/m also expressed as mJ/m ), γ NP/water is the interfacial energy of the NP/water interface (mJ/m2), and γ NP/oil and γ NP/water are the interfacial energies of the NP-oil and JNP-water interfaces, respectively. 2

130

6. The fundamental equations of interfaces

FIG. 6.8 Cartoons depicting the graphical interpretation of Dupre’s formalism for the work of adhesion of (A) NP to oil and (B) NP to water, with the initial state of the particle at the interface without a preferential orientation (left) and the final state of the particle completely immersed in either of the bulk phases (right). Modified from D. Wu, B.P. Binks, A. Honciuc, Modeling the interfacial energy of surfactant-free amphiphilic janus nanoparticles from phase inversion in pickering emulsions, Langmuir 34 (2018) 1225–1233. doi:10.1021/acs.langmuir.7b02331. Copyright © 2017 The American Chemical Society.

To gauge the relative strength of the work of adhesion for the nanoparticles to each of the phases, the work of adhesion to water and to oil can be related through a proportionality constant: JNP=oil

Wadh

1 JNP=water ¼  Wadh f

(6.43)

is the work of adhesion of oil to the NP and WJNP/water is the work of adhesion of water to the NP. where WJNP/oil adh adh By relating the work of adhesion of the NP to each of the phases with the help of the parameter f in Eq. (6.42) is to a first approximation a gauge of how much stronger the particle surface is wetted by one of the liquids compared with the other. The parameter f can take any value for which f > 0. The better spreading of oil or water on the NP surface in Fig. 6.8 should be interpreted by the immersion depth of the NP in one of the phases. Practically, the proposed constant 1/f could be determined empirically and related to the volume ratio of water-to-oil in the emulsion. An emulsion phase can be changed in three ways: (a) by changing the polarity of the particle, as depicted in the x-axis in Fig. 6.9, (b) by changing oil-to-water volumetric fraction, as depicted on the y-axis in Fig. 6.9, and (c) by changing the solvent polarity. The emulsion phase inversion boundary for several different solvents and water as a function of the particle polarity and the oil-to-water volumetric fraction are given in Fig. 6.10. It has been shown that in a homologous series of interfacially active snowman-type Janus nanoparticles (JNPs) consisting of one polar polymer lobe and another nonpolar surface lobe, the polarity can be changed gradually by varying the relative size of the lobes, as shown in the SEM images of the top row in Fig. 6.9 [32]. Based on the experimental observations in Figs. 6.9 and 6.10 Wu et al. [32] proposed the following relationship derived from Eq. (6.42), to include relate the strength of the work of adhesion of the particle to solvent and water as a function of solvent polarity, particle polarity, and oil-to-water volumetric ratio:  1 1  (6.44) γ oil=water +  γ JNP=water  γ JNP=oil ¼  γ oil=water + γ JNP=oil  γ JNP=water f f Which upon rearrangement results in a simple relationship: ðf  1Þγ oil=water ¼ ðf + 1Þγ JNP=oil  2γ JNP=water

(6.45)

With the help of Eq. (6.44), the relative interfacial energies of JNP/water and JNP/oil were evaluated by creating a linear system of equations consisting of five equations corresponding to each of the five oils having six unknowns being five γ JNP/oil interfacial energies plus the γ JNP/water interfacial energy. The system of linear equations could be solved and a global minimum was identified and the change in interfacial energy of the solvents with each nanoparticle is given in Fig. 6.11 Upon the analysis of these data, it can be seen that (i) interfacial energy of the JNPs with

6.10 Case study: Pickering emulsions and energy of adhesion of nanoparticles to immiscible phases

131

FIG. 6.9 Formation-composition maps with corresponding fluorescence microscopy images (scale bar ¼ 200 μm) for the Pickering emulsions obtained from varying toluene: water ratios with the homologous series of JNPs. The top row depicts PS seed nanoparticles and five JNPs with increasing P(3TSPM) lobe sizes (scale bar ¼ 100 nm), while the subsequent three rows represent a different volume ratio of toluene to water (given). From D. Wu, B.P. Binks, A. Honciuc, Modeling the interfacial energy of surfactant-free amphiphilic janus nanoparticles from phase inversion in pickering emulsions, Langmuir 34 (2018) 1225–1233. doi:10.1021/acs.langmuir.7b02331, with permission, Copyright © 2017 The American Chemical Society.

water and the more polar liquids dichloromethane (DCM) and methyl methacrylate (MMA) decreases with the increase in the particle surface polarity, suggesting large energy of adhesion; (ii) the interfacial energy of the JNPs with the least polar solvents such as heptane (Hep) and toluene (Tol) show an increase in interfacial energy with an increase in the polarity of the particle, suggesting small energy of adhesion; and (iii) for styrene liquid the interfacial energy with JNPs appear to evolve as an intermediary case between the two sets of solvents. This proposed model [32] provides a straightforward relationship between the experimentally acquired emulsification data with useful interfacial parameters. Besides, this model represents a useful conceptual tool which helps one understand the role of relative magnitudes of the interfacial tension between particles and liquid phases that eventually determine the emulsion phase.

132

6. The fundamental equations of interfaces

FIG. 6.10

Summary of emulsification results obtained for the PS seed nanoparticles and the homologous series of JNPs with different oils: DCM, MMA, Sty, Tol, and Hep. The curves represent the boundary between the different types of emulsion with o/w below the curves and w/o above them. The y-axis is the oil volume fraction in each emulsion, ϕo ¼ Voil/(Voil + Vwater). The overall concentration of the JNPs was 2.22 mg/mL. The cartoon insets depict the curving of the interface toward oil and water. The vertical error bars correspond to the smallest volume fraction step for which the emulsion type could be reliably determined. From D. Wu, B.P. Binks, A. Honciuc, Modeling the interfacial energy of surfactant-free amphiphilic janus nanoparticles from phase inversion in pickering emulsions, Langmuir 34 (2018) 1225–1233. doi:10.1021/acs.langmuir.7b02331, with permission, Copyright © 2017 The American Chemical Society.

FIG. 6.11 Evolution of the interfacial energies of JNP/water and JNP/liquids vs lobe size for different oils; the lobe size “0” mL 3-TSPM refers to the PS seed particles. The increase in polarity of the JNPs with the P(3-TSPM) lobe size can be spotted from the relative strong decrease in the JNP/ water interfacial tension. The error bars associated with the interfacial energies of JNP/water and JNP/oil correspond to the standard deviation obtained by propagating the errors of f in the corresponding system of equations using Eq. (6.44). From D. Wu, B.P. Binks, A. Honciuc, Modeling the interfacial energy of surfactant-free amphiphilic janus nanoparticles from phase inversion in pickering emulsions, Langmuir 34 (2018) 1225–1233. doi:10.1021/acs.langmuir.7b02331, Copyright © 2017 The American Chemical Society.

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Chibowski, Surface free energy components and flotability of barite precovered with sodium dodecyl sulfate. Langmuir 8 (1992) 303–308, https://doi.org/10.1021/la00037a055. [26] P. Prokopovich, S. Perni, An investigation of microbial adhesion to natural and synthetic polysaccharide-based films and its relationship with the surface energy components. J. Mater. Sci. Mater. Med. 20 (2009) 195–202, https://doi.org/10.1007/s10856-008-3555-6. [27] M. Gindl, S. Tschegg, Significance of the acidity of wood to the surface free energy components of different wood species. Langmuir 18 (2002) 3209–3212, https://doi.org/10.1021/la011696s. [28] U.V. Shah, D. Olusanmi, A.S. Narang, M.A. Hussain, M.J. Tobyn, J.Y.Y. Heng, Decoupling the contribution of dispersive and acid-base components of surface energy on the cohesion of pharmaceutical powders. Int. J. Pharm. 475 (2014) 592–596, https://doi.org/10.1016/j. ijpharm.2014.09.018. [29] A. Terzis, E. Sauer, G. Yang, J. Groß, B. Weigand, Characterisation of acid–base surface free energy components of urea–water solutions. Colloids Surf. A Physicochem. Eng. Asp. 538 (2018) 774–780, https://doi.org/10.1016/j.colsurfa.2017.11.068. [30] T.H.J. van Osch, J. Perelaer, A.W.M. de Laat, U.S. Schubert, Inkjet printing of narrow conductive tracks on untreated polymeric substrates. Adv. Mater. 20 (2008) 343–345, https://doi.org/10.1002/adma.200701876. [31] A. Matavž, V. Bobnar, B. Malic, Tailoring ink–substrate interactions via thin polymeric layers for high-resolution printing. Langmuir 33 (2017) 11893–11900, https://doi.org/10.1021/acs.langmuir.7b02181. [32] D. Wu, B.P. Binks, A. Honciuc, Modeling the interfacial energy of surfactant-free amphiphilic janus nanoparticles from phase inversion in pickering emulsions. Langmuir 34 (2018) 1225–1233, https://doi.org/10.1021/acs.langmuir.7b02331.

C H A P T E R

7 Elements of thermodynamics of interfaces The internal energy U is a sum of the kinetic and the potential energy of the molecules in the thermodynamic system, including the cohesion, bonding, and other interaction energies. The first law of thermodynamics states that to change the internal energy of a system by dU, work or heat must be exchanged with the environment: dU ¼ Q + W

(7.1)

To describe the system when it undergoes a transformation and predict in which direction the system can evolve with changes in pressure or temperature, thermodynamic potentials must be used, such as the Helmholtz and the Gibbs free energy. A thermodynamic system is at equilibrium when these potentials are at their minimum. The thermodynamic potentials are the difference between the internal energy of the system and “thermal energy” and the tendency to disorder is given by the TS term. At constant temperature, the Helmholtz free energy is F ¼ U  TS

(7.2)

G ¼ H  TS

(7.3)

and at constant pressure, the Gibbs free energy is

where S is the entropy, the most probable state of the system at the given temperature. The thermodynamic potentials are at their minimum when the entropy or degree of disorder is maximum. At high temperatures, the liquid and gaseous states have a higher entropy than the solid state. The thermodynamic parameter H is the enthalpy, or the latent heat of transformation: H ¼ U + PV

(7.4)

The enthalpy can be understood as follows: when the system undergoes a transformation at constant temperature (melting, vaporization), it consumes energy not only to break the bonds between the molecules (given by the U term) but also to impinge on the environment, to make room for the new state of the system, due to its changes in volume and pressure, PV [1]. Eq. (7.4) satisfies the bulk phases, but the enthalpy of the interfacial layer should be treated differently. Redefinition of the enthalpy for the interfacial layer is most useful and essential for understanding the later thermodynamic parameters and further deduction of new equations and relationships. In the bulk phase, all the forces acting at any point in the phase are homogeneous and symmetric. This is, however, not the case at the interface, which is not homogeneous, but there is a gradual change of the properties from Phase A to Phase B, see Fig. 7.1A. The interface is a thin layer with a certain thickness, τ. The unit volume of this interfacial layer can be represented by a rectangular cuboid (rectangle with l—horizontal dimension and τ is the thickness of the interface, l  τ—the cross-sectional area, l2—interfacial area). Its volume expands with an infinitesimal amount dV when applying the pressure P to the system (by convention, if there is work done to the system, then this will be taken with the minus sign)  PdV. The force operating horizontally from the exterior on the system is P  l  τ, Fig. 7.1. At the same time, there is an opposing force due to in-plane interfacial tension force acting to minimize the area, due to intermolecular forces, and these are equal to γ  l. The resultant force acting on a cross section of the interface is Plτγl

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(7.5)

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7. Elements of thermodynamics of interfaces

FIG. 7.1 (A) Unit volume of an interface between Phase A and Phase B represented by a rectangular cuboid with the interfacial area A ¼ l  l and thickness τ. (B) To expand the volume of the interface unit volume by dV, the dA and dτ must change under the action of the resultant of the forces acting on each facet.

Consequently, the work done to expand the lateral area by dA is ðP  τ  γ Þ  dA

(7.6)

The force acting on the other facets in the vertical plane to expand the thickness of the interface by dτ is P  A  dτ

(7.7)

The total work done on the interfacial system will be the sum of the above equations: P  dV + γ  dA

(7.8)

Now, we can reexpress the first law of thermodynamics applied to an interface as dU ¼ q  P  dV + γ  dA

(7.9)

q is the heat exchanged with the environment and is equal to the change in the entropy of the system with temperature, TdS: dU ¼ T  dS  P  dV + γ  dA

(7.10)

This last equation includes the γ  dA term that does not appear for a bulk phase. Thus, we can also explicitly redefine the enthalpy of the system as H ¼ U + PV  γA

(7.11)

The expression of the thermodynamic potentials can be rewritten as G ¼ U + PV  γA  TS

(7.12)

dG ¼ dU + PdV  VdP  γdA  Adγ  TdS  SdT

(7.13)

which by differentiation becomes which under conditions of constant T, P, and γ yields dG ¼ dU + PdV  γdA  TdS

(7.14)

The above treatment of the interface was for a closed system, but the interface is an open system, that is, it can exchange matter with the bulk, as in the case of adsorption at interface. For an open system, the internal energy change is X dU ¼ T  dS  P  dV + γ  dA + μ dni (7.15) i i where μ is the chemical potential of the species i and n the number of moles of species i. dH ¼ dU + PdV + VdP  γdA  Adγ Replacing dU in the equation above, we obtain dH ¼ T  dS  P  dV + γ  dA +

X

μ dn + PdV i i

dH ¼ T  dS + VdP  Adγ +

(7.16)

+ VdP  γdA  Adγ

(7.17)

μ dni i i

(7.18)

X

7.3 Choice of the boundary thickness, Gibbs dividing line, and excess function

And for the Gibbs free energy, we have dG ¼ dH  TdS  SdT ¼ SdT + VdP  Adγ +

X

μ dni i i

And integrating the above equation for the constant intensive variables p, T, and γ, we obtain X G¼ μ dni i i

137

(7.19)

(7.20)

This last equation is important; the Gibbs free energy of the interface is defined as the product of the chemical potential and the concentration of species at the interface.

7.1 Gibbs-Duhem equation for interfaces The Gibbs-Duhem equation is useful to relate the changes in the chemical potential of the system dμi due to component i and other thermodynamic parameters. X dG ¼ SdT + VdP  Adγ + μ dni i i And from the equivalent expression: dG ¼

X

μ dn + i i

X

n dμi i i

And by subtracting the two, we obtain the Gibbs-Duhem equation: X SdT  VdP + Adγ + n dμi ¼ 0 i i

(7.21)

(7.22)

which is equivalent to the Gibbs-Duhem equation for a bulk phase, except that it excludes the Adγ term.

7.2 Gibbs adsorption isotherm The Gibbs adsorption isotherm relates the quantity of the adsorbed species at interface and the surface tension. This can be derived from the Gibbs-Duhem equation at constant temperature and pressure: X Adγ ¼ n dμi (7.23) i i In the above equation, we can write the surface concentration of the surface species ni (mol/m2) in the unit area of the interphase with Γ i: Γi ¼

ni A

(7.24)

The Gibbs adsorption isotherm relates the change of the surface tension to the concentration of the species ni per unit of interface: X dγ ¼ Γ dμi (7.25) i i where Γ i depends on the choice of the boundary line of the interface. Γ i is also defined as the excess concentration per unit area of interface of the component i over that of an arbitrarily chosen plane crossing the bulk solution. In other words, how much more amount of solute is present at the interface than what it would be if the bulk concentration would have been homogeneous all the way through interface. This is an important parameter for interfacially active compounds.

7.3 Choice of the boundary thickness, Gibbs dividing line, and excess function As mentioned, the interphase region is the transition region where properties of the system gradually change from one phase to the other. For example the water-air interface: the boundary line is contained in the region AA0 DD0 ; in this

138

7. Elements of thermodynamics of interfaces

Bulk gas

Bulk liquid

Bulk gas

Interface region

A

S

Concentration

D

solvent

A‘

Gibbs dividing line

Concentration

Interface region

O

S‘

(A)

Distance

S

D

B

O‘

C

solute

A‘

D‘ D‘‘

S‘‘

A solvent

(B)

Gibbs dividing line

Bulk liquid

O

S‘ S‘‘

D‘ D‘‘

Distance

FIG. 7.2 The graphic definition of excess functions of the Gibbs dividing line in the interphase region between the water phase and the air phase. (A) the one-component system and (B) two-component system.

transition region of finite thickness, the concentration of the water molecules drops not in a sharp and abrupt way, but smoothly to almost zero as we depart from the bulk into the air phase, as in Fig. 7.2. This is easy to imagine, but because the concentration of the molecules as we approach the air-water boundary gradually changes, the water concentration at the interface will depend on where exactly we draw the interface line, or the Gibbs dividing line. The location of this Gibbs dividing line is critical for the magnitude of Γ i. To eliminate the arbitrariness of choosing a dividing line, the thermodynamic excess functions were defined, which express the deviation of the concentration in the interphase region as compared to each of the bulk phases. The concentration excess function Γ ex i is the difference between the concentrations of the molecules given by the area below the Gibbs dividing line, SS00 , (Fig. 7.2) in the interphase region, minus the concentration of molecules in bulk phase below the dividing line plus the concentrations of the molecules given by the area above the Gibbs dividing line in the interphase region, minus the concentration of molecules in bulk phase above the dividing line, as defined by the textured fields in Fig. 7.2A:     air bulkðS’ S00 D00 D0 Þ interface ðAA0 S0 OÞ water bulk ðAA0 S0 SÞ interface ðOS00 D00 D0 Þ ex  Γ water  Γ water + Γ water Γ water ¼ Γ water If the Gibbs dividing line is chosen to be AA0 , then the first term is zero and the area AA0 D0 (below the curve AODʹ) is the excess function. However, if the dividing line is at SS00 , the excess function will be zero because the first term is negative and second term is positive (the textured area AOS is equal to the textured area OS0 D0 (Fig. 7.2A)). The latter choice in positioning of the dividing line has significant advantages in a two-component system. For an interfacially active solute, such as surfactant, dissolved in water, its concentration is described by the area below the BODʹ curve (BA0 D0 area (Fig. 7.2B)); in the interfacial region, its concentration drops slower than that of the solvent. Therefore, the Gibbs adsorption isotherm for a two-component system can be written as: dγ ¼ Γ water dμwater + Γ solute dμsolute

(7.26)

The above equation can be simplified with the help of excess functions. Choosing the Gibbs dividing line at SS00 (Fig. ex 7.2B), for example, the solute, the surface excess of the solvent is zero Γ ex water ¼ 0 and Γ solute is     air bulk ðS’ S00 D0 D0 Þ interphase ðBA0 S0 OÞ interphaseðOS00 D00 D0 Þ water bulk ðBAS0 O0 Þ ¼ Γ  Γ  Γ + Γ Γ ex solute solute solute solute solute

7.4 Interfacial adsorption isotherms and surface tension

139

With such a defined excess function, the Gibbs adsorption isotherm, Eq. (7.26), in the two-component system can be written only as a function of the solute: dγ ¼ Γ ex solute dμsolute

(7.27)

Differentiation of the chemical potential equation for the solute is dμsolute ¼ RT

dCsolute Csolute

and the Gibbs adsorption equation for a dilute nonelectrolyte binary system becomes: Γ ex solute ¼

Csolute dγ RT dCsolute

The right-hand-side term in the above equation can be multiplied by a factor 1/f with 1  f  2 depending on the degree of the ionization of the solute, when the solute and other components in the system are electrolytes.

7.4 Interfacial adsorption isotherms and surface tension Adsorption isotherms are relationships between the concentration of adsorbed species to their concentration in bulk: Γ ex solute ¼ f ðCsolute ÞT¼const Csolute is the bulk concentration of a solute, such as surfactants. For a multicomponent system, the adsorption isotherm will also depend on the other solutes present: Γ ex solute1 ¼ f ðCsolute1 , Csolute1 , …ÞT¼const For liquid-gas interfaces, it is convenient to measure the surface tension as a function of bulk concentration of the solute: γ ¼ f ðCsolute ÞT¼const The isotherm can be therefore rigorously derived from the surface tension equation using the Gibbs adsorption equation. Surface tension of diluted solutions of organic substances and surfactants is described by a semiempirical equation derived by Szyszkowski [2, 3]: γ ¼ γ 0 ð1  A ln ð1 + BCsolute ÞÞ where γ 0 is the surface tension of the pure solvent and A and B are empirical constants. The theoretically derived expression for the Langmuir isotherm is Γ ex solute ¼

aCsolute 1 + bCsolute

where a and b are constants. Relating to the Szyszkowski empirical equation with the Langmuir isotherm, we obtain the relationship between the constants: a¼

γ 0 AB and b ¼ B RT

A plot of the surface tension data vs. surfactant concentration is the typical experimental result for any surfactant (Fig. 7.3) usually presented as a semilog plot. Three distinct regions may appear in the surface tension vs. bulk concentration of the surfactant, namely, the first one is at extremely dilute concentrations for which the surfactant molecules are too few to change the surface tension of pure water, 72.4 mN/m at 21°C, BCsolute ≪ 1. The Szyszkowski equation gives: γ ¼ γ0

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7. Elements of thermodynamics of interfaces

FIG. 7.3 The semilog plot of the change in surface tension with concentration of a typical surfactant.

The second region is still in the dilute domain for which the surface tension of water slowly decreases due to the adsorption of surfactants, and in this case BCsolute ≫ 1. The Szyszkowski equation is γ ¼ γ 0 ½1  A ln ðBCsolute Þ and the Langmuir isotherm is linear and the slope is the constant a: Γ ex solute ¼

γ 0 ABCsolute RT

The third region is the surface tension plateau at saturation for which the interfacial saturation is reached at the critical micelle concentration (CMC). At interfacial saturation, for which a and b are very large, compared to unity, a monolayer is obtained: a Aγ 0 Γ ex solute ¼ Γ M ¼ ¼ b RT In the CMC concentration mentioned above, the interfacial tension should remain constant. The addition of surfactants in bulk will only contribute to the formation of micelles and the interfacial adsorption remains negligible. At the liquidgas interfaces, the interfacial adsorption is fully described by the Langmuir isotherm. However, at the solid-liquid interfaces, the adsorption of the surfactants can be described by either the Langmuir isotherm or Freundlich isotherm, which allows for adsorption of multilayers or formation of surface anchored self-assembly structures such as hemimicelles: 1=n Γ ex solute ¼ kCsolute

where k and n are constant.

References [1] M.W. Zemansky, Pure substances, in: Heat and Thermodynamics, fifth ed., McGraw-Hill, New York, 1968, , pp. 275–334 (Chapter 11). [2] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, sixth ed., John Wiley & Sons, Inc., New York, 1997 [3] J.C. Berg, The role of surfactants. in: Textile Science and Technology, Elsevier, 2002, , pp. 149–198, https://doi.org/10.1016/S0920-4083(02)80008-1.

C H A P T E R

8 Populated interfaces and their reactivity 8.1 Partitioning of solute between immiscible phases Partitioning is the natural tendency of a substance soluble in two immiscible phases to distribute between two phases until equilibrium is reached. For example, a solute partially soluble in the oil and water phase will begin slowly to diffuse, absorb, and desorb in each phase back and forth until the equilibrium concentrations of the substance in both phases are achieved. The chemical potential at equilibrium of the solute i in two immiscible phases A and B at equilibrium, constant temperature, and pressure must be equal: A 0B B μ0A i + RT lnxi ¼ μi + RT ln xi

(8.1)

where x is the molar fraction of the component i in each phase, whereas the behavior of the solute is considered ideal (concentration instead of activity coefficients) and μ0A i is the standard chemical potential of the component i. By rearranging the previous equation, we arrive at an equivalent form: ΔG ¼ 

0A μ0B xB i  μi ¼ kB T ln Ai ¼ kB T ln D NA xi

(8.2)

where D is called the distribution coefficient or by the older designation partitioning coefficient:
 ΔG D ¼ RT exp  RT

(8.3)

The partition coefficient of a substance between the n-octanol oil and water phases is an important parameter used in pharmacology to establish the bioavailability of a drug designed to be absorbed through the intestinal tract into the body.

8.2 Partitioning and adsorption at liquid interfaces Some molecules, such as surfactants, and nanoparticles can partition at the interface between two immiscible bulk phases. Surfactants initially dissolved in water will in a very short time adsorb at water-air, water-oil, and water-solid interfaces. The free energy of the system is minimized when the nonpolar part of the amphiphile is partially dehydrated or ejected from water into the nonpolar phase, while the polar part remains in water. The adsorption of surfactants at interfaces proceeds until the available interfacial area is fully occupied with a monolayer of molecules.

8.3 Soluble films—Gibbs monolayers Gibbs monolayers are self-assembled monolayers formed at the interface of two immiscible phases due to spontaneous adsorption of a soluble compound in one of the phases—adsorption monolayers. For example, the adsorption of a surfactant at the water-air interface. Depending on the bulk concentration of the surfactants, the interface can be saturated with molecules packed in a monolayer. The interfacial concentration of the surfactant solute is equal to

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8. Populated interfaces and their reactivity

the surface excess Γ ex solute, which can be obtained from the Gibbs adsorption isotherm whose expression was derived in the previous chapter. This form of Gibbs adsorption equation applies to all low-dimensional objects such as nanoparticles, graphene sheets, and amphiphilic proteins whose adsorption at interfaces results in the formation of monolayers. The expression of the chemical potential of the solute i in a multicomponent system is given by μi ¼ μ0i + RT ln ci where molar fraction was replaced by the concentration ci (true for solutions below 102 M or less, otherwise is the concentration of the surfactant that can be replaced with the activity ai ¼ fci). Differentiating the last expression, we obtain dμi ¼ RTdð ln ci Þ ¼

RT dc c

(8.4)

This result can be substituted into the Gibbs’ isotherm equation applied to a surfactant dissolved in water yields ex dγ ¼ Γ ex surfactant RTdð ln ci Þ ¼ Γ surfactant RT

dc c

(8.5)

Thus, the value of Γ ex surfactant can be calculated from the measurement of the surface tension as a function of concentration for nonionic surfactants. For ionic surfactants of the AB-type electrolyte, such as sodium dodecyl sulfonate (SDNa), which is completely dissociated in water SD + Na+, the previous equation becomes   ex ex (8.6) dγ ¼ RT Γ ex A dð ln cA Þ + Γ B + dð ln cB + Þ ¼ 2RTΓ AB dð ln cAB Þ ex to preserve neutrality at the interface we can presume that Γ ex A ¼ Γ B+. Thus, for dilute solutions of ionic surfactant, the surface concentration can be obtained from the slope of a plot of surface tension γ and log C at constant temperature: ! 1 dγ   (8.7) Γ ex AB ¼  2:303 RT d log cAB

which is in units of mol/1000 m2, if R ¼ 8.31 J/mol K, and γ in mN/m or mJ/m2 and in units of mol/cm2 when R ¼ 8.31  107 erg/mol/K and γ in dyn/cm or ergs/cm2. One can further calculate the area occupied by a single molecule from the surface excess concentration by the following formula: a¼

1016 NΓex AB

(8.8)

2 where N is Avogadro’s number and Γ ex AB is in mol/cm . A typical curve of γ vs log c is given in Fig. 7.3 and in the low concentration domain is linear, above a certain concentration value a break in the curve is observed at the critical micelle concentration (CMC); above CMC the surface is considered saturated with surfactants and self-assembled structures begin to form in bulk, such as micelles.

8.4 Insoluble films—Langmuir monolayers In contrast to Gibbs monolayers that form by spontaneous adsorption of soluble molecules, Langmuir monolayers form at the interface due to spreading of insoluble molecules at the interface—also known as “spread monolayers.” For example, Langmuir monolayers form at the water-air interface by spreading long-chain fatty acids, such as arachidic acid (C19H39COOH), which are not soluble in water. The fatty acids can be initially dissolved in a volatile solvent such as dichloromethane and deposited on the water surface dropwise with a precision syringe. Next, the solvent quickly evaporates, and the surfactant remains trapped on the water surface. The amount of surfactant spread at interface can be chosen in such a way to either fully pack into a monolayer on the available surface or be less than the available surface which can be compressed to give rise to an insoluble tightly packed Pockels-Langmuir (PL) monolayer of

8.5 Langmuir-Blodgett monolayers—Manipulation of a monolayer of molecules

143

surfactants. The presence of a PL monolayer at the interfaces affects the surface tension of the liquid. The difference in the surface tension of the pristine interface γ 0 and the surface tension γ of the interface in the presence of the surfactants is called surface pressure Π: Π ¼ γ0  γ

(8.9)

8.5 Langmuir-Blodgett monolayers—Manipulation of a monolayer of molecules The Langmuir-Blodgett (LB) technique for deposition of organic monolayers on solid substrates [1] has its origins in the pioneering work of Agnes Pockels (1891), Irving Langmuir (1917), William Harkins (1917), and Katharine Blodgett and Vincent Schaefer (1929–33). The LB technique of transferring a monolayer or multilayers onto a solid substrate consists of first forming a monolayer of amphiphilic molecules at the air-water interface, a PL monolayer. This PL monolayer can be then transferred onto solid substrates as a monolayer, or, if repeated, as multilayers: these are referred to as the Langmuir-Blodgett (LB) films (if the substrate is held perpendicular to the PL monolayer) or Langmuir-Schaefer (LS) monolayer (if the substrate is held parallel to the PL monolayer). In the PL method, insoluble monolayer is prepared at the water-air interface by spreading or dropping a solution of high vapor pressure solvent (e.g., chloroform) containing surfactants onto the water surface: the solvent evaporates, but the molecules are insoluble in water and do not sink but are forced to float on the surface. If the available area on the surface is very large compared to the area occupied by surfactants, the monolayer is in two-dimensional (2D) gaseous state, can be mechanically compressed by moveable barriers into a 2D liquid and 2D solid contiguous monolayer. A typical example of a surfactant forming an ideal LP monolayer is arachidic acid (C19H39-COOH), which has a long hydrophobic alkyl chain of 19C atoms, and a hydrophilic dCOOH group at one end of the chain. Langmuir designed an ingenious instrument that allowed the compression of the molecules at the air-water interface, while simultaneously measuring the surface tension with a piece of paper (Whilhelmy plate), or Pt wire just barely immersed in the water surface (to avoid buoyancy and measure the pull down due to surface tension) hanging from a balance or piezoelectric sensor—force transducer. Upon change in surface tension of the water surface, the paper or the wire immersed on the wire is being pulled down by the water surface with a different force and the piezoelectric sensor registers a weight change. This apparatus is called a Langmuir-Blodgett (LB) trough or film balance and with it Langmuir could introduce his concepts of a monolayer and for the first time the 2D materials and the physicochemical description of his findings; for his work, Irving Langmuir received the Nobel Prize in Chemistry in 1932. The earlier work on this subject predates that of Langmuir, and was done namely by Agnes Pockels, who conducted surface tension measurements with monolayers of surfactants and measured the surface tension by hanging a shirt button from balance through a wire, she published her work in Nature in 1891. Katherine Blodgett is yet another pioneer, the first scientist woman working in 1917 at General Electrics, United States who had a major contribution in developing the LB technology and applications such as monolayer deposition on glass lenses to reduce glare for many applications. A schematic representation and a picture of a Langmuir trough are depicted in Fig. 8.1. The governing principle of the apparatus is to keep the available surface area of the water equal to (or larger than) the total area occupied by a laterally packed monolayer of molecules spread on the surface (thus, no multilayers can form at the air-water interface). Amphiphilic molecules, e.g., long-chain fatty acids, will orient at the air-water interface, such that the hydrophobic groups are held out of the water (in which they cannot dissolve), while the hydrophilic groups are attracted into the water. Therefore, the molecular area determined with the LB method is the vertical projection of the molecular area in the given orientation, over the water surface (subphase). In a Langmuir trough, upon compression, the amphiphilic molecules are forced closer together, and the short-range intermolecular forces are activated. This creates a change in water surface tension. The surface tension of pure water, γ 0, decreases to γ in the presence of the PL monolayer. The surface pressure, Π is the positive difference between γ0 and γ as given in Eq. (8.9). The surface tension of the water is reduced by the presence of the Langmuir monolayer, as first explained by Benjamin Franklin in 1757. However, the lowering of the surface tension upon compression depends on the structure of the surfactant and the cohesion forces that exist between these molecules at the interface. Langmuir monolayers can be made from a wide range of molecules, carrying different properties and functionalities. The most important indicator on the behavior of an organic monolayer at the air-water interface is a plot of surface pressure Π as a function of the available area A. This is most often referred to as the pressure-area isotherm (Π-A), as it is measured at a constant temperature. The Π-A isotherm is the 2D equivalent of the pressure-volume (P-V) isotherm of a “three-dimensional (3D)” gas. An ideal

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8. Populated interfaces and their reactivity

FIG. 8.1 Cartoon and photograph of a Langmuir-Blodget instrument. (A) Schematics of a Langmuir-Blodget instrument showing the main components (1) main water trough, (2) water well for dipping long samples, (3) surface tension sensor, (4) barriers for sweeping the water surface and compressing the surface water monolayer, and (5) sample. (B) After closing the barriers, the monolayer is being compressed and surface tension recorded. (C) Actual photograph of a Langmuir-Blodgett system from Kibron. This instrument could be equipped with further accessories such as Kelvin probe, Brewster angle microscope, polarized angle FTIR, and X-ray reflectivity for measurement of the monolayer properties.

organic monolayer, as is that of arachidic acid, exhibits three phases: gaseous, liquid, and solid. After the initial spreading of the molecules onto the “subphase” (water), the amphiphilic molecules are very far apart, and there is no interaction between them: this produces a negligible change in the surface tension and the molecules behave as a 2D gas (Fig. 8.2, region 1). Upon compression of the monolayer, the film exhibits some ordering, and behaves as a 2D liquid (Fig. 8.2, region 2). A further compression of the monolayer will compact the molecules even further, and molecular ordering becomes stronger. In this region, the monolayer behaves as a 2D solid, with the molecules fewer degrees of freedom and produces a sharp increase in surface pressure (Fig. 8.2, region 3). Arachidic acid and long-chain fatty acids in general exhibit isotherms that have all three of the regions discussed above with easily identifiable transitions between them (Fig. 8.2). Other molecules or even nanoparticles may behave differently. Some molecules exhibit a direct transition from the gas phase into the solid phase; others show only a gas and liquid phase. The intermolecular forces that occur at the water surface are electrostatic (for charged species) and van de Waals. The electrostatic forces act mostly between the polar groups that are submerged into the water; electrostatic forces are proportional to 1/r2, where r is the intermolecular distance. The van der Waals forces act mostly between the hydrophobic tails and are proportional to 1/r6 and 1/r12 [2].

145

Pressure / mN m–1

8.5 Langmuir-Blodgett monolayers—Manipulation of a monolayer of molecules

FIG. 8.2 Pressure-area (Π-A) isotherm of arachidic acid, at 17°C. The hydrophilic part of the molecule is represented by the white circle; the hydrophobic tail is represented by the zig-zag segments; and Π C and Ac are the pressure and the area per molecule at the collapse point.

The monolayer collapse takes place, when the compression forces become too strong for confinement of a single layer of molecules in two dimensions. The molecules will be either injected into the subphase (water) or into the superphase (air), or forced to overlap each other, forming local multilayers [1]. The collapse pressure, Π C, is therefore an important characteristic of the monolayer, since it is the pressure at which the molecules occupy a minimum area before they collapse onto each other. The external forces that act on the monolayer are mostly due to environmental vibrations, which produce shock waves on the water surface. The quality of the monolayer is greatly affected by the cleanliness of the environment. Molecular orientation, film thickness, and stability can be inferred from the Π-A isotherms. It is widely accepted that under ideal conditions, the LB films can exhibit both long-range ordering and a crystal-like structure. X-ray and polarized microscopy studies show that fatty acids in LB monolayers have a hexagonal close-packed translational ordering (each molecule has six nearest neighbors) [3–6]. The structural organization of the fatty acids differs only slightly from that of a true solid-state crystal. Some LB multilayers can be categorized by liquid-crystal-like phases: hexatic smectic B (perpendicular to the surface), F, I (tilted at an angle from the surface normal), and crystalline smectic phases. Another method frequently used to characterize the formation of the organic monolayer in the Langmuir-Blodgett trough is by measuring ΔV, the change in the Volta potential at the water surface. A plot of Volta potential change, as a function of the monolayer area A, is called the potential-area isotherm, ΔV-A. The molecular dipole moment μ can be estimated from ΔV-A isotherm, using the Helmholtz [7] relation: μ ¼ ΔVεr ε0 A

(8.10)

where ε0 is the electrical permittivity of vacuum, εr is the relative electrical permittivity of the monolayer, and A is the area per molecule. The Langmuir balance is mainly used to transfer the PL films, from the air-water interface onto solid substrates, by a vertical dipping method. Transfer of the monolayer is achieved at a fixed pressure, simultaneous dipping of the substrate, and compression of the monolayer. The best transfer pressure is chosen so that the monolayer is in a solid phase; this assumes a previously measured isotherm. As a function of the direction of dipping and the substrate wetting properties, the molecules can be transferred either with the hydrophobic moiety or hydrophilic moiety closer to the surface, as shown in Fig. 8.3. The exact forces that facilitate the monolayer transfer are not completely understood, however, the “carpet model” deposition is widely accepted. According to the “carpet model” [8], the monolayer transfer occurs that is similar to

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8. Populated interfaces and their reactivity

Vertical lifting (hydrophilic substrate)

Vertical dipping (hydrophobic substrate) Compression

H2O

H2O

FIG. 8.3 (Left) Vertical lifting of the substrate from water and the formation of an LB monolayer, with the hydrophilic end of each molecule closer to the hydrophilic surface (Z-type transfer) and (right) vertical dipping of a hydrophobic substrate and deposition of an LB monolayer with the hydrophobic end of each molecule closer to the substrate (X-type transfer).

pulling a carpet, with a slight flexing and deformation, but no change in the film structure or organization, although defects often occur. The crystal-like structure of the PL monolayer is preserved in the LB monolayer. This is believed to be the case for the subsequent few layers, transfer of subsequent layers on top of the first. The quality of the transferred monolayers depends on many factors: deposition speed, substrate roughness, compression speed, film stability, and intermolecular forces in the film. Therefore, an extensive knowledge of the PL monolayer at the air-water interface is required prior to any deposition attempt. Numerous X-ray diffraction studies show that the LB monolayer can be highly ordered on the transferred surfaces. The diffraction patterns of various fatty acid molecules show specific peaks, which do not change overtime. In rare cases, the LB films achieve epitaxy with the substrate. Usually, the molecular packing is dominated by the intermolecular forces, which are preexistent in the monolayer before the transfer from the air-water interface. The ability to make and control a thin monolayer of molecules has attracted a lot of interest not only for the functionalization of substrates but also for study organic conductors, magnets, nonlinear optic, rectifiers [7, 9–11], and intermolecular charge transfer [12]. Many other applications of the LB technology have been found [13]. Furthermore, this technology has attracted a fundamental interest for making monolayers of nanoparticles and nanoparticle assemblies. However, due to their fragility, the molecule LB films cannot be chemically modified after preparation.

8.6 Self-assembled monolayers Self-assembled monolayers (SAMs) are monomolecular layers, which are spontaneously formed upon immersing a solid substrate into a solution containing amphiphilic molecules. The driving force for the SAM formation is the lowering of Gibbs interfacial free energy and thus lowering the interfacial tension [14]. At the solid-liquid interfaces, the adsorption processes of surfactants are like those at the liquid-gas interfaces, but surfactants can adsorb irreversibly via chemisorption and physisorption. The best studied examples are silanes, which are used to modify silica [15], glass and quartz surfaces, alkanethiols which have an affinity for gold, silver [16], platinum, copper [17–19] and fatty acid carboxylates which adsorb on alumina and sapphire [20], alkyl phosphonic acids on aluminum oxide substrates [21], etc. Historically, according to Schwartz [14] and Ulman [22], Zisman is credited with originating the SAM concept in an article [23] from 1946, whereas in the early 1980s Nuzzo and Allara introduced SAMs from thiols on gold [24] and in the mid-1980s Maoz and Sagiv introduced SAMs of trichlorosilanes on silicon oxide [25]. The practical interest in the SAMs is for potential applications such as control surface polarity and wetting [26], adhesion and friction [27], chemical resistance, surface functionalization, biosensing applications, unimolecular electronics [10, 28], immobilization of biological components including (oligo-) nucleotides, proteins, antibodies and receptors as well as polymers [29], cells and DNA immobilization [30], tuning the metal electrode work function [31], etc. In most cases, the fully formed SAMs from single alkyl groups are constituted from highly ordered and tightly packed molecules [14], while those derived from branched fatty chain units are less ordered than the former [32], as well as other bulky structures carrying ligands and other type of molecules that are too bulky and irregular in structure for tight 2D packing. For the interested reader

8.6 Self-assembled monolayers

147

in the fundamentals mechanism of SAMs formation, Schwartz [14] and Ulman [22] have written some excellent reviews. Mixed SAM films have also been reported [33]. Alkyl thiol attachment on gold. Experimental evidence suggests that the alkyl thiol attach on gold via oxidative chemisorption resulting in the formation of strong covalent SdAu bond, like that in thiolates RS M+. The exact chemical mechanism for the adsorption of the alkyl thiols on the surface of Au has been subject of debate mainly to elucidate whether chemisorption proceeds via dissociative adsorption, meaning that SdH breaks during the attachment of sulfur to gold with the formation of a SdAu covalent bond, or is it in fact a coordinative bond between sulfur and gold, while the hydrogen atom remains attached. The coexistence of both situations has also been computed [34]. Some experimental evidence by Kankate et al. [35] on the deposition of the nitroaromatic thiols from vapor on gold proceeded with the partial reduction of the nitro groups into amine groups, which suggest that the adsorption on the gold surface proceeded with the release of atomic hydrogen with the homolytic cleavage of the SdH bond, the formation of the thiyl radical followed by chemisorption [36]. Vericat et al. [19] point out that despite the controversy related to the SdH bond scission, the most accepted hypothesis is that the hydrogen atoms react to generate H2, as shown in reaction, which is supported by the computational studies [37]:

An acidic environment seems to inhibit the dissociation of the SdH bond, while an alkaline environment favors the breaking of this bond. SdH bonds are about 20% weaker than the CdH bonds [36]. The energy of physisorption scales with the length of the alkane chain. The van der Waals physisorption energy with a metal surface per unit of CH2 is about 6.2 kJ/mol (2.5 kT) in a linear chain, while the SH group physisorption energy on gold is about 24.1 kJ/mol (9.7 kT) (Fig. 8.4A). The computed and experimentally determined SdAu chemical bond energy is about 52.5 kT and 130.2 kJ/mol [37, 38]. Alkyl silane attachment on hydroxylated surfaces. A class of widely produced SAMs is based on n-alkyltrichlorosilane, n-alkyltrimethoxysilane, and n-alkyltreethoxysilane precursor molecules, which through hydrolysis of the chloro, methoxy, and ethoxy groups produce alkylsiloxane SAMs. Octadecyltrichlorosilane (OTS) is often used as a model system, which forms very robust SAMs. Due to the hydrolysable bond, the OTS molecules can be covalently bound to substrate hydroxyl groups, as well as cross-linked within the neighboring molecules in the SAM layer. The commonly accepted mechanism for the attachment of the OTS on a hydroxylated surface such as silica is believed to take place in three steps: (i) hydrolysis of the chlorosilane bonds and the production of the silanetriol, (ii) physisorption on to the hydroxylated substrate driven by the hydrogen bonding with the silanol group, and (iii) chemisorption and siloxane SidOdSi covalent bond formation (Fig. 8.4B). The hydrolysis of the chlorosilane groups was also thought to be promoted by an adsorbed water on the substrate, for example, by the formation of OTS SAMs hydroxyl-free gold surfaces as pointed out in the review of Onclin et al. [39]. However, the preparation of substrate and the solvent greatly affects the coverage of OTS on substrate and the formation of good SAMs, for an in-depth discussion see the work of Manifar et al. [40]. Due to the versatility of the alkylchlorosilanes, they attach on any substrates with hydroxylated surface, such as cellulose [41], Ag, or various other metal oxides such as TiO2, ZrO2, and Ta2O5 [42], therefore, a preparation of the substrate. The bond energy of SidO is around 182.5 kT or 452 kJ/mol. Attachment of alkyl carboxylic acids on Al2O3 surfaces. Alkyl carboxylic acids attach on aluminum oxide surfaces and form SAMs, as first shown by Allara and Nuzzo [43, 44] in the mid-1980s. Alkyl carboxylic acids undergo physisorption on aluminum oxide through hydrogen bond in aprotic environments and through electrostatic double-layer interaction in protic environment. It has been hypothesized that following physisorption, the alkyl carboxylic acids undergo chemisorption on aluminum oxide, via acid-base interactions with the formation of the RCOO Aln+ (n  3) salt between the carboxylate ion and the metal cation surface centers [45]. Some other authors suggest that the main interaction is the formation of ester bonds with hydroxyls present on aluminum oxide surface due to increase acidity of OH bonds [46]:

Brand et al. [47] found a linear correlation between the number density of hydroxyl groups on alumina and the amount of adsorbed alkyl carboxylic acids. The larger the amount of surface hydroxyls the more adsorbed alkyl

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8. Populated interfaces and their reactivity

FIG. 8.4 (A) Formation of SAM from alkylthiols in two steps, physisorption of the alkylthiols driven by van der Waals interactions with the metal, followed in the second step by covalent bond formation. (B) Formation of SAM from n-alkyltrichlorosilane precursor molecules in three steps: (i) hydrolysis of the chlorosilane bonds and the production of the silanetriol, (ii) physisorption on to the hydroxylated substrate driven by the hydrogen bonding with the silanol group, and (iii) chemisorption and SidOdSi covalent bond formation. (C) Formation of SAMs from n-alkyl carboxylic acids with aluminum oxide surfaces, the physisorption is driven by the H-bond interaction of the carboxyl functional surfaces with alumina surfaces, or acid-base interaction with Al + centers, followed by chemisorption with suggested bridging of two Al + centers, covalent binding or chelate bond formation.

carboxylic acids were observed in their studies with the reflection absorption infrared spectroscopy (RAIRS), moreover, the AldOH groups were consumed in the reaction process. Barron [48] hypothesized that the carboxylate groups may be capable of bridge binding two aluminum Lewis acid centers on the surface of boehmite, an aluminum oxide mineral. This conundrum was summarized in a recent review by Pujari et al. [42] who have summarized the literature results, presenting the current working hypothesis that there are several modes of carboxyl binding on oxide surfaces, through “outer-sphere” adsorption complexes and “inner-sphere” adsorption complexes. In the former case, the H-bond and acid-base interaction with the formation of an ionic complex [49] is important while in the latter case either

8.6 Self-assembled monolayers

149

a bridging of two metal center, a coordinative metal-ester bond or a chelate-type binding are conceivable (see Fig. 8.4C). For the alkyl carboxylic acids, it has been pointed out in a recent study by Taylor and Schwartz [50] that a freshly annealed surface of Al2O3 is essential to a good SAM formation of octadecanoic acid in aprotic hexadecane, because in normal atmospheric conditions the AldOdAl slowly converts into the AldOH surface functional groups; the AldOdAl can be regenerated by annealing. In the same study, it is shown that on a hydrated sapphire surface, when AldOH groups are present SAMs do form but can be easily washed off by water rinse. On the other hand, when sapphire surface is freshly annealed and the surface fully dehydrated, the octadecanoic acid SAMs form, films are very sturdy and cannot be rinsed off by water. Bidentate dialkyl dicarboxylic acids are shown to form much sturdier SAMs than those formed by the alkyl carboxylic acids, resisting rinse off by water [47]. Similarly, due to the multidentate nature, the alkylphosphonic acids are known to form sturdier SAMs on sapphire than the alkyl carboxylic acids [50]. The computed single covalent bond energy in the (H2O)5Al-OOC-R complex is 149 kT and for the chelate binding of the carboxyl to the metal center in the (H2O)4Al ¼ OOC-R complex is 254.3 kT [51] (see Fig. 8.4C). These computed binding energies of the Al-OOC are larger than the binding energy of the SdAu bond. However, experimentally it is known that the thiol SAMs are significantly sturdier than the SAMs formed by the alkyl carboxylic acids, namely, they cannot be washed off by water rinse. So, it may not be the case that the alkyl carboxylic acids form covalent or coordinative bonds with the aluminum oxide surfaces stronger than that of thiols to gold. Lapouge and Cornard [51] showed that the formation of a chelate bond requires a high activation energy barrier so it is unlikely that chemisorption of alkyl carboxyls form under normal condition chelates with the Al centers on aluminum oxide surfaces. Since water displaces alkyl carboxylic acids SAMs during the rinse off from the surface, one could hypothesize that those SAMs were in fact either only physiosorbed, or a purely acid–base interaction with salt formation RCOO Aln+ (n  3)+ has occurred, with much smaller binding energies than that of the hypothesized single ester AldOOC ester covalent bond or Al]OOC chelate bond. A mixed covalent bonding of alkyl carboxylic acids with aluminum oxide has also been put in evidence by experimental studies [20]. In the study of octadecanoic acid adsorption on sapphire surface, Taylor and Schwartz [50] have shown that the hydroxyl bonds are not needed for SAM formation. In fact, the acid-base interaction is underlying interaction for other type of SAMs such as between the Lewis acid octadecyltrimethylammoniumbromide (C18TAB) and the Lewis base mica surface, which has a negative surface zeta potential at neutral pH [52]. For the sake of caution to dismiss any of the hypothesis presented, which are based either on direct or indirect experimental evidence with respect to alkyl carboxylic acid binding on various aluminum oxide surfaces, one can conclude that the binding mode is not unique for these alkyl carboxylic acids on aluminum oxide, and in a single SAM both outer and inner complexes are possible, depending on the exact conditions of the reaction and substrate treatment. Reactivity of self-assembled monolayers. Simple organic reactions can be carried on SAMs containing functional groups such as carboxyls, amines, hydroxyl, or bromine. Ideally, these reactions should have high yield, occur in mild conditions, and have no by-products as the purification would be difficult. In this way, the surface functionalization and reactivity can be controlled. For these, bifunctional molecules containing both a surface anchoring group, dSH, dCOOH, dSi(EtO)3, etc., and a chemically reactive group which should be chosen such that it does not react to the substrate, dNH2, dOH, dCOOH, dBr, dSH, dC^Cd, etc. The pathways to chemical modification of SAMs have been extensively reviewed [53, 54]. Carboxyl-amine coupling. The coupling of a carboxyl and amine groups can proceed via carboxyl activation with dicyclohexylcarbodiimide (DCC) or 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) followed by the reaction with an amine to create and amide bond (Fig. 8.5). This reaction is also exploited in biomolecules attachment on surfaces, such as enzymes and antibodies for biosensing applications [55, 56]. Because the reaction in solvent is not suitable for biomolecule attachment, Frey and Corn [57] reported a water-based amine-carboxyl coupling reaction using water-soluble carbodiimide coupling agent, EDC, and N-hydroxysulfosuccinimide (NHSS) to convert the carboxylic acids to NHSS esters (see Fig. 8.5). The typical carboxyl coupling N-hydroxysuccinimide (NHS) agent is relatively water insoluble, suitable more for organic solvents, while NHSS is water soluble [58]. The activated MUA-NHSS ester monolayer with an aqueous solution of an amine leads to the formation of an amide bond with the surface. Biomolecule attachment on this activated ester was reported for biosensing applications. However, the immobilization of protein on the surface with this reaction is based on the reaction of an activated carboxyl from the surface with a random amine from the protein, therefore, the biomolecules will not be oriented on the surface which may affect its activity [59]. The activated carboxyl groups can be further reacted also with alcohols to produce esters. The amine terminal group in SAMs can be reacted with acylating agents, acylclorides, quinones, etc. Azide-alkyne reactions. The azide-alkyne reaction also known as the Huisgen 1,3-dipolar addition, between alkyne and a 1,3 dipolar azide leads to the formation of triazole [60]. The Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) can be used for the modification of SAMs, either by first formation of a SAM bearing either a terminal azide or an alkyne group (see Fig. 8.6). The azide and alkyne do not react in the absence of a catalyst at room temperature, but

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8. Populated interfaces and their reactivity

FIG. 8.5 Carboxyl-amine coupling of a SAM with a carboxyl group functionality.

FIG. 8.6

Azide-alkyne reactions.

react immediately in the presence of the Cu(I) catalyst at room temperature; this feature can be in fact used for surface pattern formation by stamp printing of the catalyst. The catalyst Cu(I) can be added externally or generated in situ, by introducing Cu(II) and sodium ascorbate (a reducing agent) in an aqueous solvent. CuAAC is used to attach a large variety of molecules and biomolecules on surfaces. The great advantage of CuAAC in protein immobilization over the amine-carboxyl immobilization pathway is the ability of the SAM surface to react with site-specific modified proteins [59], which may preserve the protein activity. Acetylene-modified proteins could be attached to azide-functionalized SAMs [54]. Thiol-ene reactions are useful reactions for surface modification and biomolecular immobilization can proceed either via free radical addition of thiols to the double bond anti-Markovnikov or via catalyzed Michael addition mechanisms. The thiol-ene “click” reactions are initiated either under UV irradiation or under heating at 70°C [61], whereas the in situ generated thiyl radicals (Fig. 8.7), are highly reactive species leading to extremely rapid reactions with alkenes. Catalyzed thiol-ene reaction is part of Michael addition class, which encompasses thiol-vinyl sulfone, thiol-acrylate, thiol-maleimide, and thiol-yne reaction [62]. SAMs with vinyl or -SH functionalities can be prepared on various substrates and can be further chemically modified with the thiol-ene reaction by attachment of other small molecules of interest (Fig. 8.7A). The thiol-ene reaction is also useful for preparing polymer brushes on surfaces. Harant et al. [63] have obtained polymer grafted films, or polymer brushes via photoinitiated thiol-ene reaction between a 1,6-hexanedithiol, triethyleneglycol divinyl ether with a silicon surface priorly modified with a thiol-terminated SAMs (Fig. 8.7B).

8.6 Self-assembled monolayers

151

FIG. 8.7 (A) General scheme of the thiol-ene reactions with the attachment of vinyl groups of SAM with thiol functionalities, (B) growth of polymer brushes by thiol-ene, and (C) formation of PEG-ylated hydrophilic surface by the thiol-ene reaction.

Oberleitner et al. [64] have successfully reacted vinyl-terminated SAM in the presence of a photoinitiator such as 2,2-dimethoxy-2-phenylacetophenone (IRGACURE 651) or 2-benzyl-2-(dimethylamino)-1-[4-(4-morpholinyl)phenyl]-1-butanone (IRGACURE 369) following a photoactivation procedure at 254 or 365 nm, respectively, in glycerol or ethylene glycol solution for about 10 s to obtain polyethylene glycol surfaces (Fig. 8.7C). The PEG surfaces are important in medical applications, to prevent biofouling, but also for the surface modification of micro- and nanoparticles. Using a photomask to control the region on the surface exposure to UV lights where the thiol-ene reaction can proceed, one can obtain a patterned surface, which is important especially for microcontact printing [65], and site-specific surface assembly of Au nanoparticles [66]. Nucleophilic substitution reactions. The nucleophilic substitution reactions performed on SAM monolayers have been extensively reviewed by Haensch et al. [67], who noted that this offers a broad spectrum of functionalization schemes for SAM surfaces. Nucleophilic SN2 displacement reactions are mainly performed on halogen, such as Br, I, terminated surfaces due to their high reactivity to the exchange by nucleophiles (Fig. 8.8). Already in 1990, Balachander and Sukenik [68] explored the nucleophilic substitution reactions for SAMs obtained from siloxane-anchored molecules with Br, CN, SCN, and SCOCH3 functionalities. For example, the Br-terminated SAM can be converted to an azide dN3

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8. Populated interfaces and their reactivity

FIG. 8.8 Nucleophilic substitution reaction of the bromide functional SAMs and the subsequent transformations.

functionality by treating the monolayer with sodium azide NaN3 in DMF at room temperature; the resulting dN3 terminated SAM is extremely versatile for the chemical attachment of other functionality via the “click” chemistry route. The azide could be subsequently transformed to dNH2 groups by reduction with LiAlH4 in ether, important for carboxyl-amine coupling of further functionalities. Br SAMs were also reacted with KSCN in DMF or Na2S2 in DMF to yield dSCN and surface bound dRSRd respectively (Fig. 8.8).

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C H A P T E R

9 Metal-organic interfaces in organic and unimolecular electronics Organic electronics makes use of organic matter for manufacturing electronic devices. The electronic devices based on organics at any scale encompass organic light-emitting devices (OLED), organic photovoltaics (OPV), organic fieldeffect transistors (OFET), organic supercapacitors (OSC), etc. In any of the organic electronic elements, there is an interface between a metallic electrode (or wire) and the organic layer (device) forming a metal-organic heterojunction. Unlike inorganic semiconductors, such as silicon, devices based on organic semiconductors are easier and often cheaper to manufacture, offering a whole range of possibilities, such as the ability to use the organic materials in conductive inks and print the circuit/device on flexible substrates, textiles, walls, etc. Therefore, the field of organic electronics offers the possibility of mass-producing cheap and reliable electronic devices, sensors, photovoltaics, etc. In addition, unlike inorganic semiconductors, no insulating oxide forms on the surface of organic semiconductors when exposed to air and can, therefore, form “clean,” meaning chemically defined interfaces with metals, and even biological organisms. This versatility of organic electronic devices triggered an intense scientific effort to understand the fundamental electronic properties such as mechanisms of the charge carrier transport across the metal-organic junctions as well as the potential barriers for carrier injection. Organic semiconductors can be divided into two categories, small molecules and conjugated polymers; some of these compounds are shown in Fig. 9.1. Due to their high charge carrier mobilities, some conductive organic polymers such as PEDOT or PPy can also be used as electrodes. The physicochemical properties of the metal-organic (MO) interface determine the interfacial transport of charge carriers and the performance of the device. But it must be mentioned at the forefront that the mechanism of electron transport across metal-organic interfaces are completely and thoroughly understood and new theoretical frameworks are being continuously developed.

9.1 Energy levels at metal-organic interfaces The starting point in the description of the interface between a metal and an organic semiconductor is to define the energy levels between metal and organic materials. To do this, it is instructive to first treat the energy levels which are initially separated at infinity and then in contact (Fig. 9.2). In the first situation, when the metal and the organic materials are separated, the representation of the energy levels is straightforward (Fig. 9.2A). In band structure theory, the Fermi level, EF, of a solid is the hypothetical energy level, at thermodynamic equilibrium, with a 50% probability of being occupied at any given time. The vacuum level is often taken as the reference for an unbound electron, or the energy required to remove an electron from a solid into the vacuum level at infinity (VL∞). By convention, the VL∞ is taken as the reference point for zero energy, below it, the energy of electrons occupying orbitals and electronic bands is taken with a negative sign to indicate they are bonded (Fig. 9.2). In practice, for metals only, the EF can be approximately determined by measuring the work function of the metal, which is the work required to remove one electron from the solid metal to the vacuum level near the surface (VLS), as the electrons still feel the effect of the metal surface [1]. The work function is a surface property because the electrons are first removed from the surface, which for the characterization of the metal-organic interfaces is a satisfactory parameter. For semiconductors, the EF lies somewhere between the conduction and valence bands. For the electroactive organic layer, the lowest unoccupied molecular orbital (LUMO) level can be approximately determined as the affinity (A) of the material to electrons and the highest occupied molecular orbital (HOMO) can be determined approximately by measuring the ionization potential Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00014-4

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FIG. 9.1

Chemical structure of some common conductive molecules and conjugated polymers used in organic electronics: fullerene (C60), [6,6]phenyl-C61-butyric acid methyl ester (PCBM), copper phthalocyanine (CuPc), pentacene, sexithiophene, N,N0 -bis(naphthalen-1-yl)-N,N0 -bis(phenyl)-benzidine (NPB), 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (BCP), polythiol (PTh), poly(3,4-dicyanothiophene) (PDCTh), Poly(3,4ethylenedioxythiophene) (PEDOT), poly(3-hexylthiophene) (P3HT), polypyrrole (PPy), polyaniline (PA), poly(N-methylaniline) (PNMA), poly (9,90 -dioctylfluorene) (PFO), poly(p-phenylene vinylene) (PPV), (poly[2-methoxy-5-(3,7-dimethyloctyloxy)-1,4-phenylen]-alt-(vinylene)) (MDMOPPV), poly[2-methoxy-5-(20 -ethylhexoxy)-1,4-phenylenevinylene] (MEH-PPV).

(IP), but also from other methods such as cyclic voltammetry, and especially direct and inverse photoelectron spectroscopies [2]. The Fermi level of the organic material falls somewhere between the HOMO and LUMO. The bandgap ΔBG can be determined from the edge of the last absorption band in the UV-vis absorption spectrum. When a contact is made the charge flows from one material to the other until the Fermi levels align (Fig. 9.2B) [1, 3]. If the Fermi level of the metal is above that of the organic, charge will flow from the metal until to the organic layer or vice versa for the case when the Fermi level of the organic is above that of the metal until the equilibrium is reached. The main consequence of the difference in the Fermi levels of the two materials is the apparition of a built-in potential Δbi, at contact, which changes the relative surface vacuum levels of the materials (Fig. 9.2B).

9.1 Energy levels at metal-organic interfaces

157

FIG. 9.2 Energy level of metal and organic material (A) separated at infinity and (B) in contact. In (B) the EF of the two metal and organic material align and a built-in potential arises ΔBI. The Wf is the work function of the metal, EF(metal) is the Fermi level of the metal, EF(organic) is the Fermi level of the organic material, A-electron affinity of the organic material, IP, ionization potential of the organic material. VL(metal), vacuum level near the metal surface; VL(organic), vacuum level near the organic surface; ΔBG, bandgap; CB, conduction band; VB, valence band.

But the built-in potential difference due to the difference in the Fermi levels at the metal-organic interface is not the only potential difference that arises at a metal-organic contact, other potential differences appear from different sources: “push-back” of the metal electron tailing, Δpb, chemisorption and hybridization of the frontier molecular orbitals Δchim, molecular dipole Δdipole, double-dipole Δddipole, etc. [4, 5]. These can enhance or minimize the metal-organic contact potential, such that the overall potential is a sum of these contributions Δpb + Δchim + Δdipole + Δddipole + …. It is an extremely difficult task for the surface scientist to exhaustively investigate all these aspects [2] and often relies on computational methods to calculate the energy-level alignment for metal-organic interfaces [5]. Therefore, in the energy level diagram representation the potential difference between the vacuum levels is neglected at the metal-organic interfaces and often many authors choose to represent the energy levels at the metal-organic contact as though they are at infinite separation. For a more in-depth discussion on energy level alignment at metal-organic interfaces, we refer the reader to the existing literature [1, 4–6]. Next, we briefly discuss the origin of a few of the above-enumerated potentials appearing at the metal-organic interfaces. The “push-back” of the metal electron tailing, Δpb: metals have an excess of electrons at their surface due to the presence of the dangling bonds. This affects the metal work function as well as the electron density of states near the surface. Upon adsorption of an organic layer at the interface, the electron tailing into space is compressed with the effect of the decreasing the metal work function by a certain value Δpb. This is called the push-back effect and is present at any metal-organic interface [4, 7]. Chemisorption and hybridization of the frontier molecular orbitals and partial charge transfer between the organic and the metal creates a potential difference at the metal-organic interface, Δchim. Strong chemisorption leads to strong metalorganic hybridization giving rise to completely new mixed metal-organic orbitals. This chemisorption induced through-bond charge transfer creates an interfacial dipole layer and as discussed by Fahlman et al. [4] transfer of electrons from the metal to the organic layer induces an additional shift in the vacuum level increasing the effective work function, while the transfer of electrons from the organic to the metal reduces the work function. Adsorbed molecules with large molecular dipole can produce a dipole potential step Δdipole at the interface, especially if the molecules have an orientation such as in the case of SAMs [8–10]. If the molecular dipole moment is oriented toward the metal surface the vacuum level is upshifted whereas a downshift results from the opposite orientation. Double-dipole potential Δddipole occurs if the adsorbate contains a permanent charge then the metal surface is polarized and forms image charges. The induced Δddipole can be quite large; for example, poly[(9,9-bis(30 -(N,N-dimethylamino) propyl)-2,7-fluorene)-alt-2,7-(9,9-dioctyl-fluorene)] (PFN) is used as an efficient interlayer material for producing lowwork-function electrodes in, for example, organic solar cells [4]. Similarly, poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)-diphenylamine) for improving the hole injection profile of poly(3,4-ethylene dioxythiophene): poly(styrene sulfonate) (PEDOT:PSS) [11]. Mastering some of these built-in potential shifts at the interface can lead to the development of strategies for metal surface passivation and reducing sensitivity to oxygen using SAMs [12].

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9. Metalrganic interfaces in organic and unimolecular electronics

9.2 Electron transport across metal-organic interface Charge carrier injection from metal into the organic semiconductor determines the performance of the electronic device. The charge injection process usually requires the promotion of a charge carrier, electron into the LUMO unoccupied states, or hole from the metal into the HOMO occupied states of the organic material (Fig. 9.3). The injection efficiency is determined by the potential barrier that exists to either electron or hole injection. The potential barrier is determined by the relative energy of the frontier orbitals of the organic layers with respect to the Fermi level of the metal (see Fig. 9.3). In a conjugated polymer organic semiconductor with well-developed energy bands, the HOMO and LUMO levels may become narrow bands due to delocalization, forming a conduction band from a LUMO and a valence band from a HOMO. In molecular organic semiconductors, the charge carrier states are highly localized on individual molecules and in case of conjugated polymers on relatively short conjugation segments and the charge transport proceeds via thermally activated hopping [3]. The potential energy barrier to electron injection is the. ϕe ¼ ELUMO  EF

(9.1)

ϕe ¼ EF  EHOMO

(9.2)

and for the hole injection.

These energy barriers are known as Schottky or contact energy barriers. Noble metals are usually used for obtaining oxide-free and chemically defined interfaces with the organic material. Atomically clean Au surface has EF 5.1–5.4 eV in UHV, it drops to 4.5–4.9 eV after exposure to HV or air [13, 14] (the exact value of the work function will depend on the composition of the actual atmosphere). The strong acceptor molecules will have LUMO levels close to the Fermi level (within 0.2 eV) of the metal and when deposited on the metal it can withdraw electrons from the metal while an organic donor molecule has a HOMO level close to the Fermi level and can withdraw hole carriers from the metal. The energy difference between the HOMO and LUMO levels is the bandgap: ΔBG ¼ EHOMO  ELUMO

(9.3)

As mentioned, when the Φe is small, the electron injection into the material is very efficient. The injection of charge carriers takes place by promoting a charge carrier from a delocalized state of a metal into a more localized state of the organic material by thermal or field-assisted tunneling (upon application of a voltage to the metal-organic junction) [3]. The potential energy barrier between a metal and a conjugated organic material can be manipulated by the insertion of an oriented dipole layer between the metal and the organic material. According to some studies [7], several minutes of Au surface exposure to UV/ozone can reduce the hole injection barrier. Campbell et al. [9, 10], have shown that the potential barrier to charge injection between the metal and the organic layer can be tuned by changing the work function of the metal over a range of more than 1 eV for Ag, by first adsorbing SAM dipole layer of electrically insulating or electrically conductive molecules. The SAMs consisting of aligned molecular dipoles were able to shift the metal work

FIG. 9.3 Energy band diagram of a metal-organic interface depicting the hole injection from the metal to the organic layer (left) and electron injection from the metal into the organic layer (right).

9.3 Basic organic electronic devices and their metal-organic interfaces

159

function to either lower or higher values function of the molecular dipole orientation. The change of metal work function by the interfacial dipole due to the deposition of the organic layer and implicitly the potential barrier height to charge carrier injection was extensively discussed by Koch [7]. The nature of the organic layer, strong acceptor or donor also greatly affects the metal work function and the charge injection barrier [7]. Choulis et al. [11] have also shown improved injection at an inorganic-organic heterojunction between indium tin oxide-coated glass and the organic semiconductor poly(3,4-ethylene dioxythiophene): poly(styrene sulfonate) (PEDOT:PSS), by using an intermediate layer of poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)-diphenylamine), to create a double-step injection profile. If at the metal-organic interface, the frontier orbital energy levels of the organic layer are aligned with those of the metal, they are referred to as resonant and the charge injection from the metal surface into the organic layer takes place without temperature activation, in the absence of a voltage bias.

9.3 Basic organic electronic devices and their metal-organic interfaces Organic rectifying diode. A diode is a two-terminal device which allows current to pass in one direction only, at “forward bias” and limiting current flow in “reverse bias,” thus acting as a valve for the charge carriers. The diode can be used in a circuit to convert the alternating current (AC) into direct current (DC), a process known as rectification. Due to this, diodes are also referred to as rectifiers. The typical inorganic semiconductor diode consists of a p-n or n-p-type junction. The organic layers in an organic rectifier are typically sandwiched between two metallic electrodes. Various organic rectifying diode designs have been proposed, from most simple ones metal1/organic/metal2, inorganic/organic/metal that have one ohmic and one asymmetric rectifying Schottky contact [15] to more complex containing several organic semiconducting layers, such as metal1/organic (n-type)/organic (p-type)/metal2 [16, 17]. In these asymmetric constructions the forward current is maximized by improving the charge carrier injection on one side of the metal/organic heterojunction [17] while on the other side, i.e., organic/inorganic or organic/metal, the carrier injection is limited due to a high Schottky contact barrier [18]. The existence of an asymmetric potential barrier to the electron injection is the underlying operating principles of a rectifying diode (Fig. 9.4A). This leads to an asymmetry in the turn ON voltage, lower at the forward bias than at reverse bias as in Fig. 9.4B. The cartoon in Fig. 9.4A shows the energy level diagram of a diode composed of an organic layer sandwiched between two electrodes with different work functions. At zero bias, V ¼ 0 V (note that the electronvolt (eV) is a unit of energy, and is related to the potential difference V ¼ eV/e, where e is the electron’s elementary charge), we chose the injection barrier to electrons to be lower for the metal1/organic layer to be lower than that of metal2/organic layer, Φe1 < Φe2. Upon application of a small voltage, V > 0, which creates a potential difference across the MOM junction between the metal1 and metal2, the energy levels of the metal1 “shifts” relative to that of the metal2 and LUMO level of the organic layer proportionally to the voltage applied. When the voltage applied V  Φe1/e, the energy levels of the metal1 and the LUMO of the organic layer become resonant and the electrons are injected into the empty orbitals of the organic molecule and then into metal2. If the voltage applied V > Φe1/e the current further increases, as described by the equation of thermionic emission as a function of applied bias [19, 20]. In the reverse bias V < 0, for an applied voltage of the energy level of the metal2 increases proportionally with the applied voltage V. When the value of the applied voltage in reverse bias j V j ¼ Φe1/e the electrons the energy level of the metal2 with the LUMO of organic level are not resonant therefore no electron injection occurs. In reverse bias, electron injection occurs only for a higher magnitude of the applied voltage j V j ¼ Φe2/e thus creating an asymmetry in the current-voltage curve (IdV) in Fig. 9.4B. A concrete example is the organic diode Al/pentacene (160–200 nm)/Au which had very good rectifying characteristics at high frequencies [21] and photodiode characteristic [22]. The HOMO of pentacene is at 6.3 eV with respect to the vacuum level [23], the reported HOMO-LUMO gap is 1.85 eV [24], which places LUMO at 4.45 eV. Other authors place the HOMO of pentacene at 5 eV while the LUMO at 3.2 eV [25]. The Al work function is between 4.04 and 426 eV and that of Au 5.10–5.47 eV. In the Al/pentacene/Au device, the Schottky barrier to hole injection at the Al/ pentacene interface is large while the Au/pentacene contact is considered ohmic. Similarly, for the Al/pentacene/ITO, the pentacene/ITO contact is ohmic [25]. He et al. [16] demonstrated an organic diode ITO glass/ p-type semiconductor N,N0 -bis(naphthalen-1-yl)-N,N0 -bis(phenyl)-benzidine (NPB, 30 nm) (Acceptor)/n-type semiconductor layer (C60, 60 nm) (Donor)/ 2,9-Dimethyl-4,7-diphenyl-1,10-phenanthroline (BCP, 7 nm)/Al(100 nm). The BCP layer was used to better align the energy levels of the C60 with that of the metal and create an ohmic contact between the C60 and Al electrode. In this way the Schottky barriers to electron injection at C60/Al and hole injection at ITO/NPB is low. Other Schottky diodes have been constructed in a similar way, for example, from the ITO glass/polymer/metal, where the first interface had an ohmic contact and the second interface a Schottky contact; the polymer was polyindole-5carboxylic acid and poly(N-vinylcarbazole) (PVK) and the metal was Al, Sn, Sb, and In [26]. Polythiophene (PTh) has been sandwiched between the Au and Al electrodes, where Al/polymer side behaved as a rectifier and the

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9. Metalrganic interfaces in organic and unimolecular electronics

(A)

(B) FIG. 9.4 (A) Schottky diode based on a metal1-organic-metal2 heterojunction (MOM). The electron injection barrier height for the metal1 is larger than that for metal2. The electrons are injected from the metal1 to the LUMO organic layer when the turn-on voltage is approximately equal to the barrier height. In reverse bias, for any applied voltage V >  Φe2/e the electron injection from metal2 into the LUMO of the organic layer is hindered. (B) The current-voltage characteristic of the MOM Schottky diode, with the turn-on voltage at the forward bias lower than that at reverse bias. Therefore, in the shaded voltage interval the MOM junction acts as an electron valve allowing electron passing only in one direction.

Au/polymer side as an ohmic contact [19]. Other asymmetric sandwiched conductive polymeric Schottky diodes have been reported from poly(p-phenylene) (PPP) [20], polyaniline (PA) [27], or poly(N-methylaniline) (PNMA) [28], etc. Non-Schottky-type organic diodes were also reported having symmetric electrode configuration: Au/ poly(3,4-dicyanothiophene) (PDCTh) (n-type, 130 nm)/poly(2-methoxy-5-(29-ethyl-hexyloxy)-1,4-phenylene vinylene) (MEH-PPV) (p-type, 100 nm)/Au junction [29, 30]. These are believed to be like inorganic semiconductor np or pn junctions. It was reported that the Au/PDCTh/Au and Au/MEH-PPV/Au junctions were completely ohmic therefore the rectification must be coming from the donor-acceptor behavior of the polymer layers [29]. In modern electronics, organic diodes could be used in printable all-plastic on flexible substrates radio frequency identification (RFID), wireless power transmission, electrostatic discharge circuits, etc. He et al. [16] pointed out that few organic semiconductors are suitable to be used in rectifying diodes due to their low intrinsic charge carrier mobilities; pentacene and C60 are among the organic semiconductors with very high charge carrier mobilities and the field is greatly improving with new structures. As an example, the hole mobilities that have been reported for the conjugated polymers range from 101 to 107 cm2/(Vs), while electron mobilities are typically lower 104–109 cm2/(V s), while for that of the crystalline silicon are in a range of 475–1500 cm2/(V s) [31]. Organic light-emitting diode (OLED) and organic photovoltaics (OPV) have similar functions being from the standpoint of view of operation, mirror devices, emission vs absorption of light. The OLED consists of an n-type organic layer on which a recombination layer for the charge carriers is deposited and on top a p-type organic semiconductor layer is sandwiched between two metallic electrodes of which one is transparent, such as indium tin oxide (ITO) glass (Fig. 9.5A). The OLED is a diode and operated at the forward bias, whereas the charge carriers, electrons, and holes are continuously injected. The holes and electrons meet in the recombination layer creating an exciton which decays with the emission of a photon. The lifetime of the exciton should be short for good efficiency of OLEDs. The photon wavelength depends on the HOMO-LUMO gap of the recombination layer.

9.3 Basic organic electronic devices and their metal-organic interfaces

161

FIG. 9.5 (A) Energy level diagram of an OLED device composed of an n-type organic semiconductor, an active recombination layer, and an organic p-type semiconductor sandwiched between two metallic electrode, of which one is transparent to light. The diode OLED is operated at the forward bias, the charge carriers, holes, and electrons are continuously injected and combine in the recombination layer to give rise to electron-hole pairs that decay with the emission of photons. (B) Energy level diagram of an organic photovoltaic device composed of an organic n-type layer, donor-acceptor organic layer and an organic p-type semiconductor. A photon excites promotes an electron from the HOMO level of the donor creating an exciton. The lifetime of the exciton is crucial for the efficiency of the photovoltaic device. The device can be operated either at zero bias or forward bias.

The OPV device consists of an organic n-type semiconductor, a donor-acceptor layer, and a p-type organic semiconductor sandwiched between two metallic electrodes of which at least one is transparent (Fig. 9.5B). Upon exposure to photons of a certain wavelength, an electron from the HOMO level of the donor is promoted in the LUMO level creating an exciton. The lifetime of the exciton, in this case, should be relatively long to enable enough time for the electron injection into the LUMO of the acceptor and the LUMO of the organic n-type semiconductor and the hole injection into the p-type organic semiconductor. The charge carriers are collected continuously at the metallic electrodes while the device is exposed to light photons. The characteristic parameters to be enhanced in a photovoltaic device (PV) are the open-circuit voltage (VOC), which is the maximum voltage attainable from a PV device in the absence of current flow, is zero; the short-circuit current (JSC) is the maximum current drawn from the PV device when the voltage is zero (short-circuited); and power conversion efficiency (PCE). The survival of the exciton so that electron injection takes place in the acceptor is key. Only excitons formed within 20 nm from the heterojunction can reach the interface and then separate into electrons and holes, while excitons created further away will recombine before reaching the interface [1]. Therefore, a flat interface p-type/n-type organic semiconductor device is expected to have low PCEs. To improve the PCE, a better design has been proposed, namely the bulk heterojunction (BHJ) devices, where the donor-acceptor contact interfacial area is increased by an interpenetrating network with nanoscale phase separation in the active layer [32]. The BHJ solar cells show substantially improved PCE. For example, PCBM and P3HT are commonly used with good performance as an active layer in OPVs, P3HT is the donor and the PCBM the acceptor [33]. The PCBM fullerene-based derivative has an energetically low lying LUMO (4.2 eV) and a HOMO (6.0 eV) which endows the molecule with a very high electron affinity making it a good acceptor in respect to conjugated polymers, and has good electron mobility [33]. For comparison, donors such as P3HT has a LUMO at 3.2 eV and HOMO at 5.2 eV, MDMO-PPV has a LUMO at 3.2 eV and a HOMO at 5.4 eV (Fig. 9.1). The current state-of-the-art OPV devices comprise organic semiconducting polymers as electron donors and fullerene derivative as electron acceptors. The exact alignment of the energy levels in an organic electronics is crucial, therefore the synthesis of conjugated organic polymers with known HOMO-LUMO levels has been intensively researched [31, 34]. Dye-sensitized solar cells: The n-type or p-type organic semiconductors can be replaced by either inorganic semiconductors or liquid electrolytes. For example, the well-known Gr€atzel’s dye-sensitized solar cell (DSSC) [35] is a typical

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9. Metalrganic interfaces in organic and unimolecular electronics

OPV device that uses an organic molecule called light sensitizer adsorbed on sintered TiO2 (inorganic n-type semiconductor) nanoparticles to provide a high surface area. The TiO2 layer is deposited on a transparent metallic glass. Synthetic efforts have been dedicated to synthesizing organic dyes such that the energy level of the excited state matches the energy level of the conduction band of the oxide TiO2. Upon exposure to light, the electrons are injected into the n-type semiconductor and the original state of the dye is subsequently restored by electron donation from the solvent containing a redox couple system, such as the iodide/triiodide couple. Therefore, the DSSC devices are generally liquid containing devices where the p-type semiconductor is replaced by a redox couple in a solvent. Ruthenium-based metal-organic complexes are molecules having the general structure ML2(X)2, where L stands for 2,20 -bipyridyl-4,40 dicarboxylic acid M is Ru and X—halide, cyanide, thiocyanate, acetylacetonate, etc., One of the most efficient dyes reported is the ruthenium complex cis-Ru(H2dcbpy)2(NCS)2 [35], where H2dcbpy is 4,40 -dicarboxylic acid-2,20 bipyridine compound 1 in Fig. 9.6. The solvent and dye desorption are the major limitations for the DSSC devices but these can be improved by the use of amphiphilic dyes such as (cis-Ru(H2dcbpy)(dnbpy)(NCS)2, where the ligand H2dcbpy is 4,40 -dicarboxylic acid-2,20 -bipyridine and dnbpy is 4,40 -dinonyl-2,20 -bipyridine) compound 2 in Fig. 9.6 and solid-state polymer gel electrolytes greatly improve the efficiency and stability of the device [13]. It has been identified that the oxygen vacancy negatively affects the electron conductivity of the TiO2. Therefore, to improve the injection efficiency at the MO junction, oxygen plasma treatment or UV/O3 pretreatment of the TiO2 surface before dye adsorption is performed. The Gr€atzel-type OPVs have achieved efficiencies over 10% and should be stable enough to sustain about 108 turnover cycles corresponding to about 20 years of exposure to natural light [35]. These are still below the conventional efficiencies of the silicon-based photovoltaics but in comparison, dyesensitized solar cells are very cost-effective photovoltaic devices because of inexpensive materials and simple fabrication process [14]. Natural dyes have been tested as alternative inexpensive dyes from the class of flavonoids and carotenoids [36]. Organic field-effect transistor. A “transfer resistor,” is an electronic element which introduces variable resistance between two terminals, whose resistance can be altered by an input signal. The transistor is also commonly used to amplify a small signal into a large signal. A field-effect transistor is also known as unipolar transistor because they involve only a single-carrier operation n-type or p-type. An OFET is a layered device and has three electrodes a source electrode, a drain electrode and a gate electrode. The schematics of the OFET devices is depicted in Fig. 9.7. The organic semiconductor layer is deposited on a dielectric insulator, e.g., Al2O3, or a Si3N4, or polymeric insulators poly(methyl methacrylate) (PMMA), etc. poly(4-vinylphenol) (PVP) which also separates it from the gate electrode [37]. The gate electrode/dielectric/organic material system should have a high capacitance either therefore materials with a high dielectric constant k should be used. The drain and the source are deposited on top of the organic layer in direct contact with it. The source and drain electrodes are chosen from the metals such as Au, Pt, Ag, or can be conductive polymers such as polythiophene (PTh), polyaniline (PANI), or polypyrrole (PPy), etc. The conductive polymers have a great

FIG. 9.6 Molecule dyes used in the sensitization of TiO2 in construction of photovoltaics.

9.3 Basic organic electronic devices and their metal-organic interfaces

163

FIG. 9.7 (A) Diagram of an OFET in the OFF state, where the gate voltage applied between the gate and the source is zero, VGS ¼ 0; the energy level diagram of an OFET in the OFF state representing the LUMO (or the conduction band), the HOMO (or the valence band) of the organic material, the energy level of the gate electrode. (B) Diagram of an OFET in the ON state, where the gate voltage applied between the gate and the source VGS > 0; due to the capacitive action of the dielectric, upon application of a positive bias on the gate electrode the negative charge carriers appear in the LUMO or the conduction band of the organic material. Under the action of the VDS the electrons appeared in the LUMO(CB) move in perpendicular to the drawing plane.

advantage over the metallic electrode in that they can be printed [37] or deposited using wet techniques. The charge flow between the source and the drain is controlled by the gate voltage, by capacitive charge accumulation. The source electrode is the charge carrier injecting electrode while the drain is the charge carrier extractor [38]. When a drainsource voltage VDS applied between two electrodes, the current flow through the organic semiconductor film is limited and the device is in OFF state. When a gate-source voltage VGS is applied, the capacitive charge accumulates at the dielectric-semiconductor interface, which move between source and drain in response to the applied VSD, and the transistor is in the ON state [39]. The charge at the semiconductor-dielectric interface is localized within one monolayer of the interface and this has been demonstrated that a field-effect transistor has been obtained from a SAM [40], which is the foundation of unimolecular electronic devices. For an in-depth discussion of the operating principles of an OFET device, the reader is directed to the work of Zaumseil and Sirringhaus [38]. Organic semiconductors used in building OFET devices can be divided into two classes, i.e., small molecules and polymers. Whereas the small molecules can be deposited by vacuum sublimation/evaporation of the organic material or from solution, the semiconducting polymers can only be deposited from the solution. For example, tetracene, pentacene, sexithiophene, bis(dithienothiophene) [41] fall into the category of small molecules while poly(9,9dioctylfluorene), poly(3,3000 -didodecylquaterthiophene), poly(2-methoxy-5-(2-ethylhexoxy)-1,4phenylenevinylene), etc. [38], fall into the category of polymers for solution processing. The key to a high-performance OFET device is the charge mobility. High electron mobility can be obtained in organic single crystals of up to 10–50 and up to 3 cm2/(V s) in solution-processed semiconducting polymer films [4], which is close to that of inorganic semiconductors [42].

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9. Metalrganic interfaces in organic and unimolecular electronics

OFETs are used as sensors [37]. OFETs are needed to create logic circuits, pixels in displays, and is the cornerstone device of organic digital electronics. One of the great feats of organic electronics is that circuits can be made via printing methods on various supports using dielectric, conducting, insulating, and semiconducting inks in the absence of clean room facilities and ultraclean environments as in the case of silicon-based manufacturing integrated circuits electronics. Certainly, the convenience comes also at the cost of performance, but high performance is not always required in majority of application. Due to its architecture the OFET can be used as chemical and biological sensor devices, to identify label-free analytes [39], to detect bio-recognition events at functionalized gate interface of an OFET.

9.4 Role of interfacial tension in organic electronic devices In organic electronic/photonic devices, the property and nature of the interfaces exhibit profound correlation with layered device performance [4, 43]. Every physicochemical aspect of the metal-organic interface counts in manufacturing and operating of the device. The number of parameters that can influence both the energy level structure and the contact adhesion of the metal-organic interface is so large that it is a difficult to be exhaustive. Regardless of the organic electronic device manufacturing method, inkjet printing, vapor phase deposition, etc., the role of interfacial tension between any of the layers of the device plays an important role. For example, spreading adhesion determine the morphology of the interface, which ultimately affects the charge scattering and injection efficiency. For example, for a wellperforming organic electronic device performance charge trapping states at the interfaces must be eliminated. The presence of the charge trapping states is mostly due to imperfections at the interface represented either by a physical factor such as roughness or a chemical factor such as stoichiometric defects or chemical functional groups that act as electron traps. For example, for the OFET devices, Cheng et al. [43, 44] have shown that the interfacial tension γ 12 between the gate material and the active organic layer plays a significant role in the performance of the device. We remind the reader of Eq. (6.19), which gives a way to calculate the interfacial tension from known surface tensions and surface tension polar and disperse components, e.g., of the metal and the organic material: qffiffiffiffiffi qffiffiffiffiffi2 qffiffiffiffiffi qffiffiffiffiffi2 p p γ d1 + γ d2 + γ1 + γ2 γ 12 ¼ where the subscripts 1 and 2 represent the different solid phases. Cheng et al. [44] have manufactured pentacene-based OFET, Si/SiO2/pentacene/Ag, where Si-wafer was used as support for the OFET, SiO2 was the gate dielectric, pentacene was thermally evaporated on the SiO2 and the Ag source and drain electrodes were deposited by PVD on top of the pentacene layer. The authors have studied the characteristics of the pentacene evaporated layer on the SiO2 gate oxide modified surface with insulating polymers with varying polarity and surface energies. The pentacene/gate oxide interfacial energy γ 12, calculated with the above equation, could be varied from close to zero to above 20 mJ/m2. The first observation that they have made is that the pentacene layer surface roughness decreased with the decrease in interfacial tension, which can be explained by a better wetting of pentacene to the substrate. By improving the roughness, the charge scattering at the interface can be minimized. In addition, they have observed that with the decrease in the interfacial tension the mobility of electron charge carriers greatly increased, which they explain by including the γ 12 into the equation for charge transfer rate between two molecules, given by Marcus’ electron transfer theory.

Numerical example 9.1 Calculate the γ 12, of SiO2/pentacene interface knowing that the pentacene γ d ¼ 38.5 mJ/m2 and γ p ¼ 2.5 mJ/m2, and for SiO2, the γ d ¼ 23 mJ/m2 and γ p ¼ 32.6 mJ/m2.

Answer γ 12 ¼ 21.7.

In a subsequent recent work, Chen et al. [43] show similar effects of the interfacial energy between the gate dielectric HfO and N,N0 -ditridecyl-3,4,9,10-perylene tetracarboxylic diimide (PTCDI-C13) organic active layer by using interface

9.5 Unimolecular electronics

165

modifiers such as polymethylmethacrylate (PMMA), poly(4-vinylphenol) (CPVP), polyimide (PI) insulators. From these, the authors conclude that a low interfacial energy improves both the roughness of the interface thus minimizing charge scattering but also improves the charge carrier mobility in the interfacial channel of the OFET. A similar observation that Au metallic electrode treated with a alkyl thiols to form a SAM improves both the morphology of a vacuum evaporated film of pentacene and improve the charge injection characteristic of an OFET device was made in a work by Bock et al. [8]. The authors attribute this to the fact that SAM-treated electrodes the de-wetting of pentacene on Au is largely suppressed and smooth films are formed. In that case an on/off ratio of 106 was observed which is four orders of magnitude larger compared to devices with untreated and alkanethiol-treated electrodes and shows a clear improvement in charge carrier injection. Moreover, a strongly reduced trap density was observed and the same observations were made by other authors [12].

9.5 Unimolecular electronics Molecular scale electronics, single-molecule electronics (SME) or unimolecular electronics (UE) [45, 46] makes use of single molecules or monolayers of oriented molecules as the electroactive component in electronic devices. This contrasts with the bulk organic electronics where the electroactive organic layer ranges in thickness from few monomolecular layers to several hundreds of nanometers. However, despite the aim of unimolecular electronics to create miniaturized electronic devices and electronic circuits out of many wired individual molecules, this proves challenging with current technologies. Unimolecular electronics remains mainly a platform for studying fundamental phenomena related to electron transport at small scale, the electron transport across the metal-organic interface, to elucidating mechanism related to electron transport within a single molecule, and electron transport at the linking point between an organic molecule and a metal. Another marked difference between the molecular scale electronic and bulk organic electronics is the fact that in the latter case the conductivity through the organic material had to be through intermolecular charge carrier hopping or intramolecularly through the delocalized molecular orbitals. In other words, the organic layer must have intrinsic conductivity. In unimolecular electronics, the electron transport across the metal-organic interface and organic molecule, when the dimensions of the later do not exceed 5 nm, takes place through tunneling and the molecule itself can have but does not need to have intrinsic electrical conductivity. A unimolecular electronic device can have in its constituency an insulator (alkyl chain), a conductor (molecular wire, a C60 molecule, a conjugated molecule or oligomer, etc.) or an insulating donor-σ-acceptor-type molecule (molecular rectifier).

9.5.1 Making electrical contacts to single molecules vs monolayers of oriented molecules Making at least two electrical contacts to single molecules is, as one can imagine, very challenging with current technologies [47]. Although three electrical contacts have been proposed [48], it is in principle possible through an electrolyte providing a gating electrode [49, 50]. There have been several methods to electrically connect single molecules with two metallic electrodes, through scanning tunneling microscopy break junctions (STM-BJ) [51, 52], mechanically controlled break junctions [53], etc. (see Fig. 9.8A–C), and many other methods recently reviewed by Xiang et al. [54]. An actual device based on true single molecules wired in an integrated circuit has not been achieved. To make molecules accessible to macroscopic electrical contacts and to take advantage of the low-dimensional aspect monolayers SAMs and LB monolayers composed of oriented molecules have been used. Mann and Kuhn [55] were the first to measure the current flow through an LB monolayer of fatty acids sandwiched between different metallic electrodes. The SAMs and LBs were first deposited on a solid metallic substrate and special deposition methods were developed [56–58], for adding a second metallic electrode on top of the monolayer to obtain a sandwiched device [59–62] (Fig. 9.8B). A gentle way to make electrical contacts on top of the monolayer after the deposition of the second electrode can be done using a liquid droplet of GaIn eutectic metal Fig. 9.8B [60, 63] (Hg would also work but it alloys well with Au). The few methods available to create top electrical contacts to monolayer have been recently reviewed by Haick and Cahen [58]. Nanoscopic electrical contacts on monolayers were also achieved in a photolithographed nanopore [64]. Electronic transport has also been measured on in situ created SAMs between Hg droplets [65]. Electronic devices based on monolayers are called ensemble molecular junctions [54] to differentiate them from true singlemolecule devices. Monolayers constituted of oriented molecules are preferentially prepared on oxide-free metallic substrates. The molecular orientation in the film must be controlled by molecular design [66] on large areas, and be as defect-free as possible [45].

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9. Metalrganic interfaces in organic and unimolecular electronics

FIG. 9.8 Electrical contact possibilities to single molecules: (A) through break junctions, metallic wires that break and trap a single molecule; (B) the LB or SAMs sandwiched between metallic electrodes, with liquid Gallium-Indium (GaIn) eutectic for making soft electrical contacts; and (C) making electrical contacts with an atomically sharp metallic tip in STM.

9.5.2 Metal-organic interfaces: Weak vs strong coupling The electron transfer across the metal-organic interface and the conductivity of the metal-organic-metal (MOM) junction is greatly affected by the chemistry of the interface and the minute differences in the chemical structure of the molecules. The results obtained thus far, backed by a large amount of experimental evidence, divide the interfacial coupling between organic molecules and metallic electrodes into “weak coupling” and “strong coupling.” In “weak coupling” regime the transmission window for charge carriers is opaque, meaning that the transport of electron from the metal to a molecule and vice versa takes place via tunneling. In a “strong coupling” regime the metal/organic interface is transparent to charge carriers, and the electron transport from the metal to organic molecules and vice versa takes place through an extended coupling of the hybridized metal-organic orbitals across the metal/organic interface with the conjugated molecular orbitals of the molecule [67]. This enables the electrons to continuously flow in the MOM junction from the metal through the molecular wire (see Fig. 9.9A and B), under an applied electric field, i.e., voltage. In electronic terms, the weak coupling is reflected into a high resistance (low conductance) of the metalorganic interface while the strong coupling by a low resistance (high conductance). The weak and strong coupling regimes of the metal-organic interfaces are controlled by the types of linkers used, the type of bonding with the metal, and by the chemical structure of the molecule. The “linkers” are chemical functional groups covalently attached to the organic molecules. Linkers can attach to metallic electrodes, such as Au, via dative bonding, covalent bonding, and presumably also via weak electrostatic attachment. Because Au is the most used metal in the unimolecular electronics, the largest body of research has been focused on studying and developing ways for molecular attachment on this metal. Therefore, it is instructive to review the anchoring possibilities of the organic molecules at the Au electrode and the influence different linkers to the coupling strength at metal-organic interfaces. Several review articles [67, 68] cover in depth the topic of chemical attachment, coupling strength to Au electrodes, and the influence of the nature of the linker group on electron transport. Dative bonding involves the electron donation from a π donor or a lone pair donor to Au. In these Lewis acid-base interactions, the organic molecules are acting as Lewis bases and the metal surface is offering Lewis acid sites. Common linkers consisting of π donors include fullerenes [69] and other π-conjugated hydrocarbons [70, 71] (see Table 9.1). Common lone pair electron donors localized on a p-orbital include dSR, dNH2, dCN, dPR2, etc. (see Table 9.1). Covalent bonding: The reaction between a molecular radical and a metallic electrode surface can lead to the formation of strong covalent metal-organic bonds. For example, AudS contacts are one of the most widely used in the SME [51, 64, 83] due to the high affinity of the dSH and dSdSd functional group to Au. The RdSH and RdSdSdR

9.5 Unimolecular electronics

(A)

(B)

(C)

(D)

167

FIG. 9.9 (A) Molecule weakly coupled to the energy level of the metals. The electron transfer from the metal to MO takes place via tunneling, depending on the molecular structure another tunneling event can occur intramolecularly and finally from the MO to the second metal. (B) Molecule strongly coupled to the metal, the electron can cross freely across the metal-organic interface, depending on the molecular structure there could be another tunneling event intramolecularly and finally, the electrons cross the second organic-metallic interface. (C) An asymmetrically coupled molecule with a tunneling barrier at the first metal-organic interfaces and ohmic contact at the second organic-metal interface. (D) Elastic and inelastic tunneling through space. Most of the electrons tunnel through space, but some of them will excite the molecular vibrational levels and lose the hv energy corresponding to the vibration they have excited. Other electrons can tunnel through molecular orbitals leading to an enhanced conductivity path.

bonds suffer a homolytic cleavage at the surface of gold followed by the formation of the very reactive thiyl radical RdS that reacts immediately to Au. The dSH linker is also the most common functional group in the formation of SAMs on Au since it has first been proposed in the mid-1980s [84]. AudC contacts have been recently used to form SAMs and couple molecules to Au. AudC covalent bonds are mainly produced by cleaving the dRdSnMe3 bond of an organotin compound [80], where R can be an arene or an alkane. Another method is the fluoride initiated desilylation, the cleavage of a dRdTMS bond with tetra-nbutylammonium fluoride (TBAF) [82]. Binding energy vs electronic coupling strength of the linker to the metallic electrode. The best platform for studying the effect of the linkers and their electronic coupling strength to gold is that of scanning tunneling microscopy break junctions (STM-BJ). STM-BJ is an in situ method performed in an electrochemically inert solvent; the molecules in the study have two end groups that bind to the tip and the substrate electrodes when the tip is brought close enough to the substrate [54]. The “coupling strength” of the linker to the Au electrode does not necessarily follow the bond strength given by the binding energy (see Table 9.1); the former depends on the Au-linkers ability to couple to the delocalized system of the molecular backbone [67, 68]. When the molecular backbone is an alkane then the electronic coupling strength to Au, reflected in the single-molecule conductivity, seems to follow the strength of the binding energy. However, when the molecular backbone is a π-conjugated system, this offers different possibilities for Au-linker to couple to the rest of the molecular backbone, and the linkers’ electronic coupling to the electrode is only weakly correlated to its binding energy to Au.

168 TABLE 9.1

9. Metalrganic interfaces in organic and unimolecular electronics

Types of linkers on Au, bonding and the coupling strength with Au electrode surface. Type

Binding energy (kT)

a

Conductivity/coupling strength to Au electrode 4

G0

Refs.

Dative bonding π-donor Au-C60

–

1,4-Bis(fullero[c]pyrrolidin-1-yl)benzene, 3  10 Weak-to-strong coupling

Dative, σ-donor Binding energy decreases in the order Pt > Cu > Au > Ag [72]

23 [52] 19.5 [73]

Diamine butane, 1.45  103 G0 [74] 1,4-Diaminobenzene 6.4  103 G0 [52] Diaminodiphenylacetylene 103.1 G0 [73] Strong coupling

[74]

Dative, σ-donor

23 [52]

1,4-Butyl methyl sulfides, 1.5  103 G0 [52] Strong coupling

[52]

Dative, σ-donor

39 [75] 34.6 [73]

4,40 -Dicyanobiphenyl, 4.7  105 G0 [75] 4,40 -(Ethyne-1,2-diyl)dibenzonitrile, 104.6 G0 [73] Weak coupling

[75]

Dative, σ-donor Isocyanate

–

Weak coupling

[76]

Dative, σ-donor dimethylphosphine

46.7 [52]

1,4-Dimethyphosphine butyl, 2  103 G0 [52] Strong coupling

[52]

Dative, σ-donor

–

Strong coupling

[77]

Dative, σ-donor pyridyl

39 [78] 35 [73]

4,40 -Bipyridylacetylene, 103.3 G0[73] Very strong

[78]

Covalent Au-S

68 [79] 93 [73]

Bis[4-(2-acetylsulfanyl)-phenyl]ethyne, 102.7 G0 [73] Very strong

Covalent Au-C

–

Butane, 0.09 G0 and decreases with one order of magnitude for every two CH2 added in the backbone[80] Very strong

Electrostatic Au + COOd but the nature of this bond is not clear [81]

3.5

Dicarboxylic acid butane, 2.7  104 G0 [74] Very weak

Covalent Au-C

–

Very strong

[69]

Covalent Au-Se

a

[82]

G0 ¼ 2e2/h  77.4 μS.

The bond formation probability and stability on Au have been determined by STM-BJ in a homologous series molecules of n-butyl bridges with different p-lone pair electron donor linkers PMe2, SMe, or NH2 and was established that the bond probability formation and stability followed the sequence Au-PMe2-R > Au-SMeR > Au-NH2-R [52], following the binding energy values see Table 9.1. The reported conductivity for the n-butyl bridges that are terminated with PMe2, SMe, or NH2 groups follows the same trend, 2  103 G0, 1.7  103 G0, and 1  103 G0 with the bonding strength [52]. The observed trend in binding strength was hypothesized to the fact that the σ-electron donation is strongest for phosphine, followed by amine and in the same time, the π back donation from the metal to the ligand is stronger in phosphines followed by sulfides and amines. The trend in conductivity was hypothesized to arise from increased availability of d-states in sulfides and phosphines which lead to π-channel opening for electron transfer through linkers [52]. In another family of molecules, conjugated tolanes symmetrically modified with pyridyl (dPy), dSH, dCN, and dNH2 linkers, have been studied for their attachment probability and stability on Au with STM-BJ and MCBJ and resulted in this sequence: dPy > dSH > dCN > dNH2 [73], while the conductivity varies in this sequence: dSH (102.7  G0) > dNH2 (103.1  G0) > dPy (103.3  G0) > dCN (104.6  G0). Amines bind favorably to Au adatoms or undercoordinated atoms and showed the least variation in conductivity [85]. Chen et al. [74]

9.5 Unimolecular electronics

169

compared the conductance of the aliphatic molecules wired with COOH, SH, and NH2 linkers. The junction conductance decrease in the following sequence SH > NH2 > COOH, following the binding energies of these functional groups with Au, as seen in Table 9.1. Other studies show that the AudC covalent bond exhibits strong electronic coupling resulting in high conductance, in part due to the high binding energy and in part due to the ability of the bond to strongly couple to the π system of the molecular backbone [67, 80]. The STM-BJ is not the only platform for studying the effect of the linker. Adaligil et al. [86] used two Hg droplets as the electrode in a solution containing the molecule of interest and found that tunneling across Hg/n-alkanethiols/Hg is more efficient than across Hg/n-alkaneselenols/Hg, attributing this to a higher resistance of the Se/Hg interface than for the S/Hg. Contact geometry: Binding of a linker to one or more types of sites on the Au surface leads to variations in conductivity, especially when single-molecule conductivity is measured in SMT-BJ setup. Molecules with amine linkers are advantageous because they bind selectively to undercoordinated adatoms on the electrode surface (with dangling bonds) also cold “high binding sites”; this leads to narrow the conductance distribution due to a narrow Au-linker contact geometry [87]. For comparison the thiol appears to bind on many different sites of Au, bridge, hollow, or top positions, leading to conductivity variations. Py, NH2, and CN bind selectively to undercoordinated gold surface sites. In the conductive measurement of an ensemble, such as sandwiched SAM or LB monolayers between Au electrodes, the ability of the linker to attach to different binding sites, would translate in an averaging of the conductivity results across many molecules, and a broadening of quantum conductivity steps observed in I-V curves in STM-BJ. Coupling of the linker orbitals to the conjugated orbitals in the molecule. The conductivities of molecules in the same families, the same molecule with different linkers, the effect of the linker onto molecular conductivity is clearly observed in STM-BJ experiments [52, 73, 74, 87–89]. The effect of the coupling of the linker to the molecular backbone was investigated experimentally by changing the molecular structure but keeping the same linker [51, 82, 85]. From all these studies there are three cases to consider: (i) the MOs are off-resonance with the EF of the electrode and there is no π-conjugation on the molecule, e.g., alkyl chain, the conductivity through the molecule increases with the increase in the binding energy of the linker to metal; (ii) when the MO of the molecular backbone is off-resonance with the EF of the electrode, the best conductivity is achieved when the linker strongly binds to the metal but in addition, it is capable of interacting with the delocalized orbitals on the molecular backbone, and (iii) MOs of the molecules are resonant with the EF of the electrode, then the nature of the linker is not relevant. For the situation (ii), several reviews [67, 68] discuss the geometry of the lone pair orbitals of the linker groups with respect to that of conjugated orbitals in the molecular backbone is critical for achieving good conductivities. In a disubstituted benzene ring in 1,4 position with various functional groups, the lone pair carrying functional groups such as dSR, dNH2, dPR2, and dSeR2, have their orbitals coplanar, with the electronically filled conjugated π-orbital of the phenyl ring. The aryl-S group is freely rotating bond but can be locked into coplanarity by incorporating the S into dihydrobenzothiphene thioether linker [71]. Su et al. [67] point out that for these linkers, the hole transport through HOMO dominates the conduction through the molecule. In contrast, when the benzene ring is substituted in the position 1,4 with pyridine, isocyanide, and cyanide the conductivity takes place primarily through the LUMO because the lone pair lies in the σ-plane of the molecule, orthogonal to the π-conjugated orbitals of the ring. Therefore, the linkers could couple only with the π*-antibonding orbitals of the LUMO. However, for electron-deficient molecules such as porphyrins [88] when the LUMO is closer to EF of the metal, therefore the LUMO conductance dominates, regardless of the linker, leads to the situation (iii).

9.5.3 Transport mechanism through MOMs The current flowing through a MOM depends on the molecular size, the voltage applied V, and temperature [90]. There are many theories and mechanism explaining the electron transport across the MOM junctions, which require in-depth knowledge of quantum mechanics, physics, and mathematics [45]. However, there are two main theoretical frameworks when treating electron transport through a MOM junction [45, 54] at a molecular scale. The first one is to regard the molecule between two electrodes as a bridge connecting two infinite electron reservoirs, known as Landauer’s formalism of ballistic transport [91]. The second one is to regard the molecule as a mere spacer between two metals, where the electrons can tunnel through this space; in doing so some of the tunneling electrons can interact with the molecule’s vibration levels and with molecular orbitals (Fig. 9.9D). The tunneling electrons across a MOM junction is treated using Simmons’ equations [92]. The two different theoretical frameworks treat events that can operate simultaneously in a MOM junction, but one operates better at the limit of the other one as discussed further.

170

9. Metalrganic interfaces in organic and unimolecular electronics

In bulk organic electronics where the thickness of the organic conductors is much larger than the electron mean free paths, the charge transport through a macroscopic conductor, follows Ohm’s law G ¼ I/V, where V is the voltage applied and the resistance is proportional to the length of the conductor. When the conductor dimensions are greatly reduced, e.g., Au wire single atom wide [93], the conductance becomes quantized: G0 ¼

2e2 h

(9.4)

which is the quantum unity of conductance [54] G0 ¼ 77.5 μS. For organic molecules, assuming an ideal coupling between the organic linker and the metallic electrodes (zero contact resistance and no electron scattering events at the interface) the electron flow can proceed through coherent transport described by Landauer’s formalism. For a molecule, whose LUMO is in resonance with the EF of the metallic electrode and no electron barrier existing at the metal-organic interface, the electron flow can take place through the LUMO, and its conductance can be equal to G0. Increasing the applied voltage will allow more modes, i.e., LUMO1, LUMO2, …, LUMON, to be included, such that the overall conductivity is N  G0. The current in the G-V curve the conductance will appear to rise in steps, because of the quantization of the wavelength [52, 73, 74, 87–89]. In a MOM junction, the electron must somehow cross from the metal to the organic molecule, then cross from the different parts of the molecules to the right side and finally from the molecule to the metal. However, not all electrons cross the metal-organic and organic-metal interface, some are reflected, and only few manage to cross the potential barrier at the interface through a mechanism called tunneling. Therefore, in a real single-molecule junction the observed conductivities are less than the quantum unit of conductance, < G0. In order to express this mathematically the previous formula must be modified to include transmission coefficients [90]: G¼

2e2 Tmetalorganic Torganic Torganicmetal h

(9.5)

where Tmetal-organic, Torganic, and Torganic-metal are the transmission coefficients indicated by the subscript and their value is unity if the transfer of electron is 100%. If the value of the coefficients is unity, then the contacts are Ohmic and if molecules have molecular orbitals at the same energy levels with the metal electrodes within the applied voltage the molecule behaves as a molecular wire. The value of the Tmetal-organic, and Torganic-metal are given by the “coupling strength” between the molecule and the metallic electrode. If the molecule is complex consisting of different donor-acceptor moieties separated by insulating bridges, the Torganic is given by Marcus’s theory of intramolecular charge transfer [45, 63] or by the conjugation length if aromatic. In Fig. 9.9A, the energy level diagram of a poorly coupled molecule is shown to be separated by a potential barrier across which the electron can cross via tunneling. In Fig. 9.9B the energy level diagram of a strongly coupled molecule for which Tmetal-organic, and Torganic-metal are unity and the electron transfer across the metal-organic interface is uninterrupted. In a recent review by Karth€ auser [90] the coupling strength between the molecule and electrode vs the transmission coefficient is reviewed. It turns out that, for example, for the AudS chemical bond (1.73 eV binding energy) the transmission coefficient Tmetal-organic ¼ 0.81 is close to unity, while for a physical bond such as Au-COOH (0.09 eV binding energy) and Au-C60 (0.09 eV binding energy) the transfer coefficients are negligibly small 0.06 and 0.1, respectively. It can be concluded that when the transmission coefficients in a MOM junction are close to unity the molecule behaves like a wire, a quantum conductor, or a molecular wire. With the increase in voltage, the conductance increases stepwise with step heights N  G 0. In the extreme case when the transmission coefficients Tmetal-organic, and Torganic-metal are approaching zero one could state that the molecule in the MOM junction merely acts as a spacer, the metal-organic coupling is very weak. The dominant electron transport mechanism is that of electron tunneling through a potential barrier as described by Simmons [92]. Tunneling is distance-dependent and depends on the molecular size and spacer. The tunneling can be through space (elastic or inelastic) and completely ignore the molecule’s energy level if the barrier height is too large within the applied voltage window, or can involve molecular orbitals in which case the molecular orbital-mediated tunneling can contribute significantly to the electron flow. As already mentioned in unimolecular electronics the small molecules, typically 1–2 nm act as a spacer and the energy of their molecular orbital as well as their exact distribution in the metal-organic-metal junction is important. Due to the narrow spacing between the metallic electrodes, the electrons can tunnel across the junction, through space. By placing a molecule in this interelectrode “space” the tunneling electrons can interact with the vibrational molecular modes (phonons) transferring some of their energy which then relaxes through the molecular vibrations [63]. In this case, the tunneling electrons arrive at the opposite electrode with less energy, and this is called inelastic tunneling

9.5 Unimolecular electronics

171

(Fig. 9.9D). The tunneling electrons also tunnel through the molecular orbitals of the molecule [63]. The molecular orbital of the molecule provides a shorter pathway for electron tunneling when resonant with the Fermi levels of the metallic electrode. To better understand the electron transport in a low-dimensional sandwiched device MOM, one must first understand the electron tunneling across a metal-insulator-metal (MIM) junction under an applied electric field. The insulator, typically with an injection barrier of at least 4 eV or space. In 1963, Simmons developed a model [92] that gives a generalized formula for the variation of the tunneling current as a function of the applied voltage in a MIM junction. This model is applicable for a potential barrier of any shape. Simmons’ equation of the current density [92]:          

 e   1 1 eV 4πl eV 1 eV 4πl eV 1 2 2 2 2  ϕ (9.6) exp  ð 2m Þ exp  ð 2m Þ  ϕ  + ϕ + ϕ J¼ e e e e 2πhl2 2 h 2 2 h 2 The first term in the above equation describes the electron flow from metal1 to metal2 and the second term describes the electron flow from metal2 to metal1. Simmons’s model identified three tunneling regimes: tunneling at near-zero voltages, at intermediate applied voltages, for V < Φe/e (where Φe is the energy of the potential barrier, and e is the electron charge), and tunneling at high applied voltages, V > Φe/e (Fig. 9.10C). For very low biases (V  0, V ≪ Φe), the Simmons model [92] gives the following current density vs voltage dependence: 0 1 1    2 1 2 ð 2mϕ Þ 4πl e A e 2 (9.7) Vexp  ð Þ J∝ @ 2mϕ e l2 h h where m is the electron mass. Since the second factor on the right-hand side of Eq. (9.7) is negligible for small-applied biases, Eq. (9.7) predicts a linear dependence of the tunneling current on the applied voltage V, i.e., a plot of J vs V should be a straight line [45, 92, 94]. This low-bias regime is also called ‘direct tunneling.’ At larger biases, e.g., V ≫ 0, the first term in Eq. (9.6) becomes dominant and the tunneling current density becomes:     

 e   1 eV 4πl eV 1 2 (9.8) exp  ð2mÞ2 ϕe  ϕe  J¼ 2πhl2 2 h 2 where l is the thickness of the insulating barrier (Fig. 9.10B).

FIG. 9.10

Energy diagram of an MIM junction: (A) the energy diagram of the metal Fermi levels and electron affinity potential of the insulator for V ¼ 0; (B) the energy level of the metal electrodes and the top of the bandgap under a moderate applied electric potential V < Φe/e, where Φe is the potential barrier height; and (C) the applied electric potential for V > Φe/e. VL is the vacuum level, EF is metal Fermi level and Wf is the metal work function [92]. Modified from A. Honciuc, New Unimolecular Rectifiers and Through-Bond Electron Tunneling Probed by IETS, (Ph.D. thesis), The University of Alabama, 2006.

172

9. Metalrganic interfaces in organic and unimolecular electronics

The last two equations illustrate that as the barrier length increases, equivalent to larger molecular spacer molecules, the tunneling currents show an exponential decrease. This length dependence is used in the experimental analysis [53, 64, 95] and adopted in a more simplified form: J ¼ J0 exp ðβlÞ 

(9.9)

2

2mφ is defined as the tunneling decay coefficient and J0 is the hypothetical zero-length gap current. ℏ2 For even higher voltages, V ≫ Φe/e the Simmons equation reduces to   1 3 8πm (9.10) ð2mÞ2 ðϕe Þ2 J∝V 2 exp  3heV

where β ¼ 2

Eq. (9.10) is well known to be characteristic to Fowler-Nordheim electron emission from cold metals (Fig. 9.10C); a plot of ln(J/V2) as a function of 1/V should yield a straight line. The Fowler-Nordheim [92] tunneling regime occurs for high biases, and the electrons emitted from electrode 1 see a considerably lower energy barrier in a MIM junction. Simmons’s model gives a qualitative picture of the current vs voltage dependence in MIM junctions and MOM junctions containing monolayers of arachidic acid, alkanethiols, or other organic monolayers. Some curve fitting of the Simmon’s equation to the I-V characteristic of the SAMs sandwiched between metallic electrodes can lead to the empirical determination of the tunneling barrier and the position of the unoccupied molecular orbitals in relation to EF.

9.5.4 Archetypal unimolecular device—The unimolecular rectifier and rectification mechanism Historically, Aviram and Ratner [96] are credited with the first idea of a single molecule rectifier based on an electron-donating moiety (donor) and an electron-withdrawing moiety (acceptor) bridged by the σ linkage as an insulating barrier for electrically separating the two segments a donor-σ-acceptor configuration, shown in Fig. 9.11 compound 1, the leitmotif of an np diode. The archetypal configuration of such device is that of a sandwiched monolayer of oriented molecules between two metallic electrodes, which leads to the simplest device—an ensemble of a single rectifying molecule (Fig. 9.8B). Although the initial idea of a molecular rectifier proposed by Aviram and Ratner were very crude it turned out to be forward-thinking and stimulating for several decades of research in electron transport across single molecules, interaction of electron with molecules, and fathered many other unimolecular electronic devices. The experimental evidence shows that monolayer constituted of molecules with a variety of chemical structures is capable of rectification. Fig. 9.11 depicts several molecules which are experimentally proven to rectify currents are shown, compounds 2-8. In addition, the direction of preferential current flow is depicted by an arrow. As it can be seen the preferential current flow changes for different molecular structures. For the chemist, the challenge was to understand a structure-activity relationship, whether the molecule must consist of a donor and acceptor, whether the D and A moieties must be separated by a σ or a π bridge or not, the linkers used, etc. In elucidating the rectification mechanisms by a molecule, the molecular orientation as well as the position of the MOs in the junction and their spatial distribution is considered. It turned out even from the first experiments that not all tested molecules followed the Aviram-Ratner rectification mechanisms and therefore several mechanisms have been proposed to explain the experimental evidence [97]. Currently, three main models have been proposed for rectification [54]: (i) Aviram-Ratner (ARmodel), (ii) Kornilovitch-Brakovsky-Williams (KBW-model), and (iii) Datta-Paulson (DP-model). In the AR-model energy levels on both the D and A part of the molecule are involved in the electron transport. The D-σ-A molecule is oriented such that D and A are each attached to the opposite metallic electrodes. At zero bias, the HOMO located on the donor is positioned slightly below the EF of the metallic electrode, while LUMO located on the Acceptor is slightly higher than the EF of the electrode. At forward bias, a voltage is applied to the MOM junction such that the cathode () is connected to the Donor part while the anode (+) is connected to the LUMO. In this configuration, the HOMO and LUMO are brought into resonance for electron transfer, by the application of a voltage. In reverse bias, the electrode polarities are inversed and the HOMO and LUMO are taken further apart and the electron transfer is not possible anymore. In the KBW model, it was proposed that a molecule to be a rectifier it does not need to be constituted of a D and A moieties. Instead, a MO of molecules placed asymmetrically in the MOM gap is enough to produce the effect of rectification. In the DP model it was proposed that a molecule which is coupled strongly to one electrode but weakly to the other electrode leads to rectification (Fig. 9.9C), much like in the case of a Schottky-based organic diode, discussed previously. In practice, it is difficult to distinguish between some of these mechanisms as they may be operating

9.5 Unimolecular electronics

173

FIG. 9.11 Several molecules that have been proven to rectify with the exception of the compound 1 proposed by Aviram and Ratner 1 [96] that was never synthesized. Compound 2 from Ref. [61], 3 from Ref. [61], 4 from Ref. [98], 5 from Ref. [99], 6 from Ref. [59], 7 from Ref. [60], 8 from Ref. [100], 9 is from Ref. [83]. The arrow indicates the experimentally determined preferred electron flow through molecule. Modified with permission from R.M. Metzger, Unimolecular electronics, Chem. Rev. 115 (2015) 5056–5115. doi:10.1021/cr500459d. Copyright© 2015 American Chemical Society.

simultaneously, which is difficult to separate experimentally. In fact, most of the available direct experimental data from a MOM junction is from I-V curves, which are obtained by recording the current passing through a MOM while ramping the voltage. The experimentalists try to fit the obtained I-V curves to different theoretical models and with the obtained fitting parameters they attempt to obtain details of the molecular orbitals in the gap in correlation with the energy of the HOMO and LUMO obtained separately with other techniques. However, in doing so, the experimenters

174

9. Metalrganic interfaces in organic and unimolecular electronics

were challenged by the ever-persisting question whether in a MOM junction the tunneling electron really interacts with the molecule or ignores it, tunneling in fact through space. Due to technical difficulties, it is a challenge to obtain direct evidence and probe the molecular orbitals in an ensemble MOM junction. Scientists were thus seeking to prove that the I-V curve does indeed contain a molecular signature. Among the few methods available to the experimentalist is that of inelastic electron tunneling spectroscopy (IETS). IETS is the only available technique with which the experimenter can directly observe the interaction of the electron with the molecular energy levels, vibrational and electronic (orbitals). The essence of the method is to record the second derivative of the current passing through a MOM junction while ramping the voltage, d2I/dV2 vs V. The IETS is the precursor of the STM methods. The IETS was first developed by Jacklevic and Lambe in 1966 [101], which observed the inelastic events, where the tunneling electrons excited the bond vibrations and arriving at the other electrode with lower kinetic energy than that which they started, E-hν, where hν is the vibration energy of the bond excited by the tunneling electrons. This appeared in the d2I/dV2 vs V as a sharp peak at V ¼ hν/e in the interaction of photon with the molecular. Because unlike the photon interaction with the molecules, in the electron interaction with the molecules there are no selection rules. Later, Hipps and Mazur greatly extended the capabilities of the IETS method performed in MOM junctions and extended the voltage scan range to higher bias to observe in addition to vibrational excitations that the tunneling electrons interact with molecules producing π-π* electronic transitions [102, 103] and direct interrogation of the unoccupied molecular orbitals π* in a MOM junction [104–107], which they have dubbed as orbital mediated tunneling (OMT). The OMT is a clear signature of elastic tunneling through the molecular orbitals. In the d2I/dV2 vs V, these OMTs appeared as bands. The OMT bands were a clear signal that MOs facilitated the electron tunneling through MOM junctions when resonance was achieved between the EF of the electrode and the MO at a certain applied electric field. The OMT bands were observed in MOM junctions also by Honciuc et al., in direct relationship with the ability of compound 7 in Fig. 9.11 [60] to rectify current. In Fig. 9.12A the I-V characteristic curve of the Al (EF ¼  4.2 eV)/LB monolayer of compound 7/Pb (EF ¼  4.25 eV) is presented, showing a clear rectification characteristic with the current flowing stronger at forward bias, Al (cathode), and Pb (anode). In Fig. 9.12B, a d2I/dV2 vs V scan is obtained for an LB monolayer of molecule 7, showing vibration energy levels for C-H stretches, and a broadband more clearly visible at forward bias attributed to OMT. At reverse bias, Al (anode) and Pb (cathode), the intensity of the OMT band is much weaker, as also seen in the normalized intensity spectrum inset of Fig. 9.12B, which means that the unoccupied molecular orbital is more clearly accessible to Al than to Pb. The EF of Al and Pb differ slightly therefore the energy of the OMT band also differs slightly at forward and at reverse bias. In the LB monolayer, the C60 moiety of molecule 7 is oriented such that the C60 is closer to the Al electrode than to Pb rectification. The data in the work of Honciuc et al. [60] indicates that the LUMO (3.9 eV) of the compound 7 lies on C60 moiety and this is asymmetrically placed in the MOM junction. The presence of OMT bands is a clear sign that the electron transfer in a junction involves only one orbital,

FIG. 9.12 (A) I-V curve of an “Al/LS monolayer of 7/Pb” junction at 4.2 K showing a rectification ratio of 5.33. measured at 4.2 K; (B) IETS of “Al/LS monolayer of 7/Pb” showing the C-H vibration peaks, excited by the tunneling electrons and a broad OMT feature at 0.65 V. The inset shows the normalized tunneling intensity spectrum, showing that the asymmetries of the OMT bands are preserved after background removal. Note that the bias voltages can be converted to the more conventional wavenumbers through the factor of 8066 cm1/V. Reproduced with permission from A. Honciuc, R.M. Metzger, A. Gong, C.W. Spangler, Elastic and inelastic electron tunneling spectroscopy of a new rectifying monolayer, J. Am. Chem. Soc. 129 (2007) 8310–8319. Copyright © 2007, American Chemical Society.

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whereas a mechanism according to AR would have to be inherently inelastic as it involves an intramolecular electron transition, which tends to confirm the KBW mechanism, saying that the asymmetric placement of a molecular orbital which can enter in resonance with the EF of the metal is sufficient to produce rectification.

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C H A P T E R

10 Main interaction forces between molecules and interfaces 10.1 van der Waals interactions between molecules and between interfaces The van der Waals (vdW) interactions cover three types of forces: (A) Debye interaction or induction force between a molecule with a permanent dipole and a molecule with an induced dipole; (B) Keesom or dipole orientation interaction, and (C) London dispersion forces, fluctuating dipole-induced dipole interactions. The strength of the forces acting between the two atoms or molecules decreases with the separation distance, namely with the sixth power of the distance [1]: Cinduction + Corient + Cdispersive wðrÞ ¼  r6  
2  u21 u22 3α1 α2 hϑ1 ϑ2 + u1 α2 + 3kT 2ðϑ1 + ϑ2 Þ w ðrÞ ¼  2 6 ð4πε0 Þ r

(10.1)

(10.2)

where c is the van der Waals interaction constant (J m6); α is the electronic polarizability of atoms 1 and 2, this polarizability is defined as the strength of the induced dipole moment in an electric field E due to the displacement of the negative charge in an atom or molecule; u is the instantaneous dipole moment of atoms 1 and 2 whose field will polarize a nearby atom—the Bohr atom has no permanent dipole moment, but if the time stops, that is, at a given moment there will be an instantaneous dipole moment, u ¼ a0e, where a0 the first Bohr radius e2/8πε0hϑ is 0.53 nm, e is the electron charge, and ε0 is the electric permittivity of vacuum. The numerator in Eq. (10.2) has three terms: (i) the first term describes the interaction between a molecule with a permanent dipole of magnitude u and another molecule with an induced dipole, whose magnitude depends on its polarizability α (the subscript indicates the atom), (ii) the second term is the Keesom energy to align and orient permanent dipoles, and (iii) the third term is the dispersive London interaction, or fluctuating dipole-induced dipole interactions. It has been confirmed experimentally that the dispersion forces, expressed by the last term of Eq. (10.2), are the dominant forces in the vdW interaction, except for the case of small polar molecules. On the other hand, the energy of the van der Waals interaction in a medium between two molecules of radius a1 and a molecule of radius a2 in a medium 3 is given by a sum of a zero-frequency term and a nonzero-frequency term (see p. 122 in Ref. [1]):
2 
    pffiffiffi 3 3 n1  n23 n22  n23 3hϑa1 a2 3kTa31 a32 ε1  ε3 ε2  ε3  wðrÞϑ¼0 + wðrÞϑ>0 ¼ 
2 1=2
2 1=2 h
2 1=2
2 1=2 i r6 ε1 + 2ε3 ε2 + 2ε3 2r6 n1 + 2n23 n2 + 2n23 n1 + 2n23 + n2 + 2n23 (10.3) where ε1, ε2, and ε3 are the static dielectric constants of the three media, the n1, n2, and n3 are the indices of refraction of the corresponding media, and ϑ ¼ 3  1015 s1. The van der Waals interaction free energy of two identical molecules 1 in a medium 3 reduces to 2   pffiffiffi 6
2 3hϑa1 n1  n23 3kTa6 ε1  ε3 2  (10.4) wðrÞϑ¼0 + wðrÞϑ>0 ¼  6 1
2 3=2 r ε1 + 2ε3 4r6 n + 2n2 1

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00008-9

179

3

Copyright © 2021 Elsevier Inc. All rights reserved.

180 TABLE 10.1

10. Main interaction forces between molecules and interfaces

van der Waals interaction between macroscopic bodies of different geometries and their separation distance D based on the Hamaker constant, A. C is the coefficient in the atom-pair potential. A negative value of the F and E means attraction. For other geometries see Israelachvili and Parsegian [1, 2]. van der Waals interaction Geometry of interacting objects

Energy

Two atoms/molecules



C r6

Force 

6C r7

r Two flat surfaces

W¼

A 12πD2

W ¼

A 6πD3

D

Two spheres or macromolecules of radii R1 and R2

R2

R1



  A R1 R2 6D R1 + R2



  A R1 R2 2 6D R1 + R2



AR 6D



AR 6D2

D Sphere or macromolecule near a flat surface

R D

With increasing separation r, above 30 nm, the dispersive interaction energy between atoms and molecules begins to decay faster than 1/r6 and approaches 1/r7 by 100 nm. Only the dispersion forces are affected by retardation, the other vdW contributions are not affected. Eq. (10.2) gives the interaction energy between two atoms or two molecules. To quantitatively calculate the van der Waals interaction between nanoscopic and macroscopic objects, one must integrate the pairwise interaction potentials of each pair of atoms at the surface of the two bodies. The final equations to calculate the van der Waals interactions as a function of their separation distance D have different expressions depending on the shape of the interacting objects; some of these equations are listed in Table 10.1 [1–3]. For a complete derivation of these equation, the reader is directed to further literature [1, 3]. The resulting interaction forces and energies obtained for different geometries are given in Table 10.1 in terms of the Hamaker constant [4]: A ¼ π 2 cρ1 ρ2

(10.5)

where ρ is the number density of the atoms or molecules in each material and c is the same constant as in Eq. (10.1). The Hamaker constant is a characteristic of the material. While Eq. (10.2) gives the interaction potential with the separation distance between the atoms, the equations listed in Table 10.1 enable the calculation the interaction forces and energies between two objects depending on the geometry and the separation distance.

Numerical example 10.1 (A) Calculate the van der Waals interaction energy of: (1) two spheres of radius R ¼ 1 cm, (2) two spheres of radius R ¼ 20 nm, and (3) of two surfaces, when these are both in contact (D ¼ 0.2 nm) and at D ¼ 10 nm separation distance in vacuum. The Hamaker constant for all objects is A ¼ 1019 J. Express the final results in both Joules and units of kT @ 298 K. (B) When two surfaces are in contact, the van der Waals interaction energy is equivalent with the energy of adhesion. How can you relate the obtained energy of adhesion of two surfaces at (3) with their surface energy γ?

10.1 van der Waals interactions between molecules and between interfaces

181

Solution (A) A ¼ 1019 J, 1 kT ¼ 4.114  1021 J at 298 K

Wadh ¼ 

  A R1  R2 , R1 ¼ R2 ¼ 1 cm ¼ 102 m, for D ¼ 0:2 nm 6D R1 + R2 1019 J  0:01 m ¼ 4:16  1013 J 12  2  1010 m 4:16  1013 J W ðkTÞ ¼ ¼ 1:013  108 kT 21 J 4:114  10 kT W¼

For D ¼ 10 nm

1019 J  0:01 m ¼ 8:3  1015 J 12  108 m 8:3  1015 J W ðkTÞ ¼ ¼ 2:03  106 kT 21 J 4:114  10 kT 1019 J ¼ 20  1019 m ¼ 8:33  1019 J W¼ 12  0:2  1019 m 8:33  1019 J W ðkTÞ ¼ ¼ 2  103 kT for D ¼ 0:2  109 m 21 J 4:114  10 kT W¼

and

1019 J  20  109 m ¼ 1:667  1020 J 12  10  109 m 1:667  1020 J W ðkTÞ ¼  ¼ 4kT for D ¼ 10  109 m 21 J 4:114  10 kT A 1019 J J ¼ W¼
2 ¼ 0:066 2 2 10 12  π  D m 12  π  2  10 m

W¼

W ðkTÞ ¼ 

0:066

J m2

4:114  1021

J kT

¼ 1:61  1019

kT for D ¼ 0:2 nm m2

and

W¼

1019 J 5 J
8 2 ¼ 2:65  10 m2 12  π  10 m

J m2 ¼ 6:45  1015 kT W ðkTÞ ¼  J m2 4:114  1021 kT 2:63  105

(B) The calculated adhesive energy should be equivalent to the interfacial energy of the two materials. However, since both surfaces are the same material, we talk above the cohesive energy, which is 2γ ¼ W.

182

10. Main interaction forces between molecules and interfaces

10.1.1 Attractive and repulsive van der Waals interactions It is important to be able to predict not only the magnitude of the van der Waals interaction but also to know whether the interaction between two macroscopic objects is repulsive or attractive. By convention, from Eq. (10.5) and Table 10.1 the interaction energy is attractive if the energy or the calculated force has a minus sign and repulsive if positive. The only factor from the mentioned equations that can change the nature of interaction to repulsive or attractive is the Hamaker constant. To know if the Hamaker constant is positive or negative, it must be calculated. One way to calculate the Hamaker constants is to use the result of Lifschitz’s theory, which is conveniently expressed in terms of the parameters of the materials and medium of interaction. Thus, the Hamaker expression for two interacting materials 1 and 2 through a medium 3 is [1–3]
2 
    n1  n23 n22  n23 3 ε1  ε3 ε2  ε3 3hϑ h i + (10.6) A ¼ kT ε1 + ε3 ε2 + ε3 4 11:3
n2 + n2 1=2
n2 + n2 1=2
n2 + n2 1=2 +
n2 + n2 1=2 1 3 2 3 1 3 2 3 where the first term is the zero-frequency term and the second one is the frequency-dependent term, which in usual calculation varies between ν ¼ 1  1015 and 5  1015 s1 corresponding to the maximum absorption band of material in UV-vis. For metals, ν ¼ 5  1015 s1, the plasma frequency for the electron gas. The above expression tells that the van der Waals interaction energy between any two materials in vacuum or air (ε3 ¼ 1, n3 ¼ 1) is always attractive, that is, A > 0 (see Table 10.2). TABLE 10.2

Nonretarded Hamaker constants for two identical media ε1 interacting in vacuum/air (ε3 ¼ 1) A11.

Medium

Dielectric constant or relative permittivity εr

Refractive index

Absorption frequency, ν (×1015 s21)

Hamaker constant, A (×10220 J)

Liquid He

1.057

1.028

5.9

0.057

Water

80

1.333

3.0

3.7

n-Pentane

1.84

1.349

3.0

3.7

n-Octane

1.95

1.387

3.0

4.5

n-Dodecane

2.01

1.411

3.0

5.0

n-Hexadecane

2.05

1.423

2.9

5.1

Diamond

5.66

2.375

2.6

28.9

Cyclohexane

2.03

1.426

2.9

5.2

Benzene

2.28

1.501

2.1

5.0

Toluene

2.38

1.49

2.7

Acetone

21

1.359

2.9

4.1

Polystyrene

2.55

1.557

2.3

6.5

PVC

3.2

1.527

2.9

7.5

PTFE

2.1

1.359

2.9

3.8

SiO2 (silica)

3.8

1.448

3.2

6.3

Mica

5.4–7.0

1.60

3.0

10

Silicone (Si)

11.6

3.44

0.80

18

*Au

∞

–

5

45.5 (33.2)

*Ag

∞

–

5

40 (48.8)

*Cu

∞

–

5

28.8 s(40.2)

*Fe

∞

–

5

21.2

Data from J.N. Israelachvili, Intermolecular and Surface Forces, third ed., Academic Press, San Diego, 2011 and marked with * from J. Visser, On Hamaker constants: a comparison between Hamaker constants and Lifshitz-van der Waals constants, Adv. Colloid Interf. Sci. 3 (1972) 331–363. https://doi.org/10. 1016/0001-8686(72)85001-2 and in parenthesis from H.-J. Butt, M. Kappl, Surface and Interfacial Forces, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010.

10.1 van der Waals interactions between molecules and between interfaces

If the two interacting objects are made from the same material, then the above expression simplifies to
2   3 ε1  ε3 2 3hϑ n21  n23 + A ¼ kT
 ε1 + ε3 4 22:6 n2 + n2 3=2 1

183

(10.7)

3

Numerical example 10.2 Demonstrate that the vdW interaction energy between any two materials 1 and 2 in vacuum or air (ε3 ¼ 1, n3 ¼ 1) is always attractive.

However, the Hamaker constant can also be negative A < 0. The first term of Eq. (10.6), the frequency independent, is referred to as the “entropic” term because it depends on kT, while the second term, the frequency-dependent one is the purely dispersive component. Sometimes the dispersion forces suffer retardation effects, the second term that is the frequency-dependent term becomes affected, due to a faster “screening” with the distance 1/r7 than the 1/r6, while the entropic terms remain unaffected. This can have consequences such that if the A(entropic) term is negative and the A(dispersive) is positive and larger at small separation distances, but it becomes smaller in magnitude at larger separation distances than A(entropic); in this case, the overall Hamaker constant will change from attractive at small separation to repulsive at larger separations. For example, water interacting with air through pentane has a Hamaker constant Awater/pentane/air ¼ 0.8  1021 J, whereas A(entropic)water/pentane/air ¼  0.8  1021 J and A(dispersive)water/pentane/air ¼ + 1.6  1021 J, so the overall interaction between water and air through pentane is attractive at short separation distances [1]. At large separation distance A(dispersive) < A(entropic) due to retardation of A(dispersive) and the overall Awater/pentane/air < 0, making the water-air interaction from pentane repulsive. This is the reason why pentane spreads on water. In the case of longer-chain alkanes, such as octane, lenses form on water surface and do not spread, because the Awater/octane/air ≫ 0, for all separation distances, see and compare these values in Table 10.3 for these two systems.

10.1.2 Combining laws applied to van der Waals interactions The combining laws are frequently used for obtaining approximate values for unknown Hamaker constants in terms of the known ones. We have previously encountered the combining laws to obtain, for example, the energy of adhesion of the solid-liquid interface from the known surface energies and surface tensions (see Chapter 6). Similarly, for a system consisting of phase 1 that interacts with phase 2 via medium 3, the Hamaker constant A132 can be calculated if A131 and A232 are known: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A132   A131 A232 (10.8) And across vacuum: A12  

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A11 A22

(10.9)

The toolbox of combinations can be expanded further. Following the same reasoning as in Chapter 6, Section 6.1, the Hamaker constant of medium 1 interreacting with medium 1 through medium 3 is the same as for the medium 3 and medium 3 interacting through medium 1. Then, A131 is the sum of the self-interaction Hamaker constant in vacuum for the both media A11 and A33 from which we must subtract twice the A13 Hamaker constant: pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 2 A131 ¼ A313  A11 + A33  2A13  A11  A33 (10.10) and equivalently for media 1 and 2 interacting via medium 3: pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi

A11  A33  A22  A33 A132 

(10.11)

Note that the combining relations can be used only when dispersion forces dominate the interactions as in the above examples but are not applicable when the dispersion forces are not dominant such as in or between highly polar media.

184

10. Main interaction forces between molecules and interfaces

TABLE 10.3

Hamaker constant for interacting materials 1 and 2 through medium 3 [1, 5].

Interacting materials, 1 and 2 through medium 3 1

3

2

Hamaker constant, A132 (×10220 J)

Air

Water

Air

3.7

Pentane

Water

Pentane

0.28

Octane

Water

Octane

0.36

Hexadecane

Water

Hexadecane

0.49

PTFE

Water

PTFE

0.29

Polystyrene

Water

Polystyrene

1.4

Silica

Dodecane

Silica

0.07

Mica

Hydrocarbon

Mica

0.35–0.81

Mica

Water

Mica

2.0

Water

Pentane

Air

0.08

Water

Octane

Air

0.51

Octane

Water

Air

0.24

Fused quartz

Water

Air

0.87

Fused quartz

Octane

Air

0.7

Fused quartz

Tetradecane

Air

0.4

Stearic acid

Water

Stearic acid

0.079–0.368

Protein

Water

Protein

5

Various biological cells

Water

Various biological cells

0.02–0.25

Hg

Water

Glass

1.51

Numerical example 10.3 Calculate the Hamaker constant of the system: (a) PTFE/water/PTFE; (b) quartz/octane/air; (c) water/pentane/air; (d) water/octane/air; and (e) hexadecane/water/hexadecane with the above equations by using the known Hamaker constants from Table 10.2 and compare your results for the constant with those given in Table 10.3. Discuss any differences.

Solution (a) PTFE/water/PTFE
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi2 One could use Eq. (10.10): A131 ¼ A11  A33 From Table 10.2, we have A1¼PTFE ¼ 3.8 and A3¼water ¼ 3.7. So, the result is 0.00068  1020, very small to what is given in Table 10.2, of 0.29–0.33. (b) quartz =octane = air A11 6:3

A33 4:5

A22 0

A132 ffi

pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi pffiffiffi pffiffiffiffiffiffiffi


 6:3  4:5  0  4:5  1020 J ffi 0:91  1020 vs:  0:7  1020 J

(c) water = pentane = air 3:7

0

3:75

A132 ffi

pffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffi pffiffiffiffiffiffiffiffiffi


 3:7  3:75  0  3:75  1020 J ffi 0:25  1021 vs:0:08  0:11  1020 J

(d) water = octane =air 3:7

4:5

0

A132 ffi 0:42  1020 J (e) hexadecane = water = hexadecane 5:2

3:7

5:2


 A131 ffi 0:127  1020 J vs:0:49  1020 J

10.2 Hydrogen bonding

185

Numerical example 10.4 Van der Waals interaction can be a driving force for interacial adsorption of nanomaterials. Consider the situation of a solid material immersed in a liquid L1 and at a distance D from the interfaces of the L1 with a second liquid L2, as depicted in the figure below. (1) Give the analytical expression of the nonretarded vdW energy of interaction W(D) of the solid material with the liquid L2 and (2) using the known combining relations for the Hamaker constant for the London (dispersive)-van der Waals interactions to calculate the ASolidL1L2 from the Aii are the corresponding self-interaction Hamaker constant for each of the interacting phases (i ¼ 1  Liquid L1, i ¼ 2  Liquid L2, and i ¼ the Solid).

Solution

A (1) W ðDÞ ¼  12πD2
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi (2) AS12 ¼ ASS  A11  A22  A11

10.1.3 Surface tension and surface energies from intermolecular forces Probably the most powerful aspect of the theory of intermolecular forces is the ability to calculate and predict measurable macroscopic parameters, such as surface tension of liquids. Recall that the work of cohesion, the energy needed to split a liquid in two halves with the formation of two new interfaces in vacuum or air and separating them to infinity is Wcoh ¼ γ LG + γ LG  γ LL ¼ 2γ LG Another way to calculate the cohesion energy, in other words the interaction energy of two surfaces resulted from cutting a bulk material in half, is to use the appropriate equation from Table 10.1: Wcoh ¼ 

A 12πD20

(10.12)

where D0 is the separation distance, which for two contacting surfaces is taken to be approximately 0.165 nm, which is the distance between two atomic centers. From the above equations, it follows that the surface tension of a material is γ

A 24π ð0:165 nmÞ2

(10.13)

This is a particularly important result because it allows the calculation of the surface tension and energy, which is a macroscopic parameter, from the first principles, only by knowing the energy of intermolecular interactions. For those materials, constituted of molecules interacting exclusively via van der Waals forces there is a rather good agreement between theory and experiment. Vice versa one can also estimate the value of A by knowing the surface tension. The last equation, however, fails to predict the surface tension of strongly polar compounds capable of H bonding and the surface energy of the metals for which the cohesion energy calculated this way is strongly underestimated (Table 10.4).

10.2 Hydrogen bonding Hydrogen bond was previously believed to be covalent because the hydrogen atom was shared between two electronegative atoms. However, hydrogen bonding is now understood as mostly an electrostatic interaction. The hydrogen bond is represented by a dotted line connecting the electronegative atom B, and a continuous line representing the covalent bond of the H-atom with the parent atom A, which is AdH ⋯ B. In hydrogen bonding, the physical

186

10. Main interaction forces between molecules and interfaces

TABLE 10.4 Surface tension of various compounds calculated with Eq. (10.6) and compared with the experimentally determined values [1]. Surface energy, γ (mJ/m2) γ

A

Material

Theoretical A (×10220 J)

Liquid helium

0.057

0.28

0.12–0.35 (4–1.6 K)

n-Perfluoro-pentane

2.59

12.6

10.3

n-Pentane

3.75

18.3

16.1

n-Octane

4.5

21.9

21.8

n-Hexadecane

5.2

25.3

27.5

PTFE

3.8

18.5

18.3

CCl4

5.5

26.8

29.7

Benzene

5.0

24.4

28.8

Polystyrene

6.6

32.1

33

PDMS

4.4

21.4

21.8

PVC

7.8

38

39

Acetone

4.1

20.0

23.7

Ethanol

4.2

20.5

22.8

Methanol

3.6

18

23

Water

3.7

18

73

Hydrogen peroxide

5.4

26

76

Glycerol

6.7

33

63

Formamide

6.1

30

58

24π ð0:165 nmÞ2

Experiment (20°C)

interaction between H atom and B atom is predominant and there is no proton exchange between A and B as in the case of acids and bases. The electronegative parent atom withdraws the electron cloud from the hydrogen leaving it partially unshielded, the hydrogen acquires partial positive charge and this effect propagates through a medium with the inverse of the square of the distance 1/r2. The H-bond acceptor B is an electronegative atom and must have an electron lone pair. For the H-bond formation, the parent atom typically participates with the type s orbitals, while the acceptor atom participates with a lone pair on a p orbital or π molecular orbital. Water has the possibility of forming two H-bonds per molecule and due to this it has an unusually high boiling point and large latent heat of vaporization (large cohesion energy) for such a small molecule. The increase in volume of water around the freezing point, the high melting point, and good ability to work as solvent are due to this ability to form hydrogen bonds. Although electrostatic in its nature, the H-bond has some covalent characteristic, which gives it an oriented and directional character. This is confirmed by the formation of three-dimensional (3D) structures in ice. The HdO bond length is about 0.1 nm in the water molecule, and the OdH ⋯ O intermolecular bond is about 0.177 nm that is slightly smaller than the sum of the two atomic radii suggesting that the H-bond has some covalent character as well. H-bond can also form with other electronegative atoms, such as F, Cl, N, etc. The strength of the hydrogen bond lies between 10 and 40 kJ/mol, equivalent to 5–10 kT at 298 K [6]. That makes the H-bond interaction stronger than the vdW interactions, around 1 kJ/mol, 1 kT at 298 K, but significantly weaker than the covalent or ionic bonds 500 kJ/mol or 100 kT. However, the H-bond is stronger than the dipole-dipole and dispersive interactions but note that the dispersive forces scale up with the size of the molecules, thus becoming increasingly important for the larger molecules. The relative strengths of different types of interactions are very well reflected in the boiling points of the substances, because the boiling points are a measure of the cohesive energy, responsible for holding the molecules together. Hydrogen bond can exist in polar but also nonpolar environment. H-bonds are particularly important in macromolecular and biological assemblies, in interaction between proteins, with the formation of the so-called “salt bridges” NdH⋯ O]C, without it the living organisms would disintegrate. The alpha-helix is formed in DNA due to the

187

10.3 Dipole-dipole interactions

hydrogen bond formation between the nucleic acids PdOH ⋯ O]P. In proteins, aminoacids, the O and N atoms are capable of H-bond formation and the ability of these to bind water is essential. Unlike the van der Waals interactions, the H-bonds are asymmetric that is an H-donor and an H-acceptor must be involved. The H-bonds do not depend on the intrinsic material properties and can be active at surfaces. Similarly, H-bonds can be formed between two surfaces or adsorbate and surface given that an H-bond donor and an H-bond acceptor are present on either side.

Numerical example 10.5 Calculate the surface tension of water from the van der Waals and hydrogen bond energy. Hydrogen bond enthalpy in water is 23.3 kJ/mol on average each water molecule is capable of two hydrogen bonds.

Solution 2 The surface tension of water calculated from the van der Waals interaction energy was γ vdW water ¼ 18 mJ/m , see Table 10.5. To calculate the surface tension from the hydrogen bond enthalpy, we use Eq. (3.8) in Section 3.5:

 bond γ HH  2  0:5  23:3 water

 kJ atoms mJ  1018  38 2 m2 m 6  1023 atoms

Therefore, the surface tension of water including the vdW and Hydrogen bond interactions is HH bond γ vdW ¼ 56 water + γ water

mJ m2

This value is closer to the total surface tension of water determined experimentally of 72.4 mJ m2 but still significantly lower, TABLE 10.5

Relative strengths of different types of interactions of reflected in the boiling points of compounds.

Molecule

Molecular weight (Da)

Dipole moment (D)

Boiling point (°C)

Ethane

CH3CH3

30

0

89

Formaldehyde

HCHO

30

2.3

21

Methanol

CH3OH

32

1.7

64

n-Butane

CH3CH2CH2CH3

58

0

0.5

Acetone

CH3COCH3

58

3.0

56.5

Acetic acid

CH3COOH

60

1.5

118

n-Hexane

CH3(CH2)4CH3

86

0

69

Ethyl propyl ether

C5H12O

88

1.2

64

1-Pentanol

CH3(CH2)4OH

88

1.7

137

suggesting that some other types of interactions were not considered, e.g., dipole-dipole interactions.

10.3 Dipole-dipole interactions When two polar molecules come close into the vicinity of one another, they interact via dipole-dipole interaction. A permanent dipole arises in molecules that have covalent bonds formed between atoms with different electronegativities. The dipole moment vector of the polar bond is oriented following the convention from the electropositive to the electronegative atoms. The total permanent dipole moment is the resultant of the vectorial additions of all the bond dipoles in the molecules. In a liquid or gas, the dipole-dipole interaction is attractive when the dipoles are head to tail and is canceled when the dipoles are aligned head to head. Therefore, the relative orientation of the dipole moment is important. If the dipole-dipole interaction energy is sufficiently large to overcome the randomizing effects of the thermal energy, then the dipoles remain oriented favorably for interaction, namely head to tail. It is, therefore, expected that the dipole-dipole interaction between water molecules in liquid is significant.

188

10. Main interaction forces between molecules and interfaces

The magnitude of the interaction energy at room temperature can be estimated from the following equation: Edipoledipole ¼

ðu1 Þ2 ðu2 Þ2

(10.14)

1025 ðDÞ6

where the u1 and u2 are the permanent dipole moments of the interacting molecules in Debye units and D is the separation distance in nm between the molecular dipole vectors (not the contact distance between molecules).

Numerical example 10.6 Calculate the surface tension of water from the van der Waals, hydrogen bond energy, and dipole-dipole interaction energy. Hydrogen bond enthalpy in water is 23.3 kJ/mol on average each water molecule is capable of two hydrogen bonds. Hint: First calculate the dipole-dipole interaction energy knowing that the dipole moment of water is 1.85 D and the water dipole separation distance is 0.3 nm.

Solution dipoledipole

Ewater

¼



dipoledipole γ water

ð1:85 DÞ2 ð1:85 DÞ2 1025 ð0:3 nmÞ6

¼ 15:6 kJ=mol

 kJ atoms mJ  1018  0:5  15:6  13 2 23 2 m m 6  10 atoms

Therefore, this last value adds to the surface tension of water calculated from the vdW and hydrogen bonding interaction: dipoledipole

vdW HH bond γ total + γ water water ¼ γ water + γ water

¼ 69

mJ m2

mJ . m2 The difference might still come from the dipole-induced dipole and other type of interactions between water molecules that have, however, a very small contribution to the total interaction energy. mJ mJ dipoledipole HH bond In addition, note that the γ vdW + γ water ¼ 51 2 which should be compared to the values for water ¼ 18 2 while the γ water m m mJ mJ disperse polar the disperse γ water ¼ 21:8 2 and γ water ¼ 51 2 contributions given in Table 6.1, which are very similar. m m This last value is significantly closer to the experimentally determined surface tension of water at room temperature of 72.4

10.4 Hydrophobic interaction The water molecules in the first solvation layer in the immediate vicinity of a nonpolar surface or molecule have reduced the capacity of H-bond formation. The nonpolar molecule or surface will block two vertexes of the tetrahedral water molecule and this results in an energetically unfavorable situation. If the solute is small, then the water molecules will try to pack in such a way around it so that it does not need to give up any of their H-bonds, resulting in so-called “clathrate” or polyhedral structures, which are cages due to oriented water molecules (Fig. 10.1). A similar ordering occurs for water molecules near a hydrophobic surface. From a thermodynamic perspective, the ordering of water molecules near a hydrophobic surface results in a low entropy state and with an increase in the Gibbs free energy of the system. The increase in the Gibbs free energy of the system due to this orientation will be roughly determined by the area by the non-hydrogen bonding region of the molecule. Between two nonpolar solutes or hydrophobic surfaces in water, there will be always an attraction, because the system will try to minimize the energy by decreasing the total area of the exposed hydrophobic surface via association and thus the number of oriented water molecules near these surfaces. Therefore, the hydrophobic interaction is entropically driven. Note that the hydrophobic interaction is not the same as the van der Waals interactions. The former takes place exclusively in water, while the latter is present in any medium including vacuum. Hydrophobic interaction differs from van der Waals interaction and is not a bond. Methane-methane interaction energy in vacuum is 2.5  1021 J and in water this is 14  1021 J, due to their hydrophobic attraction. The strength of the hydrophobic interaction is given by the surface area the system can exclude/hide from exposure to water, and thus it scales up with the surface area of the molecule or the object. For example, the Gibbs free energy change with the change in the solvent accessible surface area (SASA) is given by Hydrophobic interaction energy ¼ ΔG ¼ γ  ΔSASA ¼ hydration free energy

(10.15)

10.4 Hydrophobic interaction

189

FIG. 10.1 Transfer of a small nonpolar molecule such as methane from its bulk phase into the water phase, followed by surface hydration. The entropy increases to the organization of water into a ordered clathrate structure, as a result the free energy change is positive.

where γ is the surface energy of the SASA. There are many scenarios where the above equation applies: (i) the hydrophobic interaction between two nonpolar molecules in water and (ii) transfer of a nonpolar molecule from its bulk phase into water phase, and its hydration (Fig. 10.1). The free energy for transferring a butane from bulk butane to water is Δ Gtransfer ¼ Δ H  T Δ S ¼  4.3 + 28.7 ¼ + 24.5 kJ mol1,where the entropic contribution is more than 85%, so we now see that this type of interaction is entropically driven [1]; (iii) adsorption of a nonpolar molecule from water onto a hydrophobic surface; (iv) self-assembly of surfactants into micelles; (v) aggregation of colloid particles; (vi) the formation of oil in water emulsion droplets, etc. The hydrophobic interaction is the driving force behind all selfassembly phenomena.

Numerical example 10.7 Knowing that the surface area of the methane molecule is 0.5 nm2, and the free energy of transfer is 14.5 kJ/mol, what is the Δ(transfer) expressed in J/m2. Make the same calculations for the butane molecules, knowing that surface area of butane is 1.0 nm2 and the ΔG(transfer) is 24.5 kJ/mol. How do these values relate to the interfacial energy γ between hydrocarbons and water?

Solution Knowing that the surface area of the methane molecule is 0.5 nm2 and the free energy of transfer is 14.5 kJ/mol, what is the Δ G(transfer) expressed in J/m2. Make the same calculation for the butane molecule, knowing that the surface area of butane is 1.0 nm2 and the Δ G(transfer) is 24.5 kJ/mol. How do these values relate to the interfacial energy γ between hydrocarbons and water? ð14:5103 Þ ΔGðtransferÞ for 14:5kJ=mol methane ¼ 6:0231023  0:51018 ¼ 0:048 mJ 2 ¼ 48 mJ=m2 ½ð Þð Þ

190

10. Main interaction forces between molecules and interfaces

ð24:5103 Þ ¼ 41 mJ=m2 ½ð6:0231023 Þð11018 Þ These values are the same as the interfacial energy γ of water/hydrocarbons. ΔGðtransferÞ for 24:5kJ=mol butane ¼

There is an analytic expression for the hydrophobic interaction with the separation distance between two surfaces at 298 K is [1, 7, 8] wH ðDÞ  20 R eðDRÞ=δH kJ mol1  8 R eðDRÞ=δH kT

(10.16)

where D is the separation distance between the hydrophobically interacting objects, R is the radius of the interacting particle or atom (for larger objects, the 1/R describes their curvature), and δH is the characteristic hydrophobic decay length of about 1 nm. Any characteristic decay length is the length at which the energy of interaction W is reduced to W  1/e, where 1/e ¼ 1/2.718  0.3679 [1]. The effective range of hydrophobic interaction is typically 1–2 nm that is much larger than that of the vdW interactions 0.25 nm, the distance after which the energy of interaction drops below that of thermal fluctuations that is 1 kT. And, it is the relatively long-range effect of the hydrophobic interaction that plays an important role in the self-assembly, protein structure formation, protein folding, hydrophobic aggregation, fusion mechanism of bilayers, and biological membranes.

Numerical example 10.8 A hydrophobic surface is a nonpolar surface, which is poorly wetted by water. For water, the surface tension γ water ¼ 72.6 mN/m at 300 K. We would like to find out what is the maximum contact angle of water hydrocarbon surface knowing that the work of adhesion WWater/Hydrocarbon ¼ 50 mJ/m2 at 300 K.

Solution To calculate this, we use the Young-Dupre equation: WWater/Hydrocarbon ¼ γ water/vapor (1 + cos θ) and we obtain a value of θ ¼ 110 degrees. So, this is the maximum contact angle achieved by water on flat hydrocarbon surfaces, e.g., polyethylene, wax, etc. Substances as hydrocarbons and fluorocarbons are known as hydrophobic substances.

Numerical example 10.9 (a) Comment on the range of the contact values of water and hydrophobicity of the surface. Example, from 0 to 10 degrees value of contact angle with water the surface is hydrophilic. (b) Is it possible to have 180 degrees water contact angles on flat surfaces? The degree of hydrophobicity of a surface can be estimated by measuring the contact angle of water on that surface. If the contact angle is low, then the surface is polar and if it high, it is nonpolar.

10.5 Repulsive hydration force Hydration force was introduced to explain several phenomena, such as: spontaneous swelling of certain clays such as montmorillonite, and superabsorbent (typically polyacrylate superabsorbents such as those found in baby diapers), the excellent dispersion of silica particles in water, stability of foam lamella, etc. When strongly polar or water loving functional groups become strongly hydrated in water, a hydration shell around these forms. Due to the creation of a hydration shell, they begin to repel other strongly hydrated molecules or functional groups. Ionic and polar functional groups that are strongly hydrated fall under this category. It turns out that the hydration sphere of oriented water molecules around a functional group acts as a steric barrier increasing the repulsive force or the effective size of the molecules. Hydration force is always repulsive. For example, mica, Fig. 10.2, is composed of layered aluminosilicate sheets, which are atomically smooth. At low salt concentration, the interaction between the sheets obeys the Derjaguin, Landau, Evert, Overbeek (DLVO) theory but at high salt concentration the short-range repulsive hydration forces take effect and the mica begins to swell.

10.6 Hildebrand and Hansen solubility parameters

191

FIG. 10.2 Pieces of mica sheets. (Shutterstock “macro shooting of natural mineral rock specimen—raw muscovite mica lamina on dark granite background” stock photo ID: 747239614, https:// www.shutterstock.com/image-photo/macro-shooting-naturalmineral-rock-specimen-747239614.)

The hydration interaction also depends on the separation distance according to the following empirically determined formula [1, 8]: W ðDÞ ¼ + W0 eD=λ0

(10.17)

where the characteristic decay length λ0 ¼ 0.6–1.1 nm in 1:1 electrolyte. This was determined by Israelachvili from forcetype experiments on mica sheets. The hydration energy is W0 ¼ 3–30 mJ m2. The strength of hydration forces increases with the strength of hydration number of cations, e.g., Hoffmeister series: Mg2 + > Ca2 + > Li + > K + > Cs +

Numerical example 10.10 Polymethylene oxide, [–CH2–O–]n, is hydrophobic, but polyethylene oxide, PEO [–CH2–CH2–O–]_n, which has one more hydrophobic CH2 group per segment, is hydrophilic and miscible with water. Give possible reasons for this.

Solution See article by Israelachvili [9]. Paradox: Both PPO and PMO are insoluble in water, while PEO is highly soluble in water. PMO has all oxygen atoms on the same side, while PEGs do not.

10.6 Hildebrand and Hansen solubility parameters Similar to the surface and interfacial tension, the Hildebrand solubility parameter for a pure liquid traces its roots in the cohesive energy of the liquid: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ΔHv  RT (10.18) δ¼ VM where Δ Hv is the latent heat of vaporization and VM is the molecular volume. Hansen proposed an extension of the Hildebrand parameters to estimate the contributions from dispersive, polar, and hydrogen bonding contributions: δ2 ¼ δ2d + δ2p + δ2HH

(10.19)

192

10. Main interaction forces between molecules and interfaces

TABLE 10.6

Hildebrand solubility parameters of common solvents [10]. Solubility parameter (MPa1/2)

Solvent

Total

δd

δH-H

δp

Benzene

18.41

18.26705

2.05

1.02

Dodecane

15.9

15.9

0

0

Toluene

18.32

18.15661

2

1.4

Ethyl acetate

18.48

14.92139

9.2

5.85

Chloroform

18.94

17.78949

5.73

3.07

Tetrahydrofuran

19.46

16.79886

8

5.7

Dichloromethane

20.79

19.00859

4.09

7.36

Dimethyl sulfoxide

26.75

18.50844

10.2

16.4

Ethanol

26.13

15.09344

19.43

8.8

Stearic acid

19.04

17.92712

5.5

3.3

Water

47.8

15.42263

42.32

16

The Hansen solubility parameters are determined empirically based on the multiple experimental solubility observations. The dispersive, polar, and hydrogen bond interactions are important toward the understanding of the solubility and miscibility of solvents (Table 10.6). Solubility parameter distance, R, is a useful parameter introduced to evaluate the solvation of a solute 2 in a solvent 1 [11]:
2 R ¼ ðδd2  δd1 Þ2 + δp2  δp1 + ðδHH2  δHH1 Þ2 From Table 10.6, we can see that the smaller the R for the pairs of listed solvent the more miscible they are. For example, ethanol and dodecane are not miscible but dimethyl sulfoxide and ethanol should be miscible according to Hansen’s prediction. If solvent 2 is fully miscible in solvent 1, then their corresponding indices of refraction must be very close: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 hpffiffiffiffiffiffi pffiffiffiffiffiffii 2
2 2
2 2
2  2 2 n1  1 n2  1  ∝ U2  U1 ∝ ðδ2  δ1 Þ2 (10.20) n2  n1 ¼

10.7 Flory-Huggins interaction parameter The Flory-Huggins solution theory is a mathematical model developed to explain the solubility and mixing of polymers. The Flory-Huggins interaction parameter can be obtained directly from Hildebrand solubility parameters and provides an indication of the miscibility of polymers. χ¼

VM ðδ1  δ2 Þ2 RT

Or involving the polar, disperse, and hydrogen bond components of the Hansen parameters [10, 12]: i
2 VM h ðδ1, d  δ2, d Þ2 + 0:25 δ1,p  δ2, p + 0:25ðδ1,HH  δ2,HH Þ2 χ¼ RT The χ parameter has important applications in estimating the miscibility of plasticizers [13], low molecular weight compounds with polymers; if χ > 0.5, then plasticizers have poor miscibility with the polymers, moderate miscibility for χ between 0.3 and 0.5, and good miscibility for χ < 1. Solubility of polymer in solvents [12]. Directed self-assembly emerged as an alternative way to photolithography for patterning large area nanostructures by self-organization and self-assembly of block copolymers, in periodic structures with the lengths scale of the order of the block polymer length [14]. Some typical copolymers used for directed self-assembly patterning are polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA), polystyrene-block-polylactide (PS-b-PLA), etc. To obtain directed self-assembly nanostructures, the χ parameter value for these polymers must be large [15].

References

193

References [1] J.N. Israelachvili, Intermolecular and Surface Forces, third ed., Academic Press, San Diego, 2011. [2] A.V. Parsegian, Van der Waals Forces a Handbook for Biologists, Chemists, Engineers, and Physicists, Cambridge University Press, New York, USA, 2006. [3] H.-J. Butt, M. Kappl, Surface and Interfacial Forces, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010. [4] H.C. Hamaker, The London—van der Waals attraction between spherical particles. Physica 4 (1937) 1058–1072, https://doi.org/10.1016/ S0031-8914(37)80203-7. [5] J. Visser, On Hamaker constants: a comparison between Hamaker constants and Lifshitz-van der Waals constants. Adv. Colloid Interf. Sci. 3 (1972) 331–363, https://doi.org/10.1016/0001-8686(72)85001-2. [6] A. Honciuc, A.W. Harant, D.K. Schwartz, Single-molecule observations of surfactant diffusion at the solutionsolid Interface. Langmuir 24 (2008) 6562–6566, https://doi.org/10.1021/la8007365. [7] J. Israelachvili, R. Pashley, The hydrophobic interaction is long range, decaying exponentially with distance. Nature 300 (1982) 341–342, https:// doi.org/10.1038/300341a0. [8] S.H. Donaldson, A. Røyne, K. Kristiansen, M.V. Rapp, S. Das, M.A. Gebbie, D.W. Lee, P. Stock, M. Valtiner, J. Israelachvili, Developing a general interaction potential for hydrophobic and hydrophilic interactions. Langmuir 31 (2015) 2051–2064, https://doi.org/10.1021/la502115g. [9] J. Israelachvili, The different faces of poly(ethylene glycol). Proc. Natl. Acad. Sci. 94 (1997) 8378–8379, https://doi.org/10.1073/pnas.94.16.8378. [10] C.M. Hansen, Hansen Solubility Parameters: A User’s Handbook, second ed., CRC Press, Boca Raton, FL, 2007. [11] A. Aghanouri, G. Sun, Hansen solubility parameters as a useful tool in searching for solvents for soy proteins. RSC Adv. 5 (2015) 1890–1892, https://doi.org/10.1039/C4RA09115A. [12] T. Lindvig, M.L. Michelsen, G.M. Kontogeorgis, A Flory–Huggins model based on the Hansen solubility parameters. Fluid Phase Equilib. 203 (2002) 247–260, https://doi.org/10.1016/S0378-3812(02)00184-X. [13] E. Langer, K. Bortel, S. Waskiewicz, M. Lenartowicz-Klik, Essential quality parameters of plasticizers. in: Plasticizers Derived From PostConsumer PET, Elsevier, 2020, , pp. 45–100, https://doi.org/10.1016/B978-0-323-46200-6.00003-9. [14] H. Hu, M. Gopinadhan, C.O. Osuji, Directed self-assembly of block copolymers: a tutorial review of strategies for enabling nanotechnology with soft matter. Soft Matter 10 (2014) 3867, https://doi.org/10.1039/c3sm52607k. [15] G.-W. Yang, G.-P. Wu, X. Chen, S. Xiong, C.G. Arges, S. Ji, P.F. Nealey, X.-B. Lu, D.J. Darensbourg, Z.-K. Xu, Directed self-assembly of polystyrene-b-poly(propylene carbonate) on chemical patterns via thermal annealing for next generation lithography. Nano Lett. 17 (2017) 1233–1239, https://doi.org/10.1021/acs.nanolett.6b05059.

C H A P T E R

11 Interactions between electrically charged interfaces 11.1 Electric double layer Helmholtz double-layer model (Fig. 11.1): Hermann von Helmholtz proposed the simplest physical model for a charged surface in water [1], which stated that the surface charge is completely neutralized by the opposite sign counterions located in the liquid phase at distance d from the surface, resembling the rigid plates of a capacitor (Fig. 11.1). The Helmholtz capacitor plates model is unrealistic for fully describing the electrical double layer, because it implies the distribution of charges as rigid layers, the counterions are immobile, nonhydrated, etc. Gouy-Chapman diffuse layer model (Fig. 11.1): M. Gouy [2] in 1910 and D.L. Chapman [3] in 1913 proposed a new model where the charged surface of the solid is surrounded by a cloud of counterions whose concentration decays exponentially away from the surface, and the distribution of these ions obeys Boltzmann’s statistics. The main difference from the previous model is that all the counterions are fully mobile and not attached to the surface so that in effect they would hover over a charged surface like a countercharge cloud. This theory is also called the “diffuse double-layer theory.” However, the current model did not explain correctly the evolution of the potential at the near surface where parts of the counterions are immobilized on the surface due to adsorption. The Stern layer (Fig. 11.1), is an improvement of the Gouy-Chapman diffuse layer theory which states that parts of the counterions are adsorbed; the distance from the surface to the center of the surface adsorbed counterions is called the Stern layer [4]. The rest of the nonadsorbed counterions are mobile and their distribution away from the surface obeys Boltzmann’s statistic like in the Gouy-Chapman diffuse layer model. Grahame [5] later improved Stern’s theory (1947) by considering that the surface and the counterions are hydrated; the distance between the surface and the center of the water molecule is the inner Helmholtz plane (IHP), whereas the distance between surface and the center of the adsorbed hydrated counterions is the outer Helmholtz plane (OHP). According to Grahame and Stern, the diffuse layer begins beyond the OHP. The potential drop between IHP and OHP would obey the Helmholtz model from the Ψ 0
ζ and beyond OHP would be described by the Gouy-Chapman’s model. ξ at the OHP is called the zeta potential, which can be measured.

11.2 Distribution of counterions in the absence of electrolyte The distribution function of the counterions and potential profiles away from a charged surface can be calculated from the chemical potential of a charged ion at distance x from a surface: μx ¼ zeΨ x + kT ln ρx

(11.1)

where Ψ is the electrostatic potential, ρx-the number density of ions of valence z at a point x away from the surface. At equilibrium, the chemical potential of the charged ions at any distance d away from the surface must be equal. By putting the equilibrium condition between two points, for example, x and x ¼ d (which could be the surface) and the corresponding potentials at each point, the concentration distribution of the ions between these points is found: zeΨ x + kT ln ρx ¼ zeΨ d + kT ln ρd

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00010-7

195

(11.2)

Copyright © 2021 Elsevier Inc. All rights reserved.

196

11. Interactions between electrically charged interfaces

FIG. 11.1 Cartoon depicting the Helmholtz (left), Gouy-Chapman (middle), and Stern/Grahame (right) double-layer theories of charged interfaces. Inner Helmholtz plane (IHP) and outer Helmholtz plane (OHP) take into account the radius of the ion and the hydrated ion, respectively, that are adsorbed at the interface. Ψ 0, potential of the charged surface, Ψ d, potential of the charged surface beyond the OHP, and ζ, zeta potential. The dark blue line represents the potential drop in the Helmholtz model, whereas the light blue line represents the potential drop in the diffuse layer model.

FIG. 11.2 The distribution profile for the counterion concentration ρx and potential ψ x between two charged interfaces separated by distance D. The boundary conditions are, x0 ¼ 0, ρx ¼ ρx and ψ 0 ¼ 0 at the midplane separating the two surfaces and xS ¼ D/2, ψ s and ρS at the surface.

which leads us to the Boltzmann distribution (the Nernst equation): ρx ¼ ρd exp ð
zeðΨ x
Ψ d Þ=kTÞ

(11.3)

The above equation indicates an exponential decay of the charge density between any two points away from the surface. The counterion distribution profiles between two charged interfaces having the same charge density, separated at distance D as in Fig. 11.2, can be calculated from Eq. (11.3) after defining the boundary conditions, Ψ 0 ¼ 0 and ρ0 at x0 ¼ 0, which is the middle of the distance separating the two surfaces and xs ¼ D/2; Ψ s is the electrostatic potential at the surface and ρs the counterion density at the surface [6]. The concentration profile ρx at any point between x0 and xs is ρx ¼ ρ0 exp ð
zeΨ x =kTÞ Poisson distribution that gives the charge distribution at a certain point x function of potential Ψ :

(11.4)

11.3 Distribution of counterions around a charged surface in the presence of electrolyte

zeρx ¼ ε0 ε

dΨ 2x dx2

197 (11.5)

By combining the above two equations, we obtain dΨ 2x zeρx zeρ0 ¼ ¼ exp ð
zeΨ x =kT Þ dx2 ε0 ε ε0 ε

(11.6)

Eq. (11.6) allows finding another expression for the counterion density at any point x: ðx

   ðx  dΨ x 2 ε0 ε dΨ x 2 d ¼ dx 2kT dx 0  2 ε0 ε dΨ x ρx ¼ ρ0 + 2kT dx

ε0 ε ρx
ρ0 ¼ dρ ¼ 2kT 0

(11.7) (11.8)

where dΨ x/dx is the electric field E at distance x. The last equation gives the concentration of the counterions at any point x function of the density of ions ρ0 at the middle of the distance between the two surfaces and the electrostatic potential Ψ x at point x. For practical reasons, it would be also useful if counterion concentration at the surface ρs can be calculated from charge density. The surface charge σ must be equal to the total counterion charge contained in the area between x ¼ 0 nm and x ¼ D/2 nm, justified by the condition of electroneutrality: ðD

ðD σ¼


2

zeρdx ¼
ε0 ε

0

2

0

    dΨ 2 dΨ s dΨ s
0 ¼
ε0 ε ¼
ε0 εEs dx ¼
ε0 ε 2 dx dx dx

(11.9)

and this gives an important relationship as it relates the surface charge density (C/m2) with the electric field at the  2 surface (V/m). dΨ from Eq. (11.9), the counterion concentration at the surface is Using the expression of the dx σ2 (11.10) ρ S ¼ ρ0 + 2ε0 εkT which relates that the concentration of the counterions at the surface depends on the surface charge density, and it shows that ρs can never drop below the value of counterion concentration farther away from the surface. For an isolated surface in the absence of electrolyte, ρ0 ! 0.

Numerical example 11.1 What is the counterion charge density (m
3) for an isolated surface with a charge density of
0.2 C/m2 (one charge per 0.8 nm2) at 293 K, in mol/L? What is the counterion density per nm2 if we consider that these are contained in a plane of 1 m2 and an OHP of thickness 0.2 nm?

Solution This is 7.0  1027  27 m
3, which is about 12 M. If the above ions occupy a layer thickness d of about 0.2 nm (OHP), the density of the counterions is about one charge per 0.7 nm2. This comes to show that most of the counterions that balance the surface charge are in the OHP.

11.3 Distribution of counterions around a charged surface in the presence of electrolyte To calculate the counterion distribution around a charged surface, the boundary conditions must be defined (see Fig. 11.3). All the charges in the system, counterions, and co-ions of the added electrolyte must be accounted for; therefore, ρi ∞ is the density of ion i in the bulk solution where Ψ ∞ ¼ 0; ρix and Ψ x are the charge density and electrostatic potential at any point between the surface x ¼ 0 and bulk x ¼ ∞; Ψ s and ρis are the potential and the ion density at the surface, respectively. The Boltzmann distribution of ion i around the charged surface becomes

198

11. Interactions between electrically charged interfaces

FIG. 11.3 Density profiles of the counterions, co-ions, and of the zeta potential away from the surface.

TABLE 11.1

Concentration of anions and cations away and at the surface [6].

Concentration of anions away from the surface

Concentration of cations at the surface

+


NA I

  x ½Na + x ¼ ½Na + ∞ exp
eΨ kT   x ½I
x ¼ ½I
∞ exp + eΨ kT

  S ½Na + S ¼ ½Na + ∞ exp
eΨ kT   S ½I
S ¼ ½I
∞ exp + eΨ kT

CA2+ 2CL
 2 +    x Ca x ¼ Ca2 + ∞ exp
2eΨ kT   x ½Cl
x ¼ ½Cl
∞ exp + eΨ kT

 2 +    S Ca S ¼ Ca2 + ∞ exp
2eΨ kT   S ½Cl
S ¼ ½Cl
∞ exp + eΨ kT

Note the change in the valence of the ions in the expressions.



zi eΨ x ρxi ¼ ρ∞i exp
kT

 (11.11)

and the concentration of ions at the surface are 

zi eΨ S ρSi ¼ ρ∞i exp
kT

 (11.12)

where ρ∞ i is the bulk concentration of the ionic species i where Ψ ∞ ¼ 0. In Table 11.1, the expression of the ion concentration is given in various electrolytes: 1:1 electrolytes (H+ OH
), (Na+ I
) and 2:1 electrolyte (Mg2+ 2Cl
). Multivalent electrolyte ions have a dramatic effect on the potential. In fact, in an electrolyte mixture of monovalent and divalent ions, the surface potential is controlled by the divalent ions even at small concentrations, about 3% from that of the monovalent ions.

Numerical example 11.2 Show by calculation that when the bulk concentration of [Ca2+]∞ is 3 mM and [Na+]∞ is 100 mM, i.e., a mixed electrolyte, the surface concentration of [Ca2+]s is larger than that of [Na+]s for a value of ψ 0 ¼
100 mV.

11.3 Distribution of counterions around a charged surface in the presence of electrolyte

Solution

199

2eѰS  2 +  Ca S ¼ Ca2 + ∞  e
kT ¼ 6:82 M ð7 MÞ

½Na + S ¼ ½Na + ∞  e
eѰS =kT ¼ 4:77 M ð5 MÞ The divalent ions adsorb more than the monovalent ones and determine the surface potential once their concentration is greater than about 3%.

In colloidal chemistry, it is known that trivalent ions such as La3+, Al3+, or Th4+ with a bulk concentration more than 10 M can completely neutralize a negatively charged surface and lead to charge reversal; this is also called surface charge titration. In the case of a colloid consisting of finely dispersed nanoparticles in water, the surface potential of the particles evolves, such that at low concentrations C1 the absolute magnitude of the surface potential decreases (see Fig. 11.4). The decrease in the absolute magnitude of the nanoparticle surface potential leads to aggregation, C2, a phenomenon also known as flocculation. Typically, in the absence of an added electrolyte, aggregation does not occur when the particles suspended in a medium, such as water, carry a sufficient charge and their electrostatic potential is high, ensuring good repulsion. Aggregation occurs when the surface potential decreases below a certain magnitude, typically 30 mV for the zeta potential; this interval is also indicated in Fig. 11.4, region C2. For example, Al2(SO4)3 is used as a flocculant in wastewater treatment stations, to remove the floating particles and eventually separate them out as mud or slurry. With a continuous increase in the concentration of the multivalent ion C3, the surface eventually becomes positively charged, and particle aggregates re-disperse, a phenomenon also known as “peptization.” Above this concentration C4, the surface potential falls again below 30 mV as the surface charges are now being screened by the very high electrolyte concentration. Generally, the greater the valence of the ions, the stronger the adsorption capacity on the oppositely charged surface. The work of Schulze [7] and Hardy [8] led to the conclusion that: “The coagulative power of a salt is determined by the valency of its ions. The coagulating ion is always the opposite electrical sign to the particle.” Typically, the colloids precipitate upon addition of: (i) salt having monovalent counterions at concentrations between 25–150 mM, (ii) salt having divalent counterions in the concentration range of 0.5–2 mM, and (iii) salt having trivalent counterions at a concentration range of 0.01–0.1 mM [9]. The capacity of adsorption decreases with the decrease in the hydration degree, charge, and volume of the ion:
5

Th4 + > Al3 + > Ba2 + > Sr2 + > Ca2 + > Mg2 + > Cs2 + > Rb + > K + > Na + > Li + SCN
> I
> NO3
> Br
> Cl
The above series are known under the name of Hoffmeister series. The Hoffmeister series of ions is divided into two categories: chaotropes and cosmotropes. Chaotropic ions interfere with intramolecular interactions mediated by noncovalent forces such as hydrogen bonds, van der Waals forces, and hydrophobic interactions included in the broader concept that of secondary interactions (primary ones are electrostatic). A chaotrope (create chaos) is an ion which disrupts the structure of, and denatures, macromolecules such as proteins and nucleic acids (e.g., DNA and RNA). A cosmotrope (create order) is an ion or substance enhancing the hydrogen bond network of water, which also (in effect) stabilizes intramolecular interactions in macromolecules such as proteins. Some examples of ions with a cosmotrope 2
4
effect are: CO3
2 , SO4 , HPO2 , etc.

FIG. 11.4 The surface potential (here expressed as the zeta potential on the Y-axis) varies with the concentration of a trivalent ion (X-axis). Region C1-particle stability, C2-surface charge titration causes particle aggregation, C3-charge reversal and aggregate re-dispersion into single particles (peptization), and C4-particle aggregation and flocculation due to screening of the surface charge.

200

11. Interactions between electrically charged interfaces

11.4 Grahame equation and Debye length The Grahame equation [5] relates the surface potential Ψ S with the charge density of the surface σ, which can be derived from the known equations: X

ρSi ¼

i

X

ρ∞i +

i

ρSi ¼ ρ∞i e

σ2 2ε0 εkT

(11.13)


zi eψ S kT

The Grahame equation for a 1:1 electrolyte or a mixture of 1:1 electrolytes is: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  eψ S σ ¼ 8Celectrolyte ε0 εkT sin h 2kT

(11.14)

where Celectrolyte is the bulk concentration of the electrolyte. The minimum value of ρ∞ i cannot be smaller than the ion concentration due to autoionization of pure water, 10
7 M. For higher valence, electrolyte ions and the analytical expression are significantly more complicated. For low surface potentials 100Þ (11.22) ε0 D

204

11. Interactions between electrically charged interfaces

In H€ uckel’s approximation, i.e., when the thickness of the electric double layer is larger than the particle radius, the case of small particles in low salt concentration, 10
5 M (Fig. 11.7) H(λDr)1: ζ¼

3μη , for λD r≪1 ðr < 0:1Þ 2ε0 D

(11.23)

The typical methods for measuring the zeta potential of the particles include dynamic light scattering (DLS), singlenanoparticle tracking analysis (NTA), and other electrophoretic methods. In the same way, the zeta potential of proteins is determined.

11.8 Case study: Constructing the interaction potentials between nanoparticles with DLVO and non-DLVO forces As already mentioned, the DLVO theory is especially important in explaining the stability of colloids as a balance between the repulsion double-layer forces and attractive van der Waals forces. In the last decades, it has become evident, however, that other forces, termed as non-DLVO, not included originally in the DLVO theory, play an important role in the stability/instability of colloids. These non-DLVO forces are attractive, such as hydrophobic interaction, depletion forces (not discussed here) and repulsive, steric, and hydration forces (not discussed here). These forces, however, are short range and depend on the detail of the particle construction or environment, with one exception, hydrophobic interaction. In water, hydrophobic interaction is almost as universal as the van der Waals interaction, especially between nonpolar or intermediately polar surfaces. Therefore, in this section, the construction of the DLVO interaction potential with separation distance between two particles is constructed step by step. In addition, we will attempt to understand the hydrophobic interaction dependence with the separation distance and generate a global interaction potential between these particles by including DLVO and non-DLVO forces. In addition to colloid stabilization, knowing how to construct an interaction potential may be useful to explain other phenomena such as selfassembly of surfactants and nanomaterials.

Numerical example 11.4 Calculate and plot in a graph the double-layer interaction energy for two polystyrene particles (Fig. 11.8), with separation distance between 1 and 180 nm, in solutions of water and 10 vol% ethanol, at three different concentrations of NaCl, 10
3, 10
4, and 10
5 M, at 298 K. The particle radius is 134 nm, the zeta potential is
56 mV. Show your calculations for the interaction constant Z at 298 K and Debye length both in the presence and absence of electrolyte. Express all the interaction energies in units of kT.

Solution For the calculation of the double-layer interaction energy with separation distance between two particles, we use the appropriate formula (row 3 in Table 11.2):

Wdouble layer ¼ 0:5RZe
λD D

(11.24)

FIG. 11.8 Two polystyrene particles interacting in an aqueous medium. Polystyrene particles are among the most common constituents of synthetic nanoparticle colloids. They are usually stabilized by the presence of sulfonate and sulfate groups on their surfaces, generated during the synthesis by the radical initiator, strong oxidizer ammonium peroxydisulfate (APS).

11.8 Case study: Constructing the interaction potentials between nanoparticles with DLVO and non-DLVO forces

205

The value of the interacting constant Z in the 1:1 electrolyte at 298 K can be calculated with the formula in Table 11.2. By taking the ζ-zeta potential value as a reasonable approximation for the surface potential Ψ 0, we obtain

  Z ¼ 64πε0 εðkT=eÞ2 tan h2 ðzeζ=4 kTÞ ¼ 9:22  10
11 tan h2 ðeζ=103Þ ¼ 2:7  10
17 J=m

Note that the dielectric constant of water +10% ethanol ¼ 73. We also assume that the zeta potential remains constant in the salt concentration interval of 10
3–10
5 M; typically, for higher salt concentrations, the zeta potential will vary more dramatically due to screening (Note that surface functional groups with permanent charge –NR+3 , –O–SO
3 , will yield a surface whose potential is largely unaffected by the concentration of binding ions H+ or OH
, functional groups such as –COOH, –NH2, will yield a surface whose potential will vary strongly with the concentration of binding ions H+ or OH
). The calculation of the Debye length yields λ1D ¼ 9:64  10
9 m (10
3 M), λ1D ¼ 3:05  10
8 m (10
4 M), λ1D ¼ 9:64  10
8 m (10
3 M). Thus, the double-layer interaction energies as a function of the separation distance in the interval of 1–190 nm can be plotted with the help of Eq. (11.24) (Fig. 11.9). It is clear that the double-layer interaction is significantly influenced by the salt concentration; for a high salt concentration, the double layer is compressed, which may affect the aggregation behavior of the particles. For this reason, it is recommended that the ionic strength of the solution is kept low when measuring the zeta potential with DLS methods.

FIG. 11.9 Double-layer interaction energy between two charged particles as a function of separation distance and 1:1 electrolyte concentration.

Numerical example 11.5 Calculate and plot in a graph the the van der Waals interaction energy for the same polystyrene nanoparticles as in the previous numerical example, with separation distance, knowing that the Hamaker constant Apolystyrene/water/polystyrene ¼ 1.4  10
20 J. All other data remain the same. Express all the interaction energies in units of kT.

Solution The vdW interaction between the Janus particles with the separation distance can be calculated with the help of the equation in Table 10.1.

206

11. Interactions between electrically charged interfaces

WvdW ¼ 0:5R

A 6D

The Hamaker constant for two polymers interacting in water  1  10
20 J. The calculation is straightforward and the results are presented in Fig. 11.10.

FIG. 11.10

vdW interaction energy between Janus nanoparticles as a function of the separation distance.

Numerical example 11.6 Calculate the total DLVO interaction potential with separation distance, between 1 and 180 nm, for the same particles as in the previous numerical examples, when their surface zeta potential is either
56 mV or
5 V. All the other conditions stay the same. Discuss if the overall interaction between particles is attractive or repulsive. The DLVO potential for the two interacting nanoparticles is obtained by adding the vdW and electrical double-layer potential curves with the separation distance (see Eq. (11.20)). By comparing the two energies, it quickly becomes evident that the electrostatic repulsion dominates over vdW interaction when the zeta potential of the particles is
56 mV. The result is presented in Figure 11.11A. If the surface potential is significantly smaller ζ ¼
5 mV, then the balance between the DLVO forces would change and the vdW interaction would dominate, especially at higher salt concentrations (see Figure 11.11B). The interaction would be sufficiently stable to aggregation, due to double-layer repulsion at a salt concentration of 10
5 M, but would aggregate at a higher salt concentration 10
3 M. Essentially, the compression of the double layer, i.e., shortening of the Debye length, due to a high electrolyte concentration when the surface potential is rather low, would lead to the aggregation of the particles due to vdW forces. For a salt concentration of 10
4 M, the height of the electrostatic repulsion barrier is lower than 1 kT, which means that this can be easily overcome by the kinetic energy of the particles at room temperature.

11.8 Case study: Constructing the interaction potentials between nanoparticles with DLVO and non-DLVO forces

207

FIG. 11.11

(A) DLVO interaction potential between the two Janus nanoparticles, when (A) the nanoparticle zeta potential is 56 mV and (B) the nanoparticle zeta potential is 5 mV.

Numerical example 11.7 For the same system of particles as in the previous examples, calculate and represent graphically the hydrophobic interaction energy knowing that the interfacial energy between particle and water +10% ethanol is γ ¼ 2 mJ/m2.

Solution The inclusion of the non-DLVO forces to construct an overall interaction potential between two objects is not difficult if the dependence of the interaction potential is known. The hydrophobic interaction energy when the two particles are in contact can be calculated by

ΔGhydrophobic ¼
γ  ΔA where ΔA is the contact area to be estimated and γ is the interfacial energy of the particle with the solvent. The effective cord theorem states that the contact area of two spheres with radius R is given by

ΔA  2πRa where a is a dimension of the range of forces in question [1]. Knowing that R ¼ 134 nm, and choosing a  1, the contact area is ΔA ¼ 8.42  10
16 m, and ΔG ¼
416 kT. The choice of a  1 is justified, since Israelachvili and Pashley [13] found experimentally that the decay length of the hydrophobic force is between 1 and 4 nm. Therefore, at larger separation distances D, the hydrophobic interaction should be

whydrophobic ðDÞ  ΔGhydrophobic e
D=δH where δH is the characteristic hydrophobic decay length of about 1 nm. The hydrophobic interaction energy with separation distance is represented in Figure 11.12A. The overall interaction potential including DLVO and non-DLVO hydrophobic interaction is represented in Figure 11.12B. From these results, it can be seen that the short-range nature of the hydrophobic interaction does not affect the large electrostatic double-layer barriers above a separation distance of cca. 10 nm.

208

11. Interactions between electrically charged interfaces

FIG. 11.12 Interaction potentials of the Janus nanoparticles: (A) DLVO interaction potentials and the hydrophobic interaction energy with separation distance D; (B) Summed DLVO and non-DLVO potentials (double layer, vdW, and hydrophobic interactions) with separation distance.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

€ ber electrische Grenzschichten. Ann. Phys. (1879) 337–382, https://doi.org/10.1002/andp.18792430702. H. Helmholtz, Studien u M. Gouy, Sur la constitution de la charge electrique a la surfaced’un electrolyte, J. Phys. 9 (1910) 457–468. D.L. Chapman, A contribution to the theory of electrocapillarity, Philos. Mag. 25 (1913) 475–481. O. Stern, Zur Theorie Der Elektrolytischen Doppelschicht. Z. Elektrochem. Angew. Phys. Chem. 30 (1924) 508–516, https://doi.org/10.1002/ bbpc.192400182. D.C. Grahame, The electrical double layer and the theory of electrocapillarity. Chem. Rev. 41 (1947) 441–501, https://doi.org/10.1021/ cr60130a002. J.N. Israelachvili, Intermolecular and Surface Forces, third ed., Academic Press, San Diego, CA, 2011. H. Schulze, Schwefelarsen in w€assriger L€ osung. Journal F€ ur Praktische Chemie 25 (1882) 431–452, https://doi.org/10.1002/prac.18820250142. W.B. Hardy, F.H. Neville, A preliminary investigation of the conditions which determine the stability of irreversible hydrosols. Proc. R. Soc. Lond. 66 (1900) 110–125, https://doi.org/10.1098/rspl.1899.0081. H.-J. Butt, M. Kappl, Surface and Interfacial Forces, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010. E.J.W. Verwey, Theory of the stability of lyophobic colloids. J. Phys. Chem. 51 (1947) 631–636, https://doi.org/10.1021/j150453a001. B. Derjaguin, On the repulsive forces between charged colloid particles and on the theory of slow coagulation and stability of lyophobe sols. Trans. Faraday Soc. 35 (1940) 203–215, https://doi.org/10.1039/TF9403500203. E.J.W. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids, American Elsevier Publishing Company, New York, NY, 1948. J. Israelachvili, R. Pashley, The hydrophobic interaction is long range, decaying exponentially with distance. Nature 300 (1982) 341–342, https:// doi.org/10.1038/300341a0.

C H A P T E R

12 Colloids and nanoparticles The term colloids probably originate from the Greek word “colos” meaning clay because after solvent evaporation clays are formed in contrast to solutions of salt that leave crystals. When two immiscible phases are not mixed at the molecular level, they form either dispersions or colloids. Colloids are finer pieces of materials than dispersions, some examples of dispersion and colloids encountered in daily life (Table 12.1). Depending on the particularities of a colloid, it can be classified into several different classes: (1) lyophobic, (2) lyophilic, (3) micellar, (4) nonliquid colloids, (5) laminar (2D) or capillary (3D) colloids, and (6) pseudo-colloids (emulsions, suspensions, pastes, etc.). In Table 12.1 several examples of different combinations of dispersed substances and dispersion media are summarized.

12.1 Lyophobic colloids Lyophobic colloids or sols are suspensions of very finely divided solid particles in a continuous medium, a liquid. In lyophobic (from the Greek word “lyos” that would loosely translate into bonding and “phobos” translated as aversion) colloids there is little interaction and weak bonding between the finely dispersed particles and the dispersion medium. These finely dispersed heterogeneous phases are thermodynamically unstable but could have kinetic stability (unlike lyophilic colloids that are thermodynamically stable). For example, a colloid consisting of metallic nanoparticles can only achieve kinetic stability in the absence of surfactant stabilizers at concentrations below 1%. Even so, these are easily destabilized by the addition of electrolytes and once precipitated, these particles cannot be re-dispersed for the regeneration of the initial colloid. Although these systems are thermodynamically irreversible and unstable, depending on the type of colloid and the concentration of the dispersed phase they can survive for very long time even hundreds of years due to this kinetic stability. The most famous example is the one made by Michael Faraday over 150 years ago from suspended gold nanoparticles in an aqueous phase that can be still seen on display in the Royal Institute of London. The stability of the lyophobic colloids can be improved by the addition of stabilizers, such as surfactants.

12.2 Preparation of the lyophobic colloids The easiest way to imagine the preparation of a colloid is the fine division of a substance solid or liquid followed by its dispersion in a continuous medium. The dispersion of a substance can be achieved through mechanical forces, such as stirring, ultrasonication, and involves a large input of energy. A large mechanical energy input is needed to create very fine particulate material with a very large surface area. With the increase in surface area the surface free energy of the material also increases significantly. Therefore, the energetic aspect of the production of colloids must be considered first. By taking, for example, an oil phase that we want to disperse in water and create an emulsion. For this, we consider the volume of the oil phase Vi and its area Ai and its final volume Vf and area Af, which corresponds to the finely divided state. The volume of oil in a dispersed state does not change ΔV ¼ 0, but what changes is its interfacial area with water as the particles of oil become smaller and smaller the interfacial area, water increases significantly, ΔA ¼ Af  Ai. Therefore, the change in the free energy of the system with the increase in the surface area is given by ΔGsystem after dispersion ¼ γ ΔA > 0, Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00016-8

209

(12.1) Copyright © 2021 Elsevier Inc. All rights reserved.

210 TABLE 12.1

12. Colloids and nanoparticles

Combination of dispersed substances and dispersion media and corresponding examples from the daily life.

Phase of colloid

Continuous phase

Dispersed phase

Example

Gas

Gas

Liquid

Fog, mist, aerosols

Gas

Gas

Solid

Aerosols, smoke

Liquid

Liquid

Gas

Foams, shaving cream, whipped cream

Liquid

Liquid

Liquid

Milk, emulsions, lotions

Liquid

Liquid

Solid

Color pigments in solvents, paint

Solid

Solid

Gas

Solid foams, sponges

Solid

Solid

Liquid

Solid emulsions, butter, sour cream

Solid

Solid

Solid

Tinted glass, ruby

where γ is the oil-water interfacial energy in mJ/m2. It is now clear that the larger the interfacial area between the dispersed and the dispersion medium the larger the increase in the free energy of the system. This change in energy is also the minimum energy input required to form the colloid.

Numerical example 12.1 (a) Calculate the Gibbs free energy change of the oil/water system when generating an oil-in-water emulsion from an initial volume V1 of 200 mL oil in 35 mL water, which contains final oil droplet volumes, V2 with diameters of 50 nm. The interfacial tension between oil and water is 50 mN/m. (b) Discuss under which circumstances and how can you lower the Gibbs free energy needed to obtain the same emulsion.

Solution ΔG ¼ γ ΔA ΔA ¼ N  4πR22  4πR21 4 R1 big particles V ¼ πR3 ¼ 200  109 m3 3 R ¼ 3:6  103 m 50  109 ¼ 25  109 m 2 A1 ¼ 4πR21 ¼ 1:65  104 m2

R2 small particles

A2 ¼ 4πR22  N, where N number of droplets 4 3 V1 3 πR1 4:7  108 N¼ ¼ ¼ ¼ 3  1015 V2 4 3 1:56  1023 πR 3 2 A2 ¼ 4  3:14  6:25  1016  3  1015 ¼ 23:5 m2 ΔA ffi A2 ΔG ¼ γ  A2 ¼ 50mN/m  23.5 m2 ¼ 1172  103 N m ¼ 1172 J.

A well-established method for the preparation of colloids is the dispersion with ultrasounds. The phenomena of cavitation take place in water where the cavities form and grow very rapidly and their implosion produces strong shear forces in the liquid. The sheer forces will typically lead to the formation of a colloid from a fine suspension. Ultrasonication can be used for the preparation of the stable sols of S, Hg, metallic hydroxides, proteins, oil, coal suspensions, and even metals, such as Au, Ag, Pt, Cu, Fe, etc. with the condition that these are already finely dispersed in the

12.4 Chemical synthesis of lyophobic colloids

211

medium. However, from an energetic perspective supplying energy to the system may not be the most advantageous way for the preparation of colloids.

12.3 Preparation of colloids by solvent replacement and physical condensation The solvent replacement method is the simplest preparation of colloids, whereas the nonmiscible compound such as sulfur, or colophonium (a solid form of resin obtained from pine trees), which is not soluble in water but is dissolved in ethanol. Then a certain volume from this solution is then poured in water under vigorous stirring and due to dilution of ethanol the solute becomes insoluble and fine lyophobic soil is formed. The sulfur colloid obtained this way has a bluish opalescent appearance due to strong blue light scattering if observed perpendicular to the incident light, and orange red if the colloid is observed from the transmitted light side. The naturally formed sulfur colloids can be seen in Hot Sulfur Springs, Colorado, Fig. 12.1 and their milky white bluish appearance. The formation of the naturally occurring sulfur colloids is due to oxidation of the hydrogen sulfide gas dissolved in thermal waters, which then in contact with oxygen forms fine sulfur sols: 2H2 S + O2 ! 2H2 O + 2S # Similarly, the opalescent or tinted glass is produced by dispersing finely divided pigments into a glass. One such example is the SnO2 which was used for a long time as an opacifier and a pigment in the manufacture of tinted glasses, enamels, and ceramic glazes, with a distinct appearance.

12.4 Chemical synthesis of lyophobic colloids Chemical method is the preferred way for the preparation of colloids and proceeds with the formation of a new finely dispersed phase in an initially homogeneous system. The colloids can be obtained from the condensation of the products resulting from redox reactions, exchange reactions, hydrolysis reactions, etc. The emergence of a new phase from the condensation process requires two stages: (1) the formation of nuclei which is characterized by the speed of formation v1 and (2) the growth of nuclei characterized by the speed of growth v2. The formation of a new phase via condensation proceeds spontaneously, similarly to dissolution or solvation, in the presence of condensation centers, nuclei or nucleation seeds; compare this to the condensation, evaporation, crystallization, melting, or sublimation phenomena. In practice both the magnitude of v1 and v2 determines the size of the particles of the resulting new phase. When nucleation speed v1 > growth speed v2 the formation of the small particles and thus of a colloidal system is favored. When v2 > v1 in the system, there are very few nuclei formed that grow fast, which will eventually

FIG. 12.1 Photograph of a hot basin in Colorado, United States, where the sulfur colloid is naturally formed and has a milky white bluish appearance due to the blue light scattering. Ute Indians believed these natural thermal springs have healing powers.

212

12. Colloids and nanoparticles

sediment out of the system, such as is the case in a precipitation reaction. Noteworthy is that when a stabilizer is added, such as a surfactant, or capping agent that inhibits the growth of the nuclei, then the formation of the colloidal system, finely dispersed particles, is favored. The formation of the colloidal phase from the reactants that are very dilute can be explained by the slow v2, either due to growth inhibition or impurities that lead to fast nucleation. The nucleation seeds may appear in the system either due to impurities or spontaneously due to the density fluctuations and statistical agglomeration of the “solute” in the systems. The natural fluctuations in the system could produce a local and instantaneous agglomeration of molecules that give birth to proto-nucleation seeds or “embryos.” However, local density variations due to the most frequent energy fluctuations, thermal 1 kT, are too low for the nucleation centers to appear. Therefore, in normal conditions, there is no spontaneous appearance of a new phase because the protonucleation seeds are continuously being destroyed by the same thermal fluctuations always present. Especially critical for the formation and survival of the proto-nuclei is the solute’s solubility; solubility is greater, around a droplet or fine particle due to the action of surface tension (see Kelvin equation). Therefore, to compensate for the nuclei’s destruction and improve its survivability the solute must be present in concentrations higher than its saturation concentration around the smallest nuclei. By increasing the concentration or pressure to supersaturation, the solute concentration equals or exceeds the solubility around the tiny droplet; thus, the critical diameter for the survival of the nuclei is lowered and these can begin to grow much faster than they are destroyed. According to von Weimarn [1] the speed with which the nuclei are formed v1 depends on the supersaturation concentration Csupersaturation, and Csaturation concentration: v1 

Csupersaturation  Csaturation Psupersaturation  Psaturation  Csaturation Psaturation

(12.2)

in which case obviously, the speed with which nuclei are formed due to fluctuations is higher when the supersaturation concentration is higher, and the solubility is lower. The Csupersaturation  Csaturation is also called the condensation pressure. Same phenomena apply to the condensation of water vapors whereas the supersaturation must be several times that of the equilibrium vapor pressure so that this occurs spontaneously. Supercooling of water must be done down to 39°C for the perfectly pure water to freeze spontaneously. Crystallization, condensation, and all other phase transformations begin from the bulk of the phase and take place by the above-described mechanism. Phenomena that begin from the surface, such as the melting of ice do not need nucleation centers due to the inherent nature of the surface. A colloidal system can be obtained by condensation of the products resulting from a variety of chemical reactions in a certain domain of reagent concentration, mixing in a specific order, and respecting the reaction conditions. Colloids from double exchange reactions: for example, the AgI colloid can result from the following reaction: AgNO3 + KI > AgI + KNO3 only if either reagent AgNO3 or KI is present in excess; the excess of electrolyte ensures that the particles are stabilized by repulsive forces due to the formation of the electric double layer on the surface of the particles. When, for example, AgNO3 is in excess then on the surface of the formed AgI nuclei n Ag+ will be adsorbed and will give the overall positive charge to the particle and it is the potential determining ion. This happens according to Fajans-Paneth’s “precipitation and adsorption rule,” which states that “the adsorption of a particular ion by an ionic lattice (here AgI nuclei) is favored when it forms a compound with the oppositely charged component of the lattice which is of low solubility” [2]. On the particle nucleus mAgInAg+, a certain amount (n x) of counterions of NO 3 will also adsorb with it, forming the colloidal particle. By convention, the resulting positively charged colloidal particle will be written x+ using the following notation: [mAgInAg+(n  x)NO 3 ] . The system formed between the colloidal particle and the diffuse layer of counterions, the remaining mobile xNO 3 is called a micelle and can be written following the notation: x+  0 {[mAgInAg+(n  x) NO 3 ] xNO3 } . On the other hand, when KI is in excess then the nucleus formed from m molecules of AgI will adsorb nI ions and this will be negatively charged, as this will be now the charge-determining ion. In this case, the formula for the micelle is given by the following formula: {[mAgInI(n x) K+]x+x K+}0. Noteworthy is the fact that stable colloids are obtained in the presence of excess electrolyte or excess of one of the reagents, the excess, however, should not be too large otherwise these lead to charge screening and thus destabilization of the colloid. Hydrolysis reaction and formation of metal hydroxide colloids: for example, the hydrolysis of FeCl3 in water: FeCl3 + 3H2 O > FeðOHÞ3 + 3HCl if FeCl3 is added in slight excess then there will be preferential adsorption of the Fe3+ ions and the particles will be positively charged, {[mFe(OH)3nFe3+ 3(n  x) Cl]3x+3x Cl}0. If instead there is a slight excess of HCl, this can react with Fe(OH)3 and FeOCl is produced and it is believed to play the role in the stabilization of the particle, due to its

12.4 Chemical synthesis of lyophobic colloids

213

ionization, such that in the end the formula of the micelle is {[mFe(OH)3nFeO+(n  x) Cl]x+xCl}0. But this colloid can also be stabilized directly by HCl when used in excess, leading to a stable micelle {[mFe(OH)3nH+(n  x) Cl]x+x Cl}0.

Numerical example 12.2 10 mL of 0.04 N of FeCl3 solution are added to 10 mL of 0.07 N K4[Fe(CN)6] solution to obtain Prussian blue sol/colloid. Establish the potential determining ion and write the formula for particle seed, particle nucleus, colloid particle, and sol micelle.

Solution The equation for the Prussian blue formation is



 4FeCl3 + 3K4 FeðCNÞ6 ! Fe4 FeðCNÞ6 3 + 12KCl

From the available concentrations we have in this reaction 10  103  0.04 ¼ 0.4  103 mol equivalents FeCl3 reacting with 10  103  0.07 ¼ 0.7  103 mol equivalents (K4[Fe(CN)6]). Because the K4[Fe(CN)6] is in excess and functions as a stabilizer for the Fe4[Fe(CN)6]3 particle core/seed; according to the Fajans-Paneth adsorption rule the [Fe(CN)6]4 will adsorb on the particle core and thus determine the negative charge of the nucleus, i.e., potential determining ion. Some of the K+ will next adsorb on the particle nucleus and form the colloid particle or sol. The rest of the K+ counterions will form the diffusive layer, which together with the colloid particle form the sol micelle. The formula of the Prussian blue colloid micelle in this case is

nh

i
 i
4 mFe4 FeðCNÞ6 3 n FeðCNÞ6 4ðn  xÞK + 4x 4  K + g0

particle core potential determining ion particle nucleus colloid particle

adsorptive layer diffuse layer

micelle

Metallic sols from the reduction of their salts: Metallic sols can be obtained from the reduction reaction of the metallic salts. For example, the Au sol can be obtained by the reduction of the AuCl3 or the hot solution of [AuCl4] H+ with a reducing agent under rapid stirring. This causes Au3+ ions to be reduced to neutral gold atoms. The neutral gold atoms continue to form and with the increase in concentration the solution becomes supersaturated with gold atoms, and subnanometer Au nuclei start forming. Additional gold atoms attach on the nuclei, which continue to grow into nanometer-sized particle. Stirring and agitation will ensure a good gold atom diffusion and are an important factor in obtaining a narrow distribution of nanoparticle sizes. To prevent aggregation of the Au nanoparticles surface stabilizing agents can be added. The obtained particles can be functionalized with various organic ligands to create functionalized and stable gold colloid particles. Colloidal gold has been of considerable interest for the scientific community not only for its unique optic and electronic properties but also for applications such as drug delivery, nanotechnology, materials sciences, biosensors, and electron microscopy whereas gold nanoparticles can be attached to different biological probes. Because of the significant interest in colloidal gold, many other different methods have been discovered and improved over the years. From these it is worth mentioning the Turkevich method in the 1950s with which gold particles of 15–20 nm size distributions can be produced. A small amount of chloroauric acid is reduced with a small amount of citric acid (Ctr-H), whereas this reducing agent also plays the role of stabilizers, or capping agent, {[mAu0nCtr(n  x)H+]x+xH+}. Obviously, the pH greatly affects the colloid stability depending on how this interacts with the functional group of stabilizing ligand, for example, in the case of dCOOH groups on the surface with pKa  3, if the pH drops below this value then the electric double layer stability is affected. The formation and growth mechanism of gold nanoparticles has been recently discussed by Polte [3] and has been hotly debated. Polte et al. [4] argue that unlike the classical theory of the Au nanoparticle formation by citrate reduction, which suggests that the nuclei formed at the initial stage act as seeds for the growth of the particles, their investigations found that the aggregation of the initial Au nuclei is responsible for the Au nanoparticle formation. Therefore in their view the mechanism proceeds as follows “fast initial formation of small nuclei, coalescence of the nuclei into bigger

214

12. Colloids and nanoparticles

particles, slow growth of particles sustained by ongoing reduction of gold precursor, and subsequent fast reduction ending with the complete consumption of the precursor species” [4]. The Brust method was developed in 1990s and it consists of the reduction of the [AuCl4] H+ with NaBH4 in Toluene in the presence of the tetraoctylammonium bromide; in this way nanoparticles as small as 5–6 nm can be produced. The gold colloid can also be obtained by the reduction of Au (III) with Sn(II). Interestingly the color of the Au colloid depends on the particle size due to localized surface plasmon resonance (LSPR). Surface plasmons are collective electron oscillations in metallic nanoparticles that can be excited by light, exhibiting optical resonances in visible or ultraviolet. The resonance frequency is determined by the size, shape, and the nature of the particle. Therefore, due to this effect, the nanoparticles with metallic and metallic alloy composition can appear intensely colored depending on the particle size, surface modifications, and the dielectric constant of the surrounding medium. The fact that the surface plasmon is sensitive to any surface modifications is the base for their use as a colorimetric sensor in the detection of various analytes. For example, metallic nanoparticles can be functionalized with a monoclonal antibody for sensing of disease-related antigens, with mannose for sensing lectin, with amine and amides for sensing changes in anion concentrations, with biotin for sensing streptavidin, etc., or simply for detecting their environment by sensing changes in the dielectric constant of the environment [5]. Also, aggregation of the colloid will lead to the change in color. The color of the gold colloid consisting of 5–10 nm particles is ruby red. If NaCl electrolyte is added in excess this will lead to charge screening of the initial particles, which will aggregate into larger particles and the solution turns to deep blue, characteristic of larger gold particles. It is of technological importance that the nanoparticles in the sols are obtained as monodisperse as possible. This can be achieved by introducing seeds or nuclei prepare a priori into the reaction so that the homogeneous nucleation doesn’t take place but instead growth takes place. This seeding method (Zsigmondy method) [6] is used to make monodisperse metallic sols, such as Au, Ag, etc. For example, such Au nuclei or seeds can be prepared separately by the reduction of the AuCl3 solution by slowly adding phosphorous dissolved in ether. Then the Au seeds can be introduced in a solution of [AuCl4] H+ which is reduced with formaldehyde and because only growth takes place monodisperse Au nanoparticles can be obtained. Peptization (re-dispersion) is another way to produce a colloid by re-dispersion of an aggregated colloid that has not been completely dried. This can be achieved by washing, for example, of a precipitate such as iron hydroxide with an electrolyte solution. In this way, the washing eliminates the cause that leads to aggregation, such as excess electrolyte that produced the compression of the electric double layer. Secondly, the washing with the electrolyte is key to future stabilization of colloid, the key ion will adsorb on the precipitate. For example, peptization of Fe(OH)3 can be achieved in the presence of an electrolyte that contains Fe3+ ion, or AgI in the presence of an electrolyte containing Ag+ ions or I ions as given by Fajans-Paneth’s rule. Purification of colloids plays an important role after synthesis by condensation methods. The first step is the removal of excess electrolyte that can lead to colloid destabilization. The removal of the excess electrolyte can be performed by dialysis. The simplest dialysis apparatus is that proposed by Graham and consists of a container containing the colloid and made from a semipermeable membrane immersed in pure water or solvent; the membrane allows solvent molecules and ions to pass but not the colloid nanoparticles. Due to concentration gradient formed the electrolyte will be slowly removed from the colloid. It is important to note that if the dialysis is performed for too long resulting in the complete removal of the electrolyte the colloid in the absence of charge stabilization will begin to aggregate. For faster removal of the electrolyte electrodialysis can be used, where the action of the current considerably speeds up the process. The electrodialysis cell consists of three compartments in series all communicating through semipermeable membranes; the unpurified colloid is placed in the middle compartment and two electrodes are immersed in the side compartment. Under the action of the current, the electrolyte gradient enhances and thus the ion mobility increases.

12.5 Interfacial forces and stability of lyophobic colloids The stability of colloids of lyophobic colloids in the absence of surfactants is generally interpreted in the light of the DLVO theory. Zeta potential value of the nanoparticles plays an important role in estimating the kinetic stability of colloids. It so follows that in the absence of the surfactant stabilizers the colloid stability can be roughly estimated so that if the double-layer interactions are assumed to be the dominant mechanism for stabilization, a zeta potential value smaller than 30 mV or larger than 30 mV is considered sufficient for good colloid stability (see Table 12.2). Below this range, the colloid will aggregate and precipitate out of the solution. Addition of excess electrolyte will compress the electrical double layer and shorten the Debye length destabilizing the colloid.

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References

TABLE 12.2 Rough guide to colloid stability function of the zeta potential of the constituting particles. Guide to colloid stability

ζ-Zeta potential (mV)

Precipitation

+5 … 5

Agglomeration

10 … 15

Medium stability

16 … 30

Good stability

41 … 60

Excellent stability

61 … 100

12.6 Lyophilic colloids Lyophilic colloids are those that have high affinity to the solvent and exhibit thermodynamic stability. Surfactant micelles are the most typical example of lyophilic colloids that are assemblies of surfactant molecules with a hydrophobic core and a hydrophilic shell. Such colloids are formed spontaneously and are driven by the entropy the system gains by the assembly of the surfactant molecules in such supra-structures as micelles. The interfacial energy between the medium and the surfactant micelles must be ultralow, asymptotically approaching zero, for this to happen. Therefore, surfactants that have strongly polar groups such as the ionic ones are strongly hydrated and the interfacial energy between the water phase and the micelle is vanishingly small. There is critical interfacial energy above which the spontaneous formation of thermodynamically stable lyophilic colloids is not possible [7]: γ  γ cr ¼

β kT d2

(12.3)

where β is the natural logarithm function of the ratio of the number of molecules in the dispersion medium N1 to the 1 number of molecules in the dispersed colloidal particles N2, i.e., ln N N2 , and d is the diameter of the structure. Because γ cr depends on the d, the spontaneous formation of the large lyophilic colloidal systems is only possible when the latter is small. For example, for a micelle of a diameter of 10 nm the γ cr must be very small, about 0.4 mJ/m2 for β ¼ 10, i.e., number of molecules in the medium is larger than in the colloid (for kT ¼ 4.11  1021 J at 298 K) and hundred times lower, 0.004 mJ/m2, than the latter value when the micellar diameter is 100 nm. Therefore, micelles are generally small structures consisting of several tens of surfactant molecules.

References [1] P.P. von Weimarn, The precipitation laws. Chem. Rev. 2 (1925) 217–242, https://doi.org/10.1021/cr60006a002. [2] R. Spence, Coprecipitation and adsorption rules. Proc. Soc. Anal. Chem. 9 (1972) 264–266, https://doi.org/10.1039/SA9720900264. [3] J. Polte, Fundamental growth principles of colloidal metal nanoparticles—a new perspective. CrystEngComm 17 (2015) 6809–6830, https://doi. org/10.1039/C5CE01014D. [4] J. Polte, T.T. Ahner, F. Delissen, S. Sokolov, F. Emmerling, A.F. Th€ unemann, R. Kraehnert, Mechanism of gold nanoparticle formation in the classical citrate synthesis method derived from coupled in situ XANES and SAXS evaluation. J. Am. Chem. Soc. 132 (2010) 1296–1301, https://doi.org/10.1021/ja906506j. [5] E. Hutter, J.H. Fendler, Exploitation of localized surface plasmon resonance. Adv. Mater. 16 (2004) 1685–1706, https://doi.org/10.1002/ adma.200400271. [6] R. Zsigmondy, The Chemistry of Colloids, first ed., John Wiley & Sons, Inc., London, 1917 [7] E.D. Shchukin, A.V. Pertsov, E.A. Amelina, A.S. Zelenev, Colloid and Surface Chemistry, first ed., Elsevier Science B.V, Amsterdam, 2001.

C H A P T E R

13 Role of interfaces in the synthesis of polymeric nanoparticles and nanostructured materials The phenomena taking place at the interface play a key role in the synthesis of polymeric nanoparticles, and surface nanostructured materials. It is, therefore, of practical interest to study these interfacial phenomena. In the first part of the chapter, the role of interfacial phenomena in emulsion polymerization is particularly underlined and brought into focus, more so than any other physicochemical aspects pertaining to the nature of the monomer, initiator, polymerization conditions, and reaction mechanisms. In the second part, Pickering emulsion polymerization is mentioned as a potential method to produce materials with nanostructured and self-organized surface structures.

13.1 Case study: Synthesis of polymeric nanoparticles via emulsion polymerization Emulsion radical polymerization is the most important method for producing polymer particle dispersions on industrial scale; the estimated worldwide production in the early 2000s is of 15 million metric tons particle dispersions and 7.5 million metric tons of dry polymer particles [1]. Currently, emulsion polymerization is performed in a large variety of different polymerization conditions, recipes, technical procedures, and chemical engineering processes, adapted to fulfill the goals in terms of production volumes and particle properties. The fundamental aspects are, however, common to all and the fundamental knowledge is prerequisite for the improvement in the existing methods, recipes, procedures, etc., and the development of future ones. In emulsion preparation, surfactant is added to lower the oil and water interface tension. Surfactant differs in their effectiveness to reduce the interfacial tension of an oil and water system. Their effectiveness depends on a variety of factors such as: oil polarity, oil solubility, ionic strength of the aqueous phase, addition of cosurfactant and cosolvents, temperature, desorption energy, and surfactant’s chemical structure and concentration. In preparing emulsions, many recipes are established empirically. Depending on the interfacial tension and the level of shear force applied emulsions with different droplet sizes can be prepared. Emulsions can be divided into two main categories: oil-in-water (o/w) with the oil being the dispersed phase and in water-in-oil (w/o) with water being the dispersed phase. The emulsions can be classified function of the droplet size such that classic emulsions have 0.5–100 μm droplet size diameters, miniemulsions 50–500 nm, and microemulsions (sometimes referred to as nanoemulsions) that have 5–50 nm droplets sizes. The first two types of emulsions have kinetic stability but are thermodynamically unstable, require external energy input in the form of mechanic shear for their preparation; the interfacial tension between oil and water is low but not negligible. The last type of emulsion is thermodynamically stable and form spontaneously, possessing a close to zero interfacial energy. In addition to the mentioned emulsion types, multiple emulsions (w/o/w or o/w/o) and high-internal phase emulsions can be obtained, but due to their particular conditions of formation are not widely used in the synthesis of nanoparticles and, therefore, will not be treated in the current work. The effective value of the interfacial tension that can be obtained between water and oil in an emulsion has a profound influence on the reaction mechanism of emulsion polymerization and the properties of nanoparticles synthesized.

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00017-X

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Numerical example 13.1 Emulsion formation requires external energy sufficient to deform and break an initially large oil droplet into smaller and smaller droplets. To break the oil droplet, the external energy input must create a pressure gradient on the scale of 2R (R is the droplet radius) that exceeds the Laplace pressure in the droplet in order to deform it or break it. Calculate the Laplace pressure of: (a) an oil droplet with R ¼ 1 mm, γ oil/water ¼ 60 mN/m and (b) an oil droplet of R ¼ 200 nm, γ oil/water ¼ 10 mN/m. Comment on the magnitude of pressure gradient one needs to generate at such small length scales, comparable to 2R.

Answer (a) Using the Laplace pressure formula and assuming that the oil droplet is spherical ΔP ¼ 120 Pa, pressure gradient to break the 2R ¼ 2 mm droplet must exceed the value of 6  104 Pa/m. (b) ΔP ¼ 105 Pa, the minimum pressure gradient necessary to break the droplet must exceed the threshold value of 2.5  1011 Pa/m. The pressure gradient in the troposphere is typically of the order of 9 Pa/m. The calculated pressure gradient produced by a high-pressure homogenizer, a device typically employed in emulsion preparation is roughly on the order of 1012 Pa/m [2]. The measured pressure gradient within a collapsing bubble due to acoustic cavitation in water is around 4  10+14 Pa/m [3]. Both methods, ultrasonication with a sonotrode (ultrasonic horn) and high-pressure homogenizer are commonly used in emulsification.

Numerical example 13.2 Calculate the minimum energy needed to create an emulsion with 1-mm droplet radius and the volume fraction of oil is Φ ¼ 0.1 and γ oil/water ¼ 10 mN/m.

Answer Calculate the surface specific area A (m2/m3) ¼ 3  105 m1, and the free energy needed to create this surface is A  γ ¼ 3 kJ.

13.1.1 Emulsion polymerization in the presence of surfactants The simplest emulsion comprises several ingredients: monomer immiscible with water capable of radical polymerization, water, surfactant (emulsifier), and water-soluble initiator. First, the o/w emulsion of the monomer in water is prepared with the aid of surfactant. In emulsions, the monomer droplets obtained are in size the range of 0.5–100 μm, depending on the interfacial tension. The size of the droplets decreases with the increase in the concentration of surfactants. The surfactant concentration used in emulsion polymerization is typically several times above the CMC value. In addition to the created oil droplets, a significant number of monomer-swollen micelles are also present in the system, with diameters in the range of 5–10 nm. Also, depending on the solubility of the monomer in water, some of the monomer molecules will be roaming freely in the water phase. The polymerization initiation proceeds with the addition of the water-soluble initiator, ammonium peroxydisulfate (APS) or potassium peroxydisulfate K2S2O8 (KPS) to the emulsion. The initiator meets the waterborne monomers and creates free radicals, which grow into oligomers. The hydrophobicity of the oligomers increases, and the hydrophobic interaction is the driving force for the radical oligomers to penetrate the monomer-swollen micelles. According to the micelle nucleation theory of Harkins [4] and Smith and Ewart [5], particle nucleation takes place inside the micelles; micelles are very efficient at capturing the free radical oligomers, due to their high surface area. Typically, the total surface area of the oil emulsion droplets is much smaller than that of micelles present in the system and are, therefore, not as effective at capturing the radicals from the solution as the micelles. In a 1-mL emulsion volume, there are roughly 1013 oil droplets coexisting with roughly 1021 of micelles of 15–20 nm sizes, so it can be concluded that micelles are most effective at capturing the radicals to initiate the polymerization. The oil droplets may become a serious competitors to micelles in capturing the free radicals, in the submicron or nanometer size ranges, such is the case in miniemulsion or microemulsion polymerization [6]. Consequently, the monomer-swollen micelles that have captured an oligomeric radical become the polymerization loci for the genesis of particle nuclei. Nucleation is the stage I of the emulsion polymerization process (Fig. 13.1). The nuclei continue to grow with monomers supplied by the oil emulsion droplet, fulfilling their function as monomer reservoirs. During the growth process, some monomer-swollen micelles that failed to capture a free radical do not become nuclei and disintegrate; the free surfactants adsorb on the increasing area of the

13.1 Case study: Synthesis of polymeric nanoparticles via emulsion polymerization

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FIG. 13.1 Cartoon representing the three stages of the nanoparticle synthesis via emulsion polymerization in the presence of surfactant stabilizers.

nucleated and growing particle, to provide colloid stability in the system. The surfactant can also come from the surface of the oil droplet as they become consumed. It is believed that the particle nucleation stage, stage I, of the emulsion polymerization, ends with the disappearance of all the surfactant micelles from the system. Smith and Ewart [5] derived a scaling relationship between the number of particles N, the surfactant micelle concentration S, and initiator concentration I: N ∝ S3=5  I 2=5

(13.1)

The particle nucleation phase is relatively short but controls the size and size distribution of nanoparticles. Nanoparticles with larger sizes can be produced by decreasing the amount of surfactant in the nucleation stage with a typically narrow size distribution. In other words, because the nucleation period is given by the time taken to complete disappearance of the micelles, a lower surfactant concentration will reduce the nucleation period, will produce lower number of particles with a narrower size distribution. In the synthesis of polystyrene nanoparticles by emulsion polymerization, Tauer et al. [7] have shown that by increasing the SDS concentration from 0.1 to 2.9 and 15 mM they achieved an effective reduction in average size of nanoparticles from 90 to 55 and 4 nm respectively, under the same reaction conditions (where the CMC value for SDS 8 mM). The Smith-Ewart equation (13.1) proved to be an accurate scaling N-Sα relationship for styrene and other water-insoluble polymers. The emulsion polymerization is typically carried at surfactant concentration at several times above the CMC. Tauer et al. [7] show that the surfactant influence

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13. Role of interfaces

is crucial, in the sense that it does not only provide the micelles as loci for nanoparticle nucleation and growth but, surfactants influence the particle nucleation kinetics in several ways: the presence of surfactants in the aqueous phase causes the formation of higher concentration of smaller monomer droplets due to spontaneous or forced emulsification, surfactants lower the interfacial tension of the particle nuclei increasing the rate of nucleation, and facilitate the transfer of monomer into the aqueous phase. Deviations with respect to the power exponents, in the above equations, increase as the monomer solubility increases; the N-Sα relationship is experimentally shown to be rather complicated and α is shown to vary wildly, 0.5–3 [7]. This led some authors [8] to propose the homogeneous nucleation mechanisms for more hydrophilic monomers, such as methyl methacrylate. In the homogeneous nucleation theory, waterborne radical monomers polymerize to form oligomers, which continue to grow to until a critical length is achieved forming a stable primary particle that precipitates or coagulates with a previously formed one [9]. Fitch and Tsai [10, 11] developed a quantitative theory for homogeneous nucleation. A realistic mechanism in emulsion polymerization should account for: (i) the micellar nucleation, (ii) homogeneous nucleation, and (iii) droplet polymerization, which can all take place with different probabilities; typically one of these mechanisms will dominate depending on the emulsion type and experimental conditions. After the completion of stage I, the particle growth, stage II begins (Fig. 13.1). Stage II of the emulsion polymerization is the particle growth process, during which most of the monomer contained in the oil droplets is consumed. The arrival of the monomer from the oil droplets to the growing nuclei takes place via diffusion through solvent. The supply of monomer to the growing particle micelle is assumed to be fast such that the growing particle micelles are always saturated with monomers. The Smith and Ewart [5] kinetic equation for particle growth is.  
 Nmicelles (13.2) Rp ¼ k p M p n NA Rp is the rate of polymerization, kp is the propagation rate constant, [Mp] is the concentration of monomer in the micelle particles, n is the average number of free radicals per micelle (where after Smith and Ewart the most probable value of n is 0.5), Nmicelles is the number of micelles in the system per cm3, and NA is Avogadro number. Although, the Harkins [4] micellar nucleation hypothesis and Smith and Ewart [5] micelle nucleation kinetics make several simplifying assumptions, which were challenged by Roe [8], the theory remains standing as being most likely scenario of particle formation in radical emulsion polymerization. The above kinetic equation has been successfully applied to explain the formation of particles from relatively insoluble monomers such as styrene and butadiene. The rate of polymerization during the stage II is assumed constant. Role of interfacial tension in particle growth stage: In the stage II of the Smith-Ewart model, the growth of latex particles is controlled by the concentration of monomer in polymer particles, and the number of free radicals per particle. During stage II, the nanoparticles absorb monomers present in the aqueous phase, which then polymerize and lead to particle growth. The particle imbibition of monomer intake is about its own weight [12]. Experimental studies show that, keeping the surface of the growing particles saturated with a layer of surfactant during stage II, will effectively double the intake of monomer, when compared to an nonsaturated surface [12]. It has been proposed that for noncrosslinked particles (no elastic stress), the only force opposing swelling is the interfacial tension. Morton et al. [12] deduced that when the swollen particle monomer is at equilibrium with the aqueous phase, then the free energy is given by the expression: ΔGm, p ¼ ΔGm + ΔGt

(13.3)

where ΔGm,p is the partial molar free energy of the monomer in the polymer particle relative to the free energy in a droplet in the water, ΔGm is the free energy of mixing the monomer with the polymer, and ΔGt is the interfacial free energy of the interface of the swollen particle with the water phase. The ΔGt term has a positive contribution to the overall term as it opposes swelling, while the ΔGm term has typically a negative contribution as the transfer of a hydrophobic monomer from the water phase into the interior of the particle is thermodynamically favored. ΔGm can be evaluated from the Flory-Huggins expression [12, 13] and ΔGt can be evaluated from the increase in the surface area of a particle by dA, which at equilibrium, Eq. (13.3), results in the following expression: h   i 2Vm ¼  ln 1  ϕp + ϕp + χϕ2p (13.4) γ RTr where Φp is the volume fraction of the polymer in the swollen particle, Vm is the molar volume of the solvent, γ is the interfacial energy between the polymer particles and aqueous solvent at swelling equilibrium, χ is the Flory-Huggins polymer-solvent interaction parameter, and r is the radius of the particle at swelling equilibrium. Eq. (13.4) shows that

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the monomer imbibition equilibrium in the particles is a direct function of the particle size and an inverse function of the interfacial energy [14]. For the same monomer for which χ is constant, the above equation predicts that by reducing the interfacial tension, or increasing the size of the particle, the equilibrium shifts such that a larger amount of monomer (or swelling agent) imbibition in the particle is expected. For different monomers and swelling agents, χ varies. To understand how χ and γ evolve for different swelling agents, the above equation can be rearranged into the new form:   ln 1  ϕp + ϕp 2Vm ¼χ +γ (13.5)  2 ϕp RTrϕ2p By making a series of experimental determinations of the polymer fraction in swollen particles, Morton et al. [12] found a linear dependence from which by extrapolation they have determined the χ from the intercept and the γ from the slope of the above equation. The authors studied the imbibition of polystyrene latex particles with styrene, toluene, and chlorocyclohexane. Their findings indicate that χ evolves as expected from best to the worst swelling agent in the series styrene (χ ¼ 0.43) < toluene (χ ¼ 0.48) < chlorocyclohexane (χ ¼ 0.53), while the interfacial energy of swollen PS particles with the corresponding monomer exhibits an opposite trend PS-Sty (γ ¼ 4.5 mN/m) > PS-toluene (γ ¼ 3.5 mN/m) > PS-chlorocyclohexane (γ ¼ 2.1 mN/m). It seems that the poorest imbibition solvent is accompanied by the lowest interfacial energy. However, when equating in the size of the nanoparticle R, the interdependence between three variables χ, γ, and R becomes more complex. Due to the lowest interfacial tension exhibited by the poorest solvent, chlorocyclohexane, it exerts a greater imbibition effect on smallest particles, than styrene [12]. For the largest particles, the smaller surface-tovolume ratio decreases the effect of surface energy and styrene shows the highest swelling volume, thus balancing the opposing effects of the χ and γ. The experimental data of Morton et al. [12] show that a better solvent shows a higher interfacial energy and the increase in swelling is not obtained in the case of smaller particles, where the increase in interfacial energy overrides the increase in solvency effect. Emulsion polymerization enters stage III (Fig. 13.1) when all the oil droplets, monomer reservoirs, have been consumed, and the polymerization effectively enters into starvation. In this stage, the rate of polymerization slows down to zero. 13.1.1.1 Surfactant-free emulsion polymerization Alternatively, the emulsion polymerization reaction can be carried in the absence of surfactants. In the absence of surfactants, transient coarse emulsions are obtained under stirring conditions during the reaction. Because surfactants are relatively difficult to completely remove from the surface of nanoparticles obtained in standard emulsion polymerization, surfactant-free emulsions polymerization is an important route for obtaining surfactant-free polymeric nanoparticles. Mechanistically the surfactant-free emulsion polymerization of monomer, initiated by a water-soluble ionic initiator, proceeds via homogeneous nucleation of the waterborne monomers. In this case, stage I of nucleation becomes mechanistically more complicated due to flocculation of nuclei and particles with the net effect of the reduction in the number of obtained particles. Tauer et al. [15] studied the effect of the emulsion polymerization of styrene in surfactant-free conditions and KPS as initiator. Their findings show that in the nucleation stage the number of nuclei formed jumped within a second to 2  1013 cm3 with an average diameter of 13 nm and particles consisted of more than one chain suggesting that the mechanism proceeds via a homogeneous nucleation and nuclei aggregation path [15–17]. One might expect that in the absence of surfactants the aggregation, collapse, and coagulation may lead to complete destruction of the forming colloids. However, in the words of Tauer et al. [15] “surfactant-free emulsion polymerization of hydrophobic monomers with hydrophilic initiators are nice examples of self-regulating systems with respect to colloidal stability.” While in the presence of surfactants, the particle stabilization against aggregation could be steric or electrostatic, in the case of surfactant-free emulsion polymerization the particle stabilization is purely electrostatic involving to a lesser extent hydration repulsion force. The ▬OSO3  functional groups generated by the KPS initiator become integrated with the surface of the synthesized particles [18] and play a significant role in the electrostatic stabilization of nanoparticles against aggregation. The primary radical attack of the initiator on styrene leads to the in situ stabilizer formation producing interfacially active oligomers R  OSO3  . The sulfate groups can be found at the nanoparticle surface due to polymer chain reorientation at the particle-water interface. In addition to the sulfate groups, dCOOH, dC]O, and dOH groups are typically detected at the surface of the nanoparticles [15, 18]. These polar groups also play a significant role in particle stabilization. The carboxyl and hydroxyl groups are the result of

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secondary reactions in the system. The reaction of the initiator with the monomer is estimated to be only around 30% of the total amount of the added initiator. The initiator also reacts with water and other organic components added in the recipe. The dOH formation is believed to be a result of the initiator reaction with water to form a hydroxyl radical, which then attacks a vinyl monomer. The dCOOH end group formation is believed to be a result of the reaction of a carbon radical with water leading to a HO• radical and formation of hydrogen peroxide; subsequently the hydrogen peroxide oxidizes a hydroxyl end group to form carbonyl and carboxyl groups [7, 15, 19, 20]. Tauer et al. [15] have studied the effect of the initiator type on the nature of the functional groups generated on the surface of the particles, and found that, a cationic radical initiator 2,20 -azobis (2-amidinopropane) dihydrochloride (V50) will generate residual cationic functional groups in addition to the hydroxyl and carboxyl groups, which are typical generated by anionic initiator KPS [15]. Therefore, different initiators can lead to different primary end groups resulting from the initiator but common to all are the dOH, dC]O, and dCOOH end groups resulting from the secondary reactions. Evidence suggests that the latex particles prepared with hydrophilic KPS initiator are typically more polar than those prepared with the hydrophobic azobisisobutyronitrile (AIBN) initiator [21]. The surfactant-free emulsion polymerization of the more hydrophilic MMA monomer was also investigated and the findings were similar, the nucleation stage takes place from the waterborne monomers [22]. The concentration of the KPS initiator in solution has both a stabilizing the effect and a destabilizing effect on the colloidal particles. The stabilizing effect, especially at low concentration, is due to the formation of sulfate end groups on the polymer, providing electrostatic stability to PMMA nanoparticles. The destabilizing effect comes into effect at higher concentrations, the compression of the electric double layer can lead to the aggregation of colloidal particles [22, 23]. An interesting experiment carried out by Wang et al. [24] in the absence of surfactants but in the presence of nanoparticle clusters, resulted in orbital-like nanoparticles. The interior of the clustered offered a hydrophobic environment for the absorption of monomer and nucleation locus, just as in the case of micelles. This shows that any hydrophobic cavity present in the aqueous system and accessible to hydrophobic monomer by diffusion will become a nucleation locus for the polymer particle.

Numerical example 13.3 How to determine the saturation concentration of the surface of the latex nanoparticles dispersed in aqueous solution by a surfactant?

Answer By measuring the surface tension of the solution and determine the offset CMC value of the surfactant in the latex solution; fully covered latex particles would allow the surfactant to form micelles in the water phase. These experiments are also known as the titration of the latex with the surfactant.

Numerical example 13.4 Consider an original latex of PS nanoparticles, containing 3 g/L SDS (10.4 mM) and with a measured surface tension of 56.8 mN/m. The titration curve, the surface tension vs. the concentration of SDS added, will exhibit a CMC-like kink [25] registered at a surfactant concentration of 36.5 mM. (A) Calculate the concentration of SDS surfactant needed to fully saturate the PS nanoparticle surface, knowing that the CMC value of the pure SDS solution is 8.2 mM. (B) What was the initial percentual surface coverage of the PS NPs by SDS?

Answer (A) Subtracting the CMC of a pure SDS solution from the CMC-like kink determined in the PS latex solution, the full particle coverage is obtained at an SDS concentration of 28.3 mM. Therefore, the initial percentual coverage of the latex surface by SDS was (10.4 mM/28.3 mM)  100 ¼ 36.74% (B). (C) The surface area of a particle with 138 nm diameter is 59,828 nm2.

13.1.1.2 Emulsion polymerization with polymerizable surfactants—Synthesis of surfactant-free nanoparticles Surfactant-free nanoparticles are important for fundamental studies of nanoparticles such as interfacial adsorption [26], emulsification [27], self-assembly [28], etc. Surfactants are generally exceedingly difficult to remove from nanoparticles prepared via emulsion polymerization methods. Therefore, methods have been devised to directly synthesize

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223

surfactant-free nanoparticles. Surfactants are used in emulsion polymerization for two main purposes: control of the particle size and the stability of the latex. Therefore, one of the most feasible methods and least interfering with the emulsion polymerization mechanism to prepare surfactant-free nanoparticles is to employ reactive polymerizable surfactants. They are known under the names INISURFS if they are used to initiate the reaction, SURFMERS when they act as comonomers, or TRANSURFS if they act as transfer agents in the controlled polymerization reactions [29]. PseudoSURFMERS such as methacrylic acid, methacrylamide, 2-sulfoethylmethacrylate, p-vinyl benzene sulfonate, etc. have also been used in obtaining surfactant-free nanoparticles. SEM images of polystyrene nanoparticles with an average diameter of 180 nm obtained with sodium p-vinyl benzene sulfonate (NaVBS) are shown in Fig. 13.2. Interfacial tension measurement of the final latex particles is a clear indication of the consumption of the SURFMERS in the reactions. SURMFER concentration of six times the CMC value used in the emulsification is completely consumed in the latex. Depending on their reactivity, the surfmers could be integrated into the core of the particle if they polymerize very fast, copolymerized if their reactivity is comparable to that of the monomer, or in the outer shell if their reactivity is slower than that of the monomer.

13.1.2 Miniemulsion polymerization The o/w miniemulsions consist of oil droplet sizes ranging from 50 to 500 nm; achieving such a large surface area requires high concentration of surfactant for stabilization. Miniemulsions do not form spontaneously and require for preparation mechanical energy input obtained with a high-power sonotrode or high-pressure homogenizer. In miniemulsion polymerization, a surfactant/co-stabilizer system is needed to retard the monomer diffusion out of the submicron droplets. The co-stabilizer for o/w miniemulsions should be highly soluble in the monomer phase and insoluble in the aqueous phase. The purpose of co-stabilizer is twofold: (i) to prevent Ostwald ripening responsible for the growth of the larger droplets at the expense of smaller droplets and (ii) to suppress the micellar or homogeneous nucleation. Ugelstad et al. [9] used hexadecanol or hexadecane as co-stabilizers, in the polymerization of styrene droplets, which both have a very low solubility in water. The surfactants are needed to prevent the droplet coalescence settling or creaming. The typical surfactants used are the anionic ones such as sodium dodecyl sulfonate (SDS) [30], but the cationic types such as cetyltrimethylammonium bromide (CTAB), alkylated polyethylene oxide surfactants [25], or SURFMERS such as sodium vinylbenzyl sulfosuccinic acid [31] have also been used in the miniemulsion generation and polymerization of styrene. After emulsion preparation, aqueous initiator is added, and the emulsion is heated at typically 70°C. If instead hydrophobic water-insoluble initiator AIBN is used, then this is added in the monomer before ultrasonication and the emulsion preparation is maintained cool to preventing the heating and triggering of the initiator during the process. In macroemulsion polymerization, the micellar and homogeneous nucleation dominate in stage I, polymerization of monomer droplet has been neglected in emulsion polymerization. In miniemulsion polymerization, the size of monomer oil droplets becomes sufficiently small [9], to become a serious competitor to micelles for radical capturing. In this way, some of the polymerization loci move into the monomer oil droplet and some remain in the micelles. In this case, typically a bimodal distribution in particle sizes resulting from micelle polymerization and oil-monomer droplet

FIG. 13.2 SEM of polystyrene (PS) nanoparticles synthesized in surfactant-free conditions using the sodium vinylbenzene sulfonate (NaVBS) pseudo-SURFMER (200 mg), APS (135 mg), Sty/DVB (27 mL) in H2O/CH3OH l (v/v ¼ 9/1) (200 mL). The average diameter of the particles 180 nm. Modified from D. Wu, J.W. Chew, A. Honciuc, Polarity reversal in homologous series of surfactant-free Janus nanoparticles: toward the next generation of amphiphiles, Langmuir 32 (2016) 6376–6386.

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polymerization will be obtained. If the monomer diffusion of the monomer is inhibited by the appropriate choice of a co-stabilizer, then monomer oil droplet nucleation becomes predominant. When the experimental conditions are perfectly tuned such that the monomer oil droplet becomes the main nucleation site, and the competing micellar and homogeneous nucleation are suppressed, a roughly 1:1 correspondence between the initial monomer droplet and final polymer particles can be obtained [9]. Therefore, the final particle size is given by the initial droplet size. The great advantage of the miniemulsion polymerization over the emulsion polymerization is that hydrophobic molecules, such as ligands, monomers, fluorescent dyes, etc., can be included in the initial oil droplet, which makes the preparation of functionalized and ligand imprinted nanoparticle possible.

13.1.3 Microemulsion polymerization Microemulsions, which are also called nanoemulsions, ultrafine emulsions or submicron emulsions, from monomers in water have been used in the synthesis of nanoparticles [32–34]. In contrast to miniemulsions, microemulsions are thermodynamically stable. In microemulsions, the oil/water interfacial tension is practically zero or extremely low. Therefore, the microemulsions form spontaneously or by a very gentle agitation and the oil-water interface has a low curvature [35–39]. They appear translucent, often bluish, unlike the milky white and opaque appearance of mini and macroemulsions. The microemulsions consist of droplet sizes between 5 and 50 nm and due to the large surface area of the system they are very efficient for capturing radicals. The main strategy in preparing microemulsions is the use of a surfactant/cosurfactant couple. The cosurfactant is chosen such that it can partition between the oil and the water phase, meaning that it exhibits some solubility in both phases. In contrast, the surfactant typically adsorbs only at the oil-water interface building a monolayer. Because very few surfactants alone can form microemulsions, an alkyl alcohol is added as a cosurfactant. For example, SDS cannot form alone microemulsions of styrene and water, therefore, 1-pentanol is added; this microemulsions can be polymerized to generate PS nanoparticles. Guo et al. [40] prepared styrene microemulsion in water using the SDS 9.05 wt%, styrene 4.85 wt%, and 1-pentanol 3.85 wt% in water. However, having an additional component in the system consisting of water monomer and surfactant can complicate the fundamental studies on the nanoparticle formation kinetics and properties [34]. It is sometimes preferred to use nanoparticle synthesis recipes containing as few components as possible, for a better control on the resulting particle characteristic and surface properties. Therefore, efforts have been dedicated to design surfactants capable of creating stable microemulsions without cosurfactants. The types of surfactants used for the formulation of microemulsions have been reviewed [32]. Most emulsions described in literature are based on the cationic dodecyltrimethylammonium bromide (DTAB), cetyltrimethylammonium bromide (CTAB), the anionic bis(2-ethylhexyl) sulfosuccinate also known as Aerosol-OT or AOT, and some nonionic surfactants such as polyethoxylated alkyls (PEO-alkyl). One strategy to make nonionic PEO-alkyl surfactants appropriate for making microemulsions is to include a polypropyleneoxide (PPO) block in between the very hydrophilic PEO-block and the very hydrophobic alkyl chain, called lipophilic and hydrophilic “linker effect” [41]. In the case of the microemulsion polymerization, to minimize the homogeneous nucleation, it could be advantageous that the initiation is done with monomer-soluble and water-insoluble initiators such as 2-20 -azobis-(2-methyl butyronitrile) or azobisisobutyronitrile (AIBN) rather than with the water-soluble KPS [40].

13.1.4 Ultrasonic-assisted surfactant-free emulsion polymerization The acoustic cavitation in water can produce bubbles with a lifetime of few microseconds, which upon collapse generate high shear forces and local hot spots that can have temperatures of 5000°C and pressures of 500 atm; sonochemistry is a well-established field in the synthesis of nanomaterials [42–44]. The local shear and heating produced by the acoustic cavitation phenomenon in water can be employed in the preparation of surfactant-free polymer nanoparticles [43–49]. Why surfactant free? Because the emulsification of a monomer demands a considerable amount of surfactant, which is a major drawback for several reasons: the produced particles are covered in surfactant, surfactants have a negative impact on the environment, surfactants can be detrimental to the surface properties of the particles, surfactants may interfere with the toxicological evaluation of nanoparticles for medical applications, etc. [50–52]. Surfactants are difficult to completely remove from the surface of the obtained nanoparticles by standard methods, i.e., centrifugation, dialysis, etc. [50, 53–57] and their removal is time consuming. Ultrasonic radiation produced by a highpower sonotrode allows for the preparation of emulsions without the need for surfactants and provides heat to drive the polymerization reaction [45]. The size of the emulsion droplets obtained depends on the sonication time, the size of the droplet decreases with the sonication time to a certain plateau value Figs. 13.3 and 13.4A in the nanometer range.

FIG. 13.3 Photographs (left) and droplet size distribution (right; diameter, nm) of the emulsions produced overtime upon acoustic treatment of an aqueous solution (35 mL) containing styrene/and divinylbenzene (200 μL) v/v ¼ 5/95. Notice the change in the appearance of the emulsion from slightly milky (dilute emulsion) to transparent as the size of the monomer droplet decreases. From M.D. Tzirakis, R. Zambail, Y.Z. Tan, J.W. Chew, C. Adlhart, A. Honciuc, Surfactant-free synthesis of sub-100 nm poly(styrene-co-divinylbenzene) nanoparticles by one-step ultrasonic assisted emulsification/polymerization, RSC Adv. 5 (2015) 103218–103228. https://doi.org/10.1039/C5RA23840D with permission from The Royal Chemical Society.

FIG. 13.4 (A) Mean droplet size of the emulsion produced after acoustic treatment of two different St/DVB (1:1, v/v) monomer concentrations (empty squares) 5.7  103 L/L and (full squares) 8.6  103 L/L with acoustic treatment time. (B) SEM images and corresponding particle size histograms of P(St/DVB) NPs prepared via acoustic emulsification/polymerization St/DVB monomer, 5.7  103 L/L in UPW for 60 min, at volumetric St:DVB ratios: 70:30. (C) Monomer/water interfacial tension values (empty circles) and the corresponding size (filled squares) of the final P(St/DVB) NPs, in the absence and in the presence of stabilizers (the trend line was added as guide to the eye). Modified from M.D. Tzirakis, R. Zambail, Y.Z. Tan, J.W. Chew, C. Adlhart, A. Honciuc, Surfactant-free synthesis of sub-100 nm poly(styrene-co-divinylbenzene) nanoparticles by one-step ultrasonic assisted emulsification/polymerization, RSC Adv. 5 (2015) 103218–103228. https://doi.org/10.1039/C5RA23840D with permission from The Royal Society of Chemistry.

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The maximum diameter of the emulsion droplet that can be prepared with ultrasonic radiation is given by the Kolmogorov scale, the size of the smallest eddies created in turbulent flow, which depends on the interfacial tension between oil-water [45] and the total ultrasonic power dissipated per volume of liquid in the unit of time: dmax  C  ε2=5  γ 3=5  ρ1=5

(13.6)

where ε is the total energy dissipated per unit volume of liquid and unit of time, γ is the interfacial tension, ρ is the density of a continuous phase, and C is a constant typically of the order of unity [58]. Tzirakis et al. [45] exploited the potential of the ultrasonic emulsification technique in the preparation of surfactantfree poly(styrene-co-divinylbenzene) [P(St/DVB)] nanoparticles, shown in Fig. 13.4B. The local energy produced in water by cavitation was sufficient to generate and stabilize the monomer into an o/w emulsion containing nanosized droplets. The emulsion droplet size generated depended on several variables: the dispersed phase volume, interfacial tension of the monomer with water, and the ultrasonication time (Fig. 13.4A). The cavitation produced by the ultrasonic radiation produced heat that drove the polymerization reaction and the nanoparticles obtained and their average size distribution is given in Fig. 13.4B. The authors concluded that the size of the [P(St/DVB)] nanoparticles obtained depends: (i) inversely on the monomer/water interfacial energy and emulsification power and (ii) directly on temperature, amount of initiator, and monomer solubility. The mechanism of homogeneous nucleation and nuclei coagulation was operating in this case. In fact, the irregular shapes of the obtained nanoparticles as well as their broad size distributions, observed in Fig. 13.4B, are an indication of an aggregative mechanism, probably enhanced by high-energy collisions during ultrasonication. Interestingly, the inverse dependence on the size of the [P(St/DVB)] nanoparticle sizes after the polymerization under ultrasonic radiation was observed for emulsions prepared with different Sty/DVB ratios in the absence of stabilizers but also for the emulsions in the presence of different interfacial stabilizers 2-sulfoethyl methacrylate (2-SEM), poly(vinyl alcohol) (PVA), and poly(ethylene glycol) (PEG400); this inverse dependence also supports a homogeneous nucleation mechanism, Fig. 13.4C, as the solubility of monomer in water increases with the decrease in droplet size as given by the Kelvin equation:   2γVm (13.7) SðrÞ ¼ S0  exp rRT where S(r) is the solubility (mol cm3) of a particle of radius r (cm), S0 is the bulk solubility (mol cm3), γ is the interfacial tension (J cm2), Vm is the molar volume of the dispersed phase (cm3), R is the gas constant (8.314 J K1 mol1), and T is the temperature (300 K). When CTAB surfactant was used, at a concentration above its CMC value, although the surface tension decreased, the presence of micelles added a competing micellar nucleation, which leads to smaller particle sizes (Fig. 13.4C).

Numerical example 13.5 Calculate the size droplet of an emulsion of styrene (Sty) and divinylbenzene (DVB) monomer mixture of 0.2 mL in water that can be obtained by ultrasonication for 40 min, when the monomer mixture Sty:DVB is 50:50, 95:5, and 5:95. The acoustic power input is 1440 J m3 s1 and the interfacial tension of the γ Sty-water ¼ 31 mJ/m2 and γ DVB-water ¼ 38 mJ/m2.

Answer The interfacial tension of the monomer mixture with water can be calculated with the formula: γ StyDVB/water ¼ fγ Sty + (1  f)γ DVB, where f is the fraction of the Sty. The result is γ Sty:DVB95:5 ¼ 31.4 mJ/m2, γ Sty:DVB50:50 ¼ 34.5 mJ/m2, and γ Sty:DVB5:95 ¼ 37.7 mJ/m2. The diameters of the emulsion droplet calculated with Eq. (13.6) are 514, 545, and 574 nm corresponding to Sty:DVB 50:50, 95:5, and 5:95, respectively. Note that the size of the particles changes with the variables: sonication time and the volume of the dispersed phase liquid.

13.1.5 Seeded emulsion polymerization for preparation of core-shell and asymmetric Janus nanoparticles Latex nanoparticles in an aqueous colloid can be swollen with another monomer that has a low solubility in water. By adding several droplets of a water-insoluble vinyl-type monomer into an aqueous polymer nanoparticle colloid under vigorous stirring, and after an induction period of several minutes to several hours, the polymerization of the monomer-swollen particle can be initiated. Depending on the polymerization parameters of the monomer-swollen

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latex particle and conditions, a variety of particles of different morphological features, ranging from dumbbell, snowman-type, two-lobe, multilobe, core-shell and inverted core-shell, or void particles [21, 57, 59–69], have been prepared by seeded emulsion polymerization techniques. Seeded emulsion polymerization resembles the emulsion polymerization to the extent that the role played by the swollen micelles is now taken by the seed nanoparticles. The transport of a water-insoluble hydrophobic monomer from an emulsion droplet in the aqueous phase to the hydrophobic interior of a nanoparticle or micelle is thermodynamically favorable. The amount of monomer intake by colloidal polymeric nanoparticles at equilibrium will depend on the particle size and inversely on its interfacial energy as described by the Morton’s equation (13.4). For cross-linked particles, one must also account for the elastic stress of the polymer network. Therefore, the partial free energy of the monomer in the particle polymer network is [70, 71] ΔGm, p ¼ ΔGm + ΔGel + ΔGt where ΔGm,p is relative to the free energy of monomer residing in a droplet in the aqueous phase, ΔGm is the free energy of mixing the monomer with the polymer, ΔGel is the elastic energy resulting from stretching the cross-linked polymer network in the seed particles, and ΔGt is the surface tension of the particle with the aqueous phase. Adding the expression of each term, the above equation takes the following form [60, 70]:  1  h   i 2Vm (13.8) ΔGm,p ¼ RT ln 1  ϕp + ϕp + χϕ2p + RTNVm ϕp3  ϕp =2 + γ r where the meaning of each parameter is the same as in the Morton’s equation. The transport of a hydrophobic monomer from a droplet, in the aqueous phase, into the hydrophobic interior of the nanoparticle is thermodynamically favored, therefore, the partial molar free energy of mixing ΔGm has a negative contribution, promoting the swelling. Because the swelling increases the elastic stress in the particle and the interfacial energy of the particle with increase in its area, ΔGel and ΔGt have a positive contribution to the free energy, restricting the swelling. Sometimes, surfactant is added or a layer of hydrophilic polymer is used to coat the seed nanoparticle to decrease the interfacial energy of the particle to drive swelling [71]. Heating increases the elastic stress and can expel the monomer, due to the contraction of the cross-linked polymer network. The effect of the elastic stress on phase separation was first proven by Sheu et al. [70] using seed polystyrene seed particles with different cross-linking degrees with divinylbenzene (DVB) in the seeded emulsion polymerization of styrene. The authors have shown that the stress is released by expelling of the monomer outside of the seed particle core upon contraction of the polymer network during heating. The relative magnitude of the interfacial energies between the monomer and water and seed nanoparticle and monomer will have a profound impact onto the shape of the particle obtained after the polymerization of a monomer-swollen seed particle. The role of interfacial tension was recognized earlier on by Chen et al. [21, 72] in determining the shape of the particles obtained by seeded emulsion polymerization. Torza and Mason [73] have worked out earlier the theoretical framework determining the equilibrium configuration of two immiscible liquids droplets, denoted by phase 1 and phase 3, insoluble in an environment denoted by phase 3. The geometrical arrangement between the three phases depends exclusively on the relative magnitude of the interfacial energies. There are three possibilities (Fig. 13.5): (1) engulfing when phase 3 completely surrounds phase 1, or vice versa, (2) phase separation with the appearance of a two-lobe droplet, and (3) complete separation with the appearance of two separated droplets from phases 1 and 3 in phase 2. Chen et al. [21, 72] have adapted this model to the case where phase 1 is the seed polymer nanoparticle, as depicted in Fig. 13.5. Responsible for this is the relative magnitude of the interfacial tension vectors, γ 12, γ 23, and γ 13 and the wetting coefficient corresponding to each liquid, S1, S2, and S3 as given in Fig. 13.5. In the initial stages of seeded polymerization, due to heating and expelling of the monomer from the seed, small protrusions appear out of the seed particle. Depending on the wetting conditions, these small protrusions can coalesce forming a larger bulge or a film surrounding the particles (Fig. 13.5). The wetting conditions can be understood by applying Young’s equation for the three-phase system: γ 12 ¼ γ 13 + γ 23 cos θ where θ is the contact angle between the monomer and the seed particle. Rearranging the above equation yields γ  γ 13 θ ¼ cos 1 12 γ 23 The contact angle θ will increase, and the bulge will become more prominent if the difference γ 12 and γ 13 decreases [71]. The polymerization process continues and for the case of partial wetting the protrusion grows into a large lobe by withdrawing the monomer from the seed particle leading to the formation of asymmetric snowman or dumbbell-shaped

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FIG. 13.5 The formation of asymmetric and core-shell particles as a function of the interfacial energy between the three phases: polymer seed nanoparticle (medium 1), monomer (3) in water (3). The corresponding interfacial energies are: γ 12 seed nanoparticle/water, γ 23 water/monomer, γ 13 seed nanoparticle/water, and are depicted by their unit vectors in the cassettes. The relative magnitude of the interfacial tension vectors will determine the sign of spreading coefficients, S1—seed particle, S2—water, and S3—monomer. Spontaneous wetting occurs for S > 0 and partial wetting for S < 0. In addition, the effect of the cross-linking of the seed nanoparticle plays a major role in the formation of multilobe type nanoparticles.

particles, named after the two-faced Roman God Janus [74, 75]. An increasing degree of seed particle cross-linking has been shown by Sheu et al. [70] to increase the phase separation and lead to the formation of anisotropic particles with multilobe architecture (Fig. 13.5). In competition with seeded emulsion nucleation, the homogeneous nucleation can also take place in aqueous environment leading to the formation of spherically homogeneous nanoparticles. The mixture between the anisotropic and homogeneous nanoparticles is not desired as it will be impossible to separate them. Therefore, to prevent the homogeneous nucleation, sodium nitrite as an aqueous phase inhibitor can be added [71]. The field of asymmetric nanoparticle synthesis by seeded emulsion polymerization has exploded in the past two decades into an exceptionally fertile ground for chemistry, materials science, and interfacial science. By varying the polymerization parameters homologous series of JNPs with precisely varying aspect ratio, degree of phase separation and overall surface properties as well the Janus balance or HLB, can be tuned [27, 28, 59, 76, 77]. For example, Kang and Honciuc [77] have produced an array of Janus nanoparticles (JNPs) with varying sizes, aspect ratio, and phase separation degree by seeded emulsion polymerization starting from surfactant-free poly(ter-butyl)acrylate (PtBA) seed nanoparticles and 3-(triethoxysilyl)propyl-methacrylate for the second lobe; the obtained array of JNPs is given in Fig. 13.6 [28, 77].

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FIG. 13.6 Synthesis of PtBA-PTPM JNPs with different geometries. (A) Synthesis of JNPs by seed emulsion polymerization. (B) Summary of JNPs used in the present study, these JNPs vary in the PTPM lobe size, phase separation degree, and overall dimension. (C) SEM images of JNPs in (B). Scale bars 150 nm. Reproduced with permission from C. Kang, A. Honciuc, Influence of geometries on the assembly of snowman-shaped Janus nanoparticles, ACS Nano 12 (2018) 3741–3750. https://doi.org/10.1021/acsnano.8b00960. Copyright 2018 The American Chemical Society.

The JNPs are important precursors for creating self-assembly suprastructures [28], for creating multifunctional nanoparticles by asymmetric chemical modifications [65], and for growing microcolloidal architectures by asymmetric chemical functionalization and controlled radical polymerization techniques [78]. For example, Mihali and Honciuc [79] have shown that JNPs can be made multifunctional by preparing homologous series of four JNPs with different lobe size ratios, whereas one JNP lobe was semiconductive polymer polypyrrole (PPy) and the other lobe was an electrical insulator poly 3-(triethoxysilyl) PTSPM. By tuning the relative size ratio of the PPy and PTSPM lobes, the overall conductivity of the PPy/PTSPM JNPs increased with the increase in the size of the conductive lobe, while the HLB balance decreased from 14 to 6. Such JNPs with tunable conductivities and surface polarities can be used in conductive inks for printing circuit elements with variable resistance. Kang and Honciuc have created various microcolloidal particles having disk, star, helmet, pumpkin, mushroom, basket, and other type of architectures using Janus nanoparticle precursors [78] (see Fig. 13.7).

13.2 Case study: Synthesis of nanostructured materials from Pickering emulsions 13.2.1 Bulk polymerization of Pickering emulsion droplets Pickering emulsions are emulsions stabilized by particles named after the S.U. Pickering (1907). The particles adsorb at the interface between oil-water and act as emulsifiers during strong agitation. The critical condition for a nanoparticle to act as emulsifier is to be partially wetted by each liquid phase. In fundamental studies, surfactant-free particles are used for the preparation of the Pickering emulsions, to avoid the falsifying effects of the surfactants. External energy input is required in the form of mechanical stirring or ultrasonication for producing Pickering emulsion. Pickering emulsions have a better kinetic stability than the standard surfactant prepared emulsions. Their stability is mainly due to the rigidity of the interfacial layer of adsorbed particles and high desorption energies, on the order of tens of thousands of kT, while for surfactant molecules the desorption energies are comparable to 1 kT. Nanoparticles have a greater emulsification power than the microparticles. A whole range of homogeneous, asymmetric polymeric, and inorganic nanoparticles can be used for stabilizing Pickering emulsions. For the preparation of a Pickering emulsions nanoparticles are first dispersed in water (typically stored as aqueous colloid), oil is added, and then high

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FIG. 13.7

Microcolloidal particles with varying shapes and architectures produced from Janus nanoparticle precursors. Reproduced from C. Kang, A. Honciuc, Growth of nano-/microcolloidal architectures from Janus seeds by ATRP, Chem. Mater. 30 (2018) 7664–7671. https://doi. org/10.1021/acs.chemmater.8b02946 with permission from The American Chemical Society.

shear forces are applied, either by ultrasonication, or high-power stirring. In this process, the high shear will cause the adsorption and trapping of the nanoparticles at the oil-water interface. Unlike small molecular surfactants, the adsorption of the nanoparticles at the interface is irreversible. The phase of the obtained emulsion is determined by the nanoparticles’ affinity to one phase or the other according to Finkle et al. [80] and Bancroft rules [81]. Thus, the surface energy of the nanoparticles is the deciding factor. For example, apolar low surface energy carbon black particles are more likely to form w/o emulsions than the high surface energy hydrophilic silica particles, due to their greater affinity to the apolar phase than to water [82]. Affinity of the particle to one of the phases can be understood by the interfacial immersion depth into one phase or the other. For example, if the particle has a higher affinity for oil phase, then its immersion depth into oil at the oil-water interface will be greater than the immersion depth of a more polar particle. In other words, the nanoparticles’ surface is wetted stronger by one of the liquid phases than the other. Because of the different immersion depths, the curvature of the oil-water interface changes toward one phase or the other, as depicted in Fig. 13.8 [27, 74]. If the immersion depth of particles in one of the phases is stronger than in the other phase, the interface becomes concave on the side of least immersion. In other words, the curvature of the interface will be such that the dispersed phase becomes the phase in which the particles are least immersed [74]. Snowman-type Janus particles are interesting model amphiphiles with demonstrated ability to function effectively as emulsifiers [27, 59, 76]. Owing to their surface polarity contrast, the JNPs can be compared to surfactants. Surfactantfree JNPs are attractive for use in emulsification of oils in water, because of the possibility to tune precisely and gradually their overall surface polarity, Janus balance, or hydrophilic-lipophilic balance (HLB). Their overall surface energy can be varied by changing the aspect ratio between lobe sizes of different polarities to the desired conditions. For example, a homologous series of five nano-sized polystyrene/poly(3-(triethoxysilyl)propyl methacrylate) Janus nanoparticles (PS/P(3-TSPM) JNPs) with different relative lobe sizes was tested for their emulsification ability of different volumetric ratios of heptane: water mixtures (heptane is a purely apolar liquid) [83]. Emulsions generated from heptane and water with this homologos series of JNPs are presented in Fig. 13.9, whereas the oil phase appears green due to a oil-soluble green fluorescent dye and the water phase appears dark. The top row in Fig. 13.9 depicts the SEM images of each particle in the homologous JNP series. The first particle is a polystyrene (PS) homogeneous nanoparticle from which the subsequent Janus particles with different P(3-TSPM) lobe sizes (brighter in SEM) were generated. The yellow line delineates the emulsion phase inversion boundary between the w/o (top of the line) and o/w (bottom of the line). The horizontal arrow shows that the phase inversion is due to the increasing polarity of the particle and the vertical arrow indicates a catastrophic phase inversion due to the change in relative volume of oil to water [59, 74]. A variety of oils such as monomers, fragrant oils, mineral or silicon oils as well as organic solvents differing in their polarity and viscosity can be emulsified in water with JNPs, as long as they partially wet the surface of the particle.

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FIG. 13.8 Cartoon depicting the emulsion phase as a function of the immersion depth (affinity) of a particle into the oil phase or the water phase (left) formation of o/w emulsions when the affinity of the particles is greater for water; (right) formation of w/o emulsion when the affinity of the particles is greater for oil. Reproduced with permission from A. Honciuc, Amphiphilic Janus particles at interfaces, in: F. Toschi, M. Sega (Eds.), Flowing Matter, Springer International Publishing, Cham, 2019, pp. 95–136. https://doi.org/10.1007/978-3-030-23370-9_4. Copyright Springer 2019.

FIG. 13.9

Formulation—composition maps with photographs of emulsions in glass vials and their corresponding fluorescence microscopy images (scale bar is 400 nm) obtained with PS/P(3-TSPM) JNPs. The top row depicts seed HPs and five PS/P(3-TSPM) JNPs with increasing P (3-TSPM) lobe sizes (scale bar is 200 nm), while the subsequent three rows represent a different volumetric ratios of heptane to water and the six columns represent the emulsification results from each particle. The yellow line indicates the w/o and o/w emulsion phase boundary; the vertical arrow indicates the catastrophic and the horizontal the “static” transitional phase inversion. The fluorescent phase is the oil phase and the dark phase the water. Reproduced with permission from D. Wu, J.W. Chew, A. Honciuc, Polarity reversal in homologous series of surfactant-free Janus nanoparticles: toward the next generation of amphiphiles, Langmuir 32 (2016) 6376–6386. Copyright 2016 American Chemical Society.

Wu et al. [27] have shown that by changing the polarity of the emulsified oil the interfacial energy of the particles with the oil and water can be estimated. If water-insoluble monomers are used, the Pickering emulsion can be polymerized resulting in microparticles with nanostructured surfaces (see Fig. 13.10) [27]. Typically, all the Pickering emulsion types w/o and o/w generated from water-insoluble vinyl monomers can be polymerized by radical polymerization.

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FIG. 13.10

(A) Polystyrene/JNP colloidosomes resulting from the polymerization of a styrene-in-water (o/w) emulsion obtained with PS/P(3-TSPM) JNPs. (B, C) Colloidosome surface showing nanostructuring due to the presence of Janus particle monolayers trapped at the oil-water interface. (C) Compact JNP packing and remaining impression after some JNPs have partially detached from the surface of the colloidosome due to ultrasonication. (D) Cross-section SEM images of the polystyrene/JNP hollow structure resulting from polymerization of a water-in-styrene (w/o) emulsion obtained with JNPs. (E) Nanostructured interface due to the presence of the JNPs. (F) Photograph of polystyrene block obtained from the polymerization of the w/o Pickering emulsion. Reproduced with permission from D. Wu, B.P. Binks, A. Honciuc, Modeling the interfacial energy of surfactant-free amphiphilic Janus nanoparticles from phase inversion in Pickering emulsions, Langmuir 34 (2018) 1225–1233. https://doi.org/10. 1021/acs.langmuir.7b02331. Copyright 2017 American Chemical Society.

If the dispersed phase is oil, then the emulsion droplets can be polymerized to result in a large spherical particle, which has the emulsion stabilizing particles trapped and immobilized at their surface, resulting in a nanostructured surface (Fig. 13.10). These types of particles are called colloidosomes [27, 59, 84], term coined by Dinsmore and coworkers [85]. AIBN and KPS can be both used for polymerization reaction. Interestingly, unlike the emulsion polymerization prepared with surfactants, in which the oil droplets act as mere monomer reservoirs for the micellar nucleation and polymerization, in Pickering emulsion polymerization the emulsion droplets seem to polymerize directly, probably due to the interfacial particle shield, which limits the monomer diffusion into water. In Pickering emulsion polymerization, there is an almost one-to-one correspondence in droplet size and the particle size obtained in Pickering emulsion polymerization. If the dispersed phase is water, w/o emulsions, the resulting material after polymerization is a polymer block containing hollow cavities, which can be separated or connected to create a high surface porous material [27] (Fig. 13.10D–F). The formed cavities can be closed or open forming a network of hollow cavities, the water liquid may be present and sealed off in the cavities. This could potentially evolve into a useful method for encapsulation and long-term storage of liquids. The polymerization of inverse w/o Pickering emulsions has received significant attention, also for manufacturing porous materials with their application as scaffold materials in tissue engineering [86]. Such materials are called polymerized high-internal phase emulsions (HIPE) [87, 88], here referred to as polymeric hollow structures. HIPE materials obtained from Pickering emulsions have an increased stability as compared to those obtained from surfactants due to reinforced wall structure by particles [89].

13.2.2 Interfacial polymerization of Pickering emulsion droplets Polymerization of oil-monomer droplets in Pickering emulsions can be used to obtain large nanoparticles or microparticles with nanostructured surfaces, called colloidosomes. This method works particularly well when using vinyl monomers as the oil phase, which polymerize via radical polymerization mechanism. Monomers which polymerize via other mechanisms, such as oxidative addition, with elimination of water is also possible, resulting in a whole different variety of structures. Mihali and Honciuc [84] have shown that Pickering emulsions of 3,4ethylenedioxythiophene (EDOT) in water can be stabilized by semiconductive JNPs, whereas the polymerization of EDOT proceeds via oxidative addition mechanism. During emulsification, the nanoparticles self-assemble into a

13.2 Case study: Synthesis of nanostructured materials from Pickering emulsions

233

monolayer at the EDOT-water interface forming protective shield around the emulsion droplet, preventing coalescence. In addition, the stability of the self-assembled monolayers of nanoparticles at the oil-water interface is key to preserving the structural integrity of the oil droplet during polymerization. The EDOT oil droplets in the Pickering emulsion were observed with the fluorescence microscope. The emulsification efficiency, smaller oil droplet, increased with the increase in particle concentration (Fig. 13.11A). After polymerization of the Pickering emulsion, microcapsules

FIG. 13.11

(A) Fluorescence images of the emulsions and the resulting PEDOT microcapsules. The size of the emulsion droplets and the capsules decreases with the increase in the concentration of the nanoparticles (NPs) 10, 25, 50, and 70 mg in 7.5 mL total emulsion volume used in generating the Pickering emulsions. The emulsion droplet diameter decreases from left to right. Scale bar fluorescence microscopy images are 40 μm and SEM 25 μm. (B) Cartoon of the emulsification and capsule polymerization process. Ammonium peroxydisulfate (APS) is used as the oxidant initiator in the water phase. The polymerization takes place exclusively at the interface. (C) SEM images showing the self-organized nanostructured wall, showing periodicity with a honeycomb-like structure on the inner side and mail armor on the outer side. Cross section of the microcapsule wall showing orientation of JNPs is such that the PANI Janus lobe (appearing darker) is pointing toward the PEDOT layer. Modified from V. Mihali, A. Honciuc, Evolution of self-organized microcapsules with variable conductivities from self-assembled nanoparticles at interfaces, ACS Nano 13 (2019) 3483–3491. https://doi.org/10.1021/acsnano.8b09625 with permission. Copyright 2019 The American Chemical Society.

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were obtained, as observed in the SEM images in Fig. 13.11A. The EDOT/water Pickering emulsion was polymerized 45°C for 12 h without stirring (Fig. 13.11B). Preliminary investigations showed that the oxidative-addition polymerization of the EDOT starts at the interface of the nanoparticle-stabilized emulsion droplet, initiated by ammonium peroxydisulfate (APS) from the water phase. The PEDOT grows at the [90] oil-water interface while continuously supplied by the monomer diffusing from the interior of the droplet, as depicted in Fig. 13.11B. The PEDOT also grows in between and around the exterior shield of nanoparticles until the oxidant or monomer is consumed. Interestingly, unlike the bulk polymerization of vinyl monomers in the Pickering emulsion, the interfacial polymerization of PEDOT around the tightly self-assembled nanoparticles at the surface of the oil droplet results in empty microcapsules with a self-organized PEDOT-nanoparticle structure with different morphologies on the inner and the outer sides, as shown in Fig. 13.11C. The wall on the interior side has a honeycomb-like morphology with one nanoparticle occupying a cell. On the outer side of the wall, a different structure can be observed, resembling a chain mail armor due to the PEDOT growing around the nanoparticles (Fig. 13.11C). Mihali and Honciuc [84] have noted that the evolution of the selforganization in the microcapsule wall resembles "morphogenesis," also known as chemical garden [91–93]. Selforganization via morphogenesis requires two compartments with different chemical environment and an unidirectional flow of reactants from one compartment to the other; whereas the reactants moving across the interface that separate the compartments, precipitate in the newly met conditions to result in a self-organized structure. In polymerization of Pickering emulsion droplets via oxidative addition, the compartmentalization was achieved by the interfacial shield of JNPs self-assembled monolayers, while the unidirectional diffusion of EDOT monomer from the emulsion droplet to the interface was driven by the interfacial polymerization reaction. As the polymerization reaction proceeded with the formation of a PEDOT membrane at the emulsion droplet surface, the diffusion of the reactants from the interior of the droplet to the interface to meet the initiator must have happened by rupturing and healing of the polymer membrane. From the SEM images of the PEDOT capsule wall, it can be seen that the JNPs are oriented and their organization is periodic. This result is significantly different from that of radical polymerization of vinyl monomers because, in the radical polymerization there is a 1:1 correspondence between the emulsion droplets and the microparticles obtained, while in the oxidative addition polymerization hollow microcapsules with nanostructured wall architectures are obtained. The size of the resulting PEDOT microcapsules is also significantly larger than the monomer emulsion droplets (Fig. 13.11A). The reason for this difference is that the polymerization mechanism of oxidative addition takes place exclusively at the monomer-water interface, whereas the radical polymerization propagates in the bulk of the monomer droplet. Interestingly, the obtained semiconducting PEDOT microcapsules from emulsions stabilized by polyaniline JNPs show to have coupled optoelectronic properties, where the particles act as dopants.

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[83] J.N. Israelachvili, Adhesion and wetting phenomena, in: Intermolecular and Surface Forces, third ed., Academic Press, 2011, , pp. 415–467. [84] V. Mihali, A. Honciuc, Evolution of self-organized microcapsules with variable conductivities from self-assembled nanoparticles at interfaces. ACS Nano 13 (2019) 3483–3491, https://doi.org/10.1021/acsnano.8b09625. [85] A.D. Dinsmore, M.F. Hsu, M.G. Nikolaides, M. Marquez, A.R. Bausch, D.A. Weitz, Colloidosomes: selectively permeable capsules composed of colloidal particles, Science 298 (2002) 1006–1009. [86] X. Liu, M. Okada, H. Maeda, S. Fujii, T. Furuzono, Hydroxyapatite/biodegradable poly(l-lactide–co-ε-caprolactone) composite microparticles as injectable scaffolds by a Pickering emulsion route. Acta Biomater. 7 (2011) 821–828, https://doi.org/10.1016/j.actbio.2010.08.023. [87] V.O. Ikem, A. Menner, T.S. Horozov, A. Bismarck, Highly permeable macroporous polymers synthesized from Pickering medium and high internal phase emulsion templates. Adv. Mater. 22 (2010) 3588–3592, https://doi.org/10.1002/adma.201000729. [88] K. Kim, S. Kim, J. Ryu, J. Jeon, S.G. Jang, H. Kim, D.-G. Gweon, W.B. Im, Y. Han, H. Kim, S.Q. Choi, Processable high internal phase Pickering emulsions using depletion attraction. Nat. Commun. 8 (2017) 14305, https://doi.org/10.1038/ncomms14305. [89] V.O. Ikem, A. Menner, A. Bismarck, Tailoring the mechanical performance of highly permeable macroporous polymers synthesized via Pickering emulsion templating. Soft Matter 7 (2011) 6571–6577, https://doi.org/10.1039/c1sm05272a. [90] D. Nguyen, H. Yoon, Recent advances in nanostructured conducting polymers: from synthesis to practical applications. Polymers 8 (2016) 118, https://doi.org/10.3390/polym8040118. [91] J.M. García-Ruiz, E. Nakouzi, E. Kotopoulou, L. Tamborrino, O. Steinbock, Biomimetic mineral self-organization from silica-rich spring waters. Sci. Adv. 3 (2017) e1602285https://doi.org/10.1126/sciadv.1602285. [92] W. Zhao, K. Sakurai, Realtime observation of diffusing elements in a chemical garden. ACS Omega 2 (2017) 4363–4369, https://doi.org/ 10.1021/acsomega.7b00930. [93] L. Cera, C.A. Schalley, Under diffusion control: from structuring matter to directional motion. Adv. Mater. 30 (2018) 1707029https://doi.org/ 10.1002/adma.201707029.

C H A P T E R

14 Adsorption and interaction of particles at interfaces 14.1 Adsorption of nanoparticles at interfaces The self-assembly of nanoparticles on a liquid-liquid interface by adsorption has been gaining increasing interest since it provides building blocks for two-dimensional functional materials in a wide range of applications [1]. In order to design nanoparticles and control their self-assembly, it is essential to understand their surface properties and adsorption energy. The current understanding is that for particles to adsorb at liquid-liquid interfaces, they must be partially wetted by each liquid. For adsorption of particles at liquid-air interfaces, it suffices to say that the particle surface is partially wetted by the liquid phase. This can be understood in terms of the relative magnitude of the interfacial energies γ 23, γ 12, and γ 13 acting at the three-phase line of an interfacially adsorbed particle, as depicted in Fig. 14.1. For example, if a particle adsorbs at the interface between two immiscible liquids, 1 and 2, the partial wetting condition is fulfilled when the spreading coefficients S1 and S2 corresponding to each liquid are negative: γ 23 < γ 13 + γ 12 where S1 ¼ γ 23  γ 13 + γ 12 < 0 and γ 13 < γ 12 + γ 23 where S2 ¼ γ 13  γ 12 + γ 23 < 0. These conditions are depicted in situations (I) and (II) in Fig. 14.1. In situation (I) in Fig. 14.1, the interfacial tension unit vectors are depicted intuitively, such that they appear equal in their magnitude γ 23  γ 12  γ 13. In this condition, the particle at the interface is about half immersed in liquid 1 and half in liquid 2. In situation (II) in Fig. 14.1, although the partial wetting by both liquids is fulfilled, the particle is wetted more by liquid 1 than liquid 2, γ 23 > γ 12, and γ 23 > γ 13, but S1 < 0, consequently the immersion depth in liquid 1 is stronger than liquid 2. In situation (III), the wetting by liquid 2 is spontaneous such that γ 13 > γ 12 + γ 23 where S2 ¼ γ 13  γ 12 + γ 23 > 0, and therefore the particle is fully immersed in liquid 2. In situation (IV), the wetting by liquid 1 is spontaneous such that γ 23 > γ 13 + γ 12 where S1 ¼ γ 23  γ 13 + γ 12 > 0, and therefore the particle is fully immersed in liquid 1. The adsorption free energy of the particle at the interface scales with R2, where R is the radius of the particle. Gibbs free energy of particles’ adsorption at a liquid-liquid interface can be calculated by taking into account the surface free energy of the particle in one of the liquid phases as the initial state and the free energy of the particle at the interface between two phases. For didactical reasons, it is easier to discuss desorption or detachment of the particle from the interface, as depicted in Fig. 14.2A. For example, if the particle is first at the interface and then completely detached into liquid 1, then ΔGdesorption ¼ E1  E12 ¼ ΔGadsorption

(14.1)

where E12 is the total interfacial energy of the particle at the interface given by the expression E12 ¼ γ 23 A23 + γ 13 A13

(14.2)

where A12 is the area of the interfacial area between Liquid 1 and Liquid 2 created by the removal of the particle from the interface, A13 is the interfacial area between the particle and Liquid 1. E1 is the interfacial free energy of the particle fully immersed in Liquid 1 and can be calculated by E1 ¼ γ 13 A0 13 + γ 12 A12

Chemistry of Functional Materials Surfaces and Interfaces https://doi.org/10.1016/B978-0-12-821059-8.00006-5

239

(14.3)

Copyright © 2021 Elsevier Inc. All rights reserved.

240

14. Adsorption and interaction of particles at interfaces

FIG. 14.1 Cartoon depicting (I) particle 3 adsorbed at the interface between two liquids 1 and 2, with the relative magnitude of the interfacial tension unit vectors; (II) particle 3 adsorbed at the interface with a stronger wetting by liquid 1 than liquid 2, reflected in the relative magnitude if the interfacial tension vectors, with γ 23 > γ 12 and γ 23 > γ 13 but γ 23 < γ 12 + γ 13; (III) particle 3 remains in liquid phase 2, γ 13 > γ 12 + γ 23, S2 > 0 is the wetting of liquid 2 of the particle surface is spontaneous; (IV) particle 3 is wetted spontaneously by liquid 1 S1 > 0 and does not adsorb at the interface.

FIG. 14.2 (A) Cartoon representing the adsorption of a particle initially immersed in Liquid 1 to the interface between Liquid 1 and Liquid 2. (B) Spherical particle adsorbed at the air-water interface. β is the contact angle of the particle with Liquid 2, a is the interfacial immersion depth of the particle measured from the center of the particle to the interface, d and d0 are the interfacial immersion depth of the particle measured from the apex of the particle in Liquid 2 and Liquid 1 to the interface, r is the radius of the circle resulting from the cross section of the interfacial plane with the particle, θ ¼ 180 degrees-β.

where A0 13 is the interfacial area of the particle fully immersed in Liquid 1 and A12 the newly created interfacial area between the two liquids upon desorption of the particle. The interfacial immersion depth of the particle at the interface can be determined in two ways: by the immersion depth parameter a, which is the distance from the center of the particle to the interface, or by the contact angle β, as depicted in Fig. 14.2B. To obtain a meaningful expression for the Eq. (14.1) as a function of the immersion depth a or contact angle β, the explicit expression for the areas A13, A12, and A23 must be found. The explicit expressions of the interfacial areas, between the particle and the liquids, can be calculated with the geometric parameters given in Fig. 14.2B:

14.1 Adsorption of nanoparticles at interfaces

241



π  A23 ¼ 2πRðR  aÞ ¼ 2πR R  R sin  β ¼ 2πR2 ð1  cos βÞ 2

π  A13 ¼ 2πRðR + aÞ ¼ 2πR R + R sin  β ¼ 2πR2 ð1 + cos βÞ 2 h
π i2 2 ¼ πR2 sin 2 β A12 ¼ πr ¼ π R cos  β 2 A0 13 ¼ 4πR2 Therefore, the total interfacial energy of the particle at the interface is E12 ¼ 2πR2 γ 23 ð1  cos βÞ + 2πR2 γ 13 ð1 + cos βÞ

(14.4)

The free energy of the particle completely immersed in water is E1 ¼ 4πR2 γ 13 + πR2 γ 12 sin 2 β

(14.5)

Inserting the explicit expressions for Eqs. (14.4), (14.5) in Eq. (14.1), the Gibbs free energy change upon detachment of the particle from interface into Liquid 1, as a function of the contact angle β, is ΔGdesorption ¼ 4πR2 γ 13 + πR2 γ 12 sin 2 β  2πR2 γ 23 ð1  cos βÞ  2πR2 γ 13 ð1 + cos βÞ

(14.6)

The interfacial immersion depth a, in Fig. 14.2B, is related to the interfacial tension with the following relationship: a ðγ  γ 13 Þ cos β ¼ ¼ 23 R γ 12

(14.7)

Inserting the result in Eq. (14.7) and regrouping the terms in Eq. (14.6), we obtain ΔGdesorption ¼ 4πR2 γ 13 + πR2 γ 12 sin 2 β  2πR2 ½ðγ 23 + γ 13 Þ + cos βðγ 13  γ 23 Þ

(14.8)

ΔGdesorption ¼ 4πR2 γ 13 + πR2 γ 12 sin 2 β  2πR2 ½ðγ 23 + 2γ 13  γ 13 Þ + cos βðγ 13  γ 23 Þ   ΔGdesorption ¼ 4πR2 γ 13 + πR2 γ 12 sin 2 β  4πR2 γ 13  2πR2 γ 12 cos β  γ 12 cos 2 β Keeping in mind that sin2(β) ¼ 1  cos2β

  ΔGdesorption ¼ πR2 γ 12 1  cos 2 β  2 cos β + 2cos 2 β

And the final result for the energy of particle detachment from the interface into Liquid 2 (Fig. 14.2A) is ΔGdesorption ¼ πR2 γ 12 ð1  cos βÞ2 ¼ ΔGadsorption

(14.9)

Case (II) for desorption from interface into liquid 2: ΔGdesorption ¼ E2  E12 ¼ ΔGadsorption where the interfacial free energy of the particle fully immersed in Liquid 2 is E2 ¼ γ 23 A0 13 + + γ 12 A12 ¼ 4πR2 γ 23 + πR2 γ 12 sin 2 β

(14.10)

Therefore, ΔGdesorption ¼ 4πR2 γ 23 + πR2 γ 12 sin 2 β  2πR2 γ 23 ð1  cos βÞ  2πR2 γ 13 ð1 + cos βÞ ΔGdesorption ¼ 4πR2 γ 23 + πR2 γ 12 sin 2 β  2πR2 ½ð2γ 23 + γ 13  γ 23 Þ + cos βðγ 13  γ 23 Þ Using the result of Eq. (14.7), we obtain from the above expression:

  ΔGdesorption ¼ 4πR2 γ 23 + πR2 γ 12 sin 2 β  4πR2 γ 23  2πR2 γ 12 cos β  γ 12 cos 2 β   ΔGdesorption ¼ πR2 γ 12 1  cos 2 β + 2 cos β + 2cos 2 β ΔGdesorption ¼ πR2 γ 12 ð1 + cos βÞ2 ¼ ΔGdesorption

(14.11)

242

14. Adsorption and interaction of particles at interfaces

Very often in different works, one finds the global expression for the adsorption or attachment energy by combining Eqs. (14.9), (14.11) for a particle of radius R at the air-water or oil-water interfaces [2]: ΔGdesorption ¼ γ 12 πR2 ð1  cos βÞ2 ¼ ΔGadsorption

(14.12)

where the sign in parenthesis is taken as negative when the particle detaches from the interface into Liquid 1 and as positive if a particle desorbs/detaches from the interface into Liquid 2. A great advantage of Eqs. (14.9), (14.11), (14.12) is that it allows the calculation of the attachment energy of a particle at the interface only by knowing the contact angle with one of the phases.

Numerical example 14.1 Calculate the desorption energy ΔGdesorption of a particle initially at the water-toluene interface, which undergoes desorption into either toluene or water, knowing the water-toluene interfacial tension γ ¼ 35.8 mJ/m2, radius of the particle R ¼ 10 nm, and the contact angles of the water phase with the particle are: (A) β ¼ 10 degrees, (B) β ¼ 40 degrees, (C) β ¼ 90 degrees, (D) β ¼ 120 degrees, (E) β ¼ 140 degrees. (F) Comment on the magnitude of energy comparing the values of the energy of attachment with the particle interfacial immersion as a function of β. (G) For the (A-E), plot a graph showing the values of ΔGdesorption with the contact angle for both cases, desorption from interface into water and desorption from interface into toluene. Comment on the curve symmetry and greatest desorption energy value.

Answer Case 1: For the desorption of the particle from interface into water, Eq. (14.9) gives (A) 0.6 kT, (B) 150 kT, (C) 2740 kT, (D) 6170 kT, (E) 8560 kT. (F) The values of the desorption energy from the interface into water increase with the increase in the contact angle, meaning that the more immersed the particle into the toluene phase is, the greater the energy needed to desorb it from the interface into the water phase. Case 2: For the desorption of the particle from the interface into toluene, the Eq. (14.11) gives: (A) 10,800 kT, (B) 8570 kT, (C) 2750 kT, (D) 689 kT, (E) 151 kT. (F) The values of the desorption energy from the interface into the toluene decrease with the increase in the contact angle, meaning that the more immersed the particle into the water phase is (for small β), the greater the detachment energy is. Conversely, when the contact angle is large, meaning the immersion into the toluene is greater, the detachment energy from interface into toluene decreases. (G) in the graph, two curves are represented, A for particle desorption into water, B for particle desorption into toluene. The desorption energy curves are fully symmetric with the interface, as given by Eq. (14.12), and the minimum desorption energy in either solvent is when the contact angle with that solvent is lowest and maximum when the contact angle is largest.

Pieranski [3] was the first to propose an analytic expression for calculating the particle energy as a function of the particle’s immersion depth “a” (Fig. 14.2B), which is the distance from the center of the particle to the interface. This can be determined experimentally with the scanning electron microscope (SEM) of cryogenized particles trapped at interfaces [4]. The expression for calculating particle energy at the interface (Fig. 14.2B), as a function of the immersion depth a0 ¼ a/R, can be found as follows: E12 ¼ 2πR2 γ 23 ð1  a0 Þ + 2πR2 γ 13 ð1 + a0 Þ The interfacial energy of the particle with the solvent plus the interfacial energy of the newly freed Liquid 1-Liquid 2 interface:   E1 ¼ 4πR2 γ 13 + πR2 γ 12 1  a20 Thus, the desorption free energy from the interface into Liquid 1 is   ΔGdesorption ¼ 4πR2 γ 13 + πR2 γ 12 1  a20  2πR2 γ 23 ð1  a0 Þ  2πR2 γ 13 ð1 + a0 Þ   ΔGdesorption ¼ 4πR2 γ 13 + πR2 γ 12 1  a20  πR2 ½2γ 23 ð1  a0 Þ + 2γ 13 ð1 + a0 Þ   ΔGdesorption ¼ πR2 a20 γ 12 + 2a0 ðγ 23  γ 13 Þ  ð2γ 13 + 2γ 23 Þ + γ 12  ðγ  γ 23 Þ ðγ + γ Þ  2 13 23 + 1 ¼ ΔGadsorption ΔGdesorption ¼ πR2 γ 12 a20  2a0 13 γ 12 γ 12

(14.13)

14.1 Adsorption of nanoparticles at interfaces

243

The quadratic Eq. (14.13) is known as Pieranski’s equation, which circumvents the difficulty of choosing the correct sign in Eq. (14.12). The a0 varies from +1 to 1, where +1 corresponds to full immersion in Liquid 1 and 1 corresponds to full immersion in Liquid 2. For the desorption of the particle into Liquid 2:   E2 ¼ 4πR2 γ 23 + πR2 γ 12 1  a20   ΔGdesorption ¼ 4πR2 γ 23 + πR2 γ 12 1  a20  2πR2 γ 23 ð1  a0 Þ  2πR2 γ 13 ð1 + a0 Þ Δ Gdesorption ¼ πR2(  γ 12a20  2a0(γ 23  γ 13)  2(γ 23 + γ 13) + γ 12)

 ðγ  γ 13 Þ ðγ + γ Þ  2 23 13 + 1 ¼ ΔGadsorption ΔGdesorption ¼ πR2 γ 12 a20  2a0 23 γ 12 γ 12

Numerical example 14.2 Using Pieranski’s equation, calculate the free energy of adsorption ΔGadsorption of a particle with radius R ¼ 10 nm initially at the water-toluene interface that desorbs into the water phase, for the following immersion depths a/R ¼ 1, 0.5, 0, 0.5, 1. γ water2 2 2 toluene ¼ 35.8 mJ/m , γ particle-toluene ¼ 10 mJ/m , γ particle-water ¼ 20 mJ/m . Comment on the magnitude of the adsorption energy with the immersion depth. Hint: plot a graph with a few extra values for the interfacial immersion depth to better explain the evolution of ΔGadsorption, comment on the curve symmetry and the maximum and minimum values.

Answer For a/R ¼ 1, ΔGdesorption ¼ 0 J; a/R ¼ 0.5 ΔGdesorption ¼ 2820 kT, a/R ¼ 0 ΔGdesorption ¼ 4270 kT, a/R ¼  0.5 ΔGdesorption ¼ 4350 kT, a/R ¼ 1 ΔGdesorption ¼ 3050 kT. The graph in Fig. 14.4 shows the evolution of ΔGdesorption with a/R. The energy of desorption is zero when the immersion depth a/R ¼ 1, meaning that the particle is fully immersed in water and touches the interface only at one point. The desorption energy increases as the particle at the interface is more immersed into the toluene phase up to a maximum value given by.

dΔGdesorption ðγ  γ 13 Þ ¼ 0,a0 maximum ¼ 23 da0 γ 12

(14.14)

In this case, a/R ¼  0.2778.

The graph in Fig. 14.4 shows the desorption energy curve with particle immersion depth. The curve is not symmetric with respect to the interface, unlike the desorption energy curve in Fig. 14.3. The different symmetries of the desorption

FIG. 14.3 Graph representing the evolution of the desorption energy with the particle at different positions in the interface given by the contact angle β: (A) desorption from interface into water, (B) desorption from interface into toluene.

244

FIG. 14.4

14. Adsorption and interaction of particles at interfaces

ΔGdesorption for a particle at different positions from the interface given by the interfacial immersion depth a/R, desorbed into the water

phase.

energy curves can be explained by the fundamental difference that exists between Eqs. (14.13) and (14.12). While the former does explicitly include the interfacial energy of the particle with each solvent, the latter equation only takes account of the interfacial tension.

14.2 Interfacial adsorption dynamics and mechanism The adsorption of partially hydrophobic colloidal particles at interfaces is mostly entropically driven. This can be understood by thinking that the overall free energy of the system decreases due to an increase in the water entropy; the ordered water layer on the hydrophobic surface of the particles is released upon particle interfacial adsorption. The dehydration and re-solvation of the particle surface generate an activation energy barrier (Fig. 14.5). Particle-interface electrostatic interactions, and particle-particle electrostatic interactions between the incoming particles and already adsorbed particles at the interface can contribute to an activation energy barrier (Fig. 14.5). On the other hand, as pointed out by Deshmukh et al. [5], the electrostatic interaction can also be involved as a driving force for particle adsorption. The experimental evidence thus far indicates that the air-water or oil-water interfaces are negatively charged, hinting that negatively charged particles may have difficulty adsorbing at the interface, and a high activation energy barrier to adsorption (Fig. 14.5), while positively charged particles are spontaneously adsorbing. Thus, surface hydrophobicity and the sign of the surface charge appear to both play a role in the mechanism of interfacial adsorption of particles. Some experimental evidence seems to lead to this conclusion: silica particles that are hydrophilic and negatively charged do not adsorb at air-water and oil-water interfaces, but upon addition of CTAB, which makes them both more hydrophobic and slightly positively charged, completely changes their interfacial adsorption properties [6, 7]. Wu and Honciuc have observed that pH-responsive Janus nanoparticles when positively charged at low pH adsorbed spontaneously at the interfaces, while no interfacial adsorption was observed when particles were negatively charged at high pH; these studies were done in surfactant-free conditions at three different interfaces: toluene-water, heptane-water, or air-water interface [8]. Such a relationship between the surface charge of particles and interfacial adsorption is not always clear, as other factors such as particle softness, particle swelling, surface amphiphilicity, as well as amphiphilicity of surface grafted polymers, do play a role. Although negatively charged particles should in theory have a high activation energy barrier to adsorption at the negatively charged air-water interface, an interfacial charge distribution mechanism appears to facilitate adsorption of hydrophobic particles at the interface [9]. Wu and Honciuc [10] have observed a contrasting interfacial adsorption mechanism between hard-sphere particles composed of cross-linked polystyrene grafted with a pH responsive polymer PDMEAEMA (PDMAEMAg-PS) and soft gel particles constituted of a similar type of pH responsive polymer PDEAEMA. The activation energy barrier to adsorption for soft gel PDEAEMA increases only slightly with increasing the pH, with no obvious relationship to surface charge. For hard particles grafted with amphiphilic polymer PDMAEMA-g-PS, the activation energy barrier to interfacial adsorption rather drops with a decrease in the positive surface charge (see Table 14.1).

245

14.2 Interfacial adsorption dynamics and mechanism

FIG. 14.5

Adsorption energy ΔE and activation energy Ea for interfacial adsorption of particles at the air-water or oil-water interface. The top cartoons depict the possible sources influencing the magnitude of the activation energy for interfacial adsorption of particles.

TABLE 14.1 Activation and adsorption energies of the PDEAEMA-1 constituted NPs and PDMAEMA-g-PS NPs at toluene-water interface and their zeta potential, effective bulk-to-surface diffusivity, for 10 mg/mL at different pH values. NPs PDEAEMA-1

PDMAEMA-g-PS

pH

Radius (nm)

Zeta potential (mV)

Deff (m2/s) 16

Ea (kBT)

ΔE (kBT)

7.8

5.3 106

2

678.5

+45

1.5 10

3

632

+48

8.6 1017

8.5

4.1 106

4

629.5

+45

3.1 1017

9.5

3.7 106

5

557.5

+59

3.3 1017

9.6

2.2 106

6.5

394.5

+60

1.2 1018

13.2

8.0 105

10

259

+40

0

∞

0

2

84

+62

0

∞

0

6.9

1.0105

15

7.2

84

+48

2.9 10

8

84

+31

5.6 1015

6.3

1.2 105

10

84

+5

1.7 1012

0.57

1.7 105

Reproduced with permission from D. Wu, A. Honciuc, Contrasting mechanisms of spontaneous adsorption at liquid–liquid interfaces of nanoparticles constituted of and grafted with pH-responsive polymers, Langmuir 34 (2018) 6170–6182. doi:10.1021/acs.langmuir.8b00877. Copyright © 2018, American Chemical Society.

The adsorption of the particles at the interface leads to a decrease in the interfacial energy. The interfacial energy can be monitored with the pendant drop tensiometer. By monitoring the decrease of the interfacial tension with time, information about particle adsorption dynamics can be obtained (Fig. 14.6). The adsorption dynamics may be diffusion limited, activation energy limited, or a combination of both. The particle adsorption experiences three adsorption stages, as depicted in Fig. 14.6: (I) the adsorption of particles at a pristine interface, where particle-interface interaction dominate, (II) adsorption of particles at a partially occupied interface, where in addition to particle-

246

14. Adsorption and interaction of particles at interfaces

FIG. 14.6 Dynamics of particle adsorption at the oil-water interface monitored by the decrease of the interfacial tension (IFT) with time. There are three main stages in the dynamics of particle adsorption: (I) initial adsorption of particles at a pristine oil-water interface, (II) adsorption of particles at a partially occupied interface, and (III) adsorption of particles at a nearly saturated interface, where the particle-particle repulsion and interfacial reorganization dominate. From A. Honciuc, Amphiphilic Janus particles at interfaces, in: F. Toschi, M. Sega (Eds.), Flow Matter, Springer International Publishing, Cham, 2019, pp. 95–136. doi:10.1007/978-3-030-23370-9_4.

interface interactions, the particle-particle interactions become present, and (III) particle adsorption at a nearly saturated interface, where the particle-particle repulsive interaction and interfacial rearrangement dominate the adsorption dynamics [11, 12]. ΔIFT in Fig. 14.6 is the difference in interfacial tension at different times, γ0-γ plateau at t0 and tplateau. The magnitude of ΔIFT encompasses several phenomena, such as the ability of the particles to adsorb at the interface, ability of the particles to form a continuous 2D network and eventually self-assemble into a monolayer, surface, and interfacial energy of the particles with both phases and the particle-particle lateral interactions. For example, amphiphilic Janus particles are more effective than homogeneous particles at lowering the IFT, and this has been theoretically predicted [13] and experimentally demonstrated [14, 15]. Amphiphilic Janus particles resemble molecular surfactants and can be constituted of two parts, one hydrophobic and one hydrophilic. In addition, the size of the particle and the shape affects ΔIFT. Gao et al. [11] observed different adsorption kinetics, different packing behaviors, and different ΔIFT values for particles constituted from the same material but having different shapes, such as spheres, disks, and rods. Dinsmore et al. [16] used the γ plateau value, reached when the interface is fully saturated with particles, to calculate the particles’ interfacial adsorption energy Δ E:
 (14.15) ΔE ¼  γ 0  γ p πR2 =η where R is the radius of the particles and n is the area fraction of particles at the interface (0.91 for close packed particles). Wu and Honciuc [17] calculated energy of attachment Δ E using Eq. (14.15) for Janus and homogeneous particles at toluene-water, heptane-water, and air-water interfaces that are summarized in Table 14.2; it appears that the Δ E values for the Janus particles are larger than those for homogeneous particles at the same interfaces within one order of magnitude. The activation energy of adsorption can be determined from the same IFT vs time curves (Fig. 14.6). As recently discussed [18], in the presence of an energy barrier, the adsorption of particles at the interface is much slower than those predicted by purely diffusive models of Ward and Tordai [19]. Instead, the theoretical effective diffusion models by Liggieri et al. [20] and Ravera et al. [21] take into account the existence of an activation energy barrier. This latter model is intuitively correct as only some of the particles arriving at the interface by diffusion may also adsorb at the interface, while some that are not able to overcome the potential barrier will diffuse back into the bulk. Therefore, the activation

247

14.3 Interaction between nanoparticles at interfaces

TABLE 14.2

Bulk-to-surface diffusion coefficients Deff, activation energies Ea and energy of interfacial adsorption ΔE of the PS-PDIPAEMA/P(3-TSPM) Janus particles (JPs) and PS-PDIPAEMA homogeneous nanoparticles (HPs) at toluenewater, heptane-water and air-water interfaces.

Interface

D0 (m2/s)

Deff (m2/s)

Ea (kBT)

ΔE (kBT)

JPs at toluene-water

1.65  1012

5.41  1015

5.8

2.2  105

JPs at heptane-water

1.65  1012

6.24  1015

5.6

2.9  105

JPs at air-water

1.65  1012

1.47  1015

7.1

7.2  104

PDIPAEMA HPs at toluene-water

4.94  1012

3.39  1015

7.3

3.0  104

PDIPAEMA HPs at heptane-water

4.94  1012

1.23  1014

6.0

6.9  104

PPDIPAEMA HPs at air-water

4.94  1012

1.83  1015

8.0

2.0  104

Reproduced from D. Wu, A. Honciuc, Design of Janus nanoparticles with pH-triggered switchable amphiphilicity for interfacial applications. ACS Appl. Nano Mater. 34 (2018) 1225–1233. doi:10.1021/acsanm.7b00356. Copyright 2017 American Chemical Society.

energy barrier can be calculated from the apparent bulk-to-surface diffusion coefficient, or the effective diffusion coefficient Deff from the IFT vs time data [22]: rffiffiffiffiffiffiffiffiffiffi Deff t (14.16) γ ¼ γ 0  2NA C0 ΔE π where C0 is the concentration of particles in bulk, γ 0—surface tension of the clean interface, Δ E thepattachment energy ffiffi calculated with Eq. (14.15). By fitting the above equation to any of the three segments of IFT vs t time curves (Fig. 14.6), one can calculate Deff for the adsorption in stages I–III. Fitting the earlier portion, stage I of Fig. 14.6, will yield information about the particle-interface interaction [22]. The activation energy for particle adsorption at a pristine oilwater or air-water interface can be thus calculated from the equation which relates the bulk diffusion coefficient D0 and bulk-to-surface effective diffusion coefficient Deff:

 Ea (14.17) Deff ¼ D0 exp  kB T kB T where Ea is the activation energy of attachment at interfaces, D0 is the Stokes-Einstein diffusion coefficient, D0 ¼ 6πμR where μ is the viscosity of water and R is the hydrodynamic radius of the particle. The values of Δ E, γ p, Deff, and D0 and Ea were recently reported by Wu and Honciuc [8] for the interfacial adsorption of two sets of particles, snowman-type polystyrene-poly[2-(diisopropylamino)ethyl methacrylate]/poly[3-(triethoxysilyl)propyl methacrylate (PS-PDIPAEMA/P(3-TSPM)) Janus particles and polystyrene-poly[2-(diisopropylamino) ethyl methacrylate] PS-PDIPAEMA homogeneous particles at three different interfaces: toluene-water, heptane-water, and air-water; these results are compared in Table 14.2. Analysis of the data shows that the bulk-to-surface diffusion coefficient, Deff is always lower than the Stokes diffusion coefficient, as expected, due to the presence of an activation energy barrier. Ea calculated using Eq. (14.17) is highest for the air-water interface and lowest for the adsorption at the heptane-water interface, which can be explained in part by the good ability of heptane to “wet” the polymer particle and replace the water hydration layer from the particle surface.

14.3 Interaction between nanoparticles at interfaces The interaction between particles at interfaces can be predominantly attractive and/or repulsive; the right balance of attractive vs repulsive forces can lead to the formation of self-assembled monolayers. The forces acting between particles at the interface are the same as those acting in bulk but with some specifics. Electrostatic interaction: a particle at the interfaces has one part immersed in water and carries surface charges due to ionization of the surface functional groups. For the part of the particle immersed in oil, a nonpolar solvent, or air, the surface charge neutralization occurs, giving rise to an asymmetric double layer, ensuing a dipole-dipole interaction, whose interaction potential energy evolves with the separation distance V(d)  1/d3. The dipole-dipole interaction between interfacially adsorbed particles was first analyzed by Pieranski [3] in the context of 2D crystal formation from polystyrene particles with ionizable surface sulfone groups at the air-water interface. Pieranski estimated the magnitude of the dipole p, oriented perpendicularly to the interface, by the surface charge Q on the surface part immersed in

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14. Adsorption and interaction of particles at interfaces

FIG. 14.7 (A) Particle adsorbed at water/oil or water/air interfaces and the formation of a dipole due to asymmetric ionization of surface charges in water and charge neutralization in air or aprotic solvents and oil. The dipole strength is estimated as the surface of the charge times the Debye length. (B) A charge may appear on the part of the particle immersed in oil or air that has residual water layers on the surface, whose thickness may be significantly less than the Debye length in water.

water and the corresponding Debye length λD ¼ k1, p ¼ Q  λD (see Fig. 14.7A). Based on intuitive reasoning, Pieranski argued that these dipoles interact through air, so it followed that the potential energy of the dipole-dipole interaction with the separation distance d is

 Q D 2 λD 2 (14.18) V ð dÞ ¼ 2 εd d2 where ε is the dielectric constant of water. The above equation was later derived by Hurd [23], which added an extra factor ε1. Furthermore, the Coulombic interaction also takes place in water between the charged surface areas, but this interaction is screened by the ions:

 d QD 2  λD e (14.19) V ðdÞ∝ εd The current experimental advances allow the measurement of the interaction forces between colloidal particles at the interface with optical tweezers [24, 25], which uses focused LASER beams to keep particles in place. Although it was previously mentioned that charge neutralization on the surface of the particle in the nonpolar solvent or air takes place, there have been experimental reports that particles in the nonpolar solvent do also carry a charge and are capable of interacting via electrostatic force, which in a low dielectric constant solvent or air is not screened and thus can be much longer ranged than in water [26]. However, the origin of this charge remains unclear. Aveyard et al. [27] also observed a very long-range electrostatic interaction in Langmuir-Blodgett studies involving the interfacial compression of particle monolayers at the octane/water and water/air interfaces, and attributed this to the presence of a charge on the surface of the particle immersed in the nonpolar medium to residual hydration layers (see Fig. 14.7B). These experimental evidences challenge the standard understanding that the charge neutralization occurs in the nonpolar solvent [5], highlighting the complexity of the particle-particle interaction at interfaces. van der Waals interaction, as is to be expected for particles at interfaces, requires a more complex treatment than in bulk. Although there have been attempts to sum this in a single equation [5], it would require a different Hamaker constant for parts of the particles interacting within a medium, water and oil/air, and across the interface. Capillary interactions have no equivalent in bulk and arise due to local deformation of the interface by the particles (Fig. 14.8). For example, due to a combination between wetting properties and gravity or buoyant forces, a solid particle deforms the surface under its own weight. The capillary forces between two particles at the interface can be attractive if both menisci are concave/convex and repulsive if one meniscus is convex and the other concave [28]

14.3 Interaction between nanoparticles at interfaces

249

FIG. 14.8 Capillary interactions between large particles and gas bubbles deforming the interface are referred to as flotation forces, while interactions between small particles that adsorb at the interface (pierce the interface) are called immersion forces. The former depends on the buoyancy and gravitation forces while the latter depends on the contact angle of the particle at the interface.

(Fig. 14.8). An example met with in practice is the aggregation of cereal flakes floating on the surface of milk or their adherence to the wall of the bowl, colloquially known as the “Cheerios effect” [29]. Similarly, for the long-lived gas bubbles trapped at the interface, which are pushing upward due to the action of buoyancy deforming the interface, they have a tendency to accumulate and migrate toward the wall of the glass. Small particles in the nano-range are considered to produce only very negligible deformations of the interface, and hence the capillary interactions are small to negligible. Kralchevsky and Nagayama [30] distinguish two situations (Fig. 14.8): (i) macroscopic particles that deform the interface under the action of gravitation/buoyancy give rise to flotation forces, for which the interaction energy drops below 1 kT for particles smaller than 5–10 μm; (ii) small particles that deform the interface due to the contact angle and wettability give rise to immersion forces, whose interaction energy remains significantly above kT, even for particle sizes in the nanometer range. The need for this distinction is that the physical origin producing the interfacial deformation is different for these forces. For two particles adsorbed at the interface, having the same radii R, the “flotation force” (large particles) is given by the expression [30, 31]: F∝

R6 K1 ðqLÞ γ

(14.20)

and the “immersion force” (small particles in the nanometer range) is given by the expression: F∝R2 K1 ðqLÞ

(14.21)

where K1 is the modified Bessel function of the first order, q is the square root of the inverse capillary length, γ is the interfacial tension, and L is the center-to-center particle separation distance. The above expressions are valid for r ≪ L ≪ q, where r is the contact line radius. From the above expressions, it can be observed that the flotation force decreases while the immersion force increases with the increase in the surface tension. The flotation forces decrease much stronger with the radius of the particle than the immersion forces, such that they become negligible for particles smaller than 5–10 μm, while the immersion forces remain significant even for particles as small as 2 nm [30]. Note that the capillary interaction forces depend on the contact angle of the particles at the interface, which is not included explicitly in the above simplified expressions, Eqs. (14.20), (14.21); for more comprehensive derivations and discussions, see Refs. [28, 30, 31]. The interaction energy due to capillary forces can be obtained by integration of Eqs. (14.20) or (14.21): ðW FðL0 ÞdL0 EðLÞ ¼ L

250

14. Adsorption and interaction of particles at interfaces

It is important to note that all the above interactions are valid for the particles as hard spheres. For soft microgel particles, the interfacial interaction is much more complex, in part because upon interfacial adsorption the microgel particles suffer elastic deformations being stretched. Due to this, the capillary interaction is assumed to be stronger due to a larger wetting radius r, while the van der Waals interaction is presumed to be negligibly small, because the microgel particles are typically strongly swollen.

14.4 Langmuir-Blodgett assembly of nanoparticles into 2D crystals The Langmuir-Blodgett method has been attracting significant interest, especially in the 1980s and early 1990s, for the deposition of molecular monolayers of amphiphilic molecules on solid substrates. Applications for the LB method branched into the preparation of supported phospholipid bilayers as biomimetic systems for cell membranes and inclusion of various receptors [32] and in unimolecular electronics for preparation of oriented monolayers of donor-acceptor molecules [33]. The uniqueness of the LB technique is the possibility to manipulate a 2D layer of molecules, by preparing it first at the air-water interface and then transferring it by dipping or raising a substrate perpendicularly to the interface, a method known also as dip-coating. Subsequent monolayers can be deposited to construct a multilayered structure on a solid substrate by multiple dipping of the substrate, a layer-by-layer (LbL) method. It was not long before the LB method was applied to particles and nanoparticles for preparation of photonic crystals, photolithographic masks, and other arrays, [34, 35]. In the LB method, the particles must be prepared or “dropped” first on the surface of water; then the interfacially “floating” particles are compressed by moving barriers sliding on the surface of the water in an LB trough. By doing so, the particles are compressed into a solid monolayer with a compact crystalline structure such as hexagonally close packing. The prerequisite is to make particles float on the surface of water. For molecules, water insoluble long-chain fatty acids are deposited on the water surface with a syringe, droplet by droplet, from a chloroform solution, and upon solvent evaporation the molecules remain trapped at the water-air interface. However, silica or polystyrene nanoparticles are obtained as colloids dispersed in water, which have a great degree of surface hydration. This water colloid cannot be directly deposited on the water surface because the particles will mostly sink. Therefore, special preparation is needed, such that surface dehydration is achieved by solvent exchange first with ethanol, methanol, and slowly to more nonpolar solvents such as chloroform, which are not miscible with water and can quickly evaporate. This is a tedious but incumbent task, and during the process the nanoparticles can irreversibly aggregate. Upon spreading the particles on the water surface and solvent evaporation, the barriers are slowly compressing the particles on the water surface. The surface pressure increases (surface tension decreases) with the particle coming together and there is an increase in the surface density until maximum possible packing is achieved. The right balance between repulsion and attractive forces ensures the formation of a compact and well-behaved monolayer as opposed to aggregation and formation of clumps, visible to the eye or with Brewster angle microscopy. After preparation, the monolayer from the water surface could be transferred to a solid substrate by uplifting a previously immersed substrate in the water phase (upstroke) or by lowering the substrate from the air into the water (downstroke). Depending on the interaction between the substrate and the amphiphilic molecules, monolayer deposition can be achieved in downstroke mode if the substrate is hydrophobic, and in upstroke mode when the substrate is hydrophilic.

Numerical example 14.3 Calculate the energy needed for transfer of a particle with R ¼ 100 nm onto a solid substrate in upstroke mode from the airwater interface and compare it with that in the downstroke mode, knowing the following parameters: (a) contact angle with water β ¼ 45 degrees; (b) contact angle with water β ¼ 15 degrees; (c) contact angle with water β ¼ 65 degrees; (d) contact angle with water β ¼ 90 degrees; (e) contact angle with water β ¼ 120 degrees. The surface tension of water is 72.4 mN/m.

Answer The energy needed to extract a particle from the air-water interface by upstroke lifting of the substrate is given by Eq. (14.11): ΔGupstroke ¼ πR2γ water (1 + cos β)2. The energy needed to force a particle from the air-water interface into bulk water by downstroke sinking of the solid substrate is given by Eq. (14.9): ΔGdownstroke ¼ πR2γ water (1  cos β)2. (a) ΔGupstroke ¼ 1.6  106 kT, ΔGdownstroke ¼ 4.7  104 kT, ΔGupstroke/ΔGdownstroke ¼ 34; (b) ΔGupstroke ¼ 2.1  106 kT, ΔGdownstroke ¼ 6.4  102 kT, ΔGupstroke/ΔGdownstroke ¼ 3335.6; (c) ΔGupstroke ¼ 1.1  106 kT, ΔGdownstroke ¼ 1.8  105 kT, ΔGupstroke/ΔGdownstroke ¼ 6; (d) ΔGupstroke ¼ 5.5  105 kT, ΔGdownstroke ¼ 5.5  105 kT, ΔGupstroke/ΔGdownstroke ¼ 1; (e) ΔGupstroke ¼ 1.4  105 kT, ΔGdownstroke ¼ 1.2  106 kT, ΔGupstroke/ΔGdownstroke ¼ 0.1.

14.5 Templated self-assembly of nanoparticles at interfaces

251

FIG. 14.9 (A) Photograph of a natural boulder opal gemstone (shutterstock photo ID:757601998); (B) photograph of the roll-to-roll slot-die coating with strips of optical adhesive NOA164 on the PET substrate with the LB monolayer of silica spheres Diameter ¼ 550 nm; (C) SEM images of the 3D colloidal photonic crystal made from silica spheres Diameter ¼ 250 nm with 5 LB layers deposited on the PET film using the roll-to-roll method. (D) cross-sectional SEM images of the two samples-sample with 4 LB layers deposited on the PET film using the roll-to-roll method. (A) From Shutterstock. (B–D) Reprinted with permission from M. Parchine, J. McGrath, M. Bardosova, M.E. Pemble, Large area 2D and 3D colloidal photonic crystals fabricated by a roll-to-roll Langmuir–Blodgett method, Langmuir 32 (2016) 5862–5869. doi:10.1021/acs.langmuir.6b01242. Copyright © 2016, American Chemical Society.

The Langmuir-Blodgett method has been used in the preparation of 2D and 3D photonic crystals. Photonic crystals are composed of periodic structures of assembled nanoparticles such that visible light is diffracted similarly to the diffraction of X-rays from an ionic or molecular crystal. Photonic crystals occur in nature, in opal rocks (Fig. 14.9A), and in the wings of some butterflies, where self-assembled silica nanoparticles in the size range of 150–300 nm are packed together, usually in hexagonal close packing crystallites [34]. The versatility of the LB method allows the preparation of photonic crystals on large surface areas, by roll-to-roll deposition, as seen in Fig. 14.9B [35]. SEM images of photonic crystals consisting of several layers of silica nanoparticles prepared by the LB method are shown in Fig. 14.9C and D.

14.5 Templated self-assembly of nanoparticles at interfaces The spontaneous or forced adsorption of particles at flat interfaces leads to the formation of two-dimensional monolayers. The geometry and curvature of the interface can be modulated, such that the adsorption of particles leads to the formation of self-assembled structures with various geometries. For example, the adsorption of particles in the watergas interface, such as gas bubbles or oil-water interface in emulsion oil droplets, leads to the formation of selfassembled monolayers that wrap around the shape of the interface, leading to the formation of different self-assembly structures [36–38]. Self-assembly structures of spherical Au/SiO2 Janus nanoparticles mediated by the interface geometry in water/n-dodecane mixtures were created by progressively increasing the fraction of water, leading to a variety of structures from micelles, wormlike micelles, and spherical emulsion droplets (Fig. 14.10) [39]; when the minority liquid is large enough, these transform into colloidosomes of Pickering emulsions [Fig. 14.10(G)–(J)]. The adsorption of particles at the air-water interface of an air bubble obtained by agitation leads to the formation of foam. Unlike molecular surfactant foams, which do not provide sufficient structural resistance and disappear during

252

14. Adsorption and interaction of particles at interfaces

FIG. 14.10

Optical microscope images showing α-dependence of the morphology in self-assembled structures, where α is the fraction of water (minority liquid) added in n-dodecane. (A–I) Optical microscope images of typical structures formed at respective α. (A) Random aggregate. (B) Small micelle-like cluster. (C–E) Rod-shaped micelle-like clusters. (F) Structure observed at a value of α where rod-shaped micelle-like clusters and spherical droplets coexist. (G–I) Spherical droplets in emulsions. (I) Hemispherical droplet attached to the bottom of the observation cell. (J) Magnified image of the framed region in (I). (K) Diagram of the α-range of the observed structures. The scale bars are 5 μm in (A) and (B), 10 μm in (C)–(H), and (J), and 50 μm in (I). Reproduced with permission from T.G. Noguchi, Y. Iwashita, Y. Kimura, Dependence of the internal structure on water/particle volume ratio in an amphiphilic Janus particle–water–oil ternary system: from micelle-like clusters to emulsions of spherical droplets, Langmuir 33 (2017) 1030–1036. doi:10.1021/acs.langmuir.6b03723. Copyright 2017 American Chemical Society.

water drainage, particle foam lamella remains as self-standing membranes after water drainage. SEM images of such membranes are shown in Fig. 14.11. Further reading on the general mechanism of foam formation and classification can be found in the recent work by Obi [40] and Horozov [41]. Particle foams and their applications can be found in a large body of literature work [7, 42–49]. Another parameter playing a significant role in the modulation of interface geometry is particle geometry. Particle geometry determines packing and a second level of modulating the shape of the interface. For example, the geometry of the snowman-type polymeric Janus nanoparticles consisting of a hydrophobic and a hydrophilic lobe can curve the oil-water interface in emulsion such that it is either convex toward oil, which leads to the formation of oil-in-water (o/w) emulsions, or convex toward water, leading to the formation of water-in-oil (w/o) emulsions (see Fig. 13.9). When o/w or w/o Pickering emulsions stabilized by particles are formed from molten paraffin wax, upon cooling,

14.5 Templated self-assembly of nanoparticles at interfaces

253

FIG. 14.11

The SEM images of the Pickering foam lamella structures formed by PDEAEMA particles at a concentration of 10 mg/mL at different pH values. (A) pH 6.3, (B) pH 8.0, (C) pH 9.0, (D) pH 5.0, (E) pH 5.0, and (F) 10.0. (G) The sketch of the setup of preparing Pickering foams by bubbling argon and digital images of the PDEAEMA emulsified Pickering foams at different times (Left: pH 3.0 and right: pH 9.0). From D. Wu, V. Mihali, A. Honciuc, pH-responsive pickering foams generated by surfactant-free soft hydrogel particles, Langmuir 35 (2019) 212–221. doi:10.1021/acs.langmuir.8b03342. Copyright © 2019, American Chemical Society.

FIG. 14.12 (A) Cross-sectional SEM image of the hollow structure resulting from cooling and solidification of the water/paraffin emulsion stabilized by the (2 mL TSPM) AIBN-JNPs and (B) magnified region showing the monolayer at the water-paraffin interface where the preferential orientation of JNPs is such that the PS lobe (darker) lies down toward paraffin. (C) SEM image of the paraffin colloidosome resulting from cooling and solidification of the paraffin/water emulsion stabilized by the (4 mL TSPM) AIBN-JNPs and (D) magnified region showing the monolayer at the colloidosome surface, where the preferential orientation of JNPs is such that the PS lobe (darker) lies down toward paraffin. The insets of (B) and (D) are cartoons depicting the type of emulsion and the orientation of the JNPs, PS (black) lobe, and P(3-TSPM) (white) lobe. Only (A) and (B) samples were Au sputtered. From D. Wu, J.W. Chew, A. Honciuc, Polarity reversal in homologous series of surfactant-free Janus nanoparticles: toward the next generation of amphiphiles, Langmuir 32 (2016) 6376–6386. Copyright 2016, The American Chemical Society.

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14. Adsorption and interaction of particles at interfaces

FIG. 14.13 SEM images of bubbles stabilized by the (A, D) Au-SiO2, (B, E) PS-g-Au-SiO2, and (C, F) PPFBEM-g-Au-SiO2 Janus particles. Panels (D–F) are magnifications of panels (A–C), respectively. Reproduced with permission from S. Fujii, Y. Yokoyama, S. Nakayama, M. Ito, S. Yusa, Y. Nakamura, Gas bubbles stabilized by Janus particles with varying hydrophilic–hydrophobic surface characteristics, Langmuir (2017). doi:10.1021/ acs.langmuir.7b02670. Copyright 2017 American Chemical Society.

the geometry of the structures obtained is solidified. SEM images of self-assembled monolayers of Janus particles resulting from the o/w and w/o emulsions of the molten paraffin wax are shown in Fig. 14.12. Gas bubbles and emulsion droplets have similar properties, e.g., the gas can be thought of as a highly hydrophobic fluid. Gas bubbles can act as templates for the self-assembly of nanoparticles upon interfacial adsorption. For example, Fujii et al. [50] obtained large mono-walled vesicles from Au/SiO2 Janus nanoparticles (Fig. 14.13).

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Nagayama, Capillary forces between colloidal particles, Langmuir 10 (1994) 23–36, https://doi.org/10.1021/la00013a004. [32] A.P. Girard-Egrot, L.J. Blum, Langmuir-Blodgett technique for synthesis of biomimetic lipid membranes, in: D.K. Martin (Ed.), Nanobiotechnology of Biomimetic Membranes (Fundamental Biomedical Technologies), Springer, Boston, MA, 2007. [33] A. Honciuc, R.M. Metzger, A. Gong, C.W. Spangler, Elastic and inelastic electron tunneling spectroscopy of a new rectifying monolayer, J. Am. Chem. Soc. 129 (2007) 8310–8319. [34] M. Bardosova, M.E. Pemble, I.M. Povey, R.H. Tredgold, The Langmuir-Blodgett approach to making colloidal photonic crystals from silica spheres, Adv. Mater. 22 (2010) 3104–3124, https://doi.org/10.1002/adma.200903708. [35] M. Parchine, J. McGrath, M. Bardosova, M.E. Pemble, Large area 2D and 3D colloidal photonic crystals fabricated by a roll-to-roll Langmuir– Blodgett method, Langmuir 32 (2016) 5862–5869, https://doi.org/10.1021/acs.langmuir.6b01242. [36] D. Patra, A. Sanyal, V.M. Rotello, Colloidal microcapsules: self-assembly of nanoparticles at the liquid-liquid Interface, Chem. Asian J. 5 (2010) 2442–2453, https://doi.org/10.1002/asia.201000301. [37] D. Wang, H. Duan, H. M€ ohwald, The water/oil interface: the emerging horizon for self-assembly of nanoparticles, Soft Matter 1 (2005) 412–416, https://doi.org/10.1039/B511911A. [38] A. B€ oker, J. He, T. Emrick, T.P. Russell, Self-assembly of nanoparticles at interfaces, Soft Matter 3 (2007) 1231–1248, https://doi.org/10.1039/ B706609K. [39] T.G. Noguchi, Y. Iwashita, Y. Kimura, Dependence of the internal structure on water/particle volume ratio in an amphiphilic Janus particle– water–oil ternary system: from micelle-like clusters to emulsions of spherical droplets, Langmuir 33 (2017) 1030–1036, https://doi.org/ 10.1021/acs.langmuir.6b03723. [40] B.E. Obi, Fundamentals of polymeric foams and classification of foam types, in: Polym. Foams Struct.-Prop.-Perform, Elsevier, 2018, pp. 93–129, https://doi.org/10.1016/B978-1-4557-7755-6.00005-7. [41] T. Horozov, Foams and foam films stabilised by solid particles, Curr. Opin. Colloid Interface Sci. 13 (2008) 134–140, https://doi.org/10.1016/j. cocis.2007.11.009. [42] B.P. Binks, T.S. Horozov, Aqueous foams stabilized solely by silica nanoparticles, Angew. Chem. Int. Ed. 44 (2005) 3722–3725, https://doi.org/ 10.1002/anie.200462470. [43] B.P. Binks, A. Rocher, M. Kirkland, Oil foams stabilised solely by particles, Soft Matter 7 (2011) 1800, https://doi.org/10.1039/c0sm01129k. [44] B.P. Binks, R. Murakami, Phase inversion of particle-stabilized materials from foams to dry water, Nat. Mater. 5 (2006) 865–869, https://doi. org/10.1038/nmat1757. [45] E. Dickinson, Food emulsions and foams: stabilization by particles, Curr. Opin. Colloid Interface Sci. 15 (2010) 40–49, https://doi.org/10.1016/j. cocis.2009.11.001. [46] A. Stocco, W. Drenckhan, E. Rio, D. Langevin, B.P. Binks, Particle-stabilised foams: an interfacial study, Soft Matter 5 (2009) 2215, https://doi. org/10.1039/b901180c. [47] T.N. Hunter, R.J. Pugh, G.V. Franks, G.J. Jameson, The role of particles in stabilising foams and emulsions, Adv. Colloid Interf. Sci. 137 (2008) 57–81, https://doi.org/10.1016/j.cis.2007.07.007. [48] D. Zabiegaj, E. Santini, E. Guzmán, M. Ferrari, L. Liggieri, V. Buscaglia, M.T. Buscaglia, G. Battilana, F. Ravera, Nanoparticle laden interfacial layers and application to foams and solid foams, Colloids Surf. Physicochem. Eng. Asp. 438 (2013) 132–140, https://doi.org/10.1016/j. colsurfa.2013.02.046. [49] S. Lam, K.P. Velikov, O.D. Velev, Pickering stabilization of foams and emulsions with particles of biological origin, Curr. Opin. Colloid Interface Sci. 19 (2014) 490–500, https://doi.org/10.1016/j.cocis.2014.07.003. [50] S. Fujii, Y. Yokoyama, S. Nakayama, M. Ito, S. Yusa, Y. Nakamura, Gas bubbles stabilized by Janus particles with varying hydrophilic– hydrophobic surface characteristics, Langmuir (2017), https://doi.org/10.1021/acs.langmuir.7b02670.

C H A P T E R

15 A short account of the role of interfaces in Integrated Circuits manufacturing 15.1 Introduction of photolithography and Integrated Circuits manufacturing Photolithography comes from the Greek words “photo” light, “lithos” stone, and “graphos” write. The substrates mostly used, on which nanometer size features can be fabricated photolithographically, are most typically silicone and rarely some other semiconductors such as Ge, In, etc. Integrated Circuits (IC) manufacturing requires the use of Si for the manufacturing of field-effect transistors (FET); therefore, all the photolithographic processes are well established on these substrates. Wafer technology currently enables the manufacturing of high purity, doped or undoped, crystalline or amorphous silicon wafers, which are thin disks, submillimeter thickness, of different diameters from 100 to 450 mm. The manufacturing of processor (chip) units is roughly 20
20 mm on the wafers; the bigger the wafer diameter, the more processor units, called dies, can be produced in one step. For high-volume manufacturing, Si wafers with larger diameters enable the production of more processors and electronic chips, thus enhancing the productivity and efficiency to support the increasing volume of smartphones, tablets, and PCs. Fig. 15.1 shows the approximate evolution of size of the wafer with time and the size and number of dies per wafer that can be produced. The principles of photolithography resemble those of photography, where the substrate (the celluloid film) is first covered by a thin photosensitive layer, called photoresist, typically 100 nm thick by spin coating. The photoresist film is tuned to respond to a wavelength of light such that it either softens (negative photoresist) or hardens (positive photoresist) after being exposed to light. The wavelength of light used is critical in determining the minimum size of the features that can be manufactured. Most of the time the Rayleigh criterion, also known as the diffraction limit, is used, where the minimum size of the feature is determined with the following formula: Size of the feature ¼

λ 2
NA

(15.1)

where λ is the wavelength of light and NA is the numerical aperture of the objective lens focusing the beam of light on the substrate. NA for typical objective lenses is below 1, but for especially wide liquid immersed lenses it can increase to 1.6 (see Fig. 15.2). The evolution of the smallest features or the "node" (typically the length of the gate of the field-effect transistor) that could be produced photolithographically with the light sources of different wavelengths is shown in Fig. 15.3. In four decades, the technology node has decreased dramatically, with about two orders of magnitude, from almost 500 nm in the mid-1980s to 5 nm or less in 2020. For the entire period spanning almost two decades, the 193 nm wavelength of light from the ArF laser has been the preferred light source in photolithography, the yellow region in Fig. 15.3. Technology nodes using a shorter wavelength of light, 157 nm from the F2 laser, such as the deep UV (DUV) photolithography, were also developed in parallel to the ArF but it remained limited in scope due to the high development cost of new materials; because normal lenses absorb the DUV light, all the optic materials were made from CaF2, in addition to new photoresist technologies, masks, etc. Because it did not bring significant competitive advantages and due to the high cost of material development, the technology for the 157 nm wavelength was abandoned in favor of the new 193i nm, using surprisingly a larger wavelength but followed by the letter “i,” which stands for immersion. The objective lens was immersed in water (or a higher index of refraction liquid) to increase the NA value and thus enable a smaller photolithographed feature size. In this way, the technology node size could be pushed down to 65 nm.

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FIG. 15.1 The time evolution of the wafer size diameters and the number of 20 mm
20 mm dies per wafer estimated for a 0.08-mm horizontal and vertical spacing and wafer edge clearance of 5 mm.

FIG. 15.2

The “dry” (left) and the water (right) immersed objective lens exposure of a wafer surface.

15.1 Introduction of photolithography and Integrated Circuits manufacturing

259

The 193-nm ArF photolithography was also the enabler of smaller nodes, called the subdiffraction limit nodes, using other strategies such as double patterning. The future development in the IC manufacturing technologies is updated on yearly bases by the International Technology Roadmap for Semiconductors (ITRS). The extreme EUV photolithographic technology has been under development for more than 20 years and has been placed under doubt several times, but as of 2019 the technology has been declared mature and will probably enter in production of chips in 2020. The challenges faced by the developers for EUV were extreme because, unlike all the other technologies, reaching sufficient intensities for production of the 13.5 nm wavelength was exceptionally difficult as molten Sn was bombarded by a high-powered CO2 laser to produce plasma, which in turn emitted the 13.5 nm light. The whole process takes place in vacuum, so that the radiation is not absorbed by air; for the same reason, only reflective optics can be used and photoresist and other materials had to be redeveloped and redesigned. Other photolithographic technologies not currently used in high-volume production of processing units, but useful in research and specialized applications, use different light or electron sources, as their name suggests: electron-beam lithography and X-ray lithography. The general photolithographic process of manufacturing ICs has two major aspects, the front-end-of-line (FEOL) and back-end-of-line (BEOL) fabrication. The FEOL starts with a pristine Si wafer covered with a thin layer of photoresist which is exposed to light through a mask. The mask is the blueprint of all the features to be imprinted on the wafer; the mask can be a shadow mask or contact mask, and the blueprint is drawn in a Cr or Mo metal layer on quartz. The highly specialized machining tool in which the exposure of the wafer is performed and manipulated to a nm scale precision level is called a “stepper”; the stepper exposes approximately 20
20-mm domains stepwise on the surface of a Si wafer (Fig. 15.4A). The photoresist is a water insoluble polymer blend between polyacrylate derivatives and photoacid generator molecules. When exposed to light, the photoacid generator decomposes into a strong acid that cleaves the ester group between some strongly hydrophobic groups grafted on the polyacrylate backbone. Upon the ester bond cleavage, the polyacrylic acid polymer becomes soluble in basic solutions, becomes soft, and can be removed away by a basic developer, typically NH4OH, tetramethyl ammonium hydroxide (TMAOH), or other bases (Fig. 15.4B). The basic solution removes the bulk photoresist that has been exposed to light, while leaving the nonexposed photoresist in place. The removal of the photoresist by the developer is not always complete, leaving often some areas with residues, the nonremoved materials or particles that are considered as defects. To improve the sharpness of the patterned features and minimize the defects, a rinse phase must be performed after the development phase (Fig. 15.4C). Typically, the rinsing phase can be done with isopropanol/water mixture or water plus surfactant solutions to clean well the trenches, remove the particles, and improve the sharpness. The rinsing phase is critical because care must be taken to ensure that the photoresist does not swell and leaves it pristine after cleaning. After

FIG. 15.3

The time evolution of IC manufacturing technologies, function of the wavelength of the light source, technology node and diagram of a field-effect transistor (FET) manufactured in Si, where the technology node is loosely associated with the gate length.

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15. The role of interfaces in Integrated Circuits manufacturing

FIG. 15.4

Front-end-of-line (FEOL) process in IC manufacturing: (A) exposure to light; (B) developing and removal of the photoresist; (C) rinsing and removal of the particles and photoresist residues; (D) transferring of the pattern into SiO2; (E) removal of the masking photoresist; and (F) formation of SiO2 gates and n or p+ doping of the Si by ion-implant.

the rinsing phase, the etching phase begins, where the layers of Si or SiO2 from the trenches not protected by the photoresist are removed after reaction with HF. Once the Si and SiO2 trenches are carved this way into desired areas, a new rinsing phase is applied to remove the unwanted rests and wash away the HF. After the ion-implantation with the formation of the drain and the source, a thin SiN insulating layer is deposited on the regions that should not be covered by metal, to prevent a short circuit between electronic elements, and finally the BEOL process can begin (see Fig. 15.5). The BEOL manufacturing starts with the deposition of the first metal layer for making of the metallic interconnects between the FETs made on the surface of the Si wafer. For interconnects, Cu metal is first deposited as a thin sheet filling all the voids. The deposition of Cu takes place electrochemically. For the Cu to deposit well inside topologically conformal into the small voids between the photolithographed structure, the electrochemical plating solution must have a sufficiently low surface tension to ensure a good wettability of the deep trenches and eliminate formation of voids. Because the thin metal layer deposited is conformal to the substrate, meaning hills and valleys follow the topography of the surface structure underneath, it needs to be planarized by chemical mechanical polishing (CMP) methods containing an “abrasive” colloidal slurry of nanoparticles to remove layers as thin as one nanometer from the surface. After the metal has been planarized, a photoresist is next applied to the wafer. After a photoresist application, the wafer is exposed to light through another mask containing the blueprint of the metallic interconnects to be fabricated in that layer. Next, the exposed photoresist is removed with a developer, the rinse phase follows, and finally the nonexposed photoresist patterns are revealed. The nonprotected metal by the photoresist is removed by etching solutions, and thus the first Cu interconnects are formed. The Cu interconnects in a fully functional processor can be regarded as a layer-by-layer network of wires connecting various circuit elements and FETs manufactured in the FEOL on the surface of the wafer. The amount of wire layers depends on the complexity of the processor, number of transistors, and the complexity of the circuit. Several hundreds or even thousands of layers of Cu interconnects can be built iteratively in BEOL in a modern processor.

15.2 Role of interfaces in photolithography Empirically founded knowledge in surface and interfacial science is extremely important in the manufacturing of IC, MEMS, photovoltaics, LEDs, etc. via photolithography. Surface and interfacial processes intervene in almost each aspect of the IC manufacturing, such as the design of liquid immersion lenses, waver cleaning, adhesion of the photoresist, rinsing of photoresist after exposure, stripping of photoresist after ion implant, wettability of the electroplating

FIG. 15.5

Main back-end-of-line (BEOL) fabrication steps for making metallic interconnects.

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solution, etc. The ramifications are so complex that it would be an impossible task to exhaustively uncover all interfacial aspects in a single chapter. As mentioned earlier, to obtain smaller nodes, some challenges were overcome by designing liquid immersion lenses to increase the NA of the lens and thus reduce the size of the features to be manufactured. The use of a liquid in a stepper meant new challenges because the water must travel with the objective on the surface of the objective to the new exposure location without leaving traces. To enable this, photoresists or photoresist topcoats that have ultralow surface energies were designed, for a large contact angle and a low contact angle hysteresis to enable the travel of the liquid droplet along with the lens to withstand rapid and accelerated movements [1]. This was provocation where the surface science knowledge was necessary. In addition, with the manufacturing of lower size features in the smaller nodes, 32, 17 nm, the surface cleanliness in terms of particle counts per wafer as well as other impurities has tightened, yet the rinsing materials used were not enough. A high surface tension liquid used as a rinsing liquid during or after development meant that the capillary force acting between the fabricated surface features was too strong, and thus the nanoscale objects on the surface could be washed away.

15.2.1 Surface tension and pattern collapse of nanometer scale structures A cleaning step intervene after each light exposure and development step. Nanometer features have a high risk of collapse during the drying process under the capillary force during drying, and these became severe after the transition from the KrF to ArF multipatterning and ultimately EUV and the decrease of the feature size [2]. The mechanism of pattern collapse has been initially described by Tanaka [3] in the early 90s and recently reevaluated by Chini and Amirfazli [4]. The geometry of features made in photolithography is decided by the circuit design needs. The deciding factor to pattern collapse is the aspect ratio (h/w, Fig. 15.6) of the feature as well as its lateral dimensions. The most prone to collapse are smaller structures with a high aspect ratio. Fig. 15.6A depicts a line-trench pattern, typically used as a

FIG. 15.6 (A) Depiction of a line-trench photoresist pattern that is prone to pattern collapse during the drying process as the interspace volume is partially filled with liquid, due to: (B) Laplace pressure and (C) surface tension force acting at the three-phase line. The parameters of the feature are: h-height, L-length, w-width of the wall, d-distance between features. (D) SEM images of photoresist collapse, (1) bend, (2) break, (3) tear, and (4) peel. Reproduced with permission from T. Tanaka, M. Morigami, N. Atoda, Mechanism of resist pattern collapse during development process, Jpn. J. Appl. Phys. 32 (1993) 6059–6064. https://doi.org/10.1143/jjap.32.6059. Copyright (1993) The Physical Society of Japan and The Japan Society of Applied Physics.

15.2 Role of interfaces in photolithography

263

model to test the effects of the rinsing solution on the pattern; the two main stress factors are the Laplace pressure and surface tension acting at the three-phase line of the features during the liquid drying process. The Laplace pressure for the line-trench pattern, Fig. 15.6B, is γ ΔP ¼ R The curvature of the meniscus of the liquid between the photoresist features 1/R is related to the distance between the photoresist lines by R¼

d 2 cos θ

Therefore, the Laplace pressure is ΔP ¼

2γ cos θ d

In the above equation, θ is the equilibrium contact angle, although the receding contact angle would be a more appropriate description of the phenomena taking place during liquid drying from the wafer surface. Thus, the force acting on the photoresist walls due to Laplace pressure is FLaplace ¼

2Lhγ cos θ d

(15.2)

From the above equation, it becomes obvious that to minimize the pressure acting on the walls of the photoresist feature, the surface tension of the rinse liquid must decrease, and the contact angle must increase. As we have seen before, the low surface tension liquids have a generally low contact angle on surfaces. Therefore, the approach to simultaneously increase the contact angle while decreasing the surface tension poses a technical challenge. The importance of finding appropriate rinse liquids for the industry can be gauged also from the significant number of patent applications [5–10] and literature studies [4, 11–13]. Formulations containing surfactants have been tested. The advantage of using surfactant formulations, in contrast to the pure solvents with low surface tension, is that specially designed surfactants can adsorb on the walls of the photoresist and modify its surface to increase the contact angle while keeping the surface tension of the liquid low. In this context, it is worth mentioning the phenomenon of autophobicity, described in Chapter 5, Section 5.12.1, that some specially designed surfactant formulations can achieve. A mixture of two surfactants, among which one is a hydrophobizer to increase the contact angle of the rinse solution on the photoresist, has also been proposed [5]. Chini and Amirfazli [4] have observed that, in addition to the Laplace pressure, the surface tension component normal to the wall of the feature, i.e., the surface tension force, is also responsible for the pattern collapse during the rinse and drying phase (see Fig. 15.6C). The surface tension force is the projection of the surface tension vector on the axis normal to the wall of the feature and is FSTF ¼ Lγ sin θ

(15.3)

where L is the length of the feature as depicted in Fig. 15.6C. In fact, by comparing Eqs. (15.2), (15.3) and assuming a contact angle θ ¼ 45 degrees, one can easily see that the magnitude of the surface tension force is comparable to the force due to Laplace pressure [4]. Also, in this case, the lowering of the surface tension would greatly reduce the pattern collapse. The best performing surfactants have a static surface tension at CMC below 19 mN/m, a very fast dynamic surface tension, required by the rapid spin-drying process, and an ultralow CMC value to minimize photoresist interactions and swelling. Surfactants have also been added in the developer for the same purpose. However, using surfactant formulations has its downsides. Surfactants are most effective at concentrations close to or above their CMC value, but at these concentrations they can swell the photoresist polymer and cause damage by penetrating the photoresists’ polymer networks. This aspect can be mitigated with specially designed surfactants that have an ultralow CMC value, which will significantly minimize the swelling of the photoresist features. The second option is to tweak the surfactants’ molecular structure to prevent penetration into the polymer network, either through bulky steric effects or by introducing functional groups that have a low mixing affinity to the photoresist’s chain network, fluorinated or trimethylsilyl functional groups, etc. Alternatively, the supercritical fluids that have no surface tension are gaining in popularity as alternatives to aqueous and solvent rinse fluids. Among these, the supercritical CO2 (sCO2) is the most popular due to its availability, nontoxic nature, and technical accessibility in terms of pressure and temperature. In addition, sCO2 has good solvation ability for many organic molecules. sCO2 has no surface tension and thus demonstrated the ability to prevent pattern

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15. The role of interfaces in Integrated Circuits manufacturing

collapse. In addition, sCO2 quickly penetrates the trenches and the intricate patterns photoresist patterns and is used either as a photoresist rinse or photoresist stripping agent after hard baking. In addition, the good solvent properties may also solvate the particle residues from the wafer surface. A cosolvent can be added to enhance cleaning such as isopropanol, water, acetone, etc. A great advantage of sCO2 is that it leaves no residues on the surface of the wafer. The supercritical sCO2 can be used either directly as a rinsing agent [14, 15] or during the drying phase, where the rinse process begins with an aqueous solution which is slowly replaced by sCO2 so that during drying the surface tension is kept at zero [15]. Because some photoresists are water based, specially designed surfactants with a good solubility in sCO2 have been used as a means to incorporate residual water in micelles and remove it [16].

15.2.2 Particle removal in IC manufacturing Micro- and nano-sized particles present on the wafer have obvious damaging effects on the manufacturing of the IC. One source of particle contamination comes from the exterior, which is mitigated as much as possible by moving the production process to a clean room environment. The ISO clean room classification is rated according to the number of particles per cubic meter allowed such that the cleanest ISO room rated ISO-1 is allowed to have a maximum of 10 particles of 0.1 μm and two particles of 0.2 μm/m3 of air. However, the main source of particle contaminants comes from the solid residues left on the wafer after the drying process, particles that can be both of organic or inorganic nature, such as salts, dissolved photoresists, particle contaminants from lenses, machine interiors, impurities in solvents, etc. The success of the removal of such particle contaminants with rinse solutions depends on the particles’ adhesion strength and interfacial energy of the particle-wafer surface. Knowledge of the nature of such bonding allows a formulator to design the appropriate rinse solution (Fig. 15.7). The general mechanisms available to the formulator for particle removal are dictated by the particle-substrate interaction. Particles can attach to the surface of the wafer via van der Waals forces, electrostatic interaction, capillary forces, or chemical bonding. Removal of physically attached particles can be done with chemical formulations containing wetting agents that displace the particle from the surface, emulsifying agents that carry organic residues away from the surface, by tuning the surface potential to promote electrostatic repulsion, etc. The chemical formulations can be combined with physical methods such as ultrasonic, UV ozone, plasma, etc. Removal of chemically attached particles is more difficult, such as that of hard-baked and cross-linked photoresist residues, which can be removed by formulations containing etching agents for particle undercutting (Fig. 15.7). The types and composition of particle residues that need to be removed are different in FEOL and BEOL. In BEOL (Fig. 15.5), the nature of post etch residue (PER) (Fig. 15.5) is ill-defined and can contain photoresist, metal, metal oxides mixed with Si which are deposited on Cu or Al interconnects and low k dielectrics. Therefore, the chemical formulations for particle removal must be tuned to the particular system. In BEOL, the organic-based solvent formulations such as N-methyl pyrrolidone (NMP) are favored over the aqueous ones, to avoid metal corrosion. However, less toxic nature aqueous formulations are constantly being developed; semiaqueous-based rinse formulations for PER removal must contain corrosion inhibitors for Cu and Al interconnect, such as amines, as well as low-k material passivating agents [17, 18]. For example, a commercially available product EKC265 of DuPont contains hydroxyl amine (corrosion inhibitor), monoethanol amine, catechol, and water to remove the PER photoresist by swelling and slow dissolution. Undercutting and liftoff of the PER photoresist can be achieved also by the addition of inorganic acids whose concentration must be tuned to achieve only a slight underetching of the metallic underlayer to enable the liftoff of the photoresist (Fig. 15.7). In addition, the aqueous and semiaqueous formulations enable the use of surfactants which can significantly improve the photoresist and particle removal. Another type of wet chemical cleaning is needed in BEOL, namely the postchemical mechanical polishing (CMP). Copper interconnects serve to electrically connect the devices on the wafer; the Cu interconnects are made by first forming trenches into a dielectric, e.g., SiO2 (see Fig. 15.5) after depositing a thin metallic barrier to avoid the Cu diffusion into the dielectric, which is followed by the deposition of Cu into the trenches. After Cu deposition, the wafer is polished using CMP. The CMP removes the excess of Cu and planarizes the surface. After CMP, a large number of particles can be found on the wafer such as inorganic particles and organic residues. These particles are typically removed by a brush-scrubbing process under continuous flow of rinse chemical formulations. These formulations are aqueous formulations containing metal corrosion inhibitors, typically amines and surfactants, and strong dispersing agents such as polyacrylates, polysulfonated polymers and copolymers thereof [19]. FEOL uses different wet chemistries than BEOL. For example, photoresist stripping is typically achieved with a strong oxidizing agent, the SPM solution, consisting of 2:1–4:1 H2SO4 (96 wt%):H2O2 (30 wt%) at 100°C. The SPM solution oxidizes the photoresist to water-soluble acids that are removed in a subsequent water rinsing step [20]. For

15.2 Role of interfaces in photolithography

FIG. 15.7

265

Cartoon depicting the types of particles attached to the substrate by physical or chemical bonding and strategies for particle and residue

removal.

particle removal, a standard cleaning step which the IC industry uses is the RCA clean, developed by Werner Kern while working for a company with the same name (Radio Corporation of America) [20]. The RCA clean consists of several steps. The first step, SC-1 or standard clean-1, can be performed with a solution containing NH4OH (29 wt %), H2O2(30 wt%), deionized water, with an overall pH ¼ 10. In this step, the particles from the wafer are removed by electrostatic repulsion, as a high pH value will render the surface of the Si wafer and that of the contaminant particles strongly negatively charged. In addition, a cca. 10 nm SiO2 layer is formed on the Si wafer surface via oxidation, which is soluble in the pH 10 solution; thus, the combined mechanisms of surface oxidation, etching, and electrostatic repulsion will contribute to the particle removal. Optionally, the SC-1 procedure can be followed by an oxide removal with the HF step. A second solution, SC-2, consists of HCl (37 wt%), H2O2 (30 wt%), deionized water, which has the role of removing the metallic contaminants (present as insoluble hydroxides) introduced in SC-1, and secondly to passivate the SiO2 surface. The RCA clean method with SC-1 and SC-2 is typically applied for clean Si wafers, but the SC-1 solution has been used at different steps in the manufacturing process [21]. The RCA method is only one of the few recently developed formulations containing high performance surfactants, to prevent the pattern collapse as previously discussed.

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15. The role of interfaces in Integrated Circuits manufacturing

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Index

Note: Page numbers followed by f indicate figures and t indicate tables.

A

Activation energy, 88–89, 94, 149, 244, 245t, 245f, 246–247 Adhesion energy, 10–11, 90–91, 117, 121 Adhesion forces, 1–2, 9–11, 22f, 120 Adhesion of cells, on rough and nanostructured surfaces, 103–104 Adsorption activation energy of, 246–247 free energy, 239–240 interfacial, 244–247 of nanoparticles at interfaces, 239–244 Adsorption energy, 243, 245t, 245f Aerosol-OT (AOT). See Anionic bis (2-ethylhexyl) sulfosuccinate Aerosol spray coatings, 36–37, 37f Agglomeration, 212 Aggregation, 188–190, 199, 202, 206, 214, 221–222 Aggregation number, 60 Aging effects, 34 AgNO3, 212 Alkane sulfonates, 47–48 Alkylated polyethylene oxide surfactants, 223 Alkyl carboxylic acids, on Al2O3 surfaces, 147 Alkyl ketene dimer (AKD), 85 Alkylphenol ethoxylate surfactants, 50 Alkylphosphate monoester surfactants, 49 Alkylpolyglycoside surfactants (APG), 52, 53f Alkyl silane attachment, on hydroxylated surfaces, 147 Alkyl thiol attachment, on gold, 147 Alternating current (AC), 159 Ammonium peroxydisulfate (APS), 232–234, 233f Amphiphiles, 2, 29–30, 43, 44f, 67–68 Amphiphilicity, 43, 64–65, 67–69 Amphoteric surfactants, 49–50, 51f Anionic bis(2-ethylhexyl) sulfosuccinate, 224 Anionic surfactants, 46–49, 47–49f Anisotropic nanoparticles, 228 Antifogging surfaces, wettability of, 94–95 Arachidic acid, 102–103, 144, 172 Archetypal unimolecular device, 172–175, 173–174f Arrhenius equation, 7 Atomic force microscopy (AFM), 82–84

Attractive van der Waals interactions, 182–183 AuCl3, 213–214 Au/SiO2 Janus nanoparticles, 254, 254f Autophilic effects, 105–106, 106f Autophobic effects, 105–106, 106f Aviram-Ratner (AR-model), 172 Axisymmetric drop shape analysis method (ADSA), 34 Azide-alkyne reactions, 149–150, 150f Azobisisobutyronitrile (AIBN), 221–222, 224 2,20 -Azobis-(2-methyl butyronitrile), 221–222

B

Bacillus subtilis, 101 Bancroft’s rule, 29–30 Barometric law, 5–6 Berthelot’s hypothesis, 119 Bidentate dialkyl dicarboxylic acids, 147–149 Binding energy vs. electronic coupling strength, 167 Biomimetic functional surfaces, 98–103, 98f Biosurfactants, 56–58 Boltzmann distribution, 1, 7, 195–196 Brust method, 213–214 Bubble pressure method, 34 Bulk heterojunction (BHJ) devices, 161 Bulk organic electronics, 170 Bulk polymerization, of Pickering emulsion, 229–232, 231–232f

C

Candida bombicola, 56 Capillary action, 25–26 Capillary forces, 108–109, 248–249 Capillary interactions, 248–249, 249f Capillary length, 1, 23–25, 34 Capillary number, 26–30, 38 Capillary rise phenomenon, 25–26, 26–27f, 32 Capillary transfer, 96 Captive air bubble method, 97f Captive bubble method, contact angle measurement with, 97–98 Carboxyl-amine coupling, 149, 150f, 151–152 Carboxylates, 46 Carpet model, 145–146 Cassie-Baxter model, 91–93, 92f, 93t Cassie-Baxter wetting state, 93–95 Cationic surfactants, 49, 50f

267

Cetyltrimethylammonium bromide (CTAB), 223–224 Chaotropes, 199 “Cheerios effect,”, 248–249 Chemical flooding, 38–39 Chemical mechanical polishing (CMP), 260, 264 Chemical potentials, 5, 141, 195–196, 200–201 Chemical synthesis, of lyophobic colloids, 211–214 Chemisorption, 147, 149, 157 Cloud point, 62 Cohesion forces, 1–3, 9, 11, 143–144 Colloidosomes, 109, 230–232, 232f, 251 Colloids classification, 209 dispersions, 209, 210t from double exchange reactions, 212 lyophilic, 215 lyophobic, 209 chemical synthesis of, 211–214 interfacial forces, 214 preparation of, 209–211 stability, 214, 215t metal hydroxide, formation of, 212 physical condensation, 211 Prussian blue formation, 213 purification of, 214 solvent replacement method, 211 sulfur, 211, 211f Condensation nuclei formation of, 211–212 growth of, 211–212 physical, 211 pressure, 212 Conductive polymers, 162–163 Contact angle, 22, 79–80, 80f, 86–88, 95 of aqueous fluid, 112 goniometer, 81f hysteresis, 88–90, 89–90f of liquids on macroscopic surfaces, 80–84 measurement of, 97–98 captive bubble method direct, 108 of micro- and nanoparticles, 107–113, 108–110f

268 Contact energy barriers, 158 Contact geometry, 169 Cosmotropes, 199 Coulombic interaction, 247–248 Covalent bonding, 69, 149, 166–167 Critical micelle concentration (CMC), 58, 62, 67, 140, 142, 263 Critical packing parameter (CPP), 60–61, 71f Critical surface tension, 126 Cross polarizers, 62 Cu interconnects, 260, 264 Curd soap, 46 Curved liquid surfaces, 27–29, 27f Cyclic voltammetry, 155–156

D

Dative bonding, 166 Datta-Paulson (DP-model), 172–174 Davies’ method, 64 Debye interaction, 179 Debye length, 60–61, 200, 203, 214, 247–248 Deep UV (DUV) photolithography, 257 Derjaguin-Landau-Verwey-Overbeek (DLVO) forces, 204–208, 204–208f theory, 201–202 Desorption free energy, 242–244, 243f Di-alkyl ketone (DAK), 85 Dichloromethane (DCM), 9, 130–131, 142–143 Dicyclohexylcarbodiimide (DCC), 149 Diffuse double-layer theory, 195 Diffusion, 96, 105–106, 222–223, 246–247 Dip-coating methods, 3 Dipole-dipole interaction, 120, 187–188, 247–248 Direct current (DC), 159 Direct tunneling, 171 Disjoining/conjoining pressure, 89–90 Distribution function, of counterions in absence of electrolyte, 195–197, 196f in presence of electrolyte, 197–199, 198t, 198f Divalent ions, 199 Divinylbenzene (DVB), 225f, 227 Dodecyltrimethylammonium bromide (DTAB), 224 Double cantilever method, 21 Double-dipole potential Δddipole, 157 Double-layer interaction force, and energy, 200–201, 201f, 202t Drop shape analysis, 32 Du No€ uy ring method, 32 Dupre equation, 117 Dye-sensitized solar cell (DSSC), 161–162 Dynamic contact angle, 86–88, 87f Dynamic light scattering (DLS), 204 Dynamic surface tension, 34–37, 67

Index

E

Electrical contacts to single molecules vs. monolayers of oriented molecules, 165, 166f Electric double layer, 195 Electroactive organic layer, 155–156 Electrodialysis, 214 Electronic coupling strength vs. binding energy, 167 Electron injection, 158–159, 160f, 161 Electron microscopy, 60–62, 109 Electron transfer, 3, 166, 167f, 168–169 Electron tunneling, 170–171, 174–175 Electrophoretic methods, 204 Electrophoretic mobility, 203 Electro-responsive surfaces, 94 Electrostatic discharge circuits, 160 Electrostatic forces, 144, 248 Electrostatic interaction, 185–186, 244, 247–248 Emulsion polymerization polymeric nanoparticles synthesis via, 217–229 with polymerizable surfactants, 222–223 in surfactants, 218–223, 219f seeded, 226–229, 228–229f surfactant-free, 221–222 ultrasonic-assisted, 224–226 Emulsion radical polymerization, 217 Emulsions, 29–30 formation, 218 micro, 217–218 mini, 217–218 oil-in-water (o/w), 217–218 self-assembly in, 63–64 water-in-oil (w/o), 217–218 Endocrine disruptors, 49–50 Energy of adhesion, 117–119, 118f Fowkes’ model for, 119–120, 120f of nanoparticles, 129–132, 130–132f Energy of cohesion, 14, 16, 118, 118f Enhanced oil recovery, interfacial tension in, 38–39 Ensemble molecular junctions, 165 Enthalpy, 135 Environmental scanning electron microscopy (ESEM), 82–83 Ethoxylated surfactants, 51f, 52, 62 3,4-Ethylenedioxythiophene (EDOT), 232–234, 233f Eutrophication, 70–73 Excess function, 137–139

F

Fajans-Paneth adsorption rule, 212–213 Fatty acids, 46, 51, 53, 142–143 Fatty acid sorbitan esters, 53, 54f Fatty alcohol ethoxylates, 50–51 Fatty amine ethoxylates, 51 Fe(OH)3, peptization of, 214 Fermi level, 155–158, 157f Fibronectin, 103–104 Field-effect transistor, 162–163, 257 First law of thermodynamics, 135 Flocculation, 199 Flory-Huggins interaction parameter, 192

Flotation force, 249 Flotation process, 111–112 Fluorosurfactants, 55–56 Foams, 29–30 self-assembly in, 63–64 sphere, 63 Forces capillary, 248–249 flotation, 249 immersion, 249 interfacial, 214 tensiometer, 37 Fowkes’ model, 119–120, 120f Fowler-Nordheim tunneling regime, 172 Fox-Zisman model, 126, 127f Fracture method, 21 FreSCA method, 108 Freundlich isotherm, 140 Functional antibiofouling surfaces, 104

G

Gangue, 111–112 Gas bubbles, 27, 30, 34–35, 63, 112, 251, 254 Gas flotation, 111 Gel-trapping technique (GTT) method, 108–109 Gemini surfactants, 56, 57f, 67 Gibbs adsorption equation, 139, 142 Gibbs adsorption isotherm, 137–138, 141–142 Gibbs dividing line, 137–139, 138f Gibbs-Duhem equation, 39, 137 Gibbs free energy, 135, 188–190, 210, 239–240 Gibbs’ isotherm equation, 142 Gibbs monolayers, 141–142 Gibb’s thermodynamic theory, 31–32 Girifalco-Good equation of state, 123 Gold, colloidal, 213–214 Gouy-Chapman diffuse layer model, 195, 196f theory, 195 Grahame equation, 200 Griffins’ method, 64 Guerbet alcohols, 50–51 Guerbet reaction, 50–51

H

Hamaker constant, 180–184, 182t, 184t, 206 Hansen solubility parameters, 191–192 Helmholtz double-layer model, 195, 196f Helmholtz free energy, 135 Highest occupied molecular orbital (HOMO), 155–156, 158–160 Highly oriented pyrolytic graphite (HOPG), 79–80, 90–91 Hildebrand solubility parameters, 191–192, 192t Hoffmeister series, 191, 199 Homogeneous nucleation, 219–220, 226, 228 H€ uckel’s approximation, 204 Hybridization, of frontier molecular orbitals, 157 Hydration force, repulsive, 190–191, 191f Hydration pressure, 125 Hydrogen bonding, 10, 119, 123–124, 185–187, 187t Hydrolysis reaction, 211–213

269

Index

Hydrophilic-lipophile balance (HLB), 64–65, 64–66t, 69, 230 Hydrophobic interaction, 188–190, 189f, 199, 204–208, 221 Hydrophobicity of, oligomers, 218–219

Kornilovitch-Brakovsky-Williams (KBWmodel), 172 Krafft point, 62 kT criterion, 7, 7f kT factor, 1

I

L

Icephobic surfaces, for aircraft industry, 101–103 Immersion depth, 109, 110f, 229–230, 231f Immersion force, 249, 249f Indium tin oxide (ITO) glass, 160 Induction force, 179 Inelastic electron tunneling spectroscopy (IETS), 172–174 Inelastic tunneling, 167f, 170–171 Inkjet printing method, 164 Inner Helmholtz plane (IHP), 195, 196f Insoluble films, 142–143 Integrated circuits (IC) manufacturing, 257–260 back-end-of-line (BEOL) fabrication, 259–260, 261f, 264–265 front-end-of-line (FEOL) fabrication, 259–260, 260f interfaces role in particle removal, 264–265, 265f surface tension and pattern collapse, 262–264, 262f time evolution of, 257–259, 259f Interfacial adsorption, 244–247 Interfacial adsorption isotherms, 139–140, 140f Interfacial energy, 10–11, 16–21, 18–20t, 18f, 21f, 215, 245–246 Interfacial forces, of lyophobic colloids, 214 Interfacial free energy, 220–221, 239–240 Interfacial models, 126–128 Interfacial polymerization, of Pickering emulsion, 232–234, 233f Interfacial tension, 217–218, 227, 239, 245–246, 246f in enhanced oil recovery, 38–39 between liquids, 14–16, 15f in particle growth stage, 220–221 surface tension measurement, 32–37, 33f, 35f with temperature, 39 unit vectors, 239, 240f International space station (ISS), 23–24 International Technology Roadmap for Semiconductors (ITRS), 257–259 Ionization potential (IP), 155–156

J

Janus balance, 68–69, 230 Janus nanoparticles, (JNPs), 228–229 seeded emulsion polymerization for preparation of core-shell and asymmetric, 226–229, 228f Janus particles (JPs), 67–69, 68f, 70–71f Jurin’s law, 26, 29

K

Kelvin equation, 30–31, 31t, 226 Kinetic stability, 29–30, 209, 214, 217–218 Kolmogorov scale, 226

Landauer’s formalism, of ballistic transport, 169–170 Langmuir balance, 145 Langmuir-Blodgett (LB) films, 143, 145 Langmuir-Blodgett (LB) method, 3, 250–251, 251f Langmuir-Blodgett (LB) monolayers, 143–146, 145–146f Langmuir isotherm, 139–140 Langmuir monolayers, 142–144 Laplace equation, 35 Laplace pressure, 27–29, 27f, 29f, 218, 262f, 263 Laplace’s law, 80 Latex nanoparticles, 226–227 Layer-by-layer (LbL) method, 250–251 Lifschitz’s theory, 124, 182 Light-emitting diodes (LEDs), 62 Light sensitizer, 161–162 Linear alkyl sulfates (LAS), 49 Line-trench pattern, Laplace pressure for, 262f, 263 Liquid crystal displays (LCDs), 62 Liquid-gas (vapor) interface, 14 Liquid-liquid interfaces, 14 adsorption of particle immersed in, 240, 240f Gibbs free energy, of particles’ adsorption, 239–240 Localized surface plasmon resonance (LSPR), 214 London dispersion forces, 179 Lowest unoccupied molecular orbital (LUMO), 155–156, 158–159 Lyophilic colloids, 215 Lyophobic colloids, 209 chemical synthesis of, 211–214 interfacial forces, 214 preparation of, 209–211 stability, 214, 215t

M

Macroscopic efficiency, 38 Macroscopic sessile droplets, 81–84, 81–84f Marangoni effect, 25, 100, 101f Marangoni flow, 100 Marcus’s theory, 170 Maximum bubble pressure method, 34 Metal-insulator-metal (MIM) junction, 171–172, 171f Metallic nanoparticles, 209, 214 Metallic sols, from reduction reaction of salts, 213–214 Metal-organic (MO) interfaces, 166–169, 167f, 168t electron transport, 158–159 energy band diagram of, 158f energy levels, 155–157 organic electronic devices and, 159–164, 160f physicochemical properties of, 155 weak vs. strong coupling, 166–169

Metal-organic-metal (MOM) junction, 160f, 166, 169–175 Methyl methacrylate (MMA), 130–131, 219–220 Micelles, 52, 212 aggregation number, 60 exterior, 59–60 interior, 59–60 inverse, 60–61 monomer-swollen, 218–219 Prussian blue colloid, 213 and self-assembly, 67 spherical, 58 structural complexity, 61–62 surfactant, 215 Microemulsions, 224 Microemulsion polymerization, 224 Microscopic sessile droplets, 81–84, 81–84f Miniemulsion polymerization, 223–224 MO interfaces. See Metal-organic (MO) interfaces Molecular dipole moment, 145, 157 Molecular rulers, 10 Molecular scale electronics, 165 Molecule dyes, 162f Monomers, 218 hydrophilic, 219–220 hydrophobic, 221–222 insoluble, 220 waterborne, 218–219 Morton’s equation, 227

N

Nanoemulsions, 224. See also Microemulsions Nanoparticles interfaces adsorption, 239–244 capillary interactions, 248–249 electrostatic interaction, 247–248 templated self-assembly, 251–254, 252f Langmuir-Blodgett (LB) method, 250–251, 251f Nanopillars, mushroom-shaped, 101, 101f Natural functional surfaces, 98–103, 98f Nernst equation, 6, 195–196 Neumann’s equation of state, 123–124 Neutron scattering techniques, 62 N-methyl pyrrolidone (NMP), 264 Non-DLVO forces, 202, 204–208, 204–208f Nonionic surfactants, 50–55 Non-Newtonian liquids, 202 Non-Schottky-type organic diodes, 160 Notched-beam technique, 21 Nucleation, 218–220 Nuclei coagulation, 226 Nucleophilic substitution reactions, 151–152, 152f

O

Octadecyltrichlorosilane (OTS), 147 Ohm’s law, 170 Oil-in-water (o/w) emulsions, 209–210, 217–218, 252–254 Oil-water interface, particle adsorption at, 245–246, 246f Oil-water interfacial energy, 209–210

270 α-Olefin sulfonates, 48 Oligomers, hydrophobicity of, 218–219 “Omniphobic” surfaces, 100–101 Open-circuit voltage (VOC), 161 Orbital mediated tunneling (OMT), 170, 174–175 Ore separation, by flotation, 111–113, 112f Organic electronics devices, 155, 156f interfacial tension in, 164–165 and metal-organic interfaces, 159–164, 160f Organic field-effect transistors (OFET), 162–164, 163f Organic light-emitting diode (OLED), 160, 161f Organic photovoltaics (OPV), 160–162 Organic rectifying diode, 159 Organic semiconductors, 163–164 Organic supercapacitors (OSC), 155 Oscillating method, 36f Ostwald ripening, 31, 223 Outer Helmholtz plane (OHP), 195, 196f Owens, Wendt, Rabel, and Kaelble (OWRK) method, 121–123, 121f, 122t, 123f Oxo process, 50–51

P

p-alkylbenzene sulfonates, 46 Palm oil methyl esters (PME), 45 Particle geometry, 68–69, 252–254 Particle-interface electrostatic interactions, 244 Particle-particle electrostatic interactions, 244 Particle removal, in integrated circuits (IC) manufacturing, 264–265, 265f Partition coefficient, 141 Partitioning and adsorption at liquid interfaces, 141 of solute between immiscible phases, 141 Pattern collapse, of nanometer scale structures, 262–264 Pendant drop tensiometer, 37, 245–246 Peptization, 199, 214 Phosphates, 49 Photolithography, 3, 257–260 deep UV (DUV), 257 interfaces role in, 260–265 particle removal, 264–265, 265f surface tension and pattern collapse, 262–264, 262f Photonic crystals, 250–251 Photoresists, 79–80, 257, 259–264, 260f Photovoltaic device (PV), 161–162 Pickering emulsions, 109, 129–132, 130–132f, 251 bulk polymerization of, 229–232, 231–232f interfacial polymerization of, 232–234, 233f Pieranski’s equation, 243 Plastron breathing, 25 Pockels-Langmuir (PL) monolayer, 142–143, 145–146 Poisson distribution, 196–197 Polarized microscopy, 145 Poly(ethylene glycol) (PEG), 104, 150–151, 226 Poly(vinyl alcohol) (PVA), 104, 226

Index

Poly(tert-butyl)acrylate (PtBA), surfactantfree, 228 Polyalkylene oxide block copolymers (EO/ PO), 52, 52f Polydimethylsiloxanes, 56 Polyethylene (PE) surface energy, 17 Polymeric nanoparticles synthesis via emulsion polymerization, 217–229 Polypyrrole (PPy), 94, 162–163, 229 Polysorbates, 53 Polystyrene/JNP colloidosomes, 232f Polystyrene (PS) nanoparticles emulsion polymerization, 219–220 with sodium p-vinyl benzene sulfonate (NaVBS), 222–223, 223f Polythiophene (PTh), 159–160, 162–163 Postchemical mechanical polishing, 264 Post etch residue (PER), 264 Potassium peroxydisulfate K2S2O8 (KPS), 218–219 Power conversion efficiency (PCE), 161 Pressure limiting apertures (PLA), 82–83 Prussian blue colloid micelle, 213 Pseudomonas aeruginosa, 56 Push-back effect, of metal electron tailing, 157

Q

Quantum dot light-emitting diodes (QLEDs), 62

R

Radical polymerization, 230–234 Radio frequency identification (RFID), 160 Raps oil methyl esters (RME), 45 Rayleigh criterion, 257 RCA clean, 264–265 Receding contact angle, 86–88, 86f Rectification, 159, 172–175, 173–174f Re-dispersion, 214 Reflection absorption infrared spectroscopy (RAIRS), 147–149 Relative humidity (RH), 82–83 Repulsive hydration force, 190–191, 191f Repulsive van der Waals interactions, 182–183, 182t RGD sequence, 103–104 Rhamnolipids, 56–58, 57f Rhodococcus Mycobacterium, 56 Roll-back mechanism, 106, 107f Roll-off advancing-receding contact angles, 88 Roll-off angle, of sessile droplet, 95–97

S

Salt bridges, 186–187 Scaling effects, 23–25, 24f Scanning tunneling microscopy break junctions (STM-BJ), 165, 167 Schottky energy barriers, 158 Seeded emulsion polymerization, 226–229 Self-assembled monolayers (SAMs), 146–152, 148f, 165 carboxyl-amine coupling of, 149, 150f dipole layer, 158–159 and LBs, 165 reactivity of, 149

Shear forces, 202, 210–211, 217–218, 224, 229–230 Silanization method, 128 Silwet-type organosilicone surfactants, 106f Simmons’ equation, 169, 171–172 Single-molecule electronics (SME), 165 Single-nanoparticle tracking analysis (NTA), 204 Si wafers, 257, 264–265 Sliding angles, of sessile droplet, 95–97 Slippery liquid-infused porous surface (SLIPS), 101, 103 Smith-Ewart equation, 219–220 Smoluchowski’s approximation, 203 Snowman-type Janus particles, 130, 230 Sodium dodecyl sulfonate (SDS), 60, 142, 223 Sodium p-vinyl benzene sulfonate (NaVBS), 222–223, 223f Sodium vinylbenzyl sulfosuccinic acid, 223 Solid-liquid interfaces, 14, 21–23, 22f Solid-solid interfaces, 3 Soluble films, 141–142 Solvent accessible surface area (SASA), 188–190 Solvent replacement method, 211 Sorbitan esters, 53 Sphingomonas elodea, 108–109 Spider silk, 99 Spinning drop method, 35 Spinning drop tensiometer, 37–39 Sponge phase, 104–105 Spread monolayers, 142–143 Stability, of lyophobic colloids, 214, 215t Stalagmometer method, 32 Stefan’s equation, 14, 16–17 Steric repulsion, 190 Stern layer, 195, 196f, 202 Stokes-Einstein diffusion coefficient, 246–247 Strong vs. weak coupling, 166–169 Sucrose fatty acid esters, 53, 54f Sugar fatty acid esters, 53, 54f Sulfates, 48 α-Sulfo fatty acid methyl esters, 48 Sulfonated surfactants, 46, 48f Sulfonates, 46 Sulfosuccinates, 48 Sulfur colloids, 211, 211f Supercritical CO2 (sCO2), 263 Superhydrophilic surfaces, 85, 95 Superhydrophobicity, 85–86, 94, 101 Superhydrophobic surfaces, 85, 86f Superspreading behavior, 104–105 Super water repellency, 85 Supra-amphiphiles (SAs), 2, 69–70, 72f Surface charge titration, 199 Surface cleaning mechanism, 106–107 Surface energy, 16, 16f components, 87–88, 88t from intermolecular forces, 185 parameters, 128 Surface hydrophobicity vs. magnitude of contact angle with water, 84–86 Surface plasmons, 214 Surface polarity, 43, 146–147, 230 Surface potential of particles, 199–200, 199f Surface pressure, 142–143, 250–251

271

Index

Surface tension (ST), 13t, 16, 36, 143–144, 186t, 212, 263 adsorption, 67 dynamic, 36–37, 67 interfacial adsorption isotherms and, 139–140, 140f from intermolecular forces, 185 of liquids, 11–14, 11–12f, 23–25, 24–25f minimum water, 67 of nanometer scale structures, 262–264 at nanoscale, 31–32 predictive models for, 14 vectors, 15f Surfactant-free emulsion polymerization, 221–222 Surfactant-free nanoparticles, 222–223 Surfactants, 2, 29–30, 43–46, 44–45f, 104–107, 141, 214 amphoteric, 49–50, 51f anionic, 46–49, 47–49f cationic, 49, 50f classes of, 46–58 effectiveness, 217–218 in emulsion polymerization, 218–223, 219f and environment, 70–73 nonionic, 50–55 self-assembly of, 58–65, 59f, 61f, 63f specialty, 55–56, 55f structure-activity relationship in, 65–69 sulfonated, 46, 48f zwitterionic, 49–50, 51f Swelling agents, 221 Switchable surfaces, 86 Szyszkowski equation, 139–140

T

Tanner’s law, 80, 104–105 Teflon coating, 117–118 Templated self-assembly, of nanoparticles at interfaces, 251–254, 252f Tensiometer method, 87–88 Ternary systems, self-assembly in, 63–64 Tetramethyl ammonium hydroxide (TMAOH), 259–260

U

Wafers (Continued) technology, 257 Washburn capillary rise method, 108, 122 Washburn equation, 109 Washburn method, 109–111, 111f Water, acoustic cavitation in, 224 Water collecting surfaces, 99–100, 100f Water-gas interface, particle adsorption, 251 Water-hexane interface, 10–11 Water-in-oil (w/o) emulsions, 129, 217–218 Water/paraffin emulsion, 252–254, 253f Waterproof clothing, 96–97 Weak coupling vs. strong coupling, 166–169 Wenzel model, 90–91, 91f, 92t Wenzel wetting state, 93–95 Wettability of antifogging surfaces, 94–95 of liquids on heterogeneously flat surfaces, 91–93 of liquids on rough and nanostructured surfaces, 90–91 of (nano-)powders, nanofibers, and porous materials, 109–111 of reservoir rocks, 17 Wetting envelope, 128–129, 129f Wicking method, 108 Wilhelmy plate method, 32, 58

V

X

Thermal energy scale, 5–8, 6f Thermodynamic system, 10–11, 135 Thiol-ene reactions, 150–151, 151f Three-phase line, 22, 79 Transfer resistor, 162–163 3-(Triethoxysilyl)propyl-methacrylate, 228 Trisiloxane surfactants, 104–105 Trouton rule, 6 Tunneling mechanism, 170 Turkevich method, 213–214 Turkey red (sulfated castor oil), 43 2D gas, 58

Ultralow interfacial tension, 37–39 Ultrasonic-assisted surfactant-free emulsion polymerization, 224–226 Ultrasonication, 29–30, 210–211, 226, 229–230 Ultrasonic radiation, 224, 226 Unimolecular electronics (UE), 165–175, 250–251 Unimolecular rectifier, 172–175, 173–174f Unipolar transistor, 162–163 Unit volume, of interfacial layer, 135, 136f Unzipping process, 104–105 UV-vis absorption spectrum, 155–156

van derWaals (vdW) interactions, 182t, 183–185, 248 between molecules and interfaces, 179–185, 180t types of forces, 179 Van Oss, Choudhury, and Good (OCG) model, 124–125, 126t Vapor phase deposition, 164 Vertical dipping method, 145 Vibrating jet method, 36 Vonnegut’s equation, 35, 37

W

Wafers silicon, 79–80, 257 size of, 257, 258f

Xanthan, 112 X-ray, 62, 145 diffraction, 146 reflectivity, 9

Y

Yong’s equation, 84 Young-Dupre equation, 79, 90–91, 117–118 Young-Laplace equation, 27–29, 27–28f, 80–81 Young’s equation, 23, 26, 79, 106, 121

Z

Zero-frequency term, 179, 182 Zeta potential, 195, 202–204, 203f, 214 Zsigmondy method, 214 Zwitterionic surfactants, 49–50, 51f