Polymer Science and Nanotechnology: Fundamentals and Applications [1 ed.] 0128168064, 9780128168066

Table of contents :
Cover
POLYMER
SCIENCE AND
NANOTECHNOLOGY
Fundamentals and Applications
Copyright
Contributors
Preface
Part I: Polymer science
1 Brief overview of polymer science
2
Nature and molecular structure of polymers
Natural vs synthetic polymers
Structure of polymers
Amorphous vs crystalline polymers
Primary structure
Monomer polarity
Secondary structure
Polymer chain configuration
Tertiary structure
Molecular weight
References
3
Polymer synthesis
Step-growth polymerization
General characteristics
Polymerization of tri- and higher-order functional monomers
Polymer types and structure
Chain-growth polymerization
General characteristics
Polymerizability (thermodynamics)
Equilibrium
Stereochemistry of chain-growth polymerization
``Living´´ versus ``controlled´´ polymerization
Free-radical polymerization
Conventional free-radical polymerization
Initiators
Initiation
Propagation
Termination
Inhibitors
Chain transfer
Chain transfer agents
Kinetics of chain-growth polymerization
Initiation
Propagation
Termination
Chain transfer
Rate of polymerization
Trommsdorff-Norrish effect or auto-acceleration or gel effect
Controlled/living radical polymerization
Nitroxide-mediated polymerization
Atom transfer radical polymerization
Monomer
Initiator
Catalysts complex
Solvent
Temperature
Reversible addition-fragmentation chain transfer (RAFT) polymerization
RAFT procedure
RAFT mechanism
Ionic polymerization
Anionic polymerization
Overview
Solvent
Initiation
Electron transfer
Nucleophilic addition to the monomer double bond
Propagation
Termination
Cationic polymerization
Initiation
Bronsted acid
Lewis acid
Propagation
Termination
Group transfer polymerization
Ring-opening polymerization
Thermodynamics
Kinetics
Coordination polymerization
Ziegler-Natta catalysts
Termination
Metallocenes
Ring-opening metathesis polymerization
Catalysts
Solution polymerization
Suspension polymerization
Process description
Size control
Quality and morphology
Emulsion polymerization
Conventional emulsion polymerization
Miniemulsion
Microemulsion
Process description
Size control
Soapless emulsion polymerization
Dispersion polymerization
Further reading
4
Copolymerization
Unspecified copolymers
Statistical copolymers
Random copolymers
Alternating copolymers
Periodic copolymers
Block copolymers
Graft copolymers
Kinetics of copolymerization
References
5
Modification of polymers
Physical methods
Self-assembled monolayers
Radiation-induced surface modification
UV-irradiation
γ-Irradiation
Laser-induced surface modifications
Chemical modification of polymer
Common chemical reactions
PEGylation
Conjugation
Method to make various polymeric architecture via chemical modification
References
Further reading
6
Polymer characterization
Measurements of molecular weight
Gel-permeation chromatography
Osmometry
Viscosity
Static light scattering
Principle of nuclear magnetic resonance
NMR equipment
Proton (1H) NMR
Carbon (13C) NMR
Relaxation time
Proton-proton correlation spectroscopy and total correlation spectroscopy
Heteronuclear multiple quantum coherence spectroscopy and heteronuclear multiple bond correlation spectroscopy
Nuclear Overhauser effect spectroscopy
Diffusion ordered spectroscopy
References
7
Polymer degradation and stability
Introduction
Aging and degradation
Influencing factors
Inherent factors
External factors
Evaluation and characterization
Evaluation
Characterization
Thermal and thermo-oxidative degradation
Thermal degradation
Thermo-oxidative degradation
Thermo-oxidation mechanism
Factors influencing thermo-oxidative degradation
Stabilization of thermal and thermo-oxidative degradation
Radical scavenger
Pro-antioxidant
Photolysis and photo-oxidative degradation
Photolysis
Photo-oxidative degradation
Stabilization of photolysis and photo-oxidative degradation
Hydrolysis and biodegradation
Hydrolysis
Biodegradation
Biodegradable polymers
Degradation and stabilization of polymer nanocomposites
References
8
Polymer processing and rheology
Polymer processing
Mixing
Polymer additives
Mixing mechanics
Mixing devices
Extrusion
Extrusion process
Single-screw extruder
Twin-screw extruder
Extrusion dies
Molding
Injection molding
Compression molding
Blow molding
Rotational molding
Calendering
Process
Arrangements of rolls
Coating
Fluid coating process
Methods
Polymer rheology
Relationship between polymer rheology and polymer processing
Non-Newtonian flow
Viscosity of polymer melts and solutions
Fitting functions for the flow and viscosity curves
Model function for ideal viscous flow behavior
Model function for shear-thinning and shear-thickening flow behavior
Model function for flow curves with a yield point
Rheometry
Capillary rheometer
Couette (concentric cylinder) rheometer
Cone-and-plate rheometer
References
9
Thermal, mechanical, and electrical properties
Thermal analysis of polymers
The melting temperature of polymers
Glass transition temperature of polymers
Thermal conductivity of polymers
Thermal diffusivity
Techniques
Differential scanning calorimeter
Differential thermal analysis
Thermomechanical analysis
Thermogravimetry
Density measurements
Mechanical properties of polymers
Basic concepts of stress and strain
Stress-strain curve
Dynamic mechanical analysis
Viscoelastic behavior of polymers
Effects of structure and composition on mechanical properties
Molecular weight
Cross-linking
Molecular configuration
Composition
Electrical properties of polymers
Conductive polymers
References
10
Hydrogels
Introduction
Synthesis of hydrogels
Physically cross-linked hydrogels
Hydrogen bonds
Electrostatic interactions
Hydrophobic interactions
Crystallization
Chemically cross-linked hydrogels
Cross-linking by chemical reactions of complementary groups
Cross-linking by free radical polymerization
Characterization of hydrogels
Physical properties
Chemical properties
Mechanical properties
Rheological properties
Biological properties
Self-healing hydrogels
Physically self-healing hydrogels
Hydrogen bonds
Hydrophobic interactions
Metal-ligand coordination
Host-guest interactions
Combination of multiple intermolecular interactions
Chemically self-healing hydrogels
Phenylboronic ester complexation
Schiff base
Acylhydrazone bonds
Disulfide bonds
Other dynamic chemical bonds and reactions
Tough hydrogels
Homogeneous hydrogels
Tetra-PEG hydrogels
Slide-ring (SR) hydrogels
Radiation cross-linked hydrogels
Mechanical energy dissipating hydrogels
Double network (DN) hydrogels
Hydrogels based on a combination of both toughening mechanisms
Nanocomposite (NC) hydrogels
Macromolecular microspheres composite (MMC) hydrogels
References
11
Biopolymers and natural polymers
Introduction
Production of biopolymers
Polysaccharides
Microbial biopolymers: A bioengineering approach
Enzymatic reactor for the production of biopolymers
Biopolymer applications
Drug delivery
Polynucleotides and protein-based therapy
3D printing in tissue engineering applications
Sustainable biopolymer for environmental remedy
Current challenges faced by bio or natural polymers
Conclusion
References
12
Smart polymers
Types of smart polymers
Temperature responsive
pH responsive
Light responsive
Magnetically responsive
Enzyme responsive
Other stimuli-responsive polymers
Shape memory polymers
References
13
Polymers in medicine
Introduction
Antimicrobial polymers
Polymeric biocides
Biocidal polymers
Biocide-releasing polymers
Polymers in gastroenterology
Polymers in cardiology
Polymers in hemodialysis
Polymers in neurology
Neural implants
Neural drug delivery
Polymers in ophthalmology
Intraocular lenses (IOLs)
Intraocular drug delivery
Polymers in dermatology
Skin grafts and skin substitutes
Dermal and transdermal drug delivery
Polymers in orthopedic surgery
Polymers in dentistry
Polymers in cancer therapy
Chemotherapeutic drug delivery
Biosensors for cancer detection
Polymers in gene therapy
Conclusions and future outlook
References
14
Polymers for advanced applications
Introduction
Polymeric membranes for gas separation
Applications of self-healing polymers
Polymers for additive manufacturing
Applications of polymers in electrical and electronics
Supercapacitors
Lithium-ion batteries
Light-emitting and sensing devices
Polymers for water purification
Polymer applications in food packaging
Conclusion and future perspectives
References
Part II: Nanotechnology
15
Nanomaterials properties
Introduction
Physical properties
Size and shape of nanomaterials
Zero dimensional
One dimensional
Two dimensional
Three dimensional
Surface effects
Quantum confinement effects
Surface charge and stability
Chemical properties
Chemical structure and composition of nanomaterials
Catalytic reactivity
Optical properties
Magnetic properties
Electrical properties
References
16
Nanomaterial synthesis
Introduction
Inorganic nanoparticles
Solution-phase synthesis of nanoparticles
Mechanism of nanoparticles synthesis
Typical methods for the synthesis of nanoparticles in solution phase
Mechanism of size and shape control of metal nanoparticles in solution phase
Affect of reaction parameters on nanoparticles growth
Template-mediated synthesis of inorganic nanostructures
Synthesis of inorganic nanoparticles by lithography
Organic nanoparticles
Bottom-up synthesis of organic nanoparticles
Controlling the shape of soft materials
Polymersomes
Top-down approach for the synthesis of organic nanoparticles
Conclusion and future outlook
References
17
Nanomaterials characterization
Introduction
Size, shape, length, and internal structure characterization
Dynamic light scattering
Microscopy
Scanning electron microscopy
Transmission electron microscopy
Atomic force microscopy
Surface charge characterization of nanoparticles (zeta potential measurements)
Optical properties
Ultraviolet-visible spectroscopy
Fluorescence spectroscopy
Magnetic properties
Composition, chemical structure, and substructure
Nuclear magnetic resonance spectroscopy
X-ray diffraction
X-ray photoelectron spectroscopy
Mechanical properties
References
18
Nanomaterials applications
Introduction
Household
Cosmetics
Textiles
Energy storage
Sports
Food and drinks
Automotive industry
Electronics
Construction and engineering materials
Medicine
References
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Back Cover

Citation preview

POLYMER SCIENCE AND NANOTECHNOLOGY

POLYMER SCIENCE AND NANOTECHNOLOGY Fundamentals and Applications Edited by

RAVIN NARAIN Professor, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada

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 © 2020 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: 978-0-12-816806-6 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisitions Editor: Edward Payne Editorial Project Manager: Emma Hayes Production Project Manager: Vijayaraj Purushothaman Cover Designer: Victoria Pearson-Esser Typeset by SPi Global, India

Contributors Surjith Kumar Kumaran Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Marya Ahmed Department of Chemistry & Faculty of Sustainable Design Engineering, University of Prince Edward Island, Charlottetown, PEI, Canada

Mingwei Mu International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

Muhammad Arshad Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, AB, Canada

Ravin Narain Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Anika Benozir Asha Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada Keshwaree Babooram Department of Chemistry, University of Alberta, Edmonton, AB, Canada

Nauman Nazeer Department of Chemistry, University of Prince Edward Island, Charlottetown, PEI, Canada

Seth Beck Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Euna Oh Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Rabin Bissessur Department of Chemistry, University of Prince Edward Island, Charlottetown, PE, Canada

Yi-Yang Peng Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Jingsi Chen Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Saadman S. Rahman Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, AB, Canada

Hyo-Jick Choi Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Shruti Srinivas Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Manika Chopra Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Aman Ullah Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, AB, Canada

Diana Diaz Dussan Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Maria Vamvakaki Department of Materials Science and Technology, University of Crete; Institute of Electronic Structure and Laser, Foundation for Research and TechnologyHellas, Heraklion, Greece

Mitsuhiro Ebara International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

Wenda Wang Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Maria Kaliva Department of Materials Science and Technology, University of Crete; Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Heraklion, Greece

Rui Yang Department of Chemical Engineering, Tsinghua University, Beijing, People’s Republic of China

ix

x

Contributors

Shin-ichi Yusa Department of Applied Chemistry, University of Hyogo, Himeji, Hyogo, Japan

Wenling Zhang Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Hongbo Zeng Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Muhammad Zubair Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, AB, Canada

Preface The fields of polymer science and nanotechnology have seen significant developments during the last few decades. A large number of technologies have been possible through a combination of knowledge from both fields, thus bringing together these fundamental aspects in one book is a convenient way to provide readers with easy access to the much sought-after information. This book is organized in two parts with the first one designed to provide a comprehensive account of the fundamental aspects of polymer science including polymer synthesis, characterization, and applications. Topics such as hydrogels, smart polymers, biopolymers, and natural polymers, which are conventionally not covered in polymer science textbooks, are also discussed. The first part also covers the fundamental aspects

of controlled radical polymerization namely nitroxide-mediated polymerization, reversible addition-fragmentation chain transfer process, and atom transfer radical polymerization. The next part focuses on nanotechnology by providing the readers with a complete description of the different types of nanomaterials, their synthesis and characterization, and their applications. I am tremendously thankful to all the contributors for dedicating their time to put together their respective chapters in a way comprehensible for a far-reaching readership. I would also like to express my sincere appreciation to Elsevier for all the support and patience throughout the entire project. Ravin Narain

xi

C H A P T E R

1

Brief overview of polymer science Keshwaree Babooram Department of Chemistry, University of Alberta, Edmonton, AB, Canada

1.1 Basic concepts The simplest definition one can use for a polymer is a long-chain molecule made up of many chemically bonded repeating units called monomers. The word polymer is of Greek origin, “poly” meaning many and “mer” meaning part [1]. In other words, “many” of the same “part” are connected to form a long chain known as a polymer. Hence, polymers have a very large number of atoms in one molecule. The number of atoms can often be in hundreds of thousands which is the reason why polymers are also called macromolecules. As an example, linking together a large number of paper clips to make a long chain, is a good illustration of how small molecules come together (in other words polymerize) to form a polymer. Polymers are everywhere and we encounter them every single day of our lives, many times a day! Right from the bottle we drink water from, to the plastic bag we carry our groceries in, to the numerous electronic devices, we have become so dependent on or attached to polymeric materials that they have become an integral part of human lives. Polymers are, however, not limited to these inanimate objects. Natural polymers like polynucleotides (deoxyribonucleic acid [DNA] and ribonucleic acid [RNA]), polysaccharides (starch and cellulose), and proteins (collagen and hemoglobin) are biologically important because they sustain life. Rubber and other protein polymers such as hair, horn, and spider silk are examples of naturally occurring polymers. Some of the latter can also be made synthetically, like polyisoprene which is the synthetic form of rubber [2]. The most common classes of polymers are composed only of carbon and hydrogen, some examples of these being polyethylene (used a lot in packaging), polypropylene (used in packaging, fashion and sports industry, and medical applications), and polystyrene (used extensively in consumer goods). While these polymers contain only carbon atoms in their backbone, other commonly manufactured polymers contain heteroatoms such as nitrogen, oxygen, silicon, and phosphorous. What makes the difference in the composition of the polymer backbone is the polymerization mechanism used in the synthesis of these polymers.

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00001-7

3

# 2020 Elsevier Inc. All rights reserved.

4

1. Brief overview of polymer science

Addition polymerization which is the sequential addition of monomers such as olefins and vinyl-based molecules, or the ring-opening polymerization of a sterically strained cyclic molecule, results in a carbon-only backbone. Condensation polymerization, on the other hand, occurs between molecules carrying different functional groups that react successively with the loss of a smaller molecule. The result is the formation of a new functional group that becomes part of the polymer backbone [3]. Polymer structures can vary depending on how monomers are brought together. In a onedimensional structure, monomers are joined to form chains, while in a two-dimensional arrangement, the chains further bond to each other through certain atoms forming a sheet. Finally, in the third type of arrangement, chains of the polymer bond to one another in three dimensions forming a more complex network. In today’s world, synthetic polymers are commonly referred to as plastics, which typically contain one or more polymers along with additives and fillers that are intended to expand their properties to fit various applications. The end uses of polymers or plastics are governed primarily by their composition, synthesis method, and structure [2, 3].

1.2 Classification of polymers Thousands of synthetic polymers are known today and there is no doubt that with the rapid advancement in the field of polymer synthesis, more will be added [2]. While all polymers can be broadly organized into two major groups based on the type of polymerization technique used in their synthesis, a more specific classification system based on polymer structure, method of polymerization, and intermolecular forces helps ease the understanding of polymer properties.

1.2.1 Polymer structure When based strictly on their structure, polymers can be classified into three types namely, linear, branched, and cross-linked polymers. Many of the commercially important polymers have a uniquely simple linear structure. Such polymers are a collection of long continuous chains in which monomers have been linked together through covalent bonds to form a backbone [3]. The chemical structure of the latter varies depending on the composition of the monomers. Linear polymers can further be broken down into polymers with (i) all-carbon backbones, typically synthesized from monomers containing carbon-carbon double bonds; (ii) heteroatoms in the backbones, resulting from the condensation polymerization of various functional groups (such as alcohols, amines, or carboxylic acids) on the monomers, and (iii) inorganic backbones that are composed of certain elements of the second or higher rows of the periodic table linked to either themselves or to oxygen or nitrogen. Linear polymers are generally of higher densities and have high melting points and tensile strength since the intermolecular forces are generally of higher magnitude, leading to the chains being wellpacked. Table 1.1 shows some examples of the different types of linear polymers and their repeating units.

I. Polymer science

TABLE 1.1 Examples of linear polymers. Type of backbone

Polymer

Monomer(s)

All-carbon

Polyethylene

CH2]CH2

Polypropylene

Polyvinylchloride (PVC)

Polystyrene

CH2]CHCH3

CH2]CHCl

CH2]CH(C6H5)

Repeating unit

H

H

C

C

H

H

H

H

C

C

H

CH3 n

H

H

C

C

H

Cl

H

H

C

C

H Presence of heteroatoms

n

n

n

Nylon 6,6

Polyethylene terephthalate (PET)

Polyethylene glycol (PEG)

Continued

TABLE 1.1 Examples of linear polymers—cont’d Type of backbone

Polymer

Monomer(s)

Inorganic

Plastic sulfur

S8

Polydimethylsiloxane (PDMS)

Polydimethylsilazane

Repeating unit

7

1.2 Classification of polymers

The second class of structural polymers results from branches of varying lengths growing from random points along the linear chain, hence the name branched polymers [3]. The presence of branches reduces the extent of close packing of the main chains, resulting in lowdensity polymers with low melting points. While branching can be due to shortfalls during polymerization, it is also occasionally intentionally introduced to tailor the properties of the polymers for specific applications. Besides, randomly branched chains and branched internal loops can also be formed. This happens when branches that are growing out of the main chain at irregular intervals recombine and form cyclic structures. Another type of branching, which is the result of many short side chains emerging from the main molecule, gives rise to a comblike structure. Fig. 1.1 depicts the difference between the different types of branching. Linear and branched polymers belong to a class of materials called thermoplastics as they can flow when heated and can, therefore, be molded into different shapes that are retained when the materials cool down. In cross-linked polymers, branches (or side chains) emerging from individual polymer chains covalently bond to one another, hence permanently connecting them. Cross-linking leads to the formation of three-dimensional networks that resist solvent attack, heat softening, and mechanical deformation. Such polymers, called thermoset plastics, are hard and brittle and tend to take on a shape that cannot be changed unless the polymer is destroyed. Bakelite and melamine are common examples of cross-linked polymers.

1.2.2 Polymerization techniques The mechanism of polymerization used in the synthesis of polymers allows for the classification of the latter into two major classes, namely, addition and condensation polymers. The former kind is produced by the repeated and sequential addition of monomers without the loss of a smaller molecule during the process. Therefore, no by-product is formed and the repeating unit of additional polymers has the same formula as the alkene or functionally-substituted alkene monomers used to make them. These addition reactions follow a stepwise mechanism

Polymer main chain Side chains (branches)

(B)

(A)

(C) FIG. 1.1 Different types of branched polymers (A) randomly branched; (B) branched with internal loop; (C) comb-like branching.

I. Polymer science

8

1. Brief overview of polymer science

that involves reactive intermediates such as radicals or ions that help in the conversion of a pi bond in the monomer into a sigma bond in the polymer. The four different polymerization techniques used in the synthesis of addition polymers are (i) radical polymerization, (ii) cationic polymerization, (iii) anionic polymerization, and (iv) coordination catalyticpolymerization [3–5]. The mechanism of radical polymerization follows three steps namely, initiation, propagation, and termination. During initiation, a molecule called a radical initiator is broken down into free radicals either thermally or photolytically. A radical then attacks the pi bond in the alkene monomer forming a covalent bond with one of the carbon atoms and turning the other one into a reactive radical. The propagation stage then follows with the latter continuously adding on more monomers and growing into a chain. Termination of chain growth finally occurs when the radical chains either combine or participate in disproportionation reactions involving pulling hydrogen from another radical chain. Cationic and anionic polymerization follows an overall similar pathway with their initiators being strong acids and Lewis acids (to covert the alkene into a cation), or strong bases, alkali metals, and organolithium compounds (to convert the alkene monomer to an anion). Fig. 1.2 summarizes the mechanism of the formation of addition polymers by radical, cationic, and anionic polymerization. Catalytic polymerization also called the Ziegler-Natta polymerization technique, employs catalysts that are transition metal-based coordination complexes derived from transition metal halides and organometallic reagents. Developed in the 1950s by Karl Ziegler and Giulio Natta, this technique allows better control over the configuration of polymers synthesized from terminal alkenes and also facilitates the production of unbranched and high molecular weight compounds, hence, stronger polyolefins at relatively lower temperature and pressure than required by other addition polymerization methods. The polymerization of ethene using a titanium-based Ziegler-Natta catalyst is shown in Fig. 1.3. H

H

C H

C R

I*

H

I

C H

H

H2C=CHR

R

(n times)

C*

H

H

C

C

H

R

n+1

I* : Initiating species; can be a radical, cation, or anion

FIG. 1.2 Mechanism of formation of addition polymers by radical, cationic, and anionic polymerization.

FIG. 1.3 Catalytic polymerization of ethene using a Ziegler-Natta catalyst.

I. Polymer science

1.2 Classification of polymers

9

The second class of polymers consisting of a large number of very useful materials are those produced by the polycondensation of monomers combined in an alternating structure. Condensation polymers are the result of the transformation of functional groups on monomers that are bi-functional so that each monomer can connect with two others. Polymerization typically proceeds with the loss of a smaller molecule which can be in the form of water, gas, or salt. One very well-known condensation polymer is nylon 6,6 which is a polyamide made from adipic acid (a dicarboxylic acid) and 1,6-hexamethylenediamine, the combination of which leads to the loss of water molecules. Nylon 6,6 finds numerous applications in the production of clothing, cooking utensils, carpets, fishing lines, and many more. Polycondensation tends to be slower than polyaddition, often requiring heating the reaction. A direct consequence of the slow polymerization is generally the formation of lower molecular weight polymers. Highly crystalline condensation polymers with high tensile strength result from strong interchain interactions when polar functional groups are present along the chains. Fig. 1.4 shows the formation of nylon 6,6 by the polycondensation of adipic acid with 1,6-hexamethylenediamine.

FIG. 1.4 Condensation polymerization of adipic acid and 1,6-hexamethylenediamine to produce nylon 6,6.

I. Polymer science

10

1. Brief overview of polymer science

1.2.3 Intermolecular forces Covalent bonds are the strong forces that hold atoms together in a molecule and they are of the intramolecular type. In a polymer backbone, they hold atoms together, making a long chain molecule. Intermolecular forces, on the other hand, are of weaker intensity and they help keep molecules closer together [6]. The presence of intermolecular forces in polymers along with their intensity help in a closer packing of the chains and heavily influence the properties and behavior of the material. Four types of polymers can be defined based on their intermolecular forces (i) elastomers; (ii) thermoplastics; (iii) thermosets; and (iv) fibers [1]. Elastomers have the characteristics of rubber, that is, they are flexible and elastic. They can be easily stretched with the application of just a little force but return to their original form once the stress is removed. For polymers to show elastic behavior, they must consist of extremely flexible chains with very weak intermolecular forces between them. Although this property allows the polymer to be stretched, for it to go back to its original shape, it is also very important that some degree of cross-linking is present between the chains as it prevents them from sliding past one another (called plastic flow or deformation). Natural rubber is sticky and very readily experiences plastic flow which limits its applications. However, its treatment with controlled amounts of elemental sulfur helps introduce cross-links between the chains which, in turn, reduces plastic flow and incorporates elasticity in rubber. The process is known as the vulcanization of rubber and produces the material used in car tires. The second type of polymers, called thermoplastics, have sufficiently strong intermolecular forces between the chains thus, preventing plastic flow at room temperature. Thermoplastics are, therefore, solid at ambient temperature but when heated they soften and turn into a thick fluid as the intermolecular forces are weakened. When allowed to cool down, they harden into a solid mass. This characteristic makes these polymers easy to transform into the desired shape by applying heat and molding. For these reasons, the recycling of the wastes of thermoplastic polymers is also made easier and nowadays they are increasingly being collected and recycled into new products of lower added value [5]. Polyethylene, polyvinylchloride, and polystyrene are very important examples of commercial thermoplastics. Thermosets, on the other hand, are materials that do not melt on heating. Thermoset polymers are generally synthesized from semi fluids composed of relatively small chains of lower molar masses. Upon heating or chemical treatment, a considerably large amount of chemical cross-linking takes place between the individual chains which cause the material to harden. The resulting three-dimensional network sets into any given shape after which, unlike thermoplastics, cannot be reshaped by heating. Such polymers will undergo degradation when heated but will not melt. They also resist mechanical deformation and attack by solvents. For these reasons, thermoset polymers are not easily recycled. Used extensively in the making of kitchenware, and electrical and automotive components because of its high resistance to heat and electricity, bakelite (made from the condensation polymerization of phenol and formaldehyde) is a well-known example of a thermosetting polymer. Polymers, that are classified as fibers are characterized by the presence of very strong intermolecular forces as well as a highly regular structure resulting in high crystallinity. The intermolecular forces are normally hydrogen bonds or strong dipole-dipole interactions that considerably lower the elasticity and increase the tensile strength of the polymer which is thread-like with a high melting point. Nylon 6,6 made from the polycondensation of adipic

I. Polymer science

1.3 Natural vs synthetic polymers

11

acid and 1,6-hexamethylenediamine, is one example of a synthetic polymer fiber with excellent heat and chemical resistance. It is widely used in the making of carpets and textiles. Other polymeric fibers like polyesters are turned into fabrics used in clothing and upholstery.

1.3 Natural vs synthetic polymers When considering the incredibly large number of polymers surrounding us, the simplest way to classify them is depending on their source, that is, natural or synthetic. Natural polymers occur in nature and originate either from plants or animals. They are designed by nature to achieve a very specific task which is primarily to sustain life [3, 5]. They belong to one of the three main categories which are polysaccharides, nucleic acids, and proteins. Polysaccharides are low molecular weight polymer chains that covalently link together sugar molecules (comprised of numerous hydroxyl groups). The most important polysaccharides are those made of glucose or its derivatives. Starch and cellulose are both glucose-based polysaccharides that make up the structure of plants. With a large number of hydroxyl groups along the polymer chains causing strong intermolecular forces through hydrogen bonding, natural cellulose is highly crystalline and very strong. For this reason, they have remarkable textile properties that are still superior to synthetic alternatives. Proteins, on the other hand, are the building blocks of animals and are polypeptides formed by the polymerization of amino acids. They can be composed of long-chain molecules or cross-linked chains, each type of protein having a characteristic sequence of amino acids and structure that determines its distinct activity or purpose. Hemoglobin, albumin, collagen, and actin are some examples of very important proteins. DNA and RNA are further examples of natural polymers found in living organisms. Responsible for storing and reading genetic information, they are linear polymers consisting primarily of sugar molecules, phosphates, and bases. Synthetic polymers are man-made and produced in a laboratory using controlled polymerization parameters that help tailor the properties of the polymers to suit specific needs. Most of the world around us is made of synthetic polymers with polyolefins like polyethylene and polypropylene, and nylon being examples of materials that are produced on a massive scale worldwide. In some cases, chemical modifications are made to natural polymers to optimize their properties and commercial value. These polymers are called semi-synthetic and one such example is vulcanized rubber which is produced by chemically cross-linking the chains in natural rubber using sulfur [5]. Rubber is a very interesting example of a polymer that occurs naturally but can also be synthesized in a laboratory. Natural rubber, composed of isoprene units, is a sticky milky liquid and therefore, hard to handle. It lacks good mechanical properties and is also not as durable as it decays with time. As mentioned earlier, one way to improve its properties is vulcanization that turns it into semi-synthetic material. Another solution to the shortcomings of natural rubber is the production of the entirely synthetic version of the polymer. The latter is preferred because synthetic rubber can be easily made from isoprene monomer which can, in turn, be produced in pure form in the laboratory. Furthermore, synthesizing rubber in a laboratory allows for a myriad of possibilities to create rubber with the desired properties by using different monomers in varying amounts.

I. Polymer science

12

1. Brief overview of polymer science

References [1] A. Rudin, The Elements of Polymer Science and Engineering: An Introductory Text and Reference for Engineers and Chemists, second ed., Academic Press, San Diego, USA, 1999. [2] J.R. Fried, Polymer Science & Technology, third ed., Prentice Hall, 2014. [3] P. Munk, T.M. Aminabhavi, Introduction to Macromolecular Science, second ed., John Wiley & Sons, New York, 2002. [4] A.E. Tonelli, M. Srinivasarao, Polymers From the Inside Out, John Wiley & Sons, New York, 2001. [5] C.E. Carraher Jr., Carraher’s Polymer Chemistry, eighth ed., CRC Press, Taylor & Francis Group, Florida, 2011. [6] C.D. Craver, C.E. Carraher Jr., Applied Polymer Science, 21st Century, Elsevier, Oxford, 2000.

I. Polymer science

C H A P T E R

2

Nature and molecular structure of polymers Yi-Yang Peng, Shruti Srinivas, Ravin Narain Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

2.1 Natural vs synthetic polymers Polymers of both natural and synthetic origin are a versatile and promising class of materials that have been used for a range of applications. These polymers have been extensively investigated because of the flexibility in modifying or synthesizing them, for instance, to match the physical and mechanical properties with various tissues and organs of the body [1–4]. Natural polymers also referred to as biopolymers have excellent biocompatibility, unique mechanical properties, and closely mimic the cellular environment. These polymers are biodegradable via both enzymatic and hydrolytic mechanism and their applications range from wound dressings and skin grafts to fibers and fabrics [5, 6]. As these polymers mimic the components of the extracellular matrix (ECM) they are readily accepted by the body and avoid chronic immunological reactions and toxicity. Some examples of natural polymers includes (i) polysaccharides, (ii) polyesters, and (iii) proteins derived from both plants and animals [7, 8]. The intermolecular interactions such as hydrogen bonding are responsible for the strength and physical properties of natural macromolecules [9]. Synthetic polymers are an attractive class of man-made polymers. They have excellent reproducibility and can be designed with appropriate physical and chemical properties. They can be tailored for specific applications by influencing their rate of degradation. Their degradation rate can be influenced by altering their mechanical or chemical properties and molecular weight [10–12]. The resulting inter/intramolecular interactions such as dipole-dipole interactions are responsible for the physical properties of the synthetic macromolecules [9]. Synthetic polymers are categorized into (i) thermoplastics, (ii) thermosets, (iii) elastomers, and (iv) synthetic fibers.

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00002-9

13

# 2020 Elsevier Inc. All rights reserved.

14

2. Nature and molecular structure of polymers

2.2 Structure of polymers 2.2.1 Amorphous vs crystalline polymers Amorphous polymers (Fig. 2.1A) are polymers that have an irregularly shaped structure with generally (but not necessarily) bulky pendent groups. The molecular packing of amorphous polymers looks like long chains that are intertwined around each other, while some polymers can form crystalline structures, their molecular packing looks more like woven threads. The chains of amorphous polymers are characterized by a short-range order of repeating units and are not capable of an orderly arrangement. Amorphous polymers are in a glassy state below their glass transition temperature (Tg), whereas above their Tg they are in a soft and rubbery state. Examples of glassy amorphous polymers include atactic PS, polycarbonates made from bisphenol A (BPA), and polymethylmethacrylate [13, 14]. The polymer chains of crystalline polymers (Fig. 2.1B) are characterized by a long-range order of repeating units that are three-dimensional and are capable of an orderly arrangement. When these polymers are cooled, the molecules tend to aggregate into a solid with very less potential energy. However, as the chains of the crystalline polymers are long, they cannot form a perfect arrangement. The degree of crystallinity varies from a few percentage to about 90% based on the conditions of crystallinity [15]. The degree of crystallinity is calculated by: degree of crystallinity ¼

ρc ðρs  ρa Þ ∗ 100 ρs ð ρc  ρa Þ

(1.1)

ρc is the density of the completely crystalline polymer and ρa is the density of the completely amorphous polymer. ρs is the density of the sample. Examples of crystalline polymers include PE and its copolymers, polypropylene, polyesters, and nylons. The three factors that lead to the metastable states in the crystals are the molecular size, flexibility, and the chemical regularity of the polymer chains [16]. The increase of crystallinity elevates the strength of the polymers. For instance, the high-density PE with 64%–80% crystallinity has a higher tensile strength (21–38 MPa) in comparison to low-density PE (4.1–16 MPa) with 42%–53% crystallinity [17]. However, not all simple organic molecules have the ability to form polymers despite the conditions being right to initiate polymerization. The condition needed for the molecules to

FIG. 2.1 Amorphous polymer (A), crystalline polymer (B), and semi-crystalline polymer (C).

I. Polymer science

2.2 Structure of polymers

15

form a polymer is based on the number of available bonding sites that a molecule constitutes to bond with other molecules under certain polymerization conditions. Based on the number of available bonding sites, the molecule can be classified as monofunctional, bifunctional, or polyfunctional. The structures of both natural and synthetic polymers are classified into three types, namely, (i) primary, (ii) secondary, and (iii) tertiary structures [15, 18].

2.2.2 Primary structure The chemical structure of the monomer make up the primary structure of the polymer. The structure of the monomer is related to the properties of the resulting polymer. Therefore, to have a fundamental understanding of the structure-property relationship of the polymers, it is necessary to know the nature of the monomer. The size of the polymer is responsible for its physical and mechanical properties while the chemistry of the monomers is responsible for the chemical and electrical properties of the polymer [15]. 2.2.2.1 Monomer polarity Polarity is a property of the molecule defined by the chemical composition and atomic arrangement within the molecule. The intramolecular attraction between the chains is affected by polarity which, in turn, affects the symmetry and regularity of the polymer structure. The properties of the polymer such as electrical nature and solubility are also affected by polarity. A polar molecule is one that has equal but opposite pairs of electrons. For example, the transfer of electrons from sodium to chlorine results in the formation of the ionic compound, sodium chloride. The electrostatic attraction between the adjacent ions in sodium chloride is due to polarity. A diatomic molecule is said to be polar if it contains equal but opposite charges and possesses a permanent dipole moment. The sharing of electrons between the constituent atoms results in the formation of covalent molecules. A diatomic molecule formed from two atoms of the same kind (e.g., H2) is said to be non-polar if the electron pair linking the two atoms is shared equally, whereas, in the case of a diatomic molecule formed from two unlike atoms (e.g., HF), the electron cloud is distributed on the more electronegative atoms. This results in the separation of positive and negative charges and the molecule is said to be polar. In the case of a polyatomic molecule, the vector sum of all the dipole moments of the groups of molecules is said to result in polarity [15].

2.2.3 Secondary structure The details about the size and shape of an isolated single molecule make up the secondary structure of the polymer. The molecular weight represents the size of the polymer and how the repeating units are linked, influences the shape or the molecular architecture of the polymer. The molecular architecture of the polymer is based on (i) configuration and (ii) conformation. 2.2.3.1 Polymer chain configuration Isomers that have the same connectivity but differ in the spatial arrangement of atoms are called stereoisomers. The repeating units between the atoms are held together by chemical

I. Polymer science

16

2. Nature and molecular structure of polymers

bonds. When these atoms undergo a relative orientation in space, the shape created is termed as configuration. The configuration of a polymer molecule may be branched, linear, or cross-linked. A polymer is said to structurally regular if its repeating units are chemically and structurally regular. The term structural regularity is classified into two types namely: (i) recurrence regularity and (ii) stereoregularity. If the repeating units occur along the polymer chain, it is referred to as recurrence regularity. The possible arrangements in the case of recurrence regularity are as follows: (i) head-to-tail configuration, (ii) head-to-head configuration, and (iii) tail-to-tail configuration. The spatial properties of a polymer molecule are termed as stereoregularity and the ability of the polymer molecule to crystallize are affected by the presence or absence of regularity. The tacticity of polymers is determined by the regularity in the configurations. The types of tacticity in polymers are (i) atacticity, (ii) isotacticity, and (iii) syndiotacticity. Examples of each type of tacticity for PS are shown in Fig. 2.2. If the R groups along the polymer chain are in a random sequence the polymer is said to be atactic. If the R groups along the polymer chain are alternately positioned on the polymer chain, the polymer is said to be syndiotactic and if the R groups on the polymer chain are aligned, the polymer is said to be isotactic. Besides, the difference in the position of chain, the tacticity influence the morphology of polymer, thus influencing the properties of the polymers. Isotactic/ syndiotactic PS form semi-crystalline/crystalline region and has Tm at 240°C/270°C.

2.2.4 Tertiary structure A large number of polymer molecules aggregate to form a solid polymeric material. This aggregation of polymers is caused by the intermolecular secondary bonding forces thereby resulting in the formation of either a crystalline or an amorphous material. The bonding

FIG. 2.2 Chemical structure of isotactic (A), atactic (B), and syndiotactic (C) polystyrene.

I. Polymer science

2.3 Molecular weight

17

energy of the secondary bonding forces ranges from 0.5 to 10 kcal/mol and the magnitude of these secondary bonding forces is responsible for the structural order of the resulting polymer. The nature of these intermolecular secondary bonding forces is related to the tertiary structure of the polymer. The dipole, induction, van der Waals forces, and hydrogen bonds form the secondary bonding forces. The attraction between the permanent dipoles associated with the polar group results in dipole forces, the attraction between the permanent and induced dipoles results in induction forces, the time-varying perturbations of the electronic clouds of neighboring atoms result in van der Waals forces. The magnitude of bond energies decreases in the order of hydrogen bond to dipole bond to van der Waals (dispersion) forces [15].

2.3 Molecular weight Besides, the structure of polymers, Mw is an essential property of the polymer as the molecular weight of the polymers affects mechanical properties and thermal properties. The molecular weight of the polymer is the summation of the molecular weight of all repeat units among the polymer chain. For a homopolymer, its molecular weight equals the molecular weight of a unit times the degree of polymerization (DP) of the unit. The DP is the number of repeat units among the polymers. For example, in Fig. 2.3, DP is the value of n. For copolymer, such as P(Ax-st-By), the molecular weight of the polymer equal to MwA times x plus MwB times y. However, in the usual case, a batch of polymers has polymeric chains with various DP and molecular weight distribution (Fig. 2.4), which leads to the polydispersity of the polymer. Thus, the average value of molecular weight is more appropriate to be used here. The number average molar weight (Mn) is defined as the arithmetic mean of the Mw (Eq 1.1). Thus, m, n, and M are mass of polymers, the number of polymers, and Mw of polymers, respectively.

FIG. 2.3 Polyethylene structure.

FIG. 2.4 The molecular weight distribution of a polymer.

I. Polymer science

18

2. Nature and molecular structure of polymers

Mn ¼

Σmi Σni Mi ¼ Σni Σni

(1.2)

The weight average molecular weight (Mw) is defined as Mw ¼

Σmi Mi Σni M2i ¼ Σmi Σni Mi

(1.3)

For monodispersed polymers, Mn equals to Mw, and Mw will be larger than Mn for a polydispersed polymer. The polydispersity index (PDI) is an indication of Mw distribution of polymer and is calculated by: PDI ¼

Mw Mn

(1.4)

For a polymeric sample with known Mn, the DP can be obtained by: DP ¼

Mn Molecular weight of a repeating unit

(1.5)

The increase of Mw leads to an increase in the tensile strength and Tg. Strength increases as the Mw increase due to the higher probability of chain entanglement. The effect of Mw on tensile strength and Tg is shown in Fig. 2.5A and B, respectively. The relationship between tensile strength and Mw is described by: σ ¼ σ∞ 

A Mw

(1.6)

σ ∞ is tensile strength for a polymer with infinity Mw and A is a constant. The Fox-Flory equation is used to describe the relationship between Mw and Tg (Eq. 1.7). Tg ¼ Tg, ∞ 

K Mw

(1.7)

Tg,∞ is the Tg for a polymer with infinity Mw and K is the Fox-Flory parameter and affected by the free volume (gaps left between entangled polymeric chains) inside the polymer.

FIG. 2.5 The influence of Mw on Strength (A) and Tg (B).

I. Polymer science

References

19

The Mw for a batch polymer can be determined either by the direct method (light scattering and ultracentrifugation) or indirect method (viscometry and gel permeation chromatography [GPC]).

References [1] S.G. Kumbar, C. Laurencin, M. Deng, Natural and Synthetic Biomedical Polymers, Elsevier Science & Technology, 2014. [2] Q. Wei, N.-N. Deng, J. Guo, J. Deng, Synthetic polymers for biomedical applications, Int. J. Biomater. 2018 (2018). [3] B.D. Ulery, L.S. Nair, C.T. Laurencin, Biomedical applications of biodegradable polymers, J. Polym. Sci. B Polym. Phys. 49 (12) (2011) 832–864. [4] L.S. Nair, C.T. Laurencin, Polymers as biomaterials for tissue engineering and controlled drug delivery, Adv. Biochem. Eng. Biotechnol. 102 (2005) 47–90. [5] L.E.K. Achenie, N. Pavurala, On the modeling of oral drug delivery, in: Quantitative Systems Pharmacology, first ed., vol. 42, Elsevier B.V., 2018, pp. 305–324 [6] R. Barbucci, Integrated Biomaterials Science, Springer Science & Business Media, 2002. [7] A. Aravamudhan, D.M. Ramos, A.A. Nada, S.G. Kumbar, Natural polymers: polysaccharides and their derivatives for biomedical applications, in: Natural and Synthetic Biomedical Polymers, Elsevier Inc, 2014, pp. 67–89. [8] S. Bhatia, Natural Polymer Drug Delivery Systems, Springer International Publishing, Cham, Switzerland, 2016. [9] J. Ouellette, J. Robert, D. Rawn, Synthetic polymers, in: Principles of Organic Chemistry, 2015, pp. 397–419. [10] M.C. Hacker, J. Krieghoff, A.G. Mikos, Synthetic polymers, in: Principles of Regenerative Medicine, third ed., Elsevier Inc., 2019, pp. 559–590 [11] C. Vyas, G. Poologasundarampillai, J. Hoyland, P. Bartolo, 3D printing of biocomposites for osteochondral tissue engineering, in: Biomedical Composites, second ed., Elsevier Ltd, 2017, pp. 261–302. [12] A. Shrivastava, Introduction to plastics engineering, in: Introduction to Plastics Engineering, William Andrew, 2018, pp. 1–16. [13] R. Schirrer, Damage mechanisms in amorphous glassy polymers: crazing, in: Handbook of Materials Behavior Models, Academic Press, 2001, pp. 488–499. [14] A.R. Rennie, Amorphous polymers, in: G.M Swallowe (Ed.), Mechanical Properties and Testing of Polymers. An A–Z Reference, Springer, Netherlands, 2013, pp. 32–33. [15] R.O. Ebewele, Polymer Science And Technology, CRC Press, Boca Raton, FL, 2000. [16] S.Z.D. Cheng, S. Jin, Crystallization Polymers and Melting of Metastable Crystalline, vol. 3, Elsevier Masson SAS, 2002. [17] T.A. Osswald, G. Menges, Chapter 3: struture of polymers, in: Materials Science of Polymers for Engineers, second ed., Hanser Gardner Pubication, Inc, Cincinnati, Ohio, USA, 2003. [18] D.R.H. Jones, M.F. Ashby, Polymer structures, in: Engineering Materials 2: An Introduction to Microstructures and Processing, fourth ed., Elsevier, 2013, pp. 405–418.

I. Polymer science

C H A P T E R

3

Polymer synthesis Seth Beck, Ravin Narain Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

3.1 Step-growth polymerization 3.1.1 General characteristics Step-growth polymerization is typically what someone would picture when thinking about polymerization for the first time. Molecule A reacts with molecule B and forms a single product A-B. This product then reacts with molecule C and forms a larger product, A-B-C. This pattern is continued until a polymer chain is created. Some general features of stepgrowth polymerization are provided in the following paragraphs. Every reaction is independent or stepwise to form a new covalent bond between the reactants. Reactants may not be necessarily individual molecules or even the same size of molecules, they could be oligomers or even polymer chains coming together to form a single longer chain. Regardless, the reactant’s length is added together. This leads to the assumption that reactivity is independent of chain length. Or in other words, the functional group on a monomer will have the same reactivity as a functional group on a polymer; this idea is elaborated in the coming sections. Since each reaction is independent this can have an important consideration, one being reaction by-products, which is typically observed in these polymerization systems. Therefore, with every reaction, a small by-product is expelled to complete the reaction and allow the reactants to come together. In many cases, this by-product is a water molecule, which is why the term condensation polymerization is used. As such a significant portion of stepgrowth polymerization processes have water as a by-product, the term condensation polymerization is often used interchangeably with step-growth polymerization. Keep in mind; as a molecular by-product is expelled the number of atoms present in the reactants will not be the same number of atoms in the product, that is, the chemistry from the reactants to products will change slightly. This is a unique feature that can assist in determining if a particular reaction proceeds via step-growth polymerization.

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00003-0

21

# 2020 Elsevier Inc. All rights reserved.

22

3. Polymer synthesis

Another consideration of each polymerization reaction occurring independently is the kinetics of step-growth polymerization. In step-growth polymerization, the chains grow randomly resulting in molecular weight (MW) that rises steadily as the reaction proceeds. Furthermore, there are three requirements for high MW linear polymers to be realized. First, for high MW, a perfect stoichiometric balance of the two difunctional monomers must be introduced. Second, the polymerization reaction must be very high-yielding with no side products, and third, the monomers introduced must be of very high purity (Fig. 3.1). Generally, monomers are classified by the number of reactive sites they possess, and this is referred to as the functionality. A monomer with two reactive sites is a bifunctional monomer and has the minimum number of reactive sites for polymerization. A monomer with three reactive sites is a trifunctional monomer and above this would become multifunctional. Typically, the functional groups consist of heteroatoms that are present in the polymer backbone; this characteristic is helpful to distinguish polymers synthesized via step-growth (Fig. 3.2). The structure, thereby, the macromolecular properties of the polymers are largely determined by the functionality of the monomers used. In the case of bifunctional monomers, the products are exclusively linear polymer chains. A high-MW product is only possible when the conversion of monomer to polymer is greater than 99%. Therefore, side reactions removing the reactivity of the growing chains cannot be tolerated in these systems, for example, the reaction of a monofunctional molecule in the system. The purity and conversion are generally the limiting factors for these reactions. Tri- and multifunctional monomers introduce branching and cross-linking among the polymer chains. As more than two ends are available for growth, the loss of reactivity for some chain ends becomes less impactful on the system. As a result, these systems have a greater tolerance to impurities and require lower conversions for high-MW products.

FIG. 3.1 The synthesis of nylon 6,6: one of the most common products synthesized via step-growth polymerization.

FIG. 3.2 Example of various functionality monomers used in step-growth polymerization.

I. Polymer science

3.1 Step-growth polymerization

23

As the concentration of tri- or multifunctional monomers increase and/or the average number of functional groups in the system increases, the degree of cross-linking increases leading to the formation of polymer networks. Many step-growth polymerization processes are reversible, and there also exists equilibrium between the reactants on one side and the macromolecular products with the expelled small molecular by-products on the other. High MW cannot be realized without further manipulation of the reaction conditions. This is best illustrated with the reaction of an acid and alcohol for the formation of an ester (Fig. 3.3). It is possible for the water to hydrolyze the ester group on the growing polymer chain, making the reaction reversible. As a result, if a large-MW product is an objective, a high conversion is necessary which is only possible by driving the reaction toward the products. This is achieved by the continuous removal of the by-product, water in this case, suppressing the reverse reaction. In many cases, a high temperature is used to drive the reaction forward while removing volatile by-products, so a large MW product can be synthesized. Although the elevated temperature results in an increased reaction rate, the vulnerability to side reactions can also increase in these conditions. Therefore, the removal of the by-product can become a significant aspect of the reaction and influences the reaction conditions along with the previous criteria mentioned. In theory, a monomer becomes a dimer, trimer, or tetramer until a high-MW polymer is formed. However, monomers, oligomers, and polymers react randomly, forming chains of various lengths at any point during the reaction. Therefore, the reactivity of the functional groups is assumed to be independent of the chain length. In other words, the reactivity between any two molecules is dictated by the nature of the functional groups and to a lesser or negligible extent, the molecule associated with those functional groups (Fig. 3.4). For example, this assumption implies that the kinetics between an acid and an amine is constant regardless of the molecules that possess these reactivity groups. This, of course, is not entirely true but becomes an excellent assumption in many cases. Let’s denote the kinetic constant as k1 in the reaction between an acid and alcohol at the early stages. And, the kinetic constant of these two reactive sites at final stages of the stepgrowth polymerization is k2. Experimentally, it has been shown that k1
k2. This is not to say the reaction rate remains constant throughout polymerization but the reactivity of functional groups is constant. However, this goes against intuition when thinking over the course of a polymerization reaction, the viscosity increases dramatically and the diffusivity of molecules decreases by approximately the same factor. To give more context to this assumption, we need to analyze a solution polymerization system a little deeper. For a reaction to proceed, it is necessary for the two reactive sites to

FIG. 3.3 Synthesis of polyethylene terephthalate.

I. Polymer science

24

3. Polymer synthesis

FIG. 3.4 Synthesis of polyimide (Kapton).

collide in a specific arrangement. If the reactive sites collide in any other arrangement the reaction will not proceed. Therefore, for every collision, there is a small probability ( p) that the reactive sites will undergo a reaction. The observed rate of reaction will be proportional to the number of collisions per unit time and the probability that a collision will lead to a reaction. The number of reactive sites that collide is clearly proportional to the number of reactive sites in the system, that is, the concentration of the reactive sites; however, it is independent of the viscosity of the system. This independence on viscosity is largely due to the cage effect. A molecule or reactive site at any given moment is surrounded by other molecules, typically solvent molecules. These molecules create a “cage” around the reactivity site, essentially encapsulating it. Within this cage, the molecules undergo a series of collisions before diffusing out or “escaping.” The rate at which molecules diffuse out or escape a specific cage is proportional to the diffusivity. The relationship between collisions, time, diffusivity, and viscosity are important to recognize before continuing. The more time molecules spend within a cage, the more collisions will occur; therefore time and collisions are proportional. Now, if diffusivity determines how fast molecules escape from a cage, it is inversely proportional to the time since a decrease in diffusivity results in an increase in time within a cage. How would diffusivity decrease? Simply increase the viscosity. Therefore, diffusivity is inversely proportional to the viscosity. This provides the framework for the following analysis. Let’s say two unique reactive sites, denoted by R1 and R2, enter the same cage, and for cases where two reactive sites are in the same cage, we will refer to this as a combined cage. Note, R1 and R2 do not refer to any specific molecule, rather the type of reactive site. Now, R1 and R2 will collide with a specific number of times while they are in a combined

I. Polymer science

3.1 Step-growth polymerization

25

cage. If we take an average the number of times R1 and R2 collide in all the combined cages we get, m. Since the number of collisions in any cage is proportional to the time spent in the cage, which is inversely proportional to the diffusivity, the average number of collisions for a combined cage, m, is proportional to viscosity. However, there is also a time delay between the two combined cages. This is proportional to the diffusivity, since an increase in diffusivity results in less time spent in combined cages, but more opportunities for combined cages, therefore the overall number of combined cages increases. Let’s denote the average number of combined cages per unit of time as M, which, by our previous analysis, is inversely proportional to viscosity. Since the average m is proportional to viscosity, M is inversely proportional to viscosity and the product of the two, mM, is independent of viscosity. Through some manipulation, it can be shown that for relatively small values of p, the probability of a reaction proceeding in a combined cage P is given by: P ¼ 1  epm And the reaction kinetics is proportional to the product of the average number of combined cages and the probability of a reaction occurring in a combined cage, MP. Now if we assume the viscosity of the system is moderate to low, the product of pm is much less than unity: MP ¼ Mð1  epm Þ
M½ð1  ð1  pmÞ
Mpm The reactivities are independent of the system’s viscosity. This verifies the assumption that the kinetic constant k1 is approximately equivalent to the kinetic constant at later stages k2. Or more concisely, the reactivity of the reaction sites is independent of chain length. If the viscosity is significantly large and pm cannot be approximated as less than unity, this assumption breaks down, however, for most commercial applications such a large viscosity is undesired therefore not considered.

3.1.2 Polymerization of tri- and higher-order functional monomers Introducing higher functionalized monomers such as tri- or multifunctional offers opportunities for branching and cross-linking in the system. As more functional groups result in more growing chains the likelihood of chains between macromolecules connecting increases considerably. Let’s say two independent molecules have three growing chains ends and one of those growing ends from each molecule react with one another. The now-single molecule has four growing chain ends and grows even faster. Therefore, the larger molecules grow substantially quicker than the smaller molecules, resulting in the MW distribution broadening. Eventually, if enough higher order functionalized monomers exist (>2 functional groups), a single infinitely networked molecule spans the entire reaction vessel creating a gel-like substance referred to as the gel point. At the gel point, the polymer becomes insoluble and loses the ability to flow and becomes elastic. Although the MW is infinite, this does not mean the reaction halts or the entire polymer is networked, in fact, the mass fraction of the polymer network is quite small, and the number averaged MW (Mn) is finite. The system just consists of a heavily branched/crosslinked polymer network. A good experimental indication of reaching the gel point is the halt of the small vapor bubbles that rise through the system during the reaction.

I. Polymer science

26

3. Polymer synthesis

FIG. 3.5 The reaction of glycerol and phthalic acid to form glyptal polyester.

An example of a system reaching the gel point is the reaction of glycerol (trifunctional) to phthalic acid (bifunctional). Replacing portions of the glycerol with glycol (bifunctional) offers a level of controllability over the branching and cross-linking of the system (Fig. 3.5). Consider two molecules A and B where A has two functional groups (A2) and B has three functional groups (B3) and both are mixed together in a 1:1 ratio. Let f be the average functionality per monomer unit, therefore, 2 +2 3 ¼ 2:5. Let N0 be the number of monomer units prior to the initiation of the polymerization reaction and let N be the total number of molecules after an arbitrary time, this includes polymers, oligomers and monomers. So, the total number of functional groups before polymerization is f  N0. However, each reaction requires two funcf N tional groups to form a bond, therefore, the number of “available” functional groups is 2 0 . This leads to the extent of reaction which can be defined as y, the number of functional groups that have reacted divided by the total number of functional groups. y¼

No  N 2ðNo  NÞ ¼ f  No f  No 2

(3.1)

The average degree of polymerization is given by Xn. No N

(3.2)

2 2yf

(3.3)

Xn ¼ Combining Eqs. (3.1) and (3.2) it follows, Xn ¼

To illustrate the importance of this relationship, let’s consider varying concentrations of the A2 and B3 monomers discussed earlier. Take a mixture, 80% of monomer A2 and 20% of monomer B3. Therefore the average functionality is: f ¼ 0:2  3 + 0:8  2 ¼ 2:2

I. Polymer science

3.1 Step-growth polymerization

Extent of reaction, y

Degree of polymerization, Xn

0.7

4.35

0.8

8.33

0.9

100

0.91

∞

27

As f increases, the extent of reaction required to achieve infinite MW decreases. This is intuitive if we think the more functionalized the monomer the more chains are available to participate in cross-linking, compared with a lower functionalized monomer. If f ¼ 4 then at a 50% conversion, Xn ¼ ∞. The conversion necessary to achieve gelation is often higher than predicted with theory due to cyclization of end groups. Instead of end groups reacting with monomers and other polymer chains, two functional groups on the same chain come together for an intramolecular reaction and do not contribute toward the growth or gelation of the system. Cyclization can be visualized as the formation of “rings” within a polymer chain (Fig. 3.6).

3.1.3 Polymer types and structure A benefit of step-growth polymerization is the wide variability in structure. Since heteroatoms are typically responsible for the reactive site, there are a number of different

FIG. 3.6 Illustration of an intramolecular cyclization reaction.

I. Polymer science

28

3. Polymer synthesis

FIG. 3.7 The general reaction scheme of carboxylic acid derivatives.

combinations of monomer compounds giving rise to unique properties and opportunities to tailor-make the product polymers. The most understood and applicable reactions in step-growth polymerization are carboxylic acid derivatives. The general structure is provided in Fig. 3.7. Where Y is the defining substituent and carries the free electron pair and R is the remaining structure. For amides, Y ¼ NR0 R00 , for acids, Y ¼ OH, for esters, Y ¼ OR0 , or for acyl chlorides, Y ¼ Cl, etc. The carbon double bonded to the oxygen carries little electron density due to the electronegativity of the oxygen, thereby polarizing the double bond. When a molecule similar to Y, denoted as X, comes, it is capable of attaching itself to the low electron density carbon completing the polarization of the bond. This intermediate either eliminates the X substituent or Y substituent. If possible, increasing the polarization of the bond with a catalyst or by protonating the oxygen facilitates the overall reaction. Polyesters—The simplest reaction scheme for polyesters involves a carboxylic acid and alcohol. Usually, the carboxylic acid structure is varied and glycol is used to derive different ester structures. These polymers typically reach equilibrium around 70% and for higher conversions require the removal of the by-product, water, usually with high temperatures and a vacuum. Side reactions are common in these systems and can occur with the monomer or among polymer chains. The side reactions involving the monomers affect the stoichiometry of the compounds whereas, the side reactions involving polymer chains “mix-and-match” sections of the chains (Fig. 3.8). However, side reactions involving the polymer chain, such as transesterification and ester/ester exchange, can also be exploited to provide the desired product (Fig. 3.9). Polyesters offer control over the properties of the bulk material by modifying the repeating monomer units. There are opportunities to incorporate ester groups in the polymer chains to increase the flexibility of the chain, or alternatively, the introduction of more carbonyl and aromatic groups that increase the rigidity of the chain. These variations in the structure allow the degree of crystallinity to be altered, offering precise control over the physical properties of the product polymer (Fig. 3.10).

FIG. 3.8 Side reactions involving the monomer in ester-based polymerizations.

I. Polymer science

29

3.1 Step-growth polymerization

FIG. 3.9 Transesterification side reaction involving the polymer chains in ester-based polymerizations. FIG. 3.10 Ester-based polymers with the corresponding melting temperature.

I. Polymer science

30

3. Polymer synthesis

Polyamides—These polymers are obtained by reaction of an amine group with either a terminal carboxylic acid group, amino acid, a lactam, or acyl chloride. They are similar to polyesters reactions; however, have a few key differences. Typically, the reaction’s equilibrium condition is shifted toward the product amides, therefore not requiring intensive by-product removal. Additionally, no catalyst is employed for these reactions. There is a huge diversity of structures and applications, with 25% of all fibers and 40% of all engineered plastics produced via step-growth of polyamides (Fig. 3.11). The properties are a result of hydrogen bonding between chains and often have high melting points. Although, aliphatic amines are the most common, aromatic amines are also used to form stronger synthetic fibers, such as Kevlar or Nomex, however, they do require stronger reaction conditions (Figs. 3.12–3.14).

FIG. 3.11

Examples of common structure classifications are provided with general applications of each.

I. Polymer science

3.2 Chain-growth polymerization

31

FIG. 3.12 Synthesis of a polyamide (Kevlar).

FIG. 3.13 Synthesis of polycarbonate.

FIG. 3.14 Synthesis of polyurethane.

3.2 Chain-growth polymerization 3.2.1 General characteristics Step-growth polymerization consists of independent reactions to build a polymer chain, whereas chain-growth polymerization has a very different mechanism. Polymerization begins by opening up a monomer double bond (or ring) and creating an active center. The active center then reacts and bonds to a monomer unit while transferring the active center to the newly added monomer, which is now the terminal molecule. Each monomer unit is individually added in rapid succession until the active center is removed (terminated), creating a polymer chain. Chain-growth polymerization can be split into three stages: initiation, propagation, and termination. Initiation involves producing an active center such as a free radical, ion, or polymer catalyst bond on a monomer molecule. Propagation is the simultaneous addition of monomer units and transfer of the active center to “grow” polymer chains. Termination is the removal of the active center on a propagating chain, creating a dead polymer chain, that is, a chain no longer capable of reacting. I. Polymer science

32

3. Polymer synthesis

The mechanistic details of chain-growth polymerization depend on the nature of the active center, however, three key characteristics are common among all the different active centers. First, once growth is initiated, the chain length is independent of the reaction time; therefore, increasing reaction time increases the number of polymer chains but does not increase the length of chains. Second, producing the active center (initiation) dictates the overall rate of reaction; therefore, a polymer solution will consist of monomers, unreacted initiating species and polymer chains; no intermediate or “growing” products. Third, the chemistry of the monomer units remains unchanged in the polymer chain, which can be used in most cases to identify whether a polymer chain was synthesized via chain-growth polymerization (Fig. 3.15).

FIG. 3.15 Examples of some common monomers with their corresponding chaingrowth polymerization mechanism. Reproduced from S. Fakirov, Fundamentals of Polymer Science for Engineers, Wiley-VCH, 2017.

I. Polymer science

3.2 Chain-growth polymerization

33

3.2.2 Polymerizability (thermodynamics) Favorability of a polymerization reaction must result in a negative change in free energy, which is independent of the nature of intermediate (free radical, anion, and cation) as it is a state function. Assuming a negligible change in temperature, the change in free energy is given by the expression as follows: ΔG ¼ ΔH  TΔS

(3.4)

As polymerization progresses, individual monomer units combine to form an ordered structure decreasing entropy. Thus, the entropy change for polymerization is unfavorable, that is, the TΔS term becomes positive. Therefore, polymerization is dictated by the change in enthalpy, H, which must be greater in absolute value than the TΔS term (Fig. 3.16). Three factors contribute to determining the magnitude of H and in the order of increasing influence are: 1. The degree of steric strain of the formed polymer. 2. The degree of resonance stabilization of the alkene bond in the monomer unit. 3. Secondary bonding and polar effects. The polymerizability of a monomer unit refers to the ease of an ability to be transformed into a polymer chain. Therefore, a low polymerizability corresponds to a monomer that has difficulty forming a polymer, and a high polymerizability corresponds to a monomer that readily forms a polymer. A low polymerizability is well-illustrated with the polymerization of the propylene system. Side reactions result in propylene acquiring the radical from growing chains and effectively stabilize the radical species through resonance. As a result, polymerizing propylene and other allyl-based monomers is challenging, requiring special reaction conditions such as copolymerizing non-allyl monomers with the desired allyl monomer. In the case of polypropylene (PP), a catalyst needs to be employed to allow successful synthesis. The following displays propylene stabilizing a free-radical species through resonance (Fig. 3.17).

FIG. 3.16 The change in enthalpy for some common monomer structures.

FIG. 3.17 Propylene stabilizing a free radical species through resonance.

I. Polymer science

34

3. Polymer synthesis

3.2.2.1 Equilibrium A thorough understanding between polymerization and equilibrium is necessary for many processes, as the product’s MW and structure are governed by these relationships. This is best illustrated through thermodynamics principles. Chain-growth propagation is due to the rapid addition of monomer units which can be expressed as: Mn  + M ! Mn + 1  Rp ¼ Kp ½Mn  ½M

(3.5)

However, the reverse is also possible, which is the depolymerization of the polymer chain, shown as: Mn  + M ! Mn + 1  Rp ¼ Kp ½Mn  ½M

(3.6)

Therefore, the overall rate of polymerization is given by the difference between the rate of propagation and the rate of depolymerization.
 (3.7) R ¼ Rp  Rd ¼ ½Mn   Kp ½M  Kd An increase in temperature results in an increase of the reaction kinetics. Therefore, the rate of propagation and depolymerization increases, however, the rate of depolymerization increases faster. For equilibrium to be established both rates must be equivalent and the change in free energy becomes zero. Rearranging expression (3.4) yields an equilibrium temperature, referred to as the ceiling temperature (Fig. 3.18). FIG. 3.18 The ceiling temperature for some monomer structures. Modified from M.P. Stevens, Polymer Chemistry, Oxford University Press, New York, 1990.

I. Polymer science

3.2 Chain-growth polymerization

Tc ¼

∂H ∂S

35 (3.8)

The ceiling temperature is a measure of the tendency of a polymer to depolymerize back to individual monomer units. At the ceiling temperature polymerization and depolymerization are equivalent. Above this temperature, the rate of depolymerization exceeds polymerization which results in the breaking of the polymer chains down to their individual monomers. Note that this relationship does not provide any information to the time component of equilibrium. Therefore, if the depolymerization process is kinetically hindered, polymers can be useful above their ceiling temperature. This is the case for poly(formaldehyde) which has a ceiling temperature of 126°C. However, it is made stable at temperature of 200°C through copolymerization, additives, and stabilizers which essentially “inhibits” depolymerization. Note, in rare circumstances, the equilibrium temperature marks the minimum temperature for favorability, above which, the rate of polymerization exceeds the rate of depolymerization. In this case, the equilibrium temperature is referred to as the floor temperature.

3.2.3 Stereochemistry of chain-growth polymerization The stereochemical arrangement of the polymer has major implications when designing polymers for different applications as it dictates the macroscopic properties. This is observed in the four main arrangements: (1) isotactic, (2) syndiotactic, (3) heterotactic, and (4) atactic (Fig. 3.19). Isotactic polymers have substituents on the same side of the polymer backbone; syndiotactic polymers have substituents on alternating sides of the polymer backbone; and heterotactic have a dyad configuration that alternates on the polymer backbone. Since each structure possesses a nonrandom orientation, they form a general class of stereoregular polymers. Stereoregular polymers are capable of packing closer together, obtaining an ordered structure, and as a result, possessing a higher degree of physical strength. As a general guideline, isotactic polymers tend to form semi-crystalline (combination of amorphous and crystalline) materials, whereas syndiotactic and heterotactic polymers form crystalline structures. To synthesize stereoselective polymers, a metal catalyst must be implemented. This includes the Ziegler-Natta initiators, metallocenes, etc. which will be discussed in later sections. Atactic polymers consist of a random stereochemical arrangement. The random arrangement restricts the polymer’s ability to pack close together and they generally form amorphous (noncrystalline) structures. This is categorized with low physical strength and higher flexibility materials, that is, soft and rubbery. Synthesis of atactic polymer always occurs unless special reaction conditions dictate otherwise. Manipulating the stereochemical arrangement of the polymer allows a level of control over the physical properties of polymers, for example, controlling the tacticity of PP. PP is an important commodity plastic utilized in diverse applications from Tic Tac lids to piping systems. However, atactic PP is rubbery and has a low strength whereas highly crystalline (50%–60%) PP is brittle, therefore a combination of the two arrangements is implemented. Metallocene catalysts allow synthesis of polymers that contain segments of isotactic PP

I. Polymer science

36

3. Polymer synthesis

FIG. 3.19 The general structure for the different stereochemical arrangement of polymers.

(crystalline) and segments of atactic PP (amorphous) in the same polymer chain, creating rubbery elastomer materials. The concentration of each arrangement gives rise to the wide range of application which PP can be used (Fig. 3.20).

3.2.4 “Living” versus “controlled” polymerization Living polymerization occurs when there is a complete absence of any substance that will deactivate the growing polymer chains or immunity to deactivation, that is, no termination mechanism occurs. Chains are initiated and grow uniformly (rate of initiation > > rate of propagation) and all monomers in the solution are consumed. Further addition of monomers

I. Polymer science

3.2 Chain-growth polymerization

37

FIG. 3.20 Illustration of controlling polypropylene tacticity.

results in the continuation of polymerization. Therefore, the growing chain end retains its active center and a “living” polymer is obtained. Proof of this can be observed if the addition of a second monomer results in a block copolymer and MW increases linearly with the degree of conversion. Living polymerization provides several benefits, including a narrow polydispersity index (PDI), control over MW, and the ability to prepare block, graft, star as well as polymers with end functional groups. However, it is challenging to achieve and usually not practical outside of the stringent laboratory settings. Controlled polymerization provides the benefit of “living” polymerization, that is, narrow PDI, control over MW, and ability to prepare diverse polymers without the requirement of strict reaction conditions. Instead of removing all potential termination mechanism in the reaction environment, controlled polymerization aims to suppress termination, decreasing the chance it takes place. For controlled polymerization, the concentration of radicals is kept low, decreasing the probability of having two radicals coming together, terminating one another. This is achieved by a reaction environment that is specifically designed to “cap” or temporary stop the growing polymer chains. This “cap” removes the active center, creating a dormant chain that can be reactivated. Whereas termination eliminates the future reaction potential of a polymer chain, this “cap” is in essence, a temporary termination. Therefore, the dormant phase protects chains from termination, while still allowing the chain to generate a new active center for further propagation.

I. Polymer science

38

3. Polymer synthesis

3.2.5 Free-radical polymerization 3.2.5.1 Conventional free-radical polymerization A subcategory of chain-growth polymerization is free-radical polymerization (FRP), where the active center is a free radical. A significant number of commercially available polymers are synthesized via free radicals. Although, there is a wide applicability of chain-growth polymerization suffering from opportunistic side reactions of the active center, removing the activity of the growing polymer chains (Fig. 3.21). Initiators

Initiating species are compounds that decompose to generate radicals when exposed to an external stimulus. Depending on the nature of bonds within the compound, decomposition can be achieved thermally (homolysis) through radiation (photolysis) or a redox reaction. The rate at which the compound breaks down is dictated by the overall molecular structure,

FIG. 3.21

Examples of chain-growth polymerizations.

I. Polymer science

3.2 Chain-growth polymerization

39

intramolecular interactions as well as the properties of the surrounding molecules, in this case the solvent/monomer mixture. Once decomposition takes place and a radical is generated, the initiating compound has two reaction pathways: react with a monomer to begin propagation or deactivate by reacting with another initiating molecule or solvent molecule. Therefore, all initiating species possess a fractional efficiency or effectiveness to account for the rate of deactivation. Fractional efficiency is largely dependent on the surrounding molecular environment, that is, choice of solvent. This is due to the cage effect. As mentioned previously, at any given time, initiating species can be surrounded and encapsulated by the solvent molecules. This “cage” influences the formation and recombination of radical species. If the cage effect is significant for a particular system, radicals are more likely to deactivate leading to a low fractional efficiency. Typically, the cage effect becomes more predominant for the recombination of initiating species as a reaction proceeds since the viscosity increases and monomer concentration decreases. The most widely used method to generate radicals is through thermal decomposition of an initiating species. This is because of the predictable kinetics since most thermal initiators follow Arrhenius temperature dependence. Some common thermal initiators include organic compounds that contain a labile group which are broken with the use of heat or irradiation. These include azo (–N]N–), peroxide (–O–O–), or disulfide (–S–S–) bonds. Although there are other methods available to generate a radical on a monomer species, the utilization of an initiating species is the most common, therefore, will be the only one considered here (Fig. 3.22). Initiation

The term “initiation” is usually used to denote a monomer that has acquired an active center, in this case, a free radical. However, initiation is a two-step process: the initiating species must decompose to generate a free radical, then that free radical must react with a monomer unit. The ability of the monomer unit to stabilize a free radical has direct implications with the polymerization of the system.

FIG. 3.22 Example of thermal initiating species.

I. Polymer science

40

3. Polymer synthesis

Naturally, the more stable arrangement will predominate. In free-radical systems, two factors typically dictate the position of the free radical. (1) The steric effect of the attack on the monomer (2) The stability of the product radical In Fig. 3.23, the attack of the initiating species on the methylene carbon is less sterically hindered therefore more likely to occur. Additionally, product radical 1 has a higher degree of radical substitution (secondary) compared to radical 2 (primary), making it a more stable formation (Fig. 3.24). Propagation

Once the monomer possesses a free radical, it can begin propagating or growing. The propagation step is marked by the rapid sequential addition of monomer units to form a growing chain. In reality, the propagation step is nearly instantaneous, with thousands of monomer units forming a chain in less than a second. Therefore, experimentally at any given time, there will be unreacted monomer units, initiating species as well as dead polymer chains, however, no growing or propagating chains. Although propagation is approximated as instantaneous, monomer units do not “randomly” arrange themselves in the growing chain. The addition of monomer units is organized and predictable. This organization is determined by the stabilization of the free radical on the monomer mentioned in the initiating section. The propagating chain will follow a similar arrangement with the initiating mechanism for every monomer addition. The growing chains gravitate toward arrangements that provide stability even if for a fraction of a second. The conformation that is capable of providing the maximum radical stability will dictate the organization of the monomer molecules in the chain (Fig. 3.25). FIG. 3.23 The two possible initiation mechanisms for majority of monomers.

FIG. 3.24

Example of the initiating step using azobisisobutyronitrile as the initiator and general monomer.

I. Polymer science

3.2 Chain-growth polymerization

41

FIG. 3.25 Example of the two propagation arrangements possible for a general monomer.

If the head-to-head arrangement was to occur, the chain end consists of a primary radical. Whereas, if a head-to-tail arrangement occurs, the chain end consists of a secondary radical, which is much more stable. Therefore, the head-to-tail predominates, however, it is not to say that the head-to-head arrangement never occurs in solution, simply less likely to occur. Termination

The final step for any growing polymer chain is where the active center is removed and a “dead” (unreactive) polymer chain is created. Termination cannot be prevented under normal reaction conditions; however, care can be given to decrease the likelihood of occurring. This is what gives rise to controlled radical polymerization which will be discussed in later sections. Two radical compounds combining together, deactivating one another is the dominant termination process which can be split into two distinct mechanisms: combination and disproportionation. It is believed that termination occurs almost entirely by combination in most radical systems; however, experimental evidence to support this is limited. Additionally, it is inferred that disproportionation becomes significant for tertiary macroradicals since more ß Hydrogens are available for transfer and combination becomes increasingly sterically hindered. Therefore, depending on the polymer system one termination mechanism could potentially be favored. Combination is when two radicals come together to form a covalent bond. The radicals combine in a head-to-head formation.

Disproportionation is when a radical removes hydrogen from another radical species resulting in both compounds terminating; one compound will have a saturated end group and another will have an unsaturated end group.

Note, unless the concentration of active initiators is unusually high (high temperature), termination of growing polymer chains via combining with initiators is negligible. However, if

I. Polymer science

42

3. Polymer synthesis

present, leads to a significantly lower average MW than what would be seen without this termination mechanism, simply due to the increase in radical concentration. Inhibitors

Compounds that drastically decrease or completely stop the rate of propagation are inhibitors. Two factors contribute to this phenomenon: first, inhibitors have a strong affinity for radicals, reacting immediately with the radicals present in the system. Second, inhibitors are capable of stabilizing the radicals to such a large extent, in many cases removing the reactivity of a radical. Depending on the objectives of the reaction inhibitors can be added to the system, however, they are more common as impurities hindering polymerization. Inhibitors do not react with the monomer or solvent in the absence of radicals. The impact on the propagation of reaction depends on the stabilization of the radical formed and concentration. If a less reactive radical is formed, such as oxygen, the propagation rate is slowed down; this is sometimes referred to as retardation. If the inhibitor is capable of stabilizing the radical through resonance, such as 2,2-diphenyl-1-picrylhydrazyl (DPPH), then the propagation rate is stopped completely, this is sometimes referred to as inhibition. Once the inhibitor is consumed polymerization will continue at a normal rate (Fig. 3.26). Chain transfer

When a radical species reacts with a non-radical species terminating the growing chain, the result is at least one radical species and an atom being transferred in the process. Depending on the new radical, it may initiate a new polymer chain; however, frequently the “new” radical will terminate another growing chain (Fig. 3.27).

FIG. 3.26 Some common inhibitors in polymerization reactions.

I. Polymer science

3.2 Chain-growth polymerization

43

FIG. 3.27 The general mechanism of chain transfer.

• Chain transfer to solvent The growing chain abstracts hydrogen from a solvent molecule and transfers the radical to the solvent molecule. This is illustrated with polystyrene in xylene solvent.

The solvent molecule can initiate a new chain; however, will usually terminate another growing chain.

• Chain transfer to monomer At lower conversion, the concentration of monomer is quite high, leading to the possibility of the growing polymer chain abstracting hydrogen from an unreacted monomer, terminating the chain. The same polymerizing rules discussed previously decide how the active monomer proceeds. Typically, it is capable of starting a new polymer chain, however, on the chance that the monomer has effective stabilization of the radical; an inhibiting response is procured, limiting the polymerization of the system.

• Chain transfer to initiator The growing chain reacts with an unreacted initiator. This generates an active initiator without external stimuli. Unlike other chain transfer mechanisms, chain transfer to initiator always allows for further propagation.

I. Polymer science

44

3. Polymer synthesis

• Chain transfer to polymer The growing chain reacts with a polymer backbone, which can be inter- or intra-chain. This results in the transfer of a radical to the backbone, which has the possibility to react with monomers and allow for propagation. This often leads to branching within the polymer network and has the tendency to occur closer to the end of the chain and intra-chain, leading to the formation of short branches. Chain transfer to polymer chains is typically observed in systems when either the radical is very reactive (has little resonance stabilization) or high conversions are achieved, resulting in large concentration of polymer.

I. Polymer science

3.2 Chain-growth polymerization

45

Chain transfer agents

Materials that are either present as impurities or deliberately added to FRP that efficiently react with the growing chains are chain transfer agents (CTAs). CTAs limit the time for propagation, which minimizes the degree of polymerization (length) of polymer chains. However, adding CTAs increases the number of radical sites available for initiation, forming more polymer chains than would be formed in their absence. The effect, length vs number of polymers is controlled by the concentration of the CTA and the associated reactivity constant of the compound. For example, thiols are commonly used due to the relatively weak RS–H and reactive RS radical (Fig. 3.28).

3.2.6 Kinetics of chain-growth polymerization The three main events: initiation, propagation, and termination were described qualitatively previously, however, they are presented with a simplified kinetic model for chaingrowth polymerization. 3.2.6.1 Initiation Introducing free radicals into the system begins the initiation step. In this case, assuming thermal decomposition of an initiating species to generate two radicals is the preferred venture. As mentioned before the true initiating step is when an initiating species reacts to generate a radical on the monomer. kd

Process: I ! 2R_ Rate expression: Rd ¼ 2fkd ½I  ki

Process: R_ + M ! R  M_ Rate expression: Ri ¼ ki ½R_½M

(3.9) (3.10)

The rate of decomposition, that is, the rate at which radicals are generated is given by Eq. (3.9), where the rate constant, kd, is determined by the temperature. Not all the decomposed initiators are successful at initiating decomposition, therefore, an efficiency or effectiveness factor, f, accounts for this. For simplicity, it is commonly chosen as 1 to simplify the analysis. In reality, f is typically between 0.4 and 0.6.

I. Polymer science

46

FIG. 3.28

3. Polymer synthesis

Additional examples of chain transfer agents (CTAs).

The “true” initiation step is given by Eq. (3.10) since it is the generation of a radical on a monomer species. However, the activation energy for Eq. (3.9) is 5 times than Eq. (3.10), consequently Eq. (3.9) becomes the rate determining step. Therefore, the rate of initiation can be satisfactorily expressed by Eq. (3.9) alone. Ri ¼ 2fkd ½I 

(3.11)

Notice, the initiating step is independent of monomer concentration. Additionally, the process is a unimolecular decomposition (individual molecule breaks down) making kd a firstorder rate constant with units of (time)1. 3.2.6.2 Propagation The propagation step is the consecutive addition of monomer molecules to grow a polymer chain. kp

kp

Process: Mx  + M ! Mx + 1  M + M ! Mx + 2  M …: It is assumed the reactivity of the radical is independent of the chain length. If this was not the case, each addition of a monomer molecule would require a new kinetic equation. This assumption, experimentally verified, that all chain lengths have equivalent reactivity makes it possible to represent the propagation step with a single kinetic equation. Rate expression: Rp ¼ kp ½Mx  ½M

(3.12)

Propagation is a bimolecular reaction (between two molecules) making kp a second-order rate constant with units of (concentration)1 (time)1.

I. Polymer science

3.2 Chain-growth polymerization

47

3.2.6.3 Termination The normal termination mechanism involves two radical species coming together for either a combination or a disproportionation termination mechanism.  2 ktc (3.13) Combination process: Mx  + My  ! P Rate expression: Rtc ¼ ktc Mx ktd

Disproportionation process: Mx  + My  ! 2P

 2 Rate expression: Rtd ¼ ktd Mx

(3.14)

Since each radical possesses equivalent reactivity, the total rate constant is expressed as the summation of each rate constant for the normal termination mechanisms, kt ¼ ktc + ktd. Then one equation can be used to express the total chain termination. Rt ¼ kt ½Mx  2

(3.15)

Since both termination mechanisms are bimolecular, they have second-order rate constants. 3.2.6.4 Chain transfer The general relationship for chain transfer can be represented by: kw

Process: Mx  + W ! Mx + W 

Rate expression: Rw ¼ kw ½Mx  ½W 

(3.16)

Where W can represent a solvent, monomer, initiator, or polymer molecule. The overall effect on the system depends on the relative polymerization rate of Mx  and the new radical W. If W has a lower rate than the monomer radical, Mx  , the polymerization rate decreases, and if W has a higher rate than vice versa. The most dramatic effect of chain transfer is seen in the MW of the product polymers. When chain transfer occurs, it is another termination mechanism, thereby reducing the overall length of the polymer chains. Of course, the exception is if chain transfer occurs with a polymer molecule. 3.2.6.5 Rate of polymerization At the beginning of the polymerization, the rate of radical generation will start at zero and increase. Nearly simultaneously the rate of termination will show a similar trend. Eventually, the rate of initiation and termination will be equivalent and the number of radicals in the system will remain constant. This marks the steady-state point and is typically reached early on in the reaction. This is also known as the steady-state assumption and is represented as: Ri ¼ Rt And d½ M   ¼0 dt

(3.17)

Since steady-state is reached early on, let’s assume that it applies to the entire polymerization process and the minor deviation from this assumption is negligible.

I. Polymer science

48

3. Polymer synthesis

 2 2fkd ½I  ¼ 2kt Mx

(3.18)

 1 fkd ½I  2 ¼ kt

(3.19)

Some rearrangement yields: 

Mx



This is an expression for the number of growing chains in terms of measurable quantities. Now the rate of polymerization is essentially the rate at which monomer molecules are consumed. The two predominant reactions of monomers are initiation and propagation. Since both of these reactions consume monomers, the concentration of monomers decreases with time, represented by a negative in the rate expression. d½M ¼ Ri + Rp dt

(3.20)

If the polymer chains are sufficiently long, only a fraction of monomers are consumed via initiation and the majority of them are consumed from propagation. Then, the polymerization rate can be well approximated by the rate of propagation. d½M
Rp dt

(3.21)

Substituting in Eq. (3.12) d½M ¼ Kp ½Mx  ½M dt Substituting in Eq. (3.19)  1 d½M fkd ½I  2 ¼ kp ½M dt kt

(3.22)

This is a differential expression for the rate of polymerization in moles of monomer per unit volume per unit time when the monomer concentration, [M] and initiator concentration, [I] is specified. Since both the monomer and initiator concentrations decrease with time, Eq. (3.17) is integrated with respect to time to obtain the amount of formed polymer in a specified interval. Eq. (3.22) was derived assuming that an initiating species is decomposing to generate radicals, however, it is possible to simplify the expression based on any initiating mechanism utilized. A couple of key features to notice: first, the instantaneous rate of polymerization is directly proportional to the monomer h i concentration and to the square root of the initiator concentration. Second, the ratio,

kp

kt 1=2

is an important and frequent relationship when deriving kinetic

equations for FRP. This is best presented with an example. Take acrylonitrile and styrene at 60°C. The kp for acrylonitrile and styrene is 2000 L/mol s and  100 L/mols, respectively. One would expect the polymerization of acrylonitrile to proceed 20 times faster hthanistyrene, however, this is not observed since the kt values provide some balance. The

kp

kt 1=2

ratio is

for acrylonitrile and 0.01 L /mol s for styrene. This is a result 0.07 L /mol s of the aromatic substituent on styrene providing stability for the radical. Since the radical 1/2

1/2

1/2

1/2

I. Polymer science

1/2

1/2

3.2 Chain-growth polymerization

49

is more stable on styrene, it does not polymerize quite as fast as acrylonitrile, however, it is not as prone to termination either. 3.2.6.6 Trommsdorff-Norrish effect or auto-acceleration or gel effect Although FRP has a wide applicability industrially as well as academically, there is particularly severe phenomenon that occurs if care is not taken during reaction conditions. Let’s take an example of polymerization reactor and initially having all free-radical mechanisms at steady state. Initiation is slow but continuous and as polymerization proceeds, the radical concentration begins to increase, and as it does the rate of termination increases by a proportional amount for the system to remain at steady state. At first, termination of radicals is controlled through diffusion of molecular species. However, as monomers are converted to polymer chains the viscosity of the solution begins to increase, hindering the movement of molecules, consequently also decreasing diffusion. As diffusion is hindered, termination of radical species slows down, resulting in an increase in the radical concentration. The increase in radicals results in more chains propagating, which in turn release more heat (exothermic reaction), leading to a higher rate of initiator decomposition to radical species. This cycle repeats and begins compounding until a runaway chain reaction occurs and if the energy is not maintained/dissipated, it can eventually lead to an explosion.

3.2.7 Controlled/living radical polymerization Radical polymerization is the most powerful tool for the synthesis of polymers from a wide range of monomers due to its tolerance toward many functional groups, solvents, additives, or impurities. Despite the fact that a truly “living” radical polymerization cannot be realized (due to the presence of rapid bimolecular radical termination reactions), it is now possible to achieve controlled/“living” radical polymerization as a dynamic equilibrium can be established between the propagating radicals and a large number of dormant species, which can be reactivated. In this section, we will describe the three most popular controlled/“living” radical polymerizations namely, nitroxide-mediated polymerization (NMP), atom transfer radical polymerization (ATRP), and reversible addition-fragmentation chain transfer polymerization (RAFT). Using these techniques, a wide range of well-defined polymers have been prepared with predetermined MW, narrow polydispersity, and a high degree of chain functionalization or chain extension. 3.2.7.1 Nitroxide-mediated polymerization NMP, invented by David Solomon, Paul Cacioli, Glen Waverley, and Ezio Rizzardo in 1986, is one of the oldest controlled stable free-radical polymerization (SFRP) processes. It allows the synthesis of polymers with narrow polydispersity, predictable MW, and composition. Using NMP, it is also possible to design and synthesize well-defined polymer architecture such as star, comb, and gradient copolymers as well as polymers with a wide range of functionality. NMP is relatively easy to perform since it requires only the addition of a stable radical nitroxide compound to an otherwise conventional FRP. With the addition of the sterically hindered nitroxide, the radical concentration in the polymerization can be kept low and hence minimizing the chance of termination mechanisms to occur. 2,2,6,6-(tetramethylpiperidin-1yl)oxyl is the structure of the first stable radical for the nitroxide FRP (Fig. 3.29). I. Polymer science

50

3. Polymer synthesis

First nitroxide reported (Solomon, 1985)

FIG. 3.29

The structure of the first nitroxide reported for controlled radical polymerization.

FIG. 3.30 The interaction between the initiating species and nitroxide compound.

First, a radical initiator is chosen to have a short half-life, this is facilitated by employing reaction conditions that promote a short half-life, usually temperature. Then, a nitroxide compound is introduced that rapidly “captures” the radicals that are generated thereby keeping the concentration of radicals low and only allowing the chains previously initiated to continue polymerizing (Fig. 3.30). Very few new chains are formed by this process. Instead, the nitroxide compound “caps” the growing polymer chains, creating dormant ones. Through temperature manipulation, these dormant chains can become reactivated allowing further propagation. The concentration of radicals is kept low (Rnitroxidecombination > > Rp)and the chains stay active (Rct and Rt < < Rp and Rnitroxidecombination) leading to a higher concentration of dormant chains as compared to active chains. The result is a low PDI ( Kactivation, however, in the case of elevated temperatures, Kdeactivation > > Kactivation, the result is an unrealistically long activation time.

I. Polymer science

3.2 Chain-growth polymerization

51

In summary, this method is not particularly versatile, however, it is capable of synthesizing well-defined polymers with a controlled MW for a limited number of monomers, such as styrene, butadiene, and methyl methacrylate. Additionally, it offers a glimpse into a relatively simple case of controlled radical polymerization (Fig. 3.31). 3.2.7.2 Atom transfer radical polymerization ATRP is a controlled radical polymerization process and is based on the reversible homolytic cleavage of the C–X bond of an alkyl halide or pseudohalide. Once again, the control of the polymerization is achieved by maintaining a low concentration of radicals throughout the polymerization. A transition metal complex is used which helps with the activation and deactivation of the growing polymer chains. Activation and deactivation occur throughout the polymerization and, ideally for good control, deactivation should be fast so that the propagating chain radicals are quickly converted to dormant species after addition of a few monomer units. The general mechanism of the ATRP process is shown in Fig. 3.32. Monomer

ATRP is suitable for the polymerization of a variety of monomers, including styrene, (meth)acrylates, (meth)acrylamides, acrylonitrile, and vinyl pyridine, essentially, any compounds that have stabilizing groups such as a phenyl or carbonyl next to the carbon radicals. However, acidic groups (methacrylic or carboxylic) tend to poison the catalyst or protonate nitrogen-based ligand groups, which leads to interference in polymerization. Although, FIG. 3.31 The simplified mechanism of controlled radical polymerization with a nitroxide compound.

I. Polymer science

52

3. Polymer synthesis

FIG. 3.32 The general mechanism for atom transfer radical polymerization (ATRP).

techniques have been developed to provide moderately successful polymerization of acidic monomers, such as carefully selected conditions (type of initiator, catalyst complex, and solvent pH) and the use of protected monomers, it still requires further development. In the absence of impurities and side reactions, the polymerization rate is dictated by the act equilibrium constant Keq ¼ KKdeact . If the equilibrium constant is too small, the polymerization rate decreases and can even cease completely. On the other hand, if the equilibrium constant is too large, termination becomes significant due to the increase in radical concentration. The equilibrium constant is largely dictated by the monomer structure, which has two direct consequences. First, under ideal conditions, the polymerization rate is essentially fixed dependent on the monomer structure. Second, it is necessary to optimize the reaction conditions: solvent, catalyst complex, initiator, concentration of components, etc. for every unique monomer. Initiator

In an ideal system, where termination and chain transfer are negligible, and initiation is sufficiently fast, the number of growing polymer chains is equivalent to the initial concentration of initiator. The rate of initiation should be much faster than the rate of propagation. Therefore, all the chains are initiated quickly and each one has an equal opportunity to grow, that is, propagate at the same rate, leading to a narrow PDI. Where the MW distribution is narrow, a low concentration of initiator leads to less chains with a higher MW compared to a higher concentration of initiator that leads to more chains with a lower MW. The diverse variety of initiators accessible for ATRP is a compelling advantage for this method. Essentially, any halogenated compound that is activated by alpha-carbonyl, phenyl, vinyl or cyano groups can be utilized. Common ones being, halogenated alkanes, benzylic halides, haloesters, alpha-haloketones, and alkyl and aryl sulfonyl chlorides. The activation rate constant, that is, the reactivity, of initiators can be assessed through four criteria and in order of significance are: 1. 2. 3. 4.

Degree of initiator substitution (Primary < Secondary < Tertiary) Leaving atom/group (Methyl-2-Halopropiaonates, Cl < Br < I) Radical stabilizing group (-Ph < -COOR 1 μm

50–500 nm

10–100 nm

Particle size

50–500 nm

50–500 nm

10–100 nm

Emulsifier concentration

Moderate

Moderate

High

Nucleation mechanism

Micellar, homogenous

Droplet

Droplet

Costabilizer type

–

Hexadecane, cetyl alcohol

Hexanol, pentanol

Duration of stability

Seconds to hours

Hours to months

Indefinitely

Homogenization method

–

Mechanical or ultrasonic

–

Modified from C.D. Anderson, E.S. Daniels, Emulsion Polymerisation and Latex Applications, Vol. 14, iSmithers Rapra Publishing, 2003.

I. Polymer science

80

3. Polymer synthesis

onto the emulsion droplets surfaces as per the adsorption isotherm (e.g., Langmuir, Freundlich, or Frumkin adsorption isotherms). The critical micelle concentration (CMC) is reached when the concentration of surfactant in the aqueous phase increases to a point at which no additional surface is soluble. Any excess surfactant, added after the CMC has reached, will associate into micelles with a hydrophobic core and a hydrophilic shell. The micellar hydrophobic core attracts monomer from the stabilized droplets, thereby causing them to swell. Initiator radicals react with monomers in the aqueous phase to form oligoradicals which can either aggregate to form primary particles by homogeneous nucleation (enter micelles containing monomers to form primary particles by micellar nucleation) or enter monomer droplets directly to cause droplets nucleation (generally low due to low droplets present in the system). Some emulsion polymerization are surfactant-free and are called emulsifier-free polymerization. In such a system, persulfate radical initiators are often used to start the polymerization through homogeneous nucleation in the aqueous phase. The generated oligoradicals form particles upon aggregation which is stabilized electrostatically by the persulfate initiator end groups at the particle surfaces. According to Harkins’ model of emulsion polymerization, the process is divided into three intervals. During the interval I, new particles are nucleated by radical entry into micelles or by homogeneous nucleation. The rate of polymerization and the particles number both increases as new particles are formed. As surfactants are used in stabilizing the new particles formed the concentration decreases below the CMC and nucleation ends. The number of particles is constant beyond this point. During interval II, the particles continue to polymerize the monomer present in the monomer droplets. As a result of the concentration gradient, the monomer is transported through the aqueous phase to the polymerization site. In the end, the monomer in the droplets is depleted. Finally, during interval III, the monomer present in the polymer particles polymerizes completely into the polymer. The concentration of monomer in the polymer particles decreases to essentially zero.

3.5.1 Conventional emulsion polymerization The majority of emulsion polymers are made by conventional emulsion polymerization. In this process, monomer droplets are dispersed in a continuous aqueous phase and are stabilized by surfactant from coalescence/aggregation. The surfactant helps polymer particle formation by homogeneous or micellar nucleation upon initiation. In this process, the monomer needs to be slightly water-soluble so that the monomer can diffuse from the droplets to the polymerization site in the growing polymer particles. A low concentration of surfactants (1–3 wt%) is generally needed in emulsion polymerization. The particle size may be controlled by the amount of surfactant present. The high concentration of surfactants can cause smaller particle sizes. The particle size can also be controlled by the concentration of the initiator and the solids content. A wide range of monomers with relatively low solubility has been polymerized by conventional emulsion polymerization. Some examples of such monomers are acrylics, methacrylics, styrene and vinyl acetate. These monomers are often used in the preparation of latexes for

I. Polymer science

3.5 Emulsion polymerization

81

paints, textile binders and adhesives. Polyesters, epoxy and urethane dispersions are applied in industrial coatings due to their higher strength. In addition, butadiene is often used to copolymerize with styrene in synthetic rubber fabrication for tire manufacture. 3.5.1.1 Miniemulsion Miniemulsions are characterized as submicron dispersions of monomer that are stabilized by surfactant from coalescence and by a costabilizer such as a hexadecane to prevent Ostwald ripening. Miniemulsions are achieved by homogenization where large droplets of a coarse emulsion are broken down into a large number of smaller droplets. Emulsions homogenized in the absence of a costabilizer are called homogenized emulsions. Miniemulsions are kinetically stable, that is, they are stable long enough for the polymerization (stability over several hours to months). The main difference between miniemulsion and conventional emulsion polymerization is the nucleation mechanism. For miniemulsion, radicals from the water phase enter the dispersed monomer droplets directly to initiate polymerization, the mechanism is referred to as droplet nucleation. Due to the small size and large surface area of the droplets, they are more competitive for radicals as compared to the homogeneous and micellar nucleation mechanism. Latex particles by this process are typically in the 50–500 nm. Monomers such as styrene, methyl methacrylate or butyl acrylate are suitable for miniemulsion due to their limited water solubility. 3.5.1.2 Microemulsion Microemulsions are thermodynamically stable dispersion droplets in the 100 nm diameter range. Microemulsions are spontaneously formed from mixtures of water and monomer containing a large amount of surfactant (10 wt%). Microemulsions can produce the smallest polymer particles (down to 10 nm) of all heterogeneous polymerization, however, the large surfactant concentration can be a significant issue for some biomedical applications. Inverse emulsion (water in oil emulsions) are emulsions where the aqueous phase is dispersed within a continuous organic phase. The organic phase is usually unreactive hydrocarbon such as xylenes or kerosenes and the water phase contains the water-soluble monomer such as acrylamide. The hydrophilic–lipophilic balance (HLB) value of the stabilizer determines the stability of the inverse emulsion. HLB values of 7 or less are considered suitable for inverse emulsion. Polyacrylamide, extensively used as a thickener, is often produced by this technique. Process description

An insoluble or scarcely soluble monomer is introduced to the polymerization medium, forming 10%–50% of the systems’ volume. With the use of a surfactant (emulsifier or soap) the monomer is emulsified in the medium. Once the surfactant concentration surpasses the CMC, the monomer is present in three ways: (1) droplets, (2) micelles, and (3) polymerization medium. The majority of the monomer, >95%, is in the form of emulsifier coated, micron-sized droplets, approximately, 1–10 μm in diameter. For context, approximately 1012 droplets are present for every milliliter of the continuous phase.

I. Polymer science

82

3. Polymer synthesis

Most of the remaining monomer creates swollen colloidal aggregates or micelles in the ˚ . This is a result of the hydrophobic and hydrophilic end of the emulsifier. range of 50–100 A If the polymerization medium is water, the hydrophilic group (or polar) end of the emulsifier is in contact with the water, sequestering the hydrophobic group (nonpolar) toward the center creating a micelle; and vice versa if the medium is oil-based (hydrophobic). Again, for context, approximately 1018 micelles are present for every milliliter of the continuous phase. The small percentage of monomer left is molecularly dissolved in the medium. The solubility of the monomer is improved due to the micelle formation since the monomer is absorbed inside the micelles. The extent of this effect depends on the concentration and structure of the surfactant as well as the nature of the monomer. An initiator, which is only soluble in the polymerization medium, is introduced; therefore, polymerization is initiated within the medium, outside of the micelles and droplets. As the monomer is approximately 50 more soluble within the micelles than the medium, monomers, and radicals formed eventually makes its way inside the micelle. These small micelle elements are largely responsible for the isolation of radicals since each one can only accommodate a single radical at a time. This isolation of radicals is what separates emulsion polymerization from the other polymerization methods. Since radical interaction is rare, termination is minimized, and large MW products are possible. The concentration of the micelles is on the order of 8 greater than droplets; therefore, the total surface area of the micelles is far greater than the monomer droplets. As a result, polymerization occurs almost entirely inside the micelles. However, the concentrated droplets emulsified throughout the medium act as a reservoir for polymerization. To elaborate, as polymerization occurs, the concentration of monomer decreases inside the micelles and a gradient is established promoting diffusion inside the micelles. Therefore, the size of the polymer particles grows gradually until the monomer is depleted. The final product is latex with particle sizes in the range of 50–300 nm (Fig. 3.58). Size control

Since the initiator is present in the medium, the size and morphology of the monomer droplets or initial micelles do not reflect the size and morphology of the final polymer product, as seen in suspension polymerization. Rather, the concentration of the dissolved monomer in the medium plays a crucial role in size. Additionally, the concentration of the emulsifier and initiator, as well as the temperature of the system, play a role in determining particle size. The sensitivity to the system’s characteristics is a large advantage for industrial competition. It is relatively easy to identify what components are responsible for a polymer product, however, it is futile to attempt to identify the reaction conditions that are responsible for a particular product.

3.5.2 Soapless emulsion polymerization The charge on the emulsifier coated micelles prevents coagulation by repelling one another electrostatically as well as providing steric stabilization of the particles. In “soapless” emulsion polymerization, the reaction takes place similar to as described above, however, with an absence of emulsifier. The result is drastically less monomer ( 1, one of the monomers is more reactive than the other monomer towards both propagating species. Therefore, a random copolymer will be obtained with a higher proportion of the more reactive monomer. When the values of r1 and r2 are very large such as r1 ¼ 10 and r2 ¼ 0.2, ideal

I. Polymer science

92

4. Copolymerization

1.0 Mole fraction M1 in copolymer, F1

FIG. 4.1 Dependence of the instantaneous copolymer composition F1 on the initial comonomer feed composition f1 for the indicated values of r1 where r1r2 ¼1. After Walling (1957). Permission of Wiley, New York from the plot in Mayo and Wallin (1950) by permission of American Chemical Society, D.C.

10

0.8

5 2

0.6

1 0.5

0.4

0.2 0.1

0.2

0 1.0

0.4 0.2 0.8 0.6 Mole fraction M1 in comonomer feed, f1

0

copolymers are formed. As an example, with a feed composition of M2 of 80% (f2 ¼ 0.8), only 18.5 mol% of M2 is incorporated in the copolymer. An appreciable amount of both monomers in the copolymer can be achieved when r1 and r2 do not differ significantly (r1 and r2 between 0.4 and 2). When r1 ¼ r2 ¼ 0, an alternating copolymer is obtained since the propagating species will add only to the other monomer type. The reactivity ratios are independent of the initiator and the solvent in a free-radical copolymerization, but there is very small temperature dependence. The figure in the following section shows the mole fraction of the monomer M1 in the copolymer as a function of the mole fraction of the monomer M1 in the feed for ideal, alternating, and partially alternating copolymerization. Table 4.2 also includes a list of reactivity ratios that apply in some important free radical polymerizations (Fig. 4.2). TABLE 4.2 Examples of reactivity ratios for free-radical copolymerization. Monomer 1 (M1)

Monomer 2 (M2)

r1

r2

r1r2

Ethylene

Vinyl acetate

0.13

1.23

0.16

Ethylene

Propylene

3.20

0.62

1.98

Styrene

Acrylonitrile

0.29

0.02

0.006

Styrene

Butadiene

0.82

1.38

1.13

Styrene

Methyl methacrylate

0.585

0.478

0.28

Methyl methacrylate

Methacrylamide

1.50

0.50

0.75

Methyl methacrylate

Butadiene

0.30

0.70

0.21

Vinyl chloride

Vinyl acetate

1.40

0.65

0.91

Vinyl chloride

Vinylidene chloride

0.205

3.068

0.63

I. Polymer science

93

4.8 Kinetics of copolymerization

FIG. 4.2 Plot of mole fraction of

1.0

monomer 1 in copolymer, F1, as a function of the mole fraction of monomer 1 in the feed, f1. Ideal, r1 ¼r2 ¼1 (—), alternating r1 ¼r2 ¼0 (–), and partially alternating copolymers (—) (copolymerization of styrene and methyl methacrylate, where r1 ¼0.585 and r2 ¼0.478).

0.8

0.6

F1 0.4

0.2

0.0 0.0

0.2

0.4

f1

0.6

0.8

1.0

There were several attempts to determine monomer reactivity ratios to predict copolymer structures. Alfrey and Price proposed an empirical scheme known as the Q-e scheme which allows the determination of reactivity ratios. Although it is not the most accurate scheme, it is the most popular due to its convenience to use, its simplicity, and clarity. The Q-e scheme assumed that each radical or monomer can be categorized based on its “general reactivity” and its polarity. Alfrey and Price proposed four propagation rate constants, k11, k12, k22, and k21, which can be expressed as k11 ¼ P1 Q1 ee1 2

k12 ¼ P1 Q2 ee1 e2 k22 ¼ P2 Q2 ee2 2

k21 ¼ P2 Q1 ee2 e1 where Pi and Qj represent the general reactivity or resonance stabilization of radical i and monomer j, respectively, and ei and ej represent the residual charges or polar properties of radical i and monomer j. The reactivity ratios r1 and r2 can, therefore, be expressed as follows: r1 ¼

k11 Q1 ½e1 ðe1 e2 Þ ¼ e k12 Q2

r2 ¼

k22 Q2 ½e2 ðe2 e1 Þ ¼ e k21 Q1

r1 r2 ¼ e½ðe1 e2 Þ  2

I. Polymer science

94

4. Copolymerization

TABLE 4.3

Q-e values for free-radical copolymerization

Monomer

Q

e

Acrylonitrile

0.48

1.23

Acrylamide

0.23

0.54

Ethylene

0.016

0.05

Butadiene

1.70

0.50

Isobutylene

0.023

1.20

Isoprene

1.99

0.55

Maleic anhydride

0.86

3.69

Methyl methacrylate

0.78

0.40

Methacrylic acid

0.98

0.62

N-Vinyl pyrrolidone

0.088

1.62

Styrene

1.00

0.80

Vinyl acetate

0.026

0.88

Vinyl chloride

0.056

0.16

Vinylidene chloride

0.31

0.34

The effective use of the Q-e scheme is first to have a selection of a representative group of similar monomers for which Q and e can be independently calculated. Styrene was chosen as a reference, with Q ¼ 1.0 and e ¼0.8, to which all other monomers were associated to. Table 4.3 shows a list of Q and e values for a list of common monomers. Monomers with more negative e values have more electron-rich double bonds and those with higher Q values are more resonance stabilized. For a large difference in polarity (i.e., e1–e2 large), r1r2 is small and for monomers with identical polarity, r1 ¼ Q1/Q2 and r2 ¼ Q2/Q1.

References [1] W. Ring, I. Mita, A.D. Jenkins, N.M. Bikales, Pure Appl. Chem. 57 (1985) 1427–1440. [2] G.E. Ham, H.F. Mark, N.C. Gaylord, N.M. Bikales (Eds.), Encyclopedia of Polymer Science and Technology, vol. 4, Wiley-Interscience, New York, 1966, p. 165. [3] A.E. Tonelli, M. Srinivasarao, Polymers From the Inside Out, Wiley, 2001, pp. 51–55. [4] A. Rudin, P. Choi, The Elements of Polymer Science and Engineering, (2013) 391. [5] G. Odian, Principles of Polymerization, third ed., (1991) 461. [6] T. Alfrey, C.C. Price, J. Polym. Sci. 2 (1) (1947) 101.

I. Polymer science

C H A P T E R

5

Modification of polymers Yi-Yang Peng, Shruti Srinivas, Ravin Narain Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

The properties of the polymer, such as strength, smart-responsiveness, therapeutic effect, conductivity, and so on are not only determined by the choice of monomers but the result of the modification. Besides, for hydrophobic polymers that are aimed to be used in an aqueous environment, the post-modification is required to make the polymer more hydrophilic to enhance the performance. Furthermore, the architecture of the polymer can also be designed through modification. In drug delivery applications, many therapeutic agents or targeting moieties can be conjugated to the polymer via modification. In this chapter, the physical and chemical modification of polymers will be introduced. These techniques are important as it allows further design of polymer to fulfill the requirement of the target application.

5.1 Physical methods Surface modification of polymers by physical methods is more advantageous in terms of precise surface modification and process control. The physical modification strategies are both simple and scalable and they eliminate surface damage, roughening, and the need for harsh chemicals to achieve the modification. In addition to this, the physical surface modification strategy helps in imparting oxygen-containing functional groups onto the polymer surface to improve the properties of polymers such as wettability, biocompatibility, printability, and adhesion [1–3].

5.1.1 Self-assembled monolayers Self-assembly is a process in which all the disordered system of components forms an organized structure or pattern without the need for external direction. Self-assembled monolayers (SAMs) are a single layer of molecules that are capable of spontaneous selfassembly on a solid surface upon the immersion of a solid substrate into a solution containing amphiphilic molecules. The surfaces can be modified by introducing SAMs of different

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00005-4

95

# 2020 Elsevier Inc. All rights reserved.

96

5. Modification of polymers

R

R

R

Functional group

R

Tail

Head group Substrate

FIG. 5.1 The representation of the SAM structure.

functionalities depending on the chemical structure of the molecules. SAMs have been usually formed on gold or silver surfaces using a siloxy linkage due to the well-known interaction between gold and n-alkane thiols [2, 4, 5]. The SAM structure is represented in Fig. 5.1. Kwok et al. had reported the development of crystalline methylene chains on polymeric surfaces via urethane linkages using isocyanate chemistry. In this study, a polymeric biomaterial poly(2-hydroxyethyl methacrylate) (pHEMA) which is commonly employed for contact lens applications was chosen to construct a SAM structure on its surface. The presence of a hydroxyl group on the side chain of the polymer makes it feasible for the polymer to undergo modifications for various biomedical applications. The results demonstrated that the reaction between the hydroxyl functional groups and dodecyl isocyanate that occurred in the presence dibutylin dilaurate resulted in the formation of an all-trans crystalline structure on the (pHEMA) substrate [5]. SAMs provide high grafting density and precise control over the surface properties based on their chemical structure and therefore, they have been widely used for implant coatings. Chan et al. had reported the design of a series of non-cytotoxic amphiphilic macromolecules (AMs) comprising of a sugar-based hydrophobic domain and a hydrophilic tail comprising of poly(ethylene glycol) to achieve their chemical adsorption to the metal cardiovascular stents. Their goal was to prevent the proliferation of smooth muscle cells (SMCs) on the stents thereby resulting in blood vessel reocclusion. The results demonstrated that the self-assembled AMs could gradually release from the metal-oxide surfaces to suppress the proliferation of SMCs [6].

5.1.2 Radiation-induced surface modification Radiation is a form of energy that is emitted when an electron in an atom drops from a higher to a lower energy level. It travels through space or a medium in the form of waves or particles. Depending on the energy of the radiated particles, radiation is usually classified into two types namely: (i) ionizing radiation and (ii) non-ionizing radiation. The unstable atoms possessing excess energy or mass are responsible for the production of ionizing radiation. This type of radiation carries more than 10 eV that can ionize atoms and molecules and break the chemical bonds. Radioactive materials containing helium nuclei, electrons or positrons, and photons that emit α, β, or γ rays are the common sources of ionizing radiation.

I. Polymer science

5.1 Physical methods

97

Non-ionizing radiation is a type of electromagnetic radiation that cannot ionize atoms or molecules as it possesses a lower amount of energy per quantum.

5.1.3 UV-irradiation UV-radiation curing is a well-accepted technology used to achieve the light-induced polymerization of multifunctional monomers in the illuminated areas. Therefore, UV-radiation is well-known to have beneficial effects in initiating polymerization [7]. The principle of UV treatment involves the activation of chemical reactions that occur in the presence of an initiator or a sensitizer that absorbs UV irradiation and is excited to a stable triplet state from a singlet state. When polymers are exposed to UV light, the surface undergoes photooxidation in the atmosphere, thereby generating reactive grafting sites by removing hydrogen present on the polymer surface. This occurs due to the excitation of the initiator present in the triplet state, thereby initiating graft polymerization between the polymer and the surrounding medium [2, 8]. The surface modification of polymers with UV radiation is both effective and economical with few processing steps involved. In a study reported by Onyiriuka [8a], the surface modification of polystyrene (PS) was obtained by exposing it to γ-rays, UV light of 254 nm wavelength, O2 plasma, X-rays, and corona discharge. The results demonstrated that exposing the polymer to UV irradiation and γ-irradiation lead to the incorporation of oxygen into the bulk layers of PS when compared to plasma or corona discharge which resulted in the deposition of oxygen in the outermost region of the PS surface [3]. Yamagishi et al. [8b] had reported the modification of hydrophobic poly(arylsulfone) ultrafiltration membranes using the UV irradiation strategy to produce highly hydrophilic surfaces. These membranes are intrinsically photoactive thereby generating free radicals upon exposure to UV light. The vinyl monomers used in this study to be introduced onto the surfaces of the membrane are 2-hydroxyethyl methacrylate (HEMA), methacrylic acid and glycidyl methacrylate (GMA). The results demonstrated photochemically modified membrane surfaces with vinyl monomers grafted to considerable depths into the membrane [4]. An increase in hydrophilicity of the modified membranes further led to an increase in the antifouling properties of the modified membranes. Pieracci et al. [8c] had reported the use of a UV-assisted graft polymerization approach to increase the antifouling properties of the membrane surfaces by increasing their hydrophilicity. The surface modification was carried out by two different techniques (i) dip modification and (ii) immersion modification. The results demonstrated that both techniques resulted in highly hydrophilic membrane surfaces with excellent fouling resistance [7]. 5.1.3.1 γ-Irradiation Surface treatment of polymers via free radical formation mechanism as a result of gammaray treatments using moderate energy of (100–300 kV) is similar to the UV-irradiation mechanism. The free radicals generated on the polymer surface are induced by photons. When the treatment is carried out in an oxygen-containing atmosphere the free radicals present on the polymer surface, react with oxygen thereby resulting in the formation of oxygenated species on the surface of the polymer. These oxygenated species enhance the mechanical properties and the adhesion tendency of the polymer. The reactions of generated free radicals are responsible for the radiation-induced modifications to the polymer surface. Soukupova´ et al. reported an increase in the surface area of the

I. Polymer science

98

5. Modification of polymers

macroreticular styrenic polymers by exposing them to gamma-irradiation [9]. Nechifor et al. studied the effect of gamma radiation on porous polymeric membranes that were obtained via the alloying of poly(hydroxy urethane) (PHU) and poly(vinyl alcohol) (PVA) in different concentrations. The results demonstrated that an increase in the dosage of gamma radiation enhanced the porosity and hydrophilic properties of the membranes [10]. Madrid et al. reported the introduction of GMA via gamma irradiation to obtain the surface modification of microcrystalline cellulose (MCC). The grafting of GMA onto the polymer surface was to impart additional functional groups to help tailor the properties of the polymer surface [11]. 5.1.3.2 Laser-induced surface modifications Surface modification of polymers using a laser is an emerging technology and offers several benefits when compared to other surface modification methods. This method enables precise surface modification that can be easily controlled and is environmentally safe. A large number of lasers operating at different wavelengths and operating modes (continuous wave or pulsed) are available as surface modification using a laser depending on the purpose of modification. The laser light is coherent and highly focused when compared to other light sources. When the atoms present in the ground state are excited to a higher energy state under a high voltage, laser light is produced. The two mechanisms involved in achieving the surface modification using laser-irradiation are (i) thermal process, and (ii) photochemical process [2, 8]. Breuer et al. reported the surface modification of polypropylene (PP) using photochemical laser action to enhance its adhesion properties. In another study, Breuer et al. reported the photolytical modification and enhancement in the adhesion properties of the surface of PP by exposure to UV-laser radiation in an oxidizing environment. The UV excimer laser treatment induces photochemical reactions on the surface further resulting in the generation of functional groups such as dOH and dC]O. These oxygen-containing functional groups are responsible for the enhanced adhesive bonding strength of the PP substrates. The adhesive strength of the substrates can also be enhanced by using the appropriate wavelength [12, 13]. Buchman et al. had reported the surface treatment of polymer composites and metal alloys by the action of an ArF excimer laser. The results demonstrated an increase in the bondable surface area and improved mechanical interlocking [14].

5.2 Chemical modification of polymer 5.2.1 Common chemical reactions Chemical modification of polymer relies on the nature of organic chemistry, and it allows polymers to have the functional groups that are not tolerated in the process of polymerization. Scheme 1 illustrates several functional groups that are aimed to possess or improve for specific properties. The disulfide is a redox-responsive moiety that will be broken when entering into the cytoplasm and will lead to intracellular targeting. Polyethylene glycol is a FDA approved biocompatible unit. Boronic ester forms a dynamic covalent bond with diol group which presents on many carbohydrate units. Furthermore,

I. Polymer science

5.2 Chemical modification of polymer

SCHEME 1

99

Examples of functional groups that are modified to the polymer to create or improve the specific

properties.

biomolecules (DNA, RNA, and protein) and the drug can be conjugated to the polymer via modification which allows the polymer to be a good drug transporter. Schiff’s base reaction, amine-epoxy reaction, thiol-ene, and thiol-yne reaction, carbodiimide cross-linked reaction, and Copper-Catalyzed Azide-Alkyne cycloaddition (CuAAC) are commonly used to modify polymer (Scheme 2).

5.2.2 PEGylation PEGylation, a process that adds polyethylene glycol polymer chain to molecules or macromolecules, is commonly used to increase the solubility of hydrophobic molecules in aqueous solution and extend the blood circulation time of a therapeutic agent by reducing renal clearance. Moreover, it is an FDA approved non-toxic agent. Casettari and his colleagues, prepared PEGylated chitosan for lowering its toxicity via carbodiimide crosslink reaction by conjugating the primary amine groups from chitosan with a carboxylic group from mPEG-COOH (Fig. 5.2) [15]. PEGylation is also a common strategy to ameliorate the therapeutic effect of biopolymers such as peptide and protein. Today, many FDA-approved drugs, which are prepared by chemical modification of peptide and protein, are available in the market [16]. Now, many polyethylene glycols with various kind functional groups at the terminal are available in the market to facile the process of PEGylation.

5.2.3 Conjugation Besides polymer, drugs can also be conjugated to the polymer via chemical modification. Doxorubicin (DOX) is a chemotherapy drug for cancer management; however, the side effects, that are triggered by the drug, and poor accumulation at the target site are the major concerns associated with administrating DOX alone to a cancer patient. To address these

I. Polymer science

100

5. Modification of polymers

SCHEME 2 Examples of reactions that were used in polymer modification.

I. Polymer science

101

5.2 Chemical modification of polymer

FIG. 5.2 PEGylaiton of chitosan via carbodiimide crosslink reaction. A, B, C, D, and E represent the value of the degree of polymerization. Reproduced with permission from L. Casettari, D. Vllasaliu, S. M. Howdle, S. Stolnik, L. Illum, Effect of PEGylation on the toxicity and permeability enhancement of chitosan. Biomacromolecules (2010) 2854–2865, American Chemistry Society.

O O

O N3

6

O O

O O

O O

O

O

O

H

6-Azidohexyl 4-formylbenzoate CuSO4 . 5H2O/Sodium Ascorbate (NaAsc)

O

O

O

O

H

O

N N

DMF, r.t., 24h

Alkyne-polyactide

O O

N

6

O

O

Aldehyde-polylactide

O O

O

O O

O O

N

O O

O

O

O

N

N

N N 6

6

N

O

O

O

O

HO

O

O

H

)

CL

.H OX (D e d A) ori chl e (TE o r n d hy lani ., 24h icin iethy , r.t DOX-polylactide b u O r t S xor DM Do O

O

O

N O O

OH

O

OH

O

O

HO

HO

O

FIG. 5.3 Preparation of acid liable DOX-polylactide by utilizing CuAAC and Schiff’s base reaction. Reproduced with permission from Y. Yu, C.-K. Chen, W.-C. Law, E. Weinheimer, S. Sengupta, P.N. Prasad, C. Cheng, Polylactide-graftdoxorubicin nanoparticles with precisely controlled drug loading for pH-triggered drug delivery. Biomacromolecules 15 (2014) 524–532, American Chemistry Society.

concerns, Yu and his colleagues conjugated DOX to polylactide by CuAAC and Schiff’s base reaction (Fig. 5.3) [17]. Aldehyde groups were modified to Azide-polylactide via CuAAC and subsequently react to primary amine from DOX to form an imine bond. The resulted DOX-Polylactide was prepared as nanoparticles by nanoprecipitation which protected the drug from the physiological environment and increased the blood circulation time by evading

I. Polymer science

102

5. Modification of polymers

the renal clearance. The release of DOX was triggered when exposed to a mildly acidic environment as the result of imine bond cleavage. In another case, Wang and his colleagues conjugated paclitaxel (taxol), a chemotherapy drug used to treat cancer, to heparin, a biocompatible natural polysaccharide, to make an amphiphilic polymer that formed a self-assemble drug nanoparticle [18]. Heparin was first modified to succinylated-heparin by reacting with succinic anhydride in the presence of trimethylamine and ethylaminopyridine. Paclitaxel with different amino acid-based spacer was conjugated to succinylated-Heparin by carbodiimide crosslinker reaction.

5.2.4 Method to make various polymeric architecture via chemical modification The architecture of the polymer strongly influences its properties. Complicate architecture of polymers such as a star-shaped polymer, comb-shaped polymer, block copolymer, and branched polymer can also be prepared via modification (Fig. 5.4). The star-shaped polymer can be prepared by synthesized linear polymer with a reactive terminal and react the terminal to a core (Fig. 5.4A). The number of arm for the star-shaped polymer is determined by the number of reacting groups in the core. The comb-shaped polymer can be prepared by reacting the terminal of linear polymers to the pendent groups among a polymer (Fig. 5.4B). Singh and his colleague synthesized poly(pentafluorophenyl methacrylate) (PFMA) and reacted PFMA with allylamine to have alkene groups. Subsequently, the alkene groups were used to conjugate with peptide via thiol-ene reaction (Fig. 5.5) [19]. Block copolymer can be easily prepared via polymer conjugation (Fig. 5.4C). Meng and others prepared Poly(styrene)-b-Poly(ethylene glycol) (PS-b-PEG) by coupling amine functional PEG with carboxylic acid functional PS by carbodiimide crosslink reaction [20]. ABA triblock copolymer can be prepared by a similar method by modifying both ends of

FIG. 5.4 Protocol in preparing various architecture of polymers via chemical modification: star-shaped polymer (A), comb-shaped polymer (B), block copolymer (C), triblock copolymer (D), and hyperbranched polymer (E).

I. Polymer science

References

103

FIG. 5.5 Preparation of comb-shaped polymer from modification of PFMA with peptide. Reproduced with permission from N.K. Singha, M. I. Gibson, B. P. Koiry, M. Danial, H.-A. Klok, Side-chain peptide-synthetic polymer conjugates via tandem “Ester-amide/thiol-Ene” post-polymerization modification of poly(pentafluorophenyl methacrylate) obtained using ATRP. Biomacromolecules, 12 (2011) 2908–2913, American Chemistry Society.

the terminal of the middle polymer with reactive groups. The hyperbranched polymer can be prepared via post-cross-linking linear polymers (Fig. 5.4E).

References [1] M. Ozdemir, C.U. Yurteri, H. Sadikoglu, Physical polymer surface modification methods and applications in food packaging polymers, Crit. Rev. Food Sci. Nutr. 8398 (2010). [2] P. Fabbri, M. Messori, 5—Surface modification of polymers: chemical, physical, and biological routes, in: Modification of Polymer Properties, Elsevier Inc., 2017 [3] S.K. Nemani, et al., Surface Modification of Polymers: Methods and Applications, vol. 1801247, (2018) pp. 1–26. [4] Z. Aguilar, Nanobiosensors, in: Nanomaterials for Medical Applications, 2012, pp. 127–169. [5] C.S. Kwok, P.D. Mourad, L.A. Crum, B.D. Ratner, Surface modification of polymers with self-assembled molecular structures: multitechnique surface characterization, Biomacromolecules 1 (2000) 139–148. [6] J.W. Chan, Y. Zhang, K.E. Uhrich, Amphiphilic macromolecule self-assembled monolayers suppress smooth muscle cell proliferation, Bioconjug. Chem. 26 (2015) 1359–1369. [7] C. Decker, The use of UV irradiation in polymerization, Polym. Int. 45 (1998) 133–141. [8] M. Ozdemir, A new and emerging technology: laser-induced surface modification of polymers, Trends Food Sci. Technol. 9 (1998) 159–167. [8a] E.C. Onyiriuka, The effects of high-energy radiation on the surface of polystyrene: a mechanistic study, J. Appl. Polym. Sci. 47 (12) (1993) 2187–2194. [8b] H. Yamagishi, J. Crivello, G. Belfort, Development of a novel photochemical technique for modifying poly(arylsulfone) ultrafiltration membranes, J. Memb. Sci. 105 (1995) 237–247. [8c] J. Pieracci, D.W. Wood, J.V. Crivello, G. Belfort, UV-assisted graft polymerization of N-vinyl-2-pyrrolidinone onto poly(ether sulfone) ultrafiltration membranes: comparison of dip versus immersion modification techniques, Chem. Mater. 12 (8) (2000) 2123–2133. [9] K. Soukupova´, A. Sassi, K. Jer, Reactive & functional polymers modifications in the morphology of poly (styreneco-divinylbenzenes) induced by gamma-ray irradiation, React. Funct. Polym. 70 (2010) 361–365. [10] C.-D. Nechifor, D.-O. Dorohoi, C. Ciobanu, The influence of gamma radiations on physico-chemical properties of some polymer membranes, Rom. J. Physiol. 54 (2009) 349–359.

I. Polymer science

104

5. Modification of polymers

[11] J.F. Madrid, L.V. Abad, Modification of microcrystalline cellulose by gamma radiation-induced grafting, Radiat. Phys. Chem. 115 (2015) 143–147. [12] J. Breuer, S. Metev, G. Sepold, Photolytical pretreatment of polymers with UV-laser radiation, Mater. Manuf. Process. (1995) 229–239. [13] G. Kr€ uger, J. Breuer, S. Metev, G. Sepold, O.D. Hennemann, H. Kollek, Laser-induced photochemical adherence enhancement, Appl. Surf. Sci. 46 (1990) 336–341. [14] A. Buchman, H. Dodiuk, M. Rotel, J. Zahavi, Laser-induced adhesion enhancement of polymer composites and metal alloys Laser-induced adhesion enliancement of polymer composites and metal alloys, J. Adhes. Sci. Technol. (1994) 1211–1224. [15] L. Casettari, D. Vllasaliu, S.M. Howdle, S. Stolnik, L. Illum, Effect of PEGylation on the toxicity and permeability enhancement of chitosan, Biomacromolecules (2010) 2854–2865. [16] Biochempeg World PEG Supplier, FDA Approved PEGylated Drugs 2019, http://www.biochempeg.com/ article/58.html, 2019. [17] Y.Y.C.-K. Chen, W.-C. Law, E. Weinheimer, S. Sengupta, P.N. Prasad, C. Cheng, Polylactide-graft-doxorubicin nanoparticles with precisely controlled drug loading for pH-triggered drug delivery, Biomacromolecules 15 (2014) 524–532. [18] Y. Wang, D. Xin, K. Liu, M. Zhu, J. Xiang, Heparin-paclitaxel conjugates as drug delivery system: synthesis, selfassembly property, drug release, and antitumor activity, Bioconjug. Chem. 20 (2009) 2214–2221. [19] N.K. Singha, M.I. Gibson, B.P. Koiry, M. Danial, H.-A. Klok, Side-chain peptide-synthetic polymer conjugates via tandem “Ester-amide/thiol-Ene” post-polymerization modification of poly(pentafluorophenyl methacrylate) obtained using ATRP, Biomacromolecules 12 (2011) 2908–2913. [20] F. Meng, G.H.M. Engbers, A. Gessner, R.H. Muller, J. Feijen, Pegylated polystyrene particles as a model system for artificial cells, J. Biomed. Mater. Res. A 70A (2004) 96–106.

Further reading S. Shahidi, J. Wiener, M. Ghoranneviss, Plasma-enhanced vapor deposition process for the modification of textile materials, in: Plasma Science and Technology—Progress in Physical States and Chemical Reactions, 2016. A. Sarangan, Physical and chemical vapor deposition, in: Nanofabrication: Principles to Laboratory Practice, 2016. P. O’Brien, Chemical vapor deposition, in: Encyclopedia of Materials: Science and Technology, 2001, pp. 1173–1176 no. Cvd. H.-Y. Chen, Y. Elkasabi, J. Lahann, Surface modification of confined microgeometries via vapor-deposited polymer coatings, J. Am. Chem. Soc. 128 (2006) 374–380.

C H A P T E R

6

Polymer characterization Shin-ichi Yusa Department of Applied Chemistry, University of Hyogo, Himeji, Hyogo, Japan

6.1 Measurements of molecular weight 6.1.1 Gel-permeation chromatography This method was called gel-permeation chromatography (GPC) as it employs porous gels to separate polymers of different sizes. GPC is a type of liquid chromatography and is also known as size exclusion chromatography (SEC) or gel filtration chromatography. Besides, there is a recent trend to use only the term SEC, because the separation mechanism is based on size exclusion. However, as this has not yet been clarified, in the polymer field it is often referred to as GPC [1–3]. Based on the principle of GPC, polymer “C,” which has the largest molecular size, goes only through a short flow path, because its size hinders the access to the deep area of the porous filler. Thus, “C” is eluted early by the chromatographic system (Fig. 6.1). In contrast, polymers with smaller molecular size go through a longer flow path, since they can reach deeper areas of the porous filler. Therefore, small polymers move and exit the column more slowly than “C.” Moreover, the retention time of “A” is higher than that of “B” since “A” with the smallest size penetrates the deeper area of the pore. If there are no interactions between the packing materials and the sample molecules, “C” with the largest size is eluted first from the column, followed by the smaller “B” and “A” polymers. According to this principle, GPC allows the sequential elution of the polymer samples starting from the components with the largest molecular size, indicating that this chromatographic method is based on the polymer size. However, GPC does not separate polymers based on their difference in molecular weight. Even when the molecular weight is the same, the molecular size varies depending on the following: 1. The molecular structure: The flexibility of a polymer chain depends on its molecular structure. Thus, the molecular size can vary even if the molecular weight is the same.

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00006-6

105

# 2020 Elsevier Inc. All rights reserved.

106

6. Polymer characterization

FIG. 6.1 Conceptual representation of the separation of different-sized polymers by GPC.

2. The affinity between the polymer and the eluent: A polymer with a high affinity for the eluent has expanded chain structure. Instead, a polymer with low affinity has a shrunk chain structure. Therefore, the GPC results may be affected by the eluent. 3. The electrostatic interactions: In polymers with repulsive functional groups, such as the same charge groups, the molecular size increases because of the polymer chain expansion. In contrast, attractive functional groups lead to smaller molecular sizes. 4. The branch: Between linear and branched polymers with the same molecular weight, a more branched polymer is smaller in size than a linear polymer. In GPC, the number-average molecular weight (Mn), weight-average molecular weight (Mw), and z-average molecular weight (Mz) can be simultaneously determined. Furthermore, Mw/Mn and/or Mz/Mw ratios are used as indicators for evaluating molecular weight distribution and are also known as polydispersity index (PDI). If these ratios are high, the polymer exhibits large molecular weight distribution. Currently, GPC is one of the most widely used methods for the determination of the molecular weight, because it offers feasible and fast measurements, unlike osmotic and static light scattering methods. Mn, Mw, and Mz can be defined by the following equations: Σ ðM i N i Þ ΣNi
Σ Mi 2 Ni Mw ¼ Σ ðMi Ni Þ
Σ Mi 3 Ni
Mz ¼ Σ Mi 2 Ni Mn ¼

(6.1) (6.2)

(6.3)

where Ni is the number of the polymer molecules and Mi is the molecular weight. According to Eq. (6.1), Mn is a simple arithmetic mean, which is sensitive to the presence of low molecular weight components. Mw is weight-average, and it is sensitive to the presence of high molecular weight components. Mz is also a weighted average using the square of the molecular weight, and it is more susceptible to the presence of high molecular weight components than Mw. Generally, the relationship between these factors is Mn  Mw  Mz (Fig. 6.2). In the case of a monodisperse polymer with no molecular weight distribution, their relationship is M n ¼ M w ¼ M z. GPC, unlike mass spectroscopic and static light scattering measurements, cannot be used to determine the absolute molecular weight of a polymer. To determine the relative molecular

I. Polymer science

6.1 Measurements of molecular weight

107

FIG. 6.2 The GPC curve and the relationship between Mn, Mw, and Mz. Mp indicates the peak of the GPC curve.

weight by GPC, the relationship between the elution time and the molecular weight should be estimated before the measurements. The plot of the relationship between the elution time and the molecular weight is called the “universal curve” or “calibration curve” (Fig. 6.3). Standard polymers of known molecular weight, narrow molecular weight distribution, and the same chemical structure as the sample polymer should also be used because the universal curve differs for each type of polymer. To that end, known polymers, such as polystyrene (PS), poly(methyl methacrylate), poly(ethylene oxide) (PEO), and sodium poly(styrene sulfonate) (PSSNa) can be used (Fig. 6.4). These conventional standard polymers with different molecular weights are commercially available, and their molecular weight and molecular weight distribution are predetermined. The molecular weight obtained by GPC measurements for a sample polymer is the relative molecular weight, assuming that it has the same chemical

FIG. 6.3 (A) GPC elution curve for standard samples with four different molecular weights, and (B) universal curve for the standard sample.

I. Polymer science

108

6. Polymer characterization

FIG. 6.4 Structures of standard polymers that are used for GPC measurements: polystyrene (PS), poly(methyl methacrylate) (PMMA), poly(ethylene oxide) (PEO), and sodium poly(styrene sulfonate) (PSSNa).

structure as the standard polymer. Therefore, if the molecular structure of the standard polymer is significantly different from that of the sample polymer, the deviation from the real molecular weight may increase. The standard sample is selected based on the eluent and the detector. For instance, when the GPC apparatus is connected to an ultraviolet (UV) detector, PEO cannot be used as the standard sample, because it cannot be detected. Moreover, when an organic solvent (e.g., tetrahydrofuran) is used as the eluent, PS is often selected as the standard sample. Besides, GPC measurements for polyelectrolytes are more efficiently obtained by adding salts or an organic solvent to the eluent to avoid unexpected interactions between the polymer and the column. The GPC system consists of a pump, a sample injector, a GPC column, and a detector (Fig. 6.5). The GPC configuration is the same as in conventional liquid chromatography, using a GPC column instead. Generally, a refractive index (RI) detector is used as the GPC detector. However, although the RI detector can detect most polymers, it displays low sensitivity and low stability due to temperature dependence. The difference in RI between the eluent mixture and the sample solution is proportional to the polymer concentration, which can thus be determined based on the RI value. Moreover, a degasser should be used for RI detection, because it is sensitive to the air in the eluent. When the RI of the polymer solution is higher than that of the eluent, the RI detected peak can be observed as a positive signal. Instead, when the RI is lower than that of the eluent, the peak is detected as a negative signal. Besides, if the RI of the polymer solution is close to that of the eluent, no peak can be detected. The RI detection sensitivity increases when the RI of the used eluent differs significantly from that of

FIG. 6.5 Schematic illustration of the GPC equipment connected to an RI detector.

I. Polymer science

6.1 Measurements of molecular weight

109

the polymer solution. An additional parameter that affects the RI is its increase against the concentration (dn/dc). Thus, dn/dc represents a differential value of the RI (n) that depends on the concentration (c). Therefore, an eluent of higher dn/dc would allow for more sensitive detection, because the RI detection sensitivity is proportional to dn/dc. The characteristics of the most commonly used detectors are presented as follows: 1. RI detector: It detects the difference in the RI between the eluent and the polymer solution. Although the RI detector is the most commonly used, it exhibits low sensitivity and low stability compared with a UV–vis absorption detector. 2. UV–vis absorption detector: It detects the absorption of the polymer sample. It is highly sensitive and stable, but it cannot detect polymers that do not absorb in the UV–vis range. 3. Multi-angle laser light scattering (MALLS) detector: The light scattering intensity of the polymer solution is detected at varying scattering angles. An absolute Mw and a radius of gyration (Rg) can be obtained by MALLS. However, this detector is sensitive to dust in the eluent, and it is generally expensive. Furthermore, to determine the absolute molecular weight by MALLS, the dn/dc of the polymer solution should be separately obtained. Alternative GPC detectors, which are still not very common, are the evaporative light scattering detector, infrared (IR), nuclear magnetic resonance (NMR), mass (MS) spectroscopy, and so on.

6.1.2 Osmometry The chemical potential of the solvent in the polymer solution is lower than that of the solvent. Therefore, when the polymer solution and solvent contact with each other across the semipermeable membrane, the solvent permeates to the solution through the membrane (Fig. 6.6). The liquid level on the polymer solution is higher than that on the solvent. When the system reaches the equilibrium state, the following equation is established.

FIG. 6.6 Simple osmometer.

I. Polymer science

110

6. Polymer characterization

Π¼

Δμ0 RT ¼ ln a0 V0 V0

(6.4)

Π ¼ ρgΔh

(6.5)

where Π is osmotic pressure, Δμ0 is the relative chemical potential of the solvent, V0 is the partial molar volume of the solvent, R is gas constant, T is absolute temperature, a0 is the activity of the solvent, Δh is the liquid level difference, and g is the gravitational acceleration. Rewriting Eq. (6.4) using the solute mass concentration, C (g cm1) gives: Π¼

RTC M

(6.6)

where M is the molecular weight. Eq. (6.6) is called as van’t Hoff equation, which is for a monodisperse solute. On the other hand, in the case of a polydisperse polymer sample, the number-average molecular weight (Mn) should be used instead of M. The following equation can be used in the low concentration region Π 1 ¼ + A2 C + ⋯ RTC Mn

(6.7)

where A2 is the second virial coefficient. 1/Mn can be obtained by extrapolating the concentration, C to zero for the plot of Π/RTC vs. C based on Eq. (6.7). From the slope of the plot of Π/RTC vs. C, A2 can be obtained. If there is a low molecular weight component including in the sample for osmotic pressure measurements, the component permeates the membrane. Therefore, it is difficult to determine the Mn values for low molecular weight oligomers. Besides, it takes a long time for the osmotic pressure to reach the equilibrium state. For these reasons, generally, osmotic pressure measurements are not so common.

6.1.3 Viscosity If the polymer structure is the same, the viscosity of the polymer solution is proportional to the molecular weight. Viscosity coefficients of solvent (η0) and solution (η) can be estimated using a capillary viscometer. Relative viscosity (ηr) and specific viscosity (ηsp) are defined as follows. η ηr ¼ (6.8) η0 ηsp ¼ ηr  1

(6.9)

The value obtained from dividing ηsp by the concentration, C, which is called reduced viscosity (ηsp/C). The limiting value obtained by extrapolating C ! 0, which is intrinsic viscosity ([η]). [η] can also be defined using ln ηr. ½η ¼ lim

C!0

ηsp C

¼ lim

C!0

lnηr C

(6.10)

(ln ηr)/C is called inherent viscosity. It is known the following relationship between viscosityaverage molecular weight (Mν) and [η] of the polymer solution experimentally.

I. Polymer science

6.1 Measurements of molecular weight

½η ¼ KMν a ð0:5  a  1:0Þ

111 (6.11)

where, K and a are constants determined by a kind of polymer, solvent, and temperature. Mν can be calculated from [η] using experimentally determining K and a. It is known that. Mν is close to weight-average molecular weight (Mw) from theory and experience. To obtain [η] experimentally, ηr is measured at various polymer concentrations to prepare a plot of ηsp/C vs. C. This plot is Huggins plot. C is extrapolated to 0 to obtain the intercept of the Y-axis which is [η]. ηsp ¼ ½η + ½η2 k0 C (6.12) C k0 is Huggins constant, which may be between 0.3  0.6. Usually, more than three polymer concentrations should be measured with ηsp ¼ 0.1  1.0 to prepare the Huggins plot. Also, the Fuoss-Mead plot of (ln ηr)/C vs. C is often used to determine [η]. Huggins and FuossMead plots give the same [η] value.

6.1.4 Static light scattering When light is irradiated to small particles, the light is scattered. Most of the scattered light caused Rayleigh scattering and has the same wavelength as the incident light. The intensity of the scattering light is a function of particle size and the number of particles. In the case of a solution, the scattering light intensity is higher than that of the solvent due to the presence of solute molecules. The excess scattering light intensity per unit scattering volume should be I with a distance (r) from scatterer at the scattering angle (θ) against the incident light intensity (I0). At this time, the Rayleigh ratio (Rθ) is defined by the following equation. Rθ ¼

Ir2 I0 ð1 + cos 2 θÞ

(6.13)

The following equation establishes between Rθ and weight-average molecular weight (Mw).   KC 1 1 2 2 ¼ 1 + s q + 2A2 C (6.14) Rθ Mw 3 where K is optical constant, C is polymer concentration, hs2i is the z-average mean-square radius of gyration, q is the magnitude of the scattering vector, and A2 is the second virial coefficient. K and q are given the following equations:   2π 2 n0 2 dn 2 K¼ (6.15) NA λ0 4 dC q¼

4π θ sin λ0 2

(6.16)

where n0 and n are the refractive indexes of solvent and solution, respectively, NA is Avogadro number, λ0 is the wavelength of the incident light, and dn/dC is refractive index

I. Polymer science

112

6. Polymer characterization

increment against the polymer concentration. The Rθ values are obtained at various θ and C. KC/Rθ and sin2(θ/2) + kC were plotted as Y- and X-axes, respectively, which is Zimm plot. k in X-axis can be selected arbitrary constant. hs2i can be obtained from the slope of the plot of KC/Rθ vs. sin2(θ/2) at C ! 0 for the Zimm plot. If the average shape of the linear flexible polymer is a sphere, hs2i1/2 corresponds to the radius. A2 can be obtained from the slope of the plot of KC/Rθ vs. C at θ ! 0 for the Zimm plot. A2 is the interaction coefficient between two polymers. It is difficult for polymers to dissolve in a poor solvent with A2  0. On the other hand, large A2 values can be observed in a good solvent, which can dissolve polymers easily. At A2 ¼ 0 it means that the interpolymer interaction disappears apparently. This situation is called theta point (Θ). Weight-average molecular weight (Mw) can be estimated from the intersection at C ! 0 and θ ! 0. Purification of the solution by filtration and/or centrifugation before measurements, because static light scattering (SLS) measurements are extremely susceptible to dust.

6.1.5 Principle of nuclear magnetic resonance The nuclear magnetic resonance (NMR) phenomenon can be observed because of the absorption and emission of nuclear spin energy under a high magnetic field. Because a nucleus has a positive charge and rotates, it can act as a small magnet that can generate a magnetic field. A magnet has a north (N) and south (S) pole, and the N pole is usually represented as an arrowhead. Normally, nuclear spin magnets are oriented in random directions. However, under a high external magnetic field, the proton (1H) nuclear spins are oriented in two directions, parallel and antiparallel to the external magnetic field. This splitting of the energy and the energy gap is known as Zeeman splitting and Zeeman energy, respectively. The energy level of the antiparallel spin is slightly higher than that of the parallel spin, whereas the number of spins at high energy levels is slightly smaller than that at low energy levels. When the energy of the irradiated radio wave pulse is equal to the Zeeman energy, the radio wave energy is absorbed and the spin at the low energy level is transferred to the high energy level. This phenomenon is called NMR. After the completion of the NMR phenomenon, the transferred magnetic spin at the high energy level returns to the low energy level. The difference between two energy levels, which are generated by Zeeman splitting due to an external magnetic field, is sensitive to the environment of the nucleus that belongs to an atom group. For example, the energy difference (Zeeman energy, ΔE) between the protons of benzene is larger than that between the protons of tetramethylsilane (TMS), where ΔE corresponds to the chemical shift. Proton (1H) and carbon (13C) nuclei are mostly measured, as they are fundamental elements of organic and polymer materials. The detection sensitivity of 1H is good because the natural abundance ratio of 1H is almost 100%. It should be also noted that NMR can be measured for nuclei with a spin quantum number (I) 6¼ 0. However, some nuclei types cannot be detected by NMR, although they have non-zero I values. Carbon nuclei exist in two stable isotopes, 12C and 13C. Although the NMR phenomena of 12 C cannot be detected because I ¼ 0, 13C has an I value of 1/2, which allows its identification. Furthermore, 13C NMR is less sensitive than 1H NMR, because the natural abundance of 13C is only 1%. Other nuclei that are frequently used in organic and polymer chemistry are 15N, 2H, 29 Si, and 31P. Each of them has a different resonance frequency; therefore, the electric circuit

I. Polymer science

6.1 Measurements of molecular weight

113

should be adjusted so that the appropriate resonance frequency for each nucleus is applied efficiently to the NMR probe. This operation is called “tuning.” The recent NMR equipment allows automatic tuning, as the nucleus can be selected on the computer software. The most important disadvantage of the NMR method is its low sensitivity. Assuming that the NMR sensitivity is 1, the sensitivity of infrared (IR) spectroscopy is 106, whereas that of mass (MS) spectroscopy is 108. The sample amount required for NMR measurement ranges from several mg to several tens mg. Because the NMR phenomenon has a long lifetime, it is difficult to detect a short, intermediate event. Furthermore, the structure of a molecule cannot be determined only by NMR. Instead, it should be analyzed in combination with other spectroscopic techniques. In this chapter, we deal mainly with solution NMR. Please refer to other text for solid-state NMR for polymers [4–6].

6.1.6 NMR equipment The NMR equipment consists of a superconducting magnet, a spectrometer, a control system, and a detector (probe). During NMR measurements, a sample solution is placed in the magnetic field and is irradiated with radio waves from a spectrometer that includes observation and irradiation systems. The bounced analog signal, called free induced decay, is amplified and digitized to obtain the corresponding NMR signals and spectrum. Moreover, the Zeeman energy increases with an increasing magnetic field intensity of the NMR equipment. Therefore, higher magnetic fields result in higher performance, good peak separation, and high detection sensitivity. In the field of NMR studies, the magnetic field strength is expressed using the resonance frequency (MHz) of protons. During NMR recordings of dissolved samples, the magnetic field around the sample solution should be uniform to obtain a good spectrum. This can be achieved by applying current to the coil that surrounds the detector. This operation is known as “shim adjustment.” Besides, to correct the fluctuation of the magnetic field during the measurement, the “NMR lock” process is applied, where the resonance frequency fluctuation of the deuterium nucleus is tracked and the uniformity of the magnetic field is automatically corrected. Therefore, in conventional solution NMR measurements, it is necessary to dissolve a sample in a deuterated solvent. An NMR sample glass tube with a diameter of 5 mm is usually used. If the edge of the tube is cracked or a sticker with the sample name is attached, the balance may be lost and uneven rotation may also be caused. Although a deuterated solvent should be typically used for conventional NMR measurements, more recent NMR equipment can measure solutions even in nondeuterated solvents. Deuterated chloroform (CDCl3) and deuterated water (D2O) are the most often used solvents for NMR measurements due to their lower cost. When the water in the air unexpectedly dissolves in CDCl3, a singlet signal is observed at around 1.5 ppm. When D2O is used, the chemical shift is determined by the peak of water at 4.8 ppm. However, it should be considered that the chemical shift of water also depends on the pH and the temperature of the sample. Furthermore, the sample concentration should be about 1% for 1H and 5% for 13C NMR. If there is any insoluble material in the NMR sample solution, it should be removed by filtration using glass wool or an alternative removal method. The solution height should generally be around 4 cm each time it is adjusted based on the NMR equipment used.

I. Polymer science

114

6. Polymer characterization

6.1.7 Proton (1H) NMR The analysis of a normal one-dimensional (1D) 1H NMR spectrum requires the understanding of the chemical shifts, integral intensity, and splitting terms. The chemical shifts correspond to the x-axis (ppm) of a 1D 1H NMR spectrum. TMS is generally used as the reference for the chemical shifts, with a singlet peak at 0 ppm. Alternatively, the signal of a nondeuterated solvent can be used as a reference for the chemical shifts. For example, when CDCl3 is used as the sample solvent, the chemical shift is adjusted using the peak of chloroform (CHCl3) at 7.26 ppm. The chemical shifts depend on the environment of the measured proton, thus allowing the identification of an atom group. Generally, 1H NMR chemical shifts can be found in the 0–12 ppm range. Fig. 6.7 shows the 1H chemical shifts of primary atom groups. Roughly, the signals 5 ppm are attributed to unsaturated hydrocarbons. The chemical shift of the proton tends to increase if its environment includes a highly electronegative atom. The process to determine which proton comes from each signal is called “assignment.” When the relative NMR signal position is explained, the terms of high and low magnetic fields are used. Currently, in actual measurements, the magnetic field strength is always fixed. High and low magnetic fields are old terms that were used for continuous-wave NMR. Specifically, the right side of an NMR spectrum is called a high magnetic field, and the left side represents the low magnetic field. The y-axis of the NMR spectra represents the intensity of the energy absorption. In the case of 1H NMR, the integral or area intensity of each signal is proportional to the number of the protons in each atom group, e.g., for the two signals of the methylene (CH2) and methyl (CH3) groups, the integral intensity ratio is 2/3. Moreover, the proton number ratio can be estimated based on the area of the signal, which is calculated by the computer software and is presented as an integral curve. A poor signal phase does not allow for a correct integral intensity ratio. Therefore, good NMR spectra should be obtained before the analysis of the integral intensity ratio. If the chemical structure of a polymer is known and the proton integral intensity ratios of the terminal and pendant groups can be obtained by the corresponding 1H NMR spectrum, the number-average degree of polymerization (DPn) and number-average molecular weight (Mn) can be determined as well. This is an end-group analysis method [7]. Adjacent nuclei with non-zero spin quantum numbers can interact with each other through chemical bonds, leading to split signals with the same width (Fig. 6.8). This interaction is

FIG. 6.7

1

H NMR chemical shifts of primary atom groups.

I. Polymer science

6.1 Measurements of molecular weight

115

FIG. 6.8 (A) without and (B) with spin-spin coupling.

called “spin-spin coupling” or “spin coupling.” The type and number of adjacent protons can be determined by the splitting pattern of each signal. When there are n equivalent protons on the adjacent carbon, the 1H NMR signal splits into (n + 1) signals. When two isolated protons, Ha and Hb (Fig. 6.8A), exist in a molecule, each one gives one (singlet) signal, whereas the Ha and Hb spin exist in two orientation states, parallel and antiparallel to the external magnetic field. When the Ha and Hb protons are bonded with adjacent carbons (Fig. 6.8B), two orientation states of Hb transmit to Ha through a shared electron pair. In other words, Ha feels the magnetic field slightly different from the external magnetic field applied, depending on the direction of the Hb spin. As a result, Ha splits into two signals (doublet) with different resonance frequencies. Hb also splits into a doublet with the same width. The width of splitting due to spin coupling is called “spin coupling constant” and is denoted with J. The unit of J is Hertz (Hz) and indicates the magnitude of the interaction, which, in turn, indicates how strongly the two nuclear spins are energetically coupled. Since the J values between spin-coupled nuclei are always equal, the nuclei with the spin-coupled partner can be identified by the corresponding J value. The NMR signal splitting due to spin coupling changes depending on the number of the interacted protons and the magnitude of J. In Fig. 6.9A, the case where a certain proton (Hc) has spin coupling with two adjacent protons (Ha and Hb) is presented. It is also assumed that the spin coupling interactions between Hc and the two adjacent protons are different with Jac ¼ Jcb (Jac < Jcb). Thus, Hc is divided into two signals by its spin coupling with Hb, whereas each signal is further divided into two additional signals by their spin coupling with Ha. Finally, two doublets appear in the NMR spectrum, resulting in four signals with equal intensity. Alternatively, the two adjacent protons can have the same spin coupling interaction (Fig. 6.9B). In this case, the two intermediate signals of the four Hc signals overlap in the same position due to Jac ¼ Jcb. Therefore, Hc displays a triplet with an intensity ratio of 1:2:1. Spin coupling takes place not only between directly bonded nuclei and protons bonded to adjacent carbons but also between non-adjacent nuclei depending on the molecular structure and the nuclei type. Moreover, the spin coupling may occur between different atoms with different nuclear spin, e.g., between 1H and 13C or between 1H and 19F. In the 1H NMR spectrum of a polymer, various features can be observed. When the molecular weight is large and the chain mobility is low, broadening of the 1H NMR signals can be observed because of their short relaxation time. Particularly in the case of high molecular weight polymers, the protons attached to the main chain cannot be easily identified

I. Polymer science

116

6. Polymer characterization

FIG. 6.9 Splitting of 1H NMR signals by spin-spin coupling. (A) Jac < Jcb and (B) Jac ¼ Jcb.

because of the broadening. Besides, the main chain protons split because of tacticity [8]. For example, the main chain methylene protons of isotactic poly(methyl methacrylate) (PMMA) split into roughly four signals, as shown in Fig. 6.10A. In contrast, the methylene protons of the syndiotactic and atactic PMMA main chain provide almost singlet signals with fine splitting (Fig. 6.10B and C).

6.1.8 Carbon (13C) NMR All the protons of an organic compound can be identified by NMR because the natural abundance of 1H is almost 100%. Carbon has two stable isotopes: 12C with a natural abundance of 99% and 13C. 12C cannot be detected by NMR (I ¼ 0), whereas the natural abundance of 13C that can be detected by NMR is about 1%, which is almost 1/100 of that of 1 H. Furthermore, the gyromagnetic ratio (γ) of 13C is 1/4 of that of 1H. The relative sensitivity of 13C is 1/6000 compared with that of 1H because the NMR sensitivity is affected by the third power of γ. This means that to measure a 13C NMR with the same resolution as 1H NMR, a 6000-fold greater sample amount is required. It should be also mentioned that more recent NMR equipment can afford good 13C NMR spectra using a sample amount of 10 mg. To avoid the decrease in the signal intensity due to splitting, normal 13C NMR measurements decouple the 1H atoms and eliminate the spin coupling with 1H. Similar to 1H NMR, TMS is often used as the reference compound for 13C NMR. The chemical shift of the TMS signal is set at 0 ppm. Generally, 13C NMR signals are observed in the range of 0–200 ppm (Fig. 6.11), which is wider than those of 1H NMR. Therefore, the 13C NMR peak separation is better than the 1H NMR, and the number of carbons can be predicted based on the 13C NMR peak number. Besides, the interpretation of the 1H NMR spectra is difficult because of the overlap of the signals in the narrow chemical shift range, which is not usually observed in 13C NMR spectra because of the wider chemical shift range. For example, the 13C NMR

I. Polymer science

6.1 Measurements of molecular weight

FIG. 6.10

1

117

H NMR spectra for (A) isotactic, (B) atactic, and (C) syndiotactic poly(methyl methacrylate)

(PMMA) [8].

signal of alkanes can be observed at the high magnetic field, whereas the typical signal of alkenes can be found at the low magnetic field and that of alkynes in the middle of the spectrum (Fig. 6.11). When the molecules bear highly electronegative atoms, the 13C NMR peaks shift to a lower magnetic field. For example, the 13C peak of a carbonyl carbon atom is detected at 160–220 ppm (Fig. 6.11). The integral intensity ratio of a conventional 13C NMR spectrum is not quantitative, because of the different nuclear Overhauser effect (NOE) that depends on the number of protons attached to the 13C nuclei. Besides, the signal intensity of 13C atoms bonded with more

FIG. 6.11

13

C NMR chemical shifts.

I. Polymer science

118

FIG. 6.12

6. Polymer characterization

Conventional 13C NMR, DEPT90, and DEPT135 spectra.

protons tends to be stronger. To obtain a quantitative integral intensity ratio of a 13C NMR spectrum, it should be recorded in an inverse gate decoupling mode. The interpretation of a 13C NMR spectrum can be further facilitated using distortionless enhancement by polarization transfer (DEPT), which allows the precise assignment of each carbon-containing functional group, i.e., CH3, CH2, CH, and C (Fig. 6.12). More specifically, in DEPT135, the CH3 and CH signals are observed upwards, whereas the CH2 signal is observed downwards. In DEPT90, only the CH signal can be detected upwards. Besides, the peak of a quaternary carbon (C) atom disappears in DEPT135 and DEPT90 measurements. Thus, the combination of these individual DEPT results provides a facile way to distinguish the signals of the CH3, CH2, CH, and C groups. Generally, both conventional and DEPT135 13 C NMR spectra are recorded, so that each functional group is determined. When it is difficult to distinguish the signals of the CH3 and CH groups, DEPT90 is also measured.

6.1.9 Relaxation time The two types of NMR relaxation time is the spin-lattice relaxation time (T1) and the spinspin relaxation time (T2). Both T1 and T2 are related to molecular mobility. In liquid samples, the NMR relaxation times for a nuclear spin with high and low mobilities are long and short, respectively. In terms of energy, these relaxation phenomena represent the process of releasing the absorbed energy and returning to the original energy distribution state. Besides, during this process, the ordered (coherent) state returns to its original random state. When the energy level of the nuclear magnetic moment splits (Zeeman split) in an external magnetic field, the number of spins parallel to the external magnetic field increases compared with the number of antiparallel spins (Fig. 6.13A). This state is then irradiated with a radio wave pulse. If the Zeeman energy matches the radio wave energy, the latter is adsorbed and the spin of the low energy level is excited to the high energy level. Nevertheless, the excited state is unstable, and the spin returns to the original low energy state. This process is called T1. Before the application of NMR, the directions of the nuclear spins are random in

I. Polymer science

6.1 Measurements of molecular weight

119

FIG. 6.13 Mechanism of (A) spin-lattice relaxation time (T1) and (B) spin-spin relaxation time (T2).

a different direction to each other (Fig. 6.13B). In this state, the precession phase is also different and corresponds to the random state. However, the precession phase changes immediately after the irradiation with a radio wave pulse from the random to the coherent state, where the nuclear spin arrows are in the same direction. The returning process of the precession phase from the coherent to the random state is called T2. In the NMR spectra of solid or high viscous liquids, the NMR signals are broader, because T2 becomes relatively short, and T1 has a minimum value with increasing molecular motion (Fig. 6.14). However, T2 decreases monotonically. When the nucleus motility is high, T1 is equal to T2. When the motility is low, T1 is significantly higher than T2. The nucleus mobility can be thus evaluated using the NMR relaxation time. Because the NMR signals broaden with the decrease in T2, the mobility can be approximately evaluated by simply comparing the half widths of the peaks under the same conditions [9].

FIG. 6.14 Relationship between the relaxation times T1 and T2 and the nucleus mobility.

I. Polymer science

120

6. Polymer characterization

6.1.10 Proton-proton correlation spectroscopy and total correlation spectroscopy In 1D 1H and 13C NMR, one signal represents one chemical shift. However, in twodimensional (2D) NMR spectra, one signal corresponds to two chemical shifts, thus providing several useful information, especially for complex structures. In 2D NMR spectra, both axes on the XY plane represent chemical shifts, whereas the Z-axis corresponds to the signal strength, which is indicated by contour lines. The higher the signal strength, the denser the contour lines. A proton-proton correlation spectroscopy (HH COSY) spectrum can be used to determine the correlation of spin coupling between adjacent protons because the correlation signal appears between the spin-coupled proton nuclei. The three signals on the diagonal line (Fig. 6.15) are called diagonal signals, and the other four peaks are called correlation signals. The diagonal signal corresponds to a 1D 1H NMR spectrum and shows the same chemical shift on both the X- and Y-axes. The correlation signal has different chemical shifts in the X and Y axes, indicating that the two protons are spin-coupled. The correlation signal is observed at a symmetric position concerning the diagonal line. Total correlation spectroscopy (TOCSY) can be observed proton spin-coupling network. TOCSY is a method where the magnetization of a proton is transferred one after another via proton spin coupling and can be used to examine the spin coupling network of proton groups (Fig. 6.16). Correlation signals appear for all the protons that belong in the same spin system. Moreover, the time required for the magnetization transfer is called “mixing time.” The magnetization continues to transfer depending on the length of the mixing time. Therefore, more correlation signals can be detected over a long mixing time. However, if the mixing time is too long, the intensity of the correlation signals will decrease.

6.1.11 Heteronuclear multiple quantum coherence spectroscopy and heteronuclear multiple bond correlation spectroscopy Heteronuclear multiple quantum coherence spectroscopy (HMQC) is used to investigate the connection by spin coupling between directly bonded 1H and 13C atoms (Fig. 6.17). The X-

FIG. 6.15

Proton-proton correlation spectroscopy (HH COSY).

I. Polymer science

6.1 Measurements of molecular weight

121

FIG. 6.16 Total correlation spectroscopy.

and Y-axes of the spectrum correspond to the 1H and 13C signals, respectively, and each signal corresponds to two chemical shifts of 1H and 13C. Thus, a correlation signal appears between the directly coupled 1H and 13C atoms. A correlation signal cannot be detected for a quaternary carbon atom because it bears no protons. Furthermore, no correlation signals are detected for 1H atoms, such as NH and OH, because they are not directly bonded to a carbon atom. Therefore, HMQC spectroscopy can facilitate the complete assignment of the 1H or 13C atoms of a compound. A correlation signal between one 13C peak and two 1H peaks implies that the 1H atom is a non-equivalent proton attached to the same carbon atom. The heteronuclear single quantum correlation spectroscopy (HSQC) provides the same information as HMQC, although the measurement principle is different. Heteronuclear multiple bond correlation spectroscopy (HMBC) is used to identify the correlation peaks between 1H and 13C that are separated by two or three bonds (Fig. 6.18). HMBC can identify quaternary carbon atoms and structures containing hetero atoms, such as O and

FIG. 6.17 Heteronuclear multiple quantum coherence spectroscopy.

I. Polymer science

122

FIG. 6.18

6. Polymer characterization

Heteronuclear multiple bond correlation spectroscopy.

N, which cannot be detected by COSY. Direct binding correlation signals of 1H and 13C can also be observed, but, unlike HMQC, they split into two signals in the X-axis direction. To avoid confusion, HMBC should be analyzed in comparison with HMQC.

6.1.12 Nuclear Overhauser effect spectroscopy When a 1H resonance signal is saturated, the resonance signal intensity of the nuclei that ˚ ) changes. This phenomenon is called the nuclear are spatially close to each other (within 5 A NOE. NOE is observed in 2D spectra by a method called nuclear Overhauser effect spectroscopy (NOESY). In the NOESY spectrum, the diagonal signals appear as negative phase and the NOE signals are positive. Sometimes, additional exchange and/or COSY signals may appear. Therefore, the NOESY analysis is performed together with HH COSY. Irrespective of the number of bonds between two 1H atoms, the NOE signals can be observed if the protons are ˚ , even between inter-molecules. Therefore, the separated by a maximum distance of 5 A NOESY provides specific information on a molecular structure. 1D NOE difference spectra focus only on a specific 1H NOE correlation, and they can be obtained with a higher digital resolution than 2D NOESY. By subtracting the normal spectrum from the spectrum that is selectively irradiated with the 1H signal, the intensity change due to NOE can be observed (Fig. 6.19). When the selectively irradiated signal is turned downward, the signal of the 1H atom that is close to the irradiated 1H atom appears upwards. The NOE intensity depends on the molecular correlation time, which indicates the restriction of the molecular motion. Generally, polymers have a long correlation time. Therefore, NOESY spectra cannot be obtained for molecules with a molecular weight that eliminates NOE at a certain magnetic field strength (Fig. 6.20). In a 500-MHz NMR apparatus, molecules with a molecular weight of about 600–1000 have zero NOE intensity. Furthermore, negative NOE signals cannot be distinguished from signals derived from a chemical exchange. In such a case, the rotating-frame Overhauser effect (ROE) spectroscopy (ROESY) is useful. The ROESY spectra provide negative diagonal signals, whereas the ROE correlation signals are obtained as positive signals. The ROE correlation signals do not turn into negative depending on the molecular weight.

I. Polymer science

6.1 Measurements of molecular weight

123

FIG. 6.19 1D nuclear Overhauser effect difference spectroscopy; (A) off resonance and (B) on resonance.

FIG. 6.20 Relationship between the NOE intensity and the correlation time.

6.1.13 Diffusion ordered spectroscopy Diffusion ordered spectroscopy (DOSY) can be used to observe the diffusion phenomena of molecules using a pulse field gradient (PFG) NMR measurement method [10]. When the peak intensity of each NMR is plotted against the magnetic field gradient, the intensity decreases with increasing magnetic field gradient. A self-diffusion coefficient (D) corresponding to each NMR peak can be obtained by analyzing the decay profile. If the range of the magnetic field gradient is too narrow, precise analysis is hindered because the peak intensity is not completely decayed. Moreover, if the range of the magnetic field gradient is too wide, the measurement point after the peak has been decayed cannot be used. Therefore, to obtain the correct D, it is important to experiment with an appropriate magnetic field gradient range. However, D cannot be easily evaluated for high molecular weight molecules and aggregates with a small D value by a commonly used probe with a magnetic field gradient 1 T/m. In that case, DOSY measurements can be performed using a special probe with a large magnetic field gradient.

I. Polymer science

124

6. Polymer characterization

In the case of 2D DOSY spectra, the X-axis represents the 1H NMR chemical shifts, whereas the Y-axis represents the diffusion coefficient. Since the 2D DOSY signals in the same molecule have the same D value, they form a horizontal line. However, the signals with different D values are observed separately in the Y-axis direction. Namely, a mixture of various molecular species can be separated by using the difference in D of each molecular species. By analyzing a mixture of a polymer and a low molecular weight molecule with extremely different D values, only the 1H NMR signal of the polymer with small D will be detected. An increase in the magnetic field gradient will rapidly reduce the NMR peak intensity of the low molecular weight molecule, but the peak intensity of the polymer will not be affected. Therefore, if the spectrum is measured at a certain magnetic field gradient intensity, where the 1H NMR peaks of the low molecular weight molecules disappear, only the 1D 1H NMR spectrum of the polymer will be obtained. Moreover, if the D values of each segment’s protons in a block copolymer are the same, the successful preparation of the block copolymer can be confirmed [11].

References [1] W. Striegel, W. Yau, J.J. Kirkland, D.D. Bly, Modern Size-Exclusion Liquid Chromatography: Practice of Gel Permeation and Gel Filtration Chromatography, John Wiley & Sons, Hoboken, 2009. [2] H. Determannz, Gel Chromatography Gel Filtration Gel Permeation Molecular Sieves: A Laboratory Handbook, second ed., Springer, Berlin Heidelberg, Berlin, 2009. [3] T. Kremmer, L. Boross, Gel Chromatography: Theory, Methodology and Applications, John Wiley & Sons, Hoboken, 1979. [4] K. Schmidt-Rohr, H.W. Spiess, Multidimensional Solid-State NMR and Polymers, Academic Press, Massachusetts, 1994. [5] T. Kitayama, K. Hatada, NMR Spectroscopy of Polymers, Springer, Berlin, 2004. [6] L.J. Mathias (Ed.), Solid State NMR of Polymers, Springer, Berlin, 1991. [7] K. Hatada, T. Kitayama, Y. Terawaki, H. Sato, F. Horii, NMR measurement of identical polymer samples by round robin method V. Determination of degree of polymerization for isotactic poly(methyl methacrylate) having a t-butyl end group, Polym. J. 15 (2003) 393–398. [8] K. Hatada, Tacticity of polymer, Kobunshi 80 (1981) 696–703. [9] Y. Iizuka, Y. Yamamoto, S. Kawahara, Latex-state 13C-NMR spectroscopy for poly(butyl acrylate), Colloid Polym. Sci. 297 (2019) 133–139. [10] K.F. Morris, C.S. Johnson Jr., Diffusion-ordered two-dimensional nuclear magnetic resonance spectroscop, J. Am. Chem. Soc. 114 (1992) 3139–3141. [11] Y. Bakkour, V. Darcos, S. Lia, J. Coudane, Diffusion ordered spectroscopy (DOSY) as a powerful tool for amphiphilic block copolymer characterization and for critical micelle concentration (CMC) determination, Polym. Chem. 3 (2012) 2006–2010.

I. Polymer science

C H A P T E R

7

Polymer degradation and stability Rui Yang Department of Chemical Engineering, Tsinghua University, Beijing, People’s Republic of China

7.1 Introduction 7.1.1 Aging and degradation During processing, storage, and application of a polymer material, its physical, chemical, or mechanical properties will deteriorate with time. One may observe yellowing, discoloration, brittleness of a coating, hardening, cracking of a tyre, or chalking and fracture of a glass fiber reinforced resin. This phenomenon is called aging. The main reaction that happened during aging is degradation (sometimes crosslinking also occurs). Various factors (inherent and external) influence the degradation behavior of a polymer material. If the degradation mechanism is clarified, methodologies to stabilize a polymer material can be developed to ensure safe practical uses and prolong the lifetime; or, methodologies to accelerate the degradation of waste can be developed to recycle it. All these efforts help to fully take advantage of the polymer material, protect the environment, and realize the sustainable development of human society. Degradation of a polymer material is a complex process, and various changes happen during this process. There are chemical changes such as molecular weight, oxidation, chain scission and crosslinking, and physical changes such as crystallization, relaxation, creep, and morphology (cracking, de-bonding, etc). The development and coupling of chemical and physical changes finally lead to property changes, such as strength, modulus, elasticity, insulation, transparency, coloring, etc. Degradation of a polymer material depends on inherent factors (organic nature), including chain structure, aggregation structure, chemical component, impurities, etc. It also relates to external factors (environmental conditions), including ultraviolet (UV) irradiation, temperature, atmosphere, humidity, chemicals, stress, microorganisms, etc. The degradation behavior is a comprehensive result of inherent and external factors.

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00007-8

125

# 2020 Elsevier Inc. All rights reserved.

126

7. Polymer degradation and stability

7.1.2 Influencing factors 7.1.2.1 Inherent factors • Chain structure There are chemical bonds with different bond energies in a polymer. A weak bond is easy to be broken, and a strong bond is more stable under the same condition. Polymers with different chemical components and structures have different stability. It was found that the degradation rate depends on the hydrogen abstraction difficulty of an initiator from a polymer, and the hydrogen abstraction difficulty depends on the CdH bond energy [1]. The bond energies rank as follows:

Therefore, hydrogen a on a branched carbon atom is easier to be abstracted than hydrogen b on methylene, and hydrogen c on the end carbon is the most stable. This is why polyethylene is more stable than polypropylene, and low-density polyethylene is less stable than highdensity polyethylene. In addition to carbon and hydrogen atoms, there are other atoms or functional groups in a polymer, which may be weak points and influence the stability. For example, unsaturated double bond, hydroxyl group, carboxyl group, amide group, and ester group are easy to be attacked and cause degradation of a polymer. Other structures, such as branching, stereoregularity, head-to-head or head-to-tail connection, and cis- or trans-isomers, also affect the degradation rate, and thus, the stability. • Aggregation structure Aggregation structures, e.g., crystal/amorphous phases and orientation, influence oxygen and water permeation and light transmission, thus may change the degradation process. Typically, an amorphous material has low density, high oxygen, and water permeation, so it is easy to be oxidized or hydrolyzed. • Filler Fillers are often added into a polymer to reinforce, toughen, improve thermal stability, and lower cost. To achieve a good dispersion of fillers in the polymer matrix, surface treatment or modification is often carried out. Both fillers and surface treatments may change the stability of a polymer significantly. By absorbing and/or screening light energy, some fillers serve as a protective agent, some are photoactive and promote the photochemical degradation of polymers [2]. Fig. 7.1 shows the variations of oxidation degrees (in terms of carbonyl index) of various fillers filled with high-density polyethylene (HDPE) during natural weathering [3]. HDPE itself is relatively stable, the oxidation degree was increased slowly with time. Wollastonite stabilized HDPE further. But other fillers accelerated the oxidation of HDPE significantly, especially kaolin and diatomite.

I. Polymer science

7.1 Introduction

127

FIG. 7.1 Effects of fillers on the carbonyl index of HDPE during natural weathering in Beijing [3].

FIG. 7.2 Effects of surface treatments on the carbonyl index of HDPE/sericite composite during natural weathering in Beijing [4]. MAH, maleic anhydride; AA, is acrylic acid.

Fig. 7.2 shows the variations of oxidation degrees of HDPE/sericite composites, in which sericite was surface treated by different coupling agents [4]. The concentration of these coupling agents is typically 0.3%, but they had great effects on stability.

I. Polymer science

128

7. Polymer degradation and stability

• Additive To improve the stability of a polymer material during thermal processing or in-service conditions, additives such as antioxidants, UV absorbers, and light stabilizers are often introduced. Hundreds to thousands of ppm are typically used. In addition, other additives, e.g., crosslinking agent, curing agent, plasticizer, etc., are often introduced to initiate crosslinking reactions, increase macromolecular mobility, and so on. Their effects on the stability of polymer materials shall be paid attention. • Impurity Impurities may also influence the stability of a polymer material. Impurities include residual initiators, catalysts, and monomers during polymerization, emulsifiers, dispersants, and trace metal ions coming from polymerization and processing equipments. During mixing and extrusion, thermoplastics are easily oxidized to chromophores under high temperature and shearing. Most of these impurities accelerate degradation. For example, Fe3+ promoted the degradation of low-density polyethylene (LDPE) at the simulated composting temperature (70°C) [5]. The degradation behavior of a polymer material is a comprehensive result of multifactors, and there may be different interactions between components. For example, during photooxidation, rutile is synergistic in stabilization with phenolic antioxidants and hindered piperidine stabilizers, but antagonistic with benzotriazole and benzophenone absorbers [6]. 7.1.2.2 External factors • Temperature Chemical reactions will be accelerated under high temperatures. So, aging and degradation will be speeded up when the ambient temperature rises. At the same time, a macromolecule chain is easy to move under high temperatures, so that stress relaxation, creep, and recrystallization may happen. When a polymer material suffers from an over-high temperature, as often occurs during melt extrusion, chemical bonds may be broken to form radicals, and these active radicals easily react with neighbor molecules to produce more radicals. As a result, the molecular weight is decreased and the mechanical properties are deteriorated. • Solar irradiation Solar irradiation is the most important factor for natural weathering. The solar light that reaches the earth’s surface is in the range of 290–3000 nm, in which UV irradiation in the range of 290–400 nm has the most significant effect on polymer materials, although it is only ca. 5% of the total energy. Table 7.1 lists the energies of various wavelengths and bond energies. It shows that UV light may cause the breakdown of most chemical bonds. Although visible and infrared light are not able to break most of the chemical bonds, they can be absorbed by polymer materials and increase the temperature, and thus accelerate the degradation. • Oxygen There is 21 vol% oxygen in the air. It is an active media. Many polymer materials can be oxidized, especially when they are under high temperatures and/or solar irradiation. As a result, thermo-oxidation and photo-oxidation happen. I. Polymer science

129

7.1 Introduction

TABLE 7.1

Light energies and chemical bond energies [1].

UV light

Visible light

Wavelength (nm)

Energy (kJ)

Chemical bond

Bond energy (kJ/mol)

300

399

OdO

138.9

400

299

CdS

259.4

500

239

CdN

291.6

600

201

CdC

347.7

700

171

CdO

351.5

NdH

390.8

CdH

413.4

OdH

462.8

800

147
1

10 –10 3

Infrared light

10 –10

6

2

• Water and humidity When water or water vapor goes into a polymer, the absorbed water may: Ø Serve as a plasticizer and increase the movability of the macromolecular chain, which may result in a water-induced re-crystallization and increase the internal stress when water is removed. In addition, Tg of a polymer absorbing water will decrease greatly. Fig. 7.3 shows that with over 10 wt% water in PA6 and over 6 wt% water in PA66, Tg is decreased by 90 K and 50 K, respectively. This means that PA changes from an engineering plastic to an elastic state at room temperature; Ø Initiate hydrolysis reactions of polymers and thus decrease the molecular weight;

Glass Transition Temperature / K

390 370 350 330 PA 6

ΔTg = 90 K

310 290 ΔTg = 50 K

PA 6,6

270 250

0

2

4

6

% Water content (w/w)

FIG. 7.3 Tg of polyamides decreased with water content [7]. I. Polymer science

8

10

12

130

7. Polymer degradation and stability

Ø Replace hydrogen bonds in polymers, in PA, for example:

Ø Extract water-soluble additives, such as plasticizers, antioxidants, and light stabilizers. Therefore, the stability of the polymer is decreased; Ø Help water-soluble chemicals to access polymer matrix and lead to further degradation; Ø Modify the surface characteristics. For example, the UV transmittance of the surface layer will change owing to the presence of the surface water layer; Ø Help microorganisms to adhere to a hydrophilic polymer and then cause biodegradation of this polymer. In composites, water may also diffuse to the polymer/filler interface, cause the debonding or delamination, and thus, the decrease of mechanical properties. • Chemicals Polymer materials often contact various kinds of chemicals during applications. Some of the chemicals can act as a solvent, which provides more flexibility and then promotes the degradation; some can react with additives or stabilizers so that the protective effect is lost and degradation is promoted; and some of the chemicals such as polycyclic aromatic hydrocarbons, nitrogen oxides, sulfur oxides, ozone, and hydrocarbons, can be adsorbed by polymer surfaces and generate chromophores. The chromophores, by absorbing UV radiation, can accelerate the photo-oxidation process [8–12]. For example, greenhouse films, mostly made of PE, would suffer the agrochemicals such as pesticide and fertilizer, and also air pollutions, such as acid rain, NOx, and SOx. Fig. 7.4 shows the rapid deterioration of the mechanical properties of PE films exposed to sulfur evaporation. • Microorganism Some microorganisms may degrade polymers to small molecules with the help of enzymes. Natural polymers are biodegradable, while most synthetic polymers are nonbiodegradable. Nowadays, synthetic biodegradable polymers such as polylactic acid (PLA) and polyhydroxybutyrate (PHB) have been developed. They will decompose to H2O and CO2 after the final disposal. Biodegradable polymers are especially encouraged in the packaging and agricultural film industry. In addition to the above factors, others factors such as stress and ozone also affect the degradation process and degradation rate, and thus, stability.

I. Polymer science

131

7.1 Introduction

The relative loss in elongation at break L, %

70 60 50 40 30 20 10 0 –10 3

6

9

12

Time, week UV;

UV-IR;

UV-IR-AD

FIG. 7.4 The relative loss in elongation at the break of films due to the effect of sulfur [8]. L ¼ (Esunonly
Esulfur andsun) ∗ 100/Enew.

7.1.3 Evaluation and characterization 7.1.3.1 Evaluation There are typically two methods to evaluate the stability of a polymer, i.e., natural weathering and laboratory accelerated aging. Natural weathering is carried out outdoors. Polymer samples are aged under the natural environment, and the real degradation behavior and lifetime are obtained. But the evaluation period lasts for years and the evaluation result is not reproducible. To realize a reproducible aging evaluation in a short period, laboratory accelerated aging instruments are developed to simulate the natural conditions. Simulated solar irradiation, ventilation, and humidity/condensation are introduced, and the evaluation period can be shortened to months. Although numerous efforts are made to simulate the real degradation behavior, there are still doubts about the correspondence to the natural weathering results. 7.1.3.2 Characterization Since there are various chemical and physical changes during the aging of a polymer material, and many degradation products formed, nearly all analytical instruments for polymer characterization can be used. Fig. 7.5 shows typical analytical techniques [13]. For example,

I. Polymer science

132

7. Polymer degradation and stability

Morphology • SEM • TEM

Physical Properties Surface analysis • ESCA

Crystallinity • XRD • DSC • TGA

Characterization of Polymer Degradation Radicals, ions • ESR • Chemiluminescence

Mechanical Properties

Chemical properties

Functional Changes • Infrared Spectroscopy • UV Spectroscopy • Photophosphoresence • Chemiluminescence

Degraded products • GC • GCMS • MALDI-TOF • LC

Molecular Weight changes • GPC (SEC) • Viscosity

• Instron • DMA

Percentage degradation

• Weight loss • LSC • CO2 Estimation (biodegradation)

FIG. 7.5 Analytical techniques in polymer degradation [13].

infrared spectroscopy (IR) is the most used technique to monitor the chemical changes, including oxidation-induced formations of carbonyl groups, hydroxyl groups, unsaturated bonds, etc. Decrease of molecular weight is determined by gel permeation chromatography (GPC) or viscosity measurement. Gas chromatography (GC) or GC coupled with mass spectroscopy (GC-MS) is powerful to qualitatively analyze gaseous degradation products. The formation of these products causes weight loss. Degradation-related crystal form and crystallinity changes are characterized by X-ray diffraction (XRD) and differential scanning

I. Polymer science

133

7.2 Thermal and thermo-oxidative degradation

calorimetry (DSC). The morphology changes are observed by using scanning electron microscopy (SEM). Mechanical property changes are determined by Instron universal testing machine or dynamic mechanical analyzer (DMA). By comprehensively understanding changes from chemical, physical, and morphological aspects, the full view of degradation can be achieved.

7.2 Thermal and thermo-oxidative degradation 7.2.1 Thermal degradation When a polymer material is heated, it may undergo chain relaxation, glass transition, crystal melting, and decomposition. Once the decomposition reactions take place, the polymer material is thermal degraded. Thermal degradation is not as popular as thermo-oxidative degradation. But during thermal processing procedure or in inert thermal environment, thermal degradation of a polymer material is mainly concerned. Thermal degradation can be regarded as a reverse process of polymerization. First, a hydrogen atom is lost from a polymer chain, or a chain is cleaved into two parts, affording corresponding radicals. Then, de-polymerization or chain transfer of these radicals results in the formation of monomers or oligomers. Finally, coupling or disproportionation of radicals terminates reactions. There are various patterns of thermal degradation [14]: • Random scission of the main chain Random scission of the main chain is often happens in vinyl polymers, giving rise to a series of fragments with different carbon numbers, with the quick decrease of the molecular weight. ð7:1Þ

When other atoms in addition to carbon are present in the main chain, the bond energy of CdX (X ¼ N, O, P, etc.) is typically less than that of CdC. Hence, chain scission easily happens on these weak points, i.e., at the α and β positions, as follows: O

Polyamide

C

α

H N C β

O

Polyester Polyether

C

C C

C

β

O α

O C

)

Polycarbonate

C

O α

O

CH3 O α

C β

CH3

I. Polymer science

O β

C α

)n

134

7. Polymer degradation and stability

When there are unsaturated bonds in the main chain, as in polybutadiene (PB) and polyisoprene (PIP), the main chain is easily cleaved at the α or β position: a C

C

C

b C

C

C

C

C

C

C.

a scission b scission

C

C

C

.C C. .C

C

ð7:2Þ C

C C

C C

C C

• Elimination of substituents For polymers such as polyvinyl chloride (PVC), HCl is eliminated by the following reaction, and C]C bonds are formed in the main chain. This reaction continues to form many C]C bonds, which are the weak positions for further reactions.

C

C

C

C

C

C

Cl

H

Cl

H

Cl

C

C

C

C

C

C

C

C

HCl

ð7:3Þ

H C

C

C

C

HCl

Cl

ð7:4Þ

• De-polymerization For α-substituted polymers such as polymethyl methacrylate (PMMA), de-polymerization often happens, with the monomer as the main thermal degradation product. CH3

CH3

CH2

C

CH2

C

CH2

C

CH2 C

O

C

O

C

O

C

O C

OCH3

CH3

OCH3

CH3

ð7:5Þ

OCH3

OCH3

• Intramolecular cyclization In addition to chain scission reactions, cyclization or crosslinking reactions may also happen in some cases. For example, when heated to approximately 200°C, polyacrylonitrile (PAN) changes to a ladder-like structure via intramolecular cyclization: H2 C

N

H2 C

H2 C

H2 C

H2 C

H2 C

CH

CH

CH

CH

CH

CH

C

C

C

C

C

C

N

N

N

I. Polymer science

N

N

ð7:6Þ

7.2 Thermal and thermo-oxidative degradation

135

FIG. 7.6 Schematic of a typical auto-oxidation procedure.

7.2.2 Thermo-oxidative degradation Under atmospheric conditions, oxygen plays a crucial role, and thermo-oxidative degradation of a polymer material happens. With the help of highly active oxygen, which is everywhere on the earth, thermo-oxidative degradation happens easier than thermal degradation. For example, low-density polyethylene (LDPE) is stable till 290°C in nitrogen but is degraded seriously at 100°C in air. Thermo-oxidative behavior of a polymer is typically an auto-oxidation procedure. The oxygen uptake or oxidation degree often shows an S-curve (Fig. 7.6), including an induction period AB, an auto-catalysis period BC, and a final plateau period CD. 7.2.2.1 Thermo-oxidation mechanism In general, there are the following reactions during thermo-oxidative degradation: • Initiation: a hydrogen atom is lost from a polymer chain to form radicals, or a polymer chain reacts with oxygen: ð7:7Þ ð7:8Þ • Propagation: alkyl radicals are easily oxidized to peroxide radicals, which in turn abstract a hydrogen atom from the main chain to form hydrogen peroxide ROOH. ROOH is quite unstable and easily cleaved to alkoxyl and hydroxyl radicals. These two active radicals continue further reactions. ð7:9Þ ð7:10Þ

I. Polymer science

136

7. Polymer degradation and stability

ð7:11Þ ð7:12Þ ð7:13Þ When ROOH accumulates to a high concentration, two ROOH molecules may meet and react to form new radicals: ð7:14Þ • Termination: two radicals react to form stable molecules. ð7:15Þ ð7:16Þ ð7:17Þ During this process, ROOH is considered as the most important product. It can be cleaved to alkoxyl, hydroxyl, and peroxide radicals, which in turn initiate more radicals. Therefore, the accumulation and decomposition of ROOH contribute the accelerated oxidation reactions.

7.2.2.2 Factors influencing thermo-oxidative degradation Thermo-oxidative degradation differs from polymers. Even for the same polymer, its stability differs from environmental conditions. Responsible factors include: • Saturated degree: unsaturated structures in a polymer decrease stability. For example, hydrogen-saturated styrene-butadiene-styrene copolymer (SBS) is more stable than SBS itself. • Branched structure: linear structure is more stable than the branched structure. That is why PE is more stable than PP, and HDPE is more stable than LDPE. • Crosslinking: crosslinking undoubtedly increases the thermal stability. In an ideal crosslinking network, a segment is connected by two ends. It is less possible to destroy all the connections at the same time. If one connection is broken, the whole network remains. • Crystallization: In the crystal phase, the oxidation is restricted by limited oxygen diffusion. Hence, high crystallinity leads to high stability. • Metal ions: metal ions, especially transition metal ions, are often present as impurities. They promote oxidation of polymers significantly by accelerating the decomposition of ROOH to radicals and thus increase the initiation rate. On one hand, metal ions harm the stability. On the other hand, this feature can be utilized to promote the composting degradation of wastes.

I. Polymer science

Concentration *103 (mol kg–1)

7.2 Thermal and thermo-oxidative degradation

137

0,6

FIG. 7.7 Concentration of antioxidant

0,5

(▪) and chain scission (⧫) in PP with exposure time at 130°C [15].

0,4 0,3 0,2 0,1 0 0

500

1000

1500

2000

2500

3000

3500

Time (h)

7.2.3 Stabilization of thermal and thermo-oxidative degradation Although one may increase thermal and thermo-oxidative stability of a polymer by changing the chemical structure, e.g., decreasing unsaturated bonds, this methodology is quite expensive and some mechanical properties may be influenced. Therefore, the introduction of antioxidants is a typical way to increase stability. Antioxidants may be introduced during polymerization (if they do not interfere with the polymerization process), during pelletization (most often), or during processing. The thermal degradation or thermo-oxidation is strongly depressed before the consumption of antioxidants, as shown in Fig. 7.7. There are typically two groups of antioxidants, i.e., radical scavenger and proantioxidant [1]. 7.2.3.1 Radical scavenger Radical scavengers react to various radicals such as peroxide radicals ROO, alkoxyl radicals RO, and hydroxyl radicals HO, so the radical chain reactions are terminated. The most often used radical scavengers include secondary aromatic amines, hindered phenols, benzoquinones, carbon black, and benzofuranone. Secondary aromatic amine has NH groups and hindered phenol has OH groups. They react to peroxide radicals ROO to form ROOH and a relatively stable radical Ar2N or ArO, which continue to terminate another peroxide radical ROO. ð7:18Þ ð7:19Þ ð7:20Þ ð7:21Þ

I. Polymer science

138

7. Polymer degradation and stability

Benzoquinones can capture alkoxyl radicals RO. Three formed radicals are stable and will not initiate further chain reactions:

ð7:22Þ

Carbon black is the most widely used antioxidant in rubbers. Phenol groups, quinone groups at edges, and aromatic complexes on the backbone can capture radicals and terminate chain reactions. Benzofuranones are excellent alkyl radical scavengers. One benzofuranone molecule can capture two macromolecular radicals. 7.2.3.2 Pro-antioxidant Pro-antioxidants decompose hydrogen peroxide without the formation of radicals. The most widely used pro-antioxidants are phosphites and organic sulfides. Phosphites (R1O)3P, in which R1 is alkyl, benzyl, or cycloalkyl group, can reduce hydrogen peroxides to corresponding alcohols. It has a synergistic effect with phenol antioxidants. ð7:23Þ Organic sulfides, e.g., thioethers (RSR), can transfer hydrogen peroxides to alcohol. ð7:24Þ

ð7:25Þ When two or more kinds of antioxidants are used together, synergistic, additional, or antagonistic effects may appear.

7.3 Photolysis and photo-oxidative degradation 7.3.1 Photolysis When a polymer is irradiated by UV light, electron beam, or X-ray, it may absorb the energy and is excited. Then, the absorbed energy may be transferred to heat or harmless

I. Polymer science

7.3 Photolysis and photo-oxidative degradation

139

long-wavelength light and release, or cause photochemical reactions of the polymer (photolysis). Photochemical reactions mainly happen in two ways. An excited molecule is broken to radicals, as shown in Eq. (7.26), or an excited molecule is decomposed to small molecules, as shown in Eq. (7.27). ð7:26Þ ð7:27Þ When a macromolecule absorbs UV irradiation and form radicals, random degradation/ crosslinking and/or depolymerization happen next. When chain scissions happen randomly on the main chain, giving rise to macromolecule radicals, next, these radicals may induce further reactions. There is a competition between radical-induced degradation and crosslinking. If degradation dominates, the molecular weight is decreased. If crosslinking dominates, the molecular weight is increased. For example, during UV exposure, chain scission exceeds crosslinking in LDPE (Fig. 7.8). Photoinduced depolymerization, as that in thermal degradation, is the reverse process of polymerization. Once a radical occurs, monomers are eliminated one by one from this site.

7.3.2 Photo-oxidative degradation When a polymer material is exposed in an outdoor condition, photo-oxidative degradation often happens. There are also initiation, propagation, and termination reactions during this process, like that during thermo-oxidative degradation. Different from thermo-oxidation, the photo-oxidation is initiated by absorbing light energy. From Table 7.1, UV energy is strong enough to break some weak bonds. The photo-oxidation reactions include: FIG. 7.8 LDPE scission and crosslinking concentration at different depth after 6 weeks of UV exposure [16].

Concentration (mmol/kg)

120 LDPE: 6 weeks

100 80

Scission

60 40

Crosslinking

20 0

0

0.5

1

1.5

Depth (mm)

I. Polymer science

140

7. Polymer degradation and stability

• Initiation: generally, saturated macromolecules are quite stable. Pure polymer does not absorb UV light. But in fact, nearly no “pure” polymer exists. All polymer materials have some impurities, such as residual catalysts from polymerization, chromophores (hydrogen peroxides, ketones, carboxylic acids, carbonyl species, aldehydes, etc.) produced by previous thermal processing, and metal ions. These impurities absorb UV energy and help to initiate photo-oxidation reactions. For example, residual ZieglerNatta catalysts are sensitizers of photo-oxidation of polyolefins. They promote the initiation. ð7:28Þ Bond energies of OdO and RdO bonds in ROOH are relatively low, so ROOH is easily broken to alkoxy, hydroxyl, alkyl, and hydrogen peroxide radicals by UV light. Hence, trace ROOH from thermal processing can also initiate photo-oxidation reactions. By β-scission of alkoxy radicals, ketones and alkyl radicals are formed. ð7:29Þ

ð7:30Þ

Aldehydes and ketones are also initiators of photo-oxidation through Norrish I and Norrish II reactions. They are often responsible for the chain scission and degradation of polymeric materials. Norrish I reaction: ð7:31Þ

Norrish II reaction: ð7:32Þ

• Propagation and transfer: ð7:33Þ ð7:34Þ

I. Polymer science

7.3 Photolysis and photo-oxidative degradation

141 ð7:35Þ ð7:36Þ ð7:37Þ ð7:38Þ ð7:39Þ ð7:40Þ

• Termination: two radicals react to form stable molecules. ð7:41Þ ð7:42Þ ð7:43Þ

7.3.3 Stabilization of photolysis and photo-oxidative degradation In principle, there are also two ways to prevent polymer materials from photolysis and photo-oxidative degradation. One is to synthesize polymers with photostable structures. This is not easy. The other is to introduce light stabilizers, which are the most effective and are widely used. There are typically four kinds of light stabilizers, i.e., light screening agents, UV absorbents, quenching agents, and hindered amine light stabilizers (HALS) [1]. • Light screening agent Light screening agents reflect or absorb UV light to protect polymer materials. Pigments such as carbon black, TiO2, and ZnO are often used. • UV absorbent UV absorbents absorb UV light and transfer the energy to heat or harmless irradiation by isomeric change. The following structures are often used as UV absorbents. O-hydroxyl benzophenone: one of the most important UV absorbents. ð7:44Þ Phenyl salicylate: photo-Fries rearrangement under UV irradiation.

I. Polymer science

142

7. Polymer degradation and stability

ð7:45Þ

O-hydroxyl benzotriazole: widely used in polyolefins. ð7:46Þ Hydroxyl phenyltriazine: strongly absorb UV of 300–400 nm. ð7:47Þ

• Quenching agent Quenching agents do not strongly absorb UV light. They quench excited macromolecules to the ground state by the inter-molecular energy transition. Quenching agents include transition metals, such as complexes of Ni and Co. • Hindered amine light stabilizer (HALS) HALS does not absorb UV light. It is a kind of multifunctional light stabilizer. It combines radical scavenging (Eqs. 7.48 7.51), hydrogen peroxide decomposition (Eqs. 7.52 and 7.53), energy transition of excited macromolecules, and singlet oxygen scavenging together. Nowadays, HALS has become the most important light stabilizer. ð7:48Þ

ð7:49Þ

ð7:50Þ

ð7:51Þ

ð7:52Þ

I. Polymer science

7.4 Hydrolysis and biodegradation

143 ð7:53Þ

7.4 Hydrolysis and biodegradation 7.4.1 Hydrolysis From Polymer Chemistry, we know that condensation polymerization between an acid and an alcohol produces a polyester; condensation polymerization between an acid and an amine produces a polyamide, both with H2O as the by-product. Reversely, with the presence of H2O, a polyester chain may be hydrolyzed to two sub-chains with carboxyl and hydroxyl ends, and a polyamide chain to two sub-chains with carboxyl and amine ends, shown in Eqs. (7.54) and (7.55). As a result, the molecular weight is decreased. Polyethylene terephthalate (PET), polyamide (PA), polycarbonate (PC), and polyurethane (PU) are sensitive to hydrolysis because of the existence of ester or amide bonds, which are easy to be attacked by water, especially in acid or alkaline conditions. ð7:54Þ ð7:55Þ For hydrophilic polymer materials, water or humidity may have a more significant impact than heat or UV light. For example, humidity has a more significant influence on PA66 than thermal oxidation, as shown in Fig. 7.9. In addition, there is an interaction between hydrolysis and thermal oxidation. Polyolefins, such as polyethylene and polypropylene, is hard to be hydrolyzed because of the hydrophobic nature.

7.4.2 Biodegradation Natural polymers are biodegradable. In a humid environment, microorganisms are easy to adhere to natural polymers and degrade them under the help of certain enzymes. Hydrolysis often happens during this process. Some synthetic polymers, especially polyolefins, are hard to be biodegraded because of their hydrophobic nature and high molecular weight. Hydrophilic synthetic polymers, such as polyurethane, polyamide, and polyester, are biodegraded. Biodegradation mainly depends on polymer structures. Polyolefins, because of the inert structure, are resistant to biodegradation. Polymers containing dNH, dCOOH, dOH, and dNCO groups, are hydrophilic and easy to be biodegraded because the absorbed water supplies a growing environment to microorganisms. A high molecular weight polymer is relatively stable. Branching and crosslinking often hinder the biodegradation. The coarse surface

I. Polymer science

144

7. Polymer degradation and stability

Average % tensile strength remaining

0

100

200

300

400 100

100

Air oven Air oven 2nd run Air oven 3rd run Argon and 100% RH Oxygen and 100% RH

90 80 70

90 80 70

60

60

50

50

40

40

30

30

20

20

10

10 0

0 0

100

200

300

400

Days exposed, 124°C

FIG. 7.9 Percent tensile strength remaining as a function exposed to 124°C [17].

is suitable for water adsorption and microorganism adherence, thus helps biodegradation of polymers than a smooth surface. Water, temperature, pH value, and oxygen also influence the biodegradation of polymers. The growth of bacteria and fungi needs water. Hence, the hygroscopicity of a polymer often decides the sensitivity to biodegradation. For example, when the humidity is lower than 20%, wood is relatively stable. The growth of microorganisms prefers a comfortable temperature range, typically 10–40°C. Hence, high or low temperature hinders the biodegradation. Many microorganisms are acid-preferable or alkaline-preferable. Most fungi grow well in a pH value of 4–7; most bacteria prefer a pH value of 7.4–8.5. Oxygen is of great importance to aerobic microorganisms, which is the main reason for biodegradation.

7.4.3 Biodegradable polymers Based on the hydrolysis and biodegradation mechanism, degradable polymer materials can be designed and produced. They will be degraded to CO2 and H2O finally under the natural environment after usage. Typical degradable polymer materials include poly (ε-caprolactone) (PCL), poly(lactic acid) (PLA), poly(3-hydroxybutyrate) (PHB), polyhydroxy valerate (PHV), poly(butylene succinate) (PBS), etc. [18] The degradation rates of biodegradable polymers differ from exposure conditions. For example, there are four stages in the degradation of PLA implanted in the body [19]. (1) Water absorption controlled by the diffusion; (2) hydrolysis controlled by the water content; (3) auto-acceleration of hydrolysis catalyzed by the accumulation of acid chain ends; (4) decrease of molecular weight accompanied by weight loss.

I. Polymer science

145

7.5 Degradation and stabilization of polymer nanocomposites

7.5 Degradation and stabilization of polymer nanocomposites In the past decades, polymer nanocomposites have attracted great attention. With a small amount of nanofillers, generally, less than 5 wt%, mechanical properties such as elastic modulus and tensile strength, heat distortion temperature, and barrier property can be significantly improved. At the same time, the effects of nanofillers on the stability of polymers must be considered. Various nanofillers, e.g., layered silicate, calcium carbonate (CaCO3), carbon nanotube (CNT), and graphene, were introduced in many polymer materials. Unfortunately, in many cases, they harm the stability of polymers and lead to a higher degradation rate than pristine polymers. Nano clay, or montmorillonite (MMT), belonging to the family of layered silicate, is the most widely used nanofiller. It has been incorporated with various polymers, such as PE, PP, PA-6, PC, and epoxy (EP). Figs. 7.10 show the carbonyl formation (as a representative to oxidation degree) of PE filled with different amounts of organo-MMT (OMMT), the effects of interlayer cations are also plotted [20]. OMMT accelerated the photo-oxidation of PE significantly, even when the OMMT concentration is only 2 wt%. Different interlayer cations lead to different oxidation rates. When graphene oxide (GO) was introduced into PBS, the increased hydrophilicity, decreased crystallinity of PBS, and the presence of defects at the PBS/GO interface by GO addition, contributed to the enhanced wettability of the composite and the largely enhanced hydrolytic degradation, as shown in Figs. 7.11 [21]. As a positive example, Figs. 7.12 show that good dispersion of multi-wall CNT (MWCNT) contributed to higher photo-oxidation and thermal oxidation stability of syndiotactic PP (s-PP) [22]. The reason is that MWCNT interacted with oxygen and prevented the oxidation at an early stage of oxidation. The introduction of nanofillers may bring many changes to a polymer material, hence change the stability.

20

OMMT-10 OMMT-5 OMMT-2 pure PE

20

15

Area of carbonyl band

Area of carbonyl band

25

10

5

0

PE/Fe-MMT PE/Ni-MMT PE/Cu-MMT PE/Na-MMT pure PE

15

10

5

0 0

50

100

Exposure time (h)

150

200

0

50

100

Exposure time (h)

150

200

FIG. 7.10 Carbonyl formation of PE filled with different amounts of OMMT (left) and various interlayer cations (right, the OMMT here is 5 wt%) [20].

I. Polymer science

146

7. Polymer degradation and stability

FIG. 7.11 Effect of GO on residual weight fraction of PBS during hydrolysis in NaOH solution at 37°C [21]. Residual weight fraction (%)

100

80 60 PBS PBS/GO-0.1 PBS/GO-0.2 PBS/GO-0.5 PBS/GO-1 PBS/GO-2

40

20 0 0

24

48

72 96 120 144 168 192 Hydrolytic degradation time (h)

FIG. 7.12 FTIR spectra of pristine syndiotactic PP (sPP) and sPP (1% MWCNT) after different time of UV exposure [22].

216 240

Absorbance (a.u.)

sPP 340h UV

sPP (1% MWCNTs) 340h UV

sPP (1% MWCNTs) exposed up to 250h UV 1900

1800

1700

1600

–1

Wavenumber (cm )

• Optical character. A nanofiller may act as a UV absorber or a UV screening agent, to accelerate or hinder photo-oxidation. TiO2 and ZnO are special examples, they are semiconductors. They exhibit photo-protection by UV reflection and photo-catalysis by radical initiation at the same time. The competence of these two effects under the ambient environment decides the final behavior of the corresponding nanocomposite. • Chemical feature. Some nanofillers have functional groups on the surface, which may be chromophores and absorb light energy to initiate the formation of radicals. These

I. Polymer science

7.5 Degradation and stabilization of polymer nanocomposites

147

functional groups also possibly take part in the interaction between filler particles and the polymer matrix. Some nanofillers, e.g., MMT or clay, have interlayer chemicals. The decomposition of ammonium ions may create acidic sites, and the photo-redox reaction of metal cations may have a catalytic effect on the degradation. • Impurities. Transition metal ions, such as Mn, Fe, Co ions, are typical impurities in nanofillers. They exhibit a catalytic effect on hydroperoxide decomposition and accelerate the oxidation of polymers. • Absorption behavior. Large specific area and porous structure of nanofillers help the adsorption of stabilizer molecules or trapping of radicals. In the former case, the stability is decreased; in the latter case, the stability is improved. • Nucleation. Nanofillers often act as nucleating agents to increase the crystallinity or change the crystal form. High crystallinity hinders the diffusion of oxygen into the polymer matrix and thus lowers the oxidation degree. A high-density crystal form is more stable than a low-density one. Since the introduction of nanofillers brings about so many changes, the aging behavior of a nanocomposite is the combinational results of the above-mentioned effects. Many nanofillers decrease the stability of polymer materials, so there are many efforts to compensate for this negative effect. For example, an organo-clay decreased the stability of linear low-density polyethylene (LLDPE) nanocomposites significantly [23] (Fig. 7.13). Two kinds of UV absorbers, i.e., UV 1164 and UV 2337, are proved to effectively counteract the catalytic effect of organo-clay by decreasing the photo-oxidation degree of the PE/clay nanocomposite. But the most effective additive is the metal deactivator (MD). It successfully decreased the photo-oxidation degree to the level of pure PE. Therefore, the negative effect of organo-clay on the stability of PE was completely counteracted.

FIG. 7.13 Variations of absorbance at 1710 cm
1 as a function of aging time (in days) of natural aging (ClermontFerrand, France) for LLDPE/clay nanocomposite films with different stabilizers (NanoB is the organo-clay, UV 1164 and UV 2337 are two UV absorbers, THT 6460 is a UV stabilizer, MD is a metal deactivator) [23].

I. Polymer science

148

7. Polymer degradation and stability

References [1] S.Y. Zhong, Q.W. Xu, G.S. Wang, Degradation and Stabilization of Polymers, Chemical Engineering Press, Beijing, 2002. [2] N.S. Allen, M. Edge, T. Corrales, A. Childs, C.M. Liauw, F. Catalina, C. Peinado, A. Minihan, D. Aldcroft, Polym. Degrad. Stab. 61 (1998) 183–199. [3] R. Yang, J. Yu, Y. Liu, K.H. Wang, Polym. Degrad. Stab. 88 (2005) 333–340. [4] R. Yang, J. Yu, Y. Liu, K.H. Wang, J. Appl. Polym. Sci. 107 (2008) 610–617. [5] J.G. Yu, X.D. Wang, Acta Polym. Sin. 1 (2001) 99–104. [6] N.S. Allen, M. Edge, T. Corrales, F. Catalina, Polym. Degrad. Stab. 61 (1998) 139–149. [7] I.F. Kaimin, A.P. Apinis, A.Y. Galvanov, Vysokomol. Soed. A 17 (1975) 41–45. [8] P.A. Dilara, D. Briassoulis, J. Agric. Eng. Res. 76 (2000) 309–321. [9] W. Schnabel, Polymer Degradation, Hanser International, New York, 1981. [10] B. Ranby, J.F. Rabek, The Effects of Hostile Environments on Coatings and Plastics, (1983) pp. 291–307. [11] P.A. Dilara, D. Briassoulis, Polym. Test. 17 (1998) 549–585. [12] F. Geoola, Y. Kashti, A. Levi, R. Brichman, Polym. Degrad. Stab. 80 (2003) 575–578. [13] J.K. Pandey, K.R. Reddy, A.P. Kumar, R.P. Singh, Polym. Degrad. Stab. 88 (2005) 234–250. [14] R. Yang, Analytical Methods for Polymer Characterization, CRC Press, New York, 2018. [15] B. Fayolle, L. Audouin, J. Verdu, Polym. Degrad. Stab. 75 (2002) 123–129. [16] I.H. Craig, J.R. White, A.V. Shyichuk, I. Syrotynska, Polym. Eng. Sci. 45 (2005) 579–587. [17] R. Bernstein, D.K. Derzon, K.T. Gillen, Polym. Degrad. Stab. 88 (2005) 480–488. [18] B. Laycock, M. Nikolic, J.M. Colwell, E. Gauthier, P. Halley, S. Bottle, G. George, Prog. Polym. Sci. 71 (2017) 144–189. [19] S.P. Lyu, J. Schley, B. Loy, D. Lind, C. Hobot, R. Sparer, Biomacromolecules 8 (2007) 2301–2310. [20] H.L. Qin, Z.G. Zhang, M. Feng, F.L. Gong, S.M. Zhang, M.S. Yang, J. Polym. Sci. B Polym. Phys. 42 (2004) 3006–3012. [21] X.C. Du, X.L. Xu, X.H. Liu, J.H. Yang, Y. Wang, X.L. Gao, Polym. Degrad. Stab. 123 (2016) 94–104. [22] L. Guadagno, C. Naddeo, M. Raimondo, G. Gorrasi, V. Vittoria, Polym. Degrad. Stab. 95 (2010) 1614–1626. [23] S. Morlat-Therias, E. Fanton, J.-L. Gardette, N.T. Dintcheva, F.P. La Mantia, V. Malatesta, Polym. Degrad. Stab. 93 (2008) 1776–1780.

I. Polymer science

C H A P T E R

8

Polymer processing and rheology Wenling Zhanga, Jingsi Chena, Hongbo Zeng Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Polymer products have been utilized for a variety of applications in our daily lives, as well as for diverse industrial applications. One of the important reasons for the growing applications of polymers in recent decades is the facile strategies to convert them into complex shapes. For the purpose of the manufacturing desired polymer products, from the production of raw materials to the preparation of finished products, many processing methods are involved, including mixing, extrusion, molding, calendering, and coating. The success of the polymer processing techniques depends upon controlling the rheological behaviors of the polymer melts/suspensions. The shear flow behaviors can be controlled by manipulating several polymer parameters like molecular weight, molecular weight distribution and chain branching, using modifiers like fillers, plasticizers and other polymers and adjusting the processing variables like temperature, shear, and pressure. Thus, the successful processing of polymeric materials requires a thorough understanding of their rheological behavior, and the characterization of the polymer melts/suspensions by relevant rheometry is critical for the control of polymer processing. In this chapter, we describe briefly some of the typical polymer processing techniques, typical rheological phenomena of polymer solutions and suspensions, and the relationships between polymer rheology and polymer processing. The introduction of rheometry and fundamentals of the relevant rheological concepts are also provided.

8.1 Polymer processing 8.1.1 Mixing 8.1.1.1 Polymer additives Since pristine polymers generally lack desirable properties for the wide range of commercial applications, polymer additives have been extensively employed to tune the properties a

W. Zhang and J. Chen contributed equally to this chapter.

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00008-X

149

# 2020 Elsevier Inc. All rights reserved.

150

8. Polymer processing and rheology

of the macromolecules, enhancing both the processability and mechanical performances of the polymers to meet the requirements of diverse applications [1]. Polymer additives are usually uniformly dispersed in the polymer matrix with a concentration in the range of 0.1–1 wt% [2], which improves several features of the material such as stiffness, toughness, durability, clarity, etc., leading to high-quality products. The most commonly used polymer additives are stabilizers, plasticizers, impact modifiers, and flame retardants. Stabilizers. Weathering plays a critical role in the service life of polymeric materials, especially when the products are utilized under outdoor conditions. Upon exposure to heat and ultraviolet (UV) light, the initiated free radicals tend to react with oxygen to form unstable peroxy radicals, which can disrupt CdH bonds in polymer chains and result in chain session or crosslinking [3]. Therefore, the polymeric materials will experience severe loss of physical and mechanical properties. The addition of antioxidants can consume the free radicals and slow down the oxidation process, and the incorporation of UV absorbers as well as quenchers either dissipate light energy or deactivate photosensitive groups, protecting the polymers against degradation [4]. Plasticizers. Plasticizers are introduced into polymers to facilitate their processability. The intermolecular interactions formed between plasticizers and polymers can increase the distance between the original polymer chains and reduce their interactions, increasing the chain mobility, and lowering the viscosity. The mechanical properties (e.g., strength, stiffness, and toughness) of the products are also altered with the addition of plasticizers [5]. Impact modifiers. A large number of plastics are brittle below their glass transition temperatures (Tg) and can be easily damaged upon stress at small deformations, such as polyvinyl chloride and polystyrene. Therefore, impact modifiers, which are generally rubbery polymers with low Tg and compatible with the host polymers, are incorporated to dissipate impact energy and induce plastic deformation. Typical impact modifiers are butadiene-modifiers, acrylic modifiers, and elastomers [6]. Flame retardants. As a kind of organic materials, lots of polymers are flammable in the presence of heat and oxygen, which has been considered as a serious hazard to human life and health. The addition of flame retardants, including halogenated, phosphorus, inorganic, and bio-based compounds, can either increase the ignition temperature or limit the spread of flame, effectively preventing the polymers from combustion [7]. 8.1.1.2 Mixing mechanics In polymer processing, the formability of the materials and the quality of the final products are highly dependent on mixing operations. The objective of mixing is to reduce the inhomogeneity of the raw materials, by either dispersing the minor components (e.g., solid particles or liquid droplets) into the continuous major phase or blending two or more polymers at different ratios [8]. The efficiency of mixing lies in the properties of raw materials, mixing procedures, and mixing equipment. There are two major mixing mechanisms: distributive mixing and dispersive mixing. Distributive mixing usually refers to the mixing of compatible liquids, where the interfacial area between different phases is enhanced by imposing large deformations to the system, and the mixing quality is determined by the spatial distribution of the minor component throughout the matrix. Dispersive mixing occurs when blending two immiscible fluids or dispersing agglomerates of solid particles in a fluid, which is achieved by the breakup of the fluid droplets

I. Polymer science

8.1 Polymer processing

151

or solid clusters via mechanical stresses. The mixing quality is usually characterized by the size of the minor component [9]. The schematics and the relationship between distributive and dispersive mixing are presented in Fig. 8.1. The mixing operations in polymer processing generally combine both distributive and dispersive processes, and the mixing of the raw materials usually takes place in the laminar regime due to the high viscosity of polymer melts, which involves shear, elongation, and reorientation of the phases [10]. When adjacent layers of dissimilar materials are stretched and folded under large deformation, the thickness of the lamella is reduced and the interfacial area between the phases is enhanced, which is known as baker’s transformation. Simultaneously, the shear stress generated due to the relative motion between different phases at small openings or slits can break the stretched-out liquids or solid aggregates into small segments, leading to desired homogenization. 8.1.1.3 Mixing devices Internal batch mixers are the most commonly utilized apparatus in mixing operations, especially for the dispersion of solid particles in polymer matrices. The typical design of an internal mixer is shown in Fig. 8.2, mainly consisting of an enclosed mixing chamber, two spiral-shaped rotors, a hopper for feeding and a door at the bottom to discharge the mixed compound. The two rotors are the key component of the equipment, which are driven by an electric motor and rotate in the operate directions at slightly different speeds [11]. Thus, complex flow can be generated in the fluid of raw materials with high localized shear stress and large shear deformation, where the mixing occurs between the rotors and the chamber wall. External cooling or heating can be realized by circulating water or stream through the hollow rotors and the chamber. The mixing quality and efficiency are dependent on several parameters. The rotor speed directly affects the total shear strain and strain rate of the fluids, but the maximum speed is

FIG. 8.1 Schematic illustration of distributive and dispersive mixing.

I. Polymer science

152

8. Polymer processing and rheology

FIG. 8.2 Schematic of an internal batch mixer.

limited by the heat generated during the operation. The gap between the rotors correlates to the minimum shear stress generated within the mixture, which should beyond a critical value to ensure the rupture of the dispersed droplets or aggregates. Temperature control, including the heating and cooling rates as well as the duration of each temperature step, also plays an important role. Moreover, high pressure exerted on the fluid can reduce the voids within the fluid and increase the shear stress during mixing [8]. Continuous mixers combine the mixing process of raw materials with other polymer processing operations and have emerged as replacements for internal batch mixers. For example, single- and twin-screw extruders usually contain special screw channels for mixing, which occurs before the melts are pumped out into the die. In a single-screw extruder, when the polymer melt travels down through the channel, the screw flights serve as the stirring mechanism and spiraling flows are generated due to the circulation of the fluid. The mixing quality is largely determined by the number of changes in the flow direction, which facilitates the division, combination, and reorientation of the flows. Introducing pins in the screw channel can efficiently disturb the flow of the fluids, especially for high-viscosity polymer melts. Homogenization of relatively low-viscosity fluids is facilitated by special screw designs such as Saxton, Dulmage, and pineapple mixing sections depicted in Fig. 8.3 [12]. Twin-screw extruders are also employed for mixing operations, and the mixing efficiency is mainly regulated by screw speed, temperature as well as screw geometry. In general, a co-rotating configuration can provide high pumping efficiency, and counter-rotating configuration results in high stress but the accompanied high-temperature pulse might be detrimental to the processing. Narrow kneading blocks on the screw promote the distributive mixing of materials around the blocks, whereas wide kneading blocks allow the fluid to enter the gap between the flight and the barrel wall, facilitating dispersive mixing. Therefore, to choose an appropriate mixing section, various factors should be taken into consideration,

I. Polymer science

8.1 Polymer processing

153

FIG. 8.3 Typical designs of mixing sections.

including the mixing type, screw length, temperature sensitivity of polymers, and shear sensitivity of polymers [13].

8.1.2 Extrusion 8.1.2.1 Extrusion process Extrusion can directly convert raw materials into finished forms. It is prevalent in producing primary products and intermediates subjected to further processing, owing to its capability to generate highly uniform polymer melts at high rates. The first step of extrusion is to feed the raw materials from a hopper and then the solids are moved through a heated barrel by a screw. Once the polymers are melted and mixed homogenously at a proper temperature, the viscous fluid is pumped out through a shaping die into a continuous, two-dimensional product with different shapes, including filaments, tubes, films, plates, and other cross-section profiles [14]. After cooling, the hardened product is cut into the desired length according to the final dimension. Extrusion has been mainly exploited for the production of thermoplastics because the melted polymers are viscous enough to be pushed out and the materials can completely solidify and maintain their shapes upon cooling. In some circumstances, special formulations are developed to maintain the strength of the polymer melts. Extrusion is a highly efficient processing method for manufacturing products with a constant cross-section, ranging from simple to moderately complex shapes. It has found wide applications in cooking, fabricating sewer pipes, paintbrushes, window components and is also used for coating electrical wires. However, due to the relatively low pressure involved in this strategy, it is difficult to yield high-quality surfaces and the products often require post-processing [15]. 8.1.2.2 Single-screw extruder Single-screw extruder is one of the most commonly utilized apparatus in the polymer industry. It can also be incorporated in diverse other processing methods such as injection molding, blow molding, and coating. As illustrated in Fig. 8.4, a single-screw extruder consists of a cylindrical barrel, whose outer wall is attached with several band heaters and

I. Polymer science

154

8. Polymer processing and rheology

FIG. 8.4 Schematic illustration of a single-screw extruder.

thermocouples for temperature control. The key component of the extruder is the screw fitted in the cylinder. The geometry of the screw is dependent on the properties of the polymers and the thermal condition, and the flights of the screw are usually coated by a layer of alloy to reduce wear. The energy required for polymer melting is mainly contributed by the rotation of the screw, and the barrel temperature is maintained by the heating/cooling system. The plasticizing process in an extruder is mainly divided into three zones: solid conveying, melting, and metering [16]. Solid conveying. In this zone, the polymer pellets are fed to the extruder through a hopper and transported to the screw channel, where they are compressed by the feeding forces into a fully compacted solid bed and moved down the channel. The compression and transport of the solid pellets are driven by the relative friction of the polymer against the barrel and the screw. When the friction at the barrel wall exceeds that at the screw surface, the solid plug will not rotate with the screw and tend to move along the axial direction. Therefore, the solid conveying can be optimized by making the polymer slip on the screw while sticking to the barrel. Melting. The polymers start to melt once the temperature of the screw and barrel surfaces is beyond the melting point. The melting occurs at the edge of the solid bed. Then a fraction of melt film is dragged by the relative motion between the solid and the barrel surface to form a melt pool. The motion of the screw flight results in circulating flow in the melt pool and the melt pressure pushes the solid bed against the leading fight to maintain the continuous melting by squeezing the melt film. The length of the melting zone depends on the polymer properties, screw geometry, and processing conditions. Metering. The function of the metering zone is to the pump the polymer melts out of the screw. Sufficient pressure is required at the screw head to drive the material through the rest parts of the system, including the beaker plate, adapter and extrusion die. The relative motion of the screw to the barrel creates a drag flow across the screw channel, which contributes to the complex flow pattern of the melt and generates the pressure to pump the fluid. The pumping capacity of the equipment is determined by the diameter of the screw.

I. Polymer science

8.1 Polymer processing

155

8.1.2.3 Twin-screw extruder Twin-screw extruders have been developed mainly to facilitate the mixing/compounding processes and are also utilized as polymerization reactors. The primary feature of the twin-screw extruders is that they can promote the uniform distribution of polymer additives without imposing high mechanical or thermal stress to the material, which is particularly beneficial for the production of polymers with solid fillers such as mineral, glass and carbon fibers. This equipment is also employed for compounding of polymer blends consisting of polymers with significantly different melting points and viscosities. Besides, due to the short retention time, the twin-screw extruders show advantages when possessing temperaturesensitive materials [17]. The two parallel screw shafts are able to rotate in the same direction or opposite directions, so the twin-screw extruders are generally categorized into co-rotating and counter-rotating systems. In each model, the distance between the screw shafts can be modulated, ranging from intermeshing to non-intermeshing. Different configurations of the screws are displayed in Fig. 8.5, through which the mixing efficiency, output rate, and heat generation can be easily regulated [18]. High pumping efficiency is achieved in co-rotating extruders because of the double transport action of two screws, and high-speed co-rotating systems are widely used for compounding resin with different kinds of additives. The counter-rotating arrangement permits high stresses due to the calendaring action between the screws, which is efficient in dispersing pigments and lubricants. This technique is commonly applied for the processing of temperature-sensitive polyvinyl chloride (PVC). The intermeshing configuration is also selfcleaning, and reactive extrusion involving chemical reactions (e.g., crosslinking, functionalization, condensation) is usually conducted in non-intermeshing systems [19]. The polymer flow patterns in intermeshing co-rotating and counter-rotating twin-screw extruders are shown in Fig. 8.6. The co-rotating configuration results in both high- and low-pressure regions of the fluid when the polymer passes from one screw to the other one, whereas the counter-rotating arrangement generates a high-pressure region at the nip where polymer enters the screw and a low-pressure region with polymer coming out.

FIG. 8.5 Different configurations of screws in twin-screw extruders.

I. Polymer science

156

8. Polymer processing and rheology

FIG. 8.6 Schematic diagrams of polymer flow patterns in co-rotating and counter-rotating screws.

8.1.2.4 Extrusion dies The last step of extrusion processing is to shape the compound melt into the final shape by an extrusion die attached to the end of the extruder. To ensure the uniformity of the product, the mass flow of the polymer must be uniform across the exit plane. Therefore, a breaker plate is placed between the screw head and an adapter connected to the die [20]. Owing to the plenty of holes distributed on the breaker plate, the polymer melt exiting the screw head is forced to flow in straight lines along the axis of the extruder, and the rotation of the fluid is inhibited. Meanwhile, the screens located in the breaker plate can filter the contaminants from the polymer melt and assist thermal homogeneity. The extrusion die should able to generate profiles with constant wall thickness and avoid thick sections as well as hollow sections. When the polymer leaves the extrusion die, the crosssection of the product tends to expand due to the viscoelastic swelling. To achieve desired dimensions of the final profile, the polymer melts are usually cooled during shaping.

8.1.3 Molding 8.1.3.1 Injection molding Process. Injection molding is a primary method to transform plastic materials into complex shapes with mass production. It can be applied for most thermoplastics with tailored rheology and some thermosets showing proper shear flow. The injection molding machine is composed of two major parts: an injection unit and a clamp unit. The injection unit is generally a reciprocating single-screw extruder that prepares the polymer melt and transfers the compound into the mold. In the clamp unit, the mold is held tightly against the pressure of injection, opened for demolding, and closed for the next shot. The equipment is mainly driven by hydraulic power with an electric motor and a hydraulic pump. The use of hydraulic systems

I. Polymer science

8.1 Polymer processing

157

FIG. 8.7 Typical events during an injection molding cycle.

allows hydraulic oil flow through the pipes, generating a maximum pressure around 14 MPa in the absence of complicated mechanical transfer elements [21]. Injection molding in a repetitive process and the sequence of events that occur during an injecting molding cycle is illustrated in Fig. 8.7. Similar to a single-screw extruder, the raw materials are fed in a barrel and plasticized into a polymer melt by the rotation of screw and external heating. When the viscosity of the polymer is reduced to a point, the melt is enforced to flow into a closed mold under high pressure until the cavity is filled. After injection, the pressure is maintained for a certain time by holding the screw. As the polymer tends to shrink after entering the relatively cool mold, some additional material is injected during the packing stage to compensate for the contraction. Then the screw retracts and the next shot of material is fed to the front of the screw. After the molded polymer is cooled and sufficiently solidified, the mold opens for the ejection of the product. Once the mold closes again, another cycle begins with the injection of a new shot of polymer [22]. The total cycle time is dominated by the time required for cooling the part. Although rapid cooling can reduce the cycle time, high-quality products are usually generated in relatively hot molds. The optimization of cycle time and quality of moldings are realized by the control system. Injection molding allows high-yield production of complex products with precise dimensions, where the three-dimensional shapes are endowed by the combination of various cavities. The resulting parts can range from flexible rubbers to rigid plastics, with highly reproducible details on the surfaces. The major limitation of injection molding is high pressure. Besides, stock temperature is required to be above the glass transition temperature of the polymer to ensure the flow, which possibly results in materials degradation due to the exposure to heat. Mold design. As high injection pressures are used to overcome the high viscosity of the plastics, all parts of the mold are made from strong materials, typically tool steels. A runner system, consisting of spruce, runners, and gates, is employed to direct the melt into the cavity of the mold. When the machine nozzle contacts the mold, the flow passes the spruce and the channels of the runners, distributing materials into different cavities through small openings called gates. To reduce the mechanical stress on the material, the geometry of the running system should minimize the flow resistance, which is affected by the cavity dimension, material properties, and processing conditions. After each ejection of the product, the material in

I. Polymer science

158

8. Polymer processing and rheology

the spruce and runners is separated from the product and fed back into the injection unit. The mold cavity is the key component to ensure the dimensions of the final part, but it should be noted that shrinkage of the plastics after cooling always leads to smaller moldings than the cavities. To guarantee the surface quality of the product, the cavities need to be polished, hardened, and generally chrome-plated [23]. The cooling system is also a critical feature of mold design. Although rapid cooling can shorten the molding cycle and enhance productivity, uniform cooling benefits the product quality by minimizing internal stresses, voids, differential shrinkage, and mold release problems. Quality control. The mechanical properties and performances of the final product are largely dependent on the manufacturing process and influenced by a variety of factors such as polymer properties during molding, product design, injection mold configuration, process conditions, and machine operations. For instance, the viscoelastic parameters of polymer melts and mold design affect the melt distribution in the mold; the shrinkage of the material throughout the cavity is impacted by packing, crystallization of polymer, mold geometry, and cooling speed; the microstructure and morphology of the material are determined by the thermomechanical history of the polymer experienced during processing. Computer modeling is an effective approach to provide an overall evaluation of the interrelated building blocks [24]. 8.1.3.2 Compression molding Process. Compression molding has been used as a common possessing technique for a long time due to its simplicity. This method is originally utilized for the fabrication of thermoset polymers and rubber compounds, and nowadays it is primarily employed in the automotive industry to produce large, thin, and strong parts. The basic process of compression molding is presented in Fig. 8.8. First, the desired amount of raw material called charge is placed inside the lower part of the heated mold, which usually covers about half of the mold surface area. The position of the charge in the mold plays an important role in the knit line formation and the final void content. Then the upper half of the mold quickly moves to the top of the charge and compresses the material slowly. During mold closure, the high pressure forces the polymer to deform and fill the mold cavity. After the squeezed charge fills the cavity completely, the pressure is maintained for a while with mold kept closed, during which the material is cured and consolidated. At last, the solidified part is ejected from the mold and cooled down outside the mold. Generally, the molding pressure is in the order of tens of MPa with processing temperature ranging from 130°C to 160°C [25].

FIG. 8.8 Compression molding process.

I. Polymer science

8.1 Polymer processing

159

Similar to injection molds, the compression molds are also machined from hardened tool steels. A high degree of hardness and polish are required to withstand the abrasion of raw materials and obtain a good surface finish. Because the polymers are generally processed below their melting temperatures, the production rate is quite high with a typical cycle time ranging from 1 to 3 min based on the size and thickness of the products. On the other hand, the limited flow of the raw materials restricts the geometric complexity of the finished parts, and imperfections such as pitting and waviness may appear on the surface [26]. Sheet molding compound (SMC). The most common material for compression molding is sheet molding compound (SMC), which are glass fiber reinforced plastics and have found principle applications in the transportation industry and construction. SMC is produced by sandwiching chopped glass fibers (usually of 25 mm) between two plastic carrier films on which specific resin pastes are spread. The reinforcing fibers can be between 10% and 60% volume fraction of the compound and are randomly oriented. The carrier films are only used to prevent the auto-adhesion of the resins and removed before the compression process [27]. During molding, the glass fibers in the charges can flow in the polymer matrix without damage and undergo rearrangements due to the applied force, resulting in preferred orientation and the anisotropy of the product. Compared to structural components made from other materials such as metal, the high strength and toughness, lightweight, and convenient manufacturing process suggest the advantages of SMC. 8.1.3.3 Blow molding Blow molding is most widely used to produce hollow plastic components, especially plastic bottles and containers, where uniform thickness distribution is not required. During the molding process, the tube of the molten polymer is expanded by airflow and then solidify during the cooling of the melt, so a broad range of thermoplastics can be employed and polyethylene (PE), polypropylene (PP), polyvinylchloride (PVC), polyethylene terephthalate (PET) are the most popular materials. As hydrophobic polymers, PE and PP show good barrier property for water but have a poor capacity to stop the diffusion of oxygen. Whereas PVC and PET can act as barrier materials for oxygen but they are less effective regarding moisture. Based on the specific applications, the polymers can be either used individually or combined to form layered products [28]. Extrusion blow molding. Large and moderately complex hollow parts are suitable to be manufactured by extrusion blow molding. As indicated in Fig. 8.9, a molten polymer tube called parison is extruded vertically from a die head into an open mold. The size of the parison is controlled by the head and the melt tends to swell and sag when it comes out of the extrusion die. Therefore, the viscous material is required to be strong enough to hold the shape and possess constant swell and sag properties. The extrusion process should also be fast. When the parison reaches the desired length, the mold is closed and the bottom of the parison is pinched. Then compressed air is fed from the head to inflate the material to fill the cavity of the mold. For a simple parison with homogeneous wall thickness, after blowing, the sections with large diameters will show a thin wall while the sections with small diameters display a thick wall. A parison of variable thickness along its length can be generated by certain modifications of the die, improving the wall thickness distribution and strength of the final part [29]. When the polymer contacts the mold surface, it starts to cool and solidify under the air pressure, which takes up the largest portion of the cycle time. The last step is to open

I. Polymer science

160

8. Polymer processing and rheology

FIG. 8.9 Extrusion blow molding.

the mold and the finished part is ejected. It is noted that extrusion blow molding is a one-wall process and depends on the extension of the material, so it is difficult to realize exquisite control of the wall thickness, especially in areas with extensive stretching. Injection blow molding. As a hybrid fabrication process, injection blow molding combines features of injection molding and blow molding, which provides better control of the shape and wall thickness compared to extrusion blow molding. It is utilized to produce small components with details and precision. The primary difference between these two methods is the parison formation. To prevent the effect of gravity and swelling on the extruded parison, in injection blow molding, the polymer is first injected into a mold with a core, and the parison is formed around the core with both well-defined inner and outer diameters and the finished bottle threads (Fig. 8.10), which is called preform. After the material is slightly cooled, the preform is transferred to the blow mold with the core, where the air is injected into the core to blow the parison into the final shape. Therefore, no trim of the part is needed, and dimensional control of the neck and the threaded closure is improved. Injection stretch blow molding. For soft-drink bottles containing carbonated products, they are required to possess high modulus to withstand the pressurization as well as barrier property to prevent the loss of carbon oxide. The bottles are usually made from PET and fabricated via injection stretch blow molding. Similar to injection blow molding, the tube-shaped preform is prepared in an injection mold. However, the raw material contains infrared absorbing

FIG. 8.10

Injection blow molding.

I. Polymer science

8.1 Polymer processing

161

FIG. 8.11 Injection stretch blow molding.

agents and the preform is then heated to a temperature above its glass transition temperature before further processing, as shown in Fig. 8.11. Following this step, it is stretched along the axial direction by a rod and expanded along the radial direction by blowing. Therefore, the ordered regions in PET are biaxially oriented, which significantly enhance the barrier properties of the material and improves the transparency as well as mechanical properties (e.g., strength and toughness) of the bottle [30]. 8.1.3.4 Rotational molding Process. Rotational molding is a unique process for manufacturing sealed hollow plastic products. It shows special advantages for the production of large parts (>2 m3) in one piece, such as tanks, buoys, kayaks, toys, etc., because the rotational mold can easily create a seamless and large cavity. Almost all the raw materials used for processing are thermoplastics and over 85% of them are PE. Other polymers including PP, PVC, polycarbonate, and nylon make up the rest of the world’s consumption [31]. Each cycle of rotational molding consists of four basic steps, namely charging, healing, cooling, and demolding. As shown in Fig. 8.12, the rotational molds fixed on the mechanical arms are driven by the motors to enter three zones during processing, where charging and demolding takes place at the same position. First, the desired amount of powder, granular, or viscous liquid is introduced into the bottom of the mold, and the initial amount of the material should ensure good coverage of the mold surface. Usually, two or more molds are utilized to balance the load on the system. When the mold enters the oven, it rotates independently in two axes at low speeds and the polymer starts to melt and stick to the heated wall. During the heating step, bubbles are formed in the molten polymer and removed by decreasing the melt viscosity and surface tension. This densification process facilitates mechanical enhancement. Then the mold moves to the cooling station with continuous rotation. The cooling system consists both of air blowers and water spray to provide different cooling rates, which determines the crystalline structure of the material. After solidification, the plastic shrinks, and the product is removed from the mold. Compared to blowing molding and injection molding, the major advantage of rotational molding is its low-cost mold and the anisotropic products with low residual stresses.

I. Polymer science

162

FIG. 8.12

8. Polymer processing and rheology

Rotational molding process.

Therefore, the parts can maintain good surface detail and sharp features. However, this processing method suffers from relatively long cycle time and the products may contain surface defects. Quality control. Rotational molding is not dependent on the centrifugal force because the rotation rates are slow. In fact, the molten polymer mainly locates at the bottom of the mold forming a melt pool, and different parts of the mold surface sequentially come down for coating. Generally, the speed ratio of the major axis and the minor axis is around 4, which offers a uniform coating of the inside surface [32]. During the heating process, bubbles are generated and slowly diminish with the increase in temperature. The quality of the product can be indicated by the bubble density through the thickness. Too many bubbles distributed through the cross-section indicate the part is undercooked. On the contrary, if no bubbles are observed, the part is most likely overcooked. A small number of bubbles near the inner surface suggest a proper heating time [33]. The cooling of the rotational mold is only from the outer surface. Slow cooling (air blowing) of the material can effectively increase the strength but impair the toughness; whereas rapid cooling (water spray) leads to good resistance to impact loading but sacrifices the stiffness.

8.1.4 Calendering 8.1.4.1 Process Calendering is mainly applied to rubbers and flexible PVC for the production of sheets and webs with different thicknesses. It is also used to coat certain substrates with thin films as well as texture or embossing surfaces. Compared to other film-production processes such as extrusion, calendering provides a shorter residence time of the melts, which reduces the use of

I. Polymer science

8.1 Polymer processing

163

FIG. 8.13 Typical calendering process.

stabilizers and is cost-saving. The typical process of calendering is depicted in Fig. 8.13. Before calendering, the raw materials are melt and mixed in an internal batch mixer, two-roll mill, or extruder, and then the melt is transferred into a calender that consists of two or more rotating metal rolls. The adjacent pairs of rolls rotate in the opposite directions, where the melt enters the nip of the rolls and is squeezed into sheets or processed into desired products. The feeding rate is controlled by the first two rolls and the subsequent rolls are employed to modulate the sheet thickness. The rolls are allowed to rotate at constant or variable speeds controlled by the drivers to meet the processing requirements of the materials. As the materials are generally of high viscosity, the force generated between the rolls is generally in the range of 2000 to 10,000 N/cm, which is sufficient to result in the bend of the rolls and uneven sheet thickness. To compensate roll bending, the rolls can be placed in a slightly crossed pattern and roll profiles can be modulated with positive or negative roll crown [34]. After passing through the calender, the sheet is further embossed to create a surface structure and cooled from both sides by a series of chilling rolls. At the end of processing, it is collected by a winder. 8.1.4.2 Arrangements of rolls Calenders are generally differentiated by the number of rolls as well as their arrangements, which are highly dependent on the property of processed materials. Most calender systems consist of four rolls and the typical arrangements are shown in Fig. 8.14. In I-type calenders, the rolls are perpendicularly stacked, which takes up the minimum floor space. However, this simple design is rarely used because at each nip the generated force tends to push the rollers away from the nip, resulting in an unstable structure. F-type calenders offer a good compromise with the first pair of rolls being horizontal. The materials can be easily supplied between the feeding gap and then passing through the subsequent working gaps. This kind of calenders is frequency applied to produce flexible vinyl films with a thickness between 0.1 and

I. Polymer science

164

FIG. 8.14

8. Polymer processing and rheology

Typical arrangements of rolls.

2 mm. L-type calenders are similar to the F-type calenders, but the feeding gap is provided by the bottom rolls. They are suitable to process rigid vinyl products. In Z-type calenders, each pair of rolls is perpendicular to the adjacent ones, so the bending of the rolls due to the pressure at the nip will have no effect on other rolls and it can improve the thickness accuracy [35].

8.1.5 Coating 8.1.5.1 Fluid coating process Fluid coating is to apply one or several layers of polymeric materials in the form of paste or liquid on a moving substrate to impart new characteristics. The substrate can be any rigid or flexible materials, including metal, inorganic, or organic wires/films/sheets. In a coating process, first, the substrate material, e.g. a flexible web, is unwound and enters the equipment under uniform tension. Then a liquid film is applied on the surface of the substrate by a coating head (e.g., knife, roll, slot) and the product is transferred into a drying oven, where the solvents are evaporated to yield a solidified and cured polymer film. To prevent the formation of crack, the solvent evaporation rate needs to be carefully controlled and it is usually realized by dividing the oven into several regions with successively increased temperature. Continuous circulation of fresh air is required in the oven to avoid the explosion of volatiles [36]. After coating, the layered product passes through cooling drums and then is rolled up for storage. The typical fluid coating methods are presented in Fig. 8.15. 8.1.5.2 Methods Knife coating is one of the most developed spread coating methods. A flexible and dry sheet is supplied by the rolls, over which a knife or blade is fixed. The position of the knife can be over the air, over the blanket, or over the roll, where the over-roll configuration is most commonly used. The direction of the knife to the substrate can be either normal or at a certain angle. The coating material is poured in front of the knife, forming a pool over the entire width. With the forward motion of the substrate, a rotatory motion occurs in the viscous material and the thickness of the coating is approximately half of the gap between the knife edge and the substrate. The coating rate is mainly determined by the evaporation rate of the solvent.

I. Polymer science

165

8.2 Polymer rheology

FIG. 8.15 Schematic representations of typical coating methods.

Roll coating feeds the coating material and the substrate at the nip between two rotating rolls. The coating material is of low viscosity and picked up by the engraved applicator roll which is submerged in the pool. When the substrate moves through the gap with the rotation of the rolls, the coating material is transferred from the applicator roll to one side of the substrate. The coating thickness can be as low as micrometers and is modulated by the viscosity of liquid as well as the nip pressure. Dip coating is a popular method to create thin-film coatings on both sides of the substrate. First, the substrate is immersed in a tank of the coating material for a certain time and moves at a constant speed. When the substrate is pulled up, the excess material on the surface is removed by passing through a pair of rolls with the deposition of a thin layer. Because the flexible substrate is not stressed during the processing, no damage or distortion is expected in the final products. Wire coating is used to produce polymer resin-protected conductive metal wires. During the coating process, the wire is pulled through an extrusion die, where the polymer melt is deposited on the surface of the wire by the drag flow. The thickness of the coating depends on the moving speed and the geometry of the die. To achieve high coating uniformity, polymer melt recirculation should be avoided in the die.

8.2 Polymer rheology 8.2.1 Relationship between polymer rheology and polymer processing The term “rheology” was first coined by Professor Eugene Bingham of Lafayette College, Indiana in 1920s, which originates from the Greek word “rheos,” meaning “everything flows upon time interval” [37, 38]. Thus, rheology is defined as the science of studying the flow and

I. Polymer science

166

8. Polymer processing and rheology

deformation of matter induced by applied shear forces. From the scope of rheology, all forms of shear behaviors, including the flow of ideal viscous liquids and the deformation of classical elastic solids, can be described by their response to external stresses. These rheological characteristics are highly dependent on the deformation process with respect to time. The time scale of the deformation process in rheology is quantified by the introduction of “Deborah number,” which was first proposed by Professor Marcus Reiner, one of the pioneers of the modern rheology [37, 39]. The Deborah number is a useful parameter for estimating the viscoelastic effects during flow: De ¼ λ=T,

(8.1)

where λ stands for the relaxation time and T is the experimental time of the relevant deformation process. A low value of Deborah number demonstrates a liquid-like behavior and a Deborah number of infinite defines an ideal elastic solid. Here is a story about the definition of the Deborah number: in the QWERTY keyboard, the letters “R” and “T” are next to each other, hence, the term “rheology” has been often incorrect to “theology.” Coincidentally, in Chapter 5 of the book “Judges in the Old Testament,” Deborah has claimed that, “The mountains flowed before the Lord…” “everything flows if you wait long enough, even the mountains.” One consequence of the above reference, Professor M. Reiner named the dimensionless group on the Deborah number (De). Fig. 8.16 is the scenery of the Horsethief Canyon, Drumheller located in the Province of Alberta, Canada. The Deborah number was first pointed out in Professor M. Reiner’s article titled “The Deborah Number” issued of Physics Today (in the January 1964). Song of Deborah Judges 5:5—“The mountains flowed before the Lord.”

Polymer rheology is literally the science that studies the deformation and flow of polymers [40, 41]. A thorough understanding of polymer rheology is essential to effective material FIG. 8.16 Horsethief Canyon, Drumheller, Alberta, Canada. Photo taken by Chen Yang.

I. Polymer science

8.2 Polymer rheology

167

design and processing techniques. For practical applications, most of the polymers show “viscoelastic” behavior during flow, indicating that they exhibit viscous behavior and elastic behavior simultaneously. The shear flow behaviors of most polymer melts and suspensions can be manipulated via controlling the polymer parameters (e.g., molecular weight Mw, molecular weight distribution, chain branching, etc.) and varying the rheological factors such as temperature, shear, and pressure. This section discusses the typical rheological phenomena of polymer melts and solutions. The introduction of rheometry will also be presented in Section 8.3.

8.2.2 Non-Newtonian flow Polymer melts and solutions are highly viscous liquids, possessing non-Newtonian and viscoelastic natures. The flow behaviors of molten polymers or solutions are becoming increasingly relevant to their engineering processing techniques. Before we discuss the nonNewtonian behaviour in polymer solution and suspension, it is important to first emphasize what Newtonian behavior is. Through Newton’s postulate, the flow curve of an ideal liquid

FIG. 8.17 Typical flow behaviors of Newtonian and non-Newtonian liquids.

I. Polymer science

168

8. Polymer processing and rheology

(curve ① in Fig. 8.17) should be a straight line and the shear viscosity (η), which is obtained via dividing the shear stress (τ) by shear rate (_γ ), remains constant and independent of shear rate [38]. All liquids exhibiting these behaviors are called “Newtonian liquids,” such as water, glycerine, alcohol, molasses, mineral oils, bitumen, etc. All other liquids showing deviation from the “ideal” flow behaviors are defined as “nonNewtonian liquids” (curves ②③④ in Fig. 8.17) [42]. Many liquids show drastic decrease of viscosity with increase of shear rate (curve ② in Fig. 8.17). The fluids showing decreased viscosity with increase in shear rate are generally called “pseudoplastic or shear-thinning fluids” [43]. Many liquid products exhibit shear-thinning behaviors, such as polymer solutions, polymer melts, and emulsions. On the contrary, another type of substances or liquids shows a dilatant behavior (increasing in viscosity) with the increase of shear rate (curve ③ in Fig. 8.17). However, dilatant liquids are less common, but they can be found in some PVC pastes and crowded filled systems [44]. The plasticity describes the pseudoplastic/shear-thinning liquids featuring a certain yield stress (curve ④ in Fig. 8.17). The pseudoplastic liquids are suspensions that can usually build up intermolecular/interparticle networks through diverse binding forces, including polar forces, van der Waals forces, etc. The mentioned forces endow the fluids resistance against free flow of particles and give the dispersions a solid-like behavior with an infinite viscosity. However, when the external forces surpasses the threshold of the shear stress (denoted as the yield point), the build-up networks rapidly collapse. In consequence, the solid-like suspension turns into a flowing liquid irreversibly. Many industrial products and daily chemical substances possess yield points, such as oil well–drilling muds, lubricating greases, lipstick balms, toothpastes, and natural rubber polymers [45–48].

8.2.3 Viscosity of polymer melts and solutions The varied viscosity of polymers with shear rate is regarded as an important characteristic in many industrial processes [49]. Most polymer processing is shear rate dominated; thus, the viscosity of the polymer melts/solutions is commonly measured using the shear-deformed instruments. For instance, Fig. 8.18 illustrates the simple shear flow behaviors generated in a sliding plate rheometer incorporated with a shear stress transducer [50]. This kind of sliding plate rheometer was first developed by Giacomin et al. at McGill University in 1987 and then commercialized by Interlaken Technology Corporation [51, 52]. When the polymer melts are squeezed between the parallel plates, the shear stress generated in the flow is defined by τ ¼ η_γ ,

(8.2)

where τ is the shear stress (the force F per unit area A required to move the plate, F/A), which is linked to the velocity gradient (i.e., shear rate) γ_ determined by U/h, and η is the viscosity. Eq. (8.2) presented reflects a simple Newtonian Fluid behavior with an intrinsic viscosity. The flow behaviors of molten polymers and solutions are more complex; they are distinguished from Newtonian liquids by their highly viscous, non-Newtonian and viscoelastic natures. Moreover, they exhibit some degree of elastic solid-like properties. Most polymer melts and suspensions are shear-thinning fluids. As mentioned earlier, the shear-thinning effect is the decrease in viscosity with increasing shear rate, which also referred to as pseudoplasticity.

I. Polymer science

8.2 Polymer rheology

169 FIG. 8.18 Configuration of a sliding plate rheometer coupled with a shear stress transducer. Modified based on Figure 3.1, Chapter 3 Melt Rheology, T.A. Osswald, Understanding Polymer Processing: Processes and Governing Equations, Hanser Publishers, 2011.

As shown in Fig. 8.19, the shear thinning or pseudoplastic behaviors of these liquids are not uniform through the whole range of shear rate. At the low shear rate range (①), all molecules or particles maintain an irregularly random orientation owing to the Brownian motion in spite of the initial shear effects. Correspondingly, these pseudoplastic liquids behave similar to Newtonian liquids, and are characterized by a sizable viscosity (equivalent to the tangent of the slope angle α1, tanα1 ¼ η0) which is called “zero shear viscosity, η0.” Then the shear-thinning phenomena occur with the increase in shear rate (②). Some possible reasons are pointed out from the rheological aspects: the molecules or particles are stretched, entangled, reshaped, and reoriented themselves parallel to the direction of the flow. Therefore, the shear-induced alignments lead to particles or molecules to pass through each other more easily, resulting in reduced the bulk viscosity. When the shear rate reaches an extremely high value (③), the equilibrium of perfect orientation will be achieved and the corresponding shear viscosity will eventually approach a constant (η∞) again.

FIG. 8.19 The shear rate dependence of shear-thinning/pseudoplastic liquids. Modified based on Fig. 8, Chapter 2.8 Substances, G. Schramm, A Practical Approach to Rheology and Rheometry, second ed., Gebrueder Haake, Germany, 2000.

I. Polymer science

170

8. Polymer processing and rheology

There are many parameters influencing non-Newtonian behaviors of the polymer melts and suspensions, including temperature, polymer melts and entanglements, molecular weight distribution, chain branching, and effect of additives and pressure [53, 54].

8.2.4 Fitting functions for the flow and viscosity curves Several mathematical model functions have been developed to describe the complex flow curves of the polymer melts and suspensions via varying the fitting parameters. However, none of them can be used for all kinds of the practical flow behaviors. There are enormous fitting functions, among which Newton [55], Ostwald-de Waele [56], Bingham [57], and Herschel/Bulkley models are most commonly used [58]. 8.2.4.1 Model function for ideal viscous flow behavior Newton model [55]. τ ¼ η_γ (see Eq. 8.2) 8.2.4.2 Model function for shear-thinning and shear-thickening flow behavior Ostwald-de Waele equation (Power law model). The power-law model proposed by W. Ostwald jun (in 1925) and A. de Waale (in 1923) is the simplest constitutive model that accurately depicts the shear-thinning region in a given shear rate range [56, 59]. The power-law model can be expressed in terms of two coefficients m and n as: τ ¼ mðTÞ_γ n or η ¼ mðTÞ_γ n1 ,

(8.3)

where m is the consistency index exhibiting the fluidity of the material, and n is the power law index representing the non-Newtonian behavior. For n ¼ 1, the constitutive equation changes to Newtonian’s law with m ¼ η. The consistency index m determinates the temperature dependence of the shear stress or viscosity, and it can be represented as mðTÞ ¼ m0 eaðTT0 Þ :

(8.4)

The simple constitutive model with only two parameters can provide approximately perfect fit for the viscosity points of most polymers melts and suspensions within the given shear rate range [60]. The primary disadvantage of this function model is its invalidity at low shear rates. For this reason, other constitutive equations predicting the correlation between polymer deformation and applied force should be established. 8.2.4.3 Model function for flow curves with a yield point Bingham equation. Many polymer melts and suspensions exhibit various complex nonNewtonian characteristics, including the yielding behavior. Several constitutive equations have been proposed to describe the significant yielding behaviors in detail. Bingham and Green (1919) proposed one of the empirical models to describe the viscoelastic behaviors of fluids with the Bingham yield point τB [57, 61]. τ ¼ τB + η_γ γ_ ¼ 0

τ  τB τ < τB

I. Polymer science

ð8:5Þ

8.3 Rheometry

171

in which τ is the shear stress, τB is the yield point, η is the shear viscosity, and γ_ is the shear rate. Typical Bingham fluids are polymer slurries and emulsions. Experimental records indicate that a critical value of shear stress (τB) must be exceeded to initiate the flow. However, the yield stress value, above which the material begins to move from the state of rest, predicted by Bingham model is very inaccurately; hence, this constitutive model should only be employed for the simple cases. Besides the ideal Bingham model, the Herschel-Bulkley model is widely used to depict the viscoelastic characteristics of fluids. The model is written as τ ¼ τy + Kεm ,

(8.6)

where τy is the yield stress, K and m are empirical parameters, which are adjusted to fit the experimental data. Similar to the Ostwald-de Waele equation (Power law model), m > 1 represents the shear thickening, m < 1 is the shear thinning, and m ¼ 1 denotes the Newtonian flow when stress is over the critical yield stress [62].

8.3 Rheometry A better understanding of the rheological properties of polymers is very important for determining the preferred industrial-scale processing conditions, as well as for achieving the desirable physical/mechanical properties in the finished products [63]. Rheometry is the measuring equipment used to assess these rheological properties. This section gives a general idea of current measuring systems: (1) capillary rheometer, (2) Couette (Concentric cylinder) rheometer, and (3) cone-and-plate rheometer.

8.3.1 Capillary rheometer A capillary viscometer/rheometer is the simplest instrument for measuring the viscosity, which was first reported to investigate the viscosity of water by Hagen and Poiseuille. Its main component is a straight circular tube or capillary. As shown in Fig. 8.20, a well-designed capillary rheometer allows the tested fluid to flow through a straight circular tube or capillary. In this situation, the shear rate varies from maximum at the capillary wall to zero at the center line. Since the pressurized viscometers employ heterogeneous flow, they can only be utilized to characterize steady shear functions/parameters such as shearing viscosity but not elastic properties. Despite its simplicity, the capillary viscometers can provide the most accurate viscosity data via modulating the capillary parameters, such as the capillary lengths, ratios of the capillary length L to its diameter D. The capillary viscometer has been proved to be an efficient measurement tool to inspect the rheological behaviors for industrial applications due to the following features: (1) there are no free surfaces in the test zone in comparison to other typical types of rheometers, including the cone and plate rheometer, which will be discussed later. (2) The capillary rheometers are capable of measuring viscosities at medium and high shear rates, which are important for optimizing the polymer melt processes such as mixing, extrusion, and injection molding. (3) The design is quite simple and basic. With respect to the commercial requirements, it just requires a pressure head at the entrance attaching with a screw- or ram-type extruder at the end. I. Polymer science

172

8. Polymer processing and rheology

FIG. 8.20 Schematic illustration of a capillary rheometer. Modified based on Figure 3.13, Chapter 3.3.2 The Capillary Viscometer, T.A. Osswald, Understanding Polymer Processing: Processes and Governing Equations, Hanser Publishers, 2011 and Figure 6.6, Chapter 6.4 The Capillary Rheometer, T.A. Osswald, and N. Rudolph, Polymer Rheology: Fundamentals and Applications, Hanser Publishers, 2015.

When a Newtonian liquid flows through a capillary tube of radius D and length L with a volume flow rate of Q, the pressure drop (ΔP) and flow rate along the tube can be employed to calculate the viscosity. At the capillary wall, the shear stress is given by the following equation: τW ¼

Dðp0  pL Þ DΔp ¼ 2L 2L

(8.7)

The shear stress in the liquids varies proportional to RΔP/2L in the immediate vicinity of the capillary wall to zero at the center line. In Eq. (8.7), a good capillary rheometer must have a long capillary length to assure fully developed flow and a small capillary diameter. Otherwise, the measured pressure differences profile related to the length of the capillary will exhibit a curvature as a consequence of the entrance effects (Fig. 8.21). End correction e has been determined to correct the entrance effects proposed by Bagley in 1957 [64, 65], the effective shear stress at the wall τW can be calculated as follows: τW ¼

ð p0  pL Þ 2ðL=D + eÞ

(8.8)

The correction e at a specific shear rate can be found by extrapolating the pressure drop as a function of capillary L/D to ΔP¼ 0, as shown in Fig. 8.22. The equation for shear stress can then be written as τγ_ z ¼

γ_ τW D

For apparent or Newtonian liquids, the shear rate at the wall (_γ aw ) is written as I. Polymer science

(8.9)

8.3 Rheometry

173

FIG. 8.21

The entrance effects in a capillary rheometer. Modified based on Figure 3.14, Chapter 3.2.2 The Capillary Viscometer, T.A. Osswald, Understanding Polymer Processing: Processes and Governing Equations, Hanser Publishers, 2011 and Figure 6.7, Chapter 6.4 The Capillary Rheometer, T.A. Osswald, and N. Rudolph, Polymer Rheology: Fundamentals and Applications, Hanser Publishers, 2015.

FIG. 8.22 Bagley plots for two different shear rates. Modified based on Figure 3.15, Chapter 3.2.2 The Capillary Viscometer, T.A. Osswald, Understanding Polymer Processing: Processes and Governing Equations, Hanser Publishers, 2011 and Figure 6.8, Chapter 6.4 The Capillary Rheometer, T.A. Osswald, and N. Rudolph, Polymer Rheology: Fundamentals and Applications, Hanser Publishers, 2015.

γ_ aw ¼

4Q πR3

(8.10)

In addition, as for the shear-thinning fluids, the Weissenberg-Rabinowitsch correction [66, 67] was employed to calculate the true shear rate at the capillary wall:
 1 dð ln QÞ γ_ w ¼ γ_ aw 3 + (8.11) 4 dð lnτÞ Finally, the viscosity can be calculated as follows: ηðγ_ w Þ ¼

τw ¼ γ_ w

πa4 ðdP=dlÞ
 3 1 d lnQ + 8Q 4 4 d ln τw

I. Polymer science

(8.12)

174

8. Polymer processing and rheology

As for the shear-thinning liquids, d(lnQ)/d(lnτw) > 1 and for the power law liquids, the value is equal to 1/n.

8.3.2 Couette (concentric cylinder) rheometer Another rheometer widely used in industry is the concentric cylinder or Couette flow rheometer [68]. When the annular gap between two coaxial cylinders is “narrow” enough, the testing liquids confined in the gap are assumed to be deformed by nearly constant shear rates. The ratio b of the radii of the inner (ri) and outer (ro) cylinders (b ¼ ri/ro) must be greater than 0.97 for the definition of “narrow gap.” As schematically shown in Fig. 8.23, the angular velocity of the inner cylinder is Ωi, then the shear rate γ_ can be given by γ_ ¼

ro Ωi : ro  ri

(8.13)

The shear rate is variable and independent of the rheological properties of the liquids. As for the couple-driven rheometer, the applied couple on the cylinder is assumed to be C, then the shear stress in the testing liquid can be given by C 2πro 2 L

(8.14)

Cðro  ri Þ , 2πro 3 Ωi L

(8.15)

τ¼ Thus, the viscosity can be calculated by η¼

where L is the effective immersed length of the shearing liquid, and it would be obtained through measuring the real immersed length without considering the end effect. However, in some specific cases (such as the liquid containing large particles, the difficulty of achieving parallel alignments, etc.), the ratio of the cylinder radii b tends to be less than 0.97, the shear rate of the liquid at the inner wall is now dependent on the rheological

FIG. 8.23

Schematic diagram of Couette rheometer.

I. Polymer science

8.3 Rheometry

175

properties of the filled liquids. Unlike the cases in narrow gap instrument, the shear stress should be manipulated by 2Ωi
2=n # ri n 1 r0

γ_ i ¼ "

(8.16)

The shear stress at the inner cylinder is given by τ¼

C 2πri 2 L

(8.17)

The viscosity can be finally calculated by

  τi Cn 1  b2=n η¼ ¼ 4πri 2 LΩI γ_ i

(8.18)

The power law index n can be calculated by plotting C versus Ωi in a logarithmiclogarithmic scale:   d log τi   n¼ (8.19) d log Ω

8.3.3 Cone-and-plate rheometer The cone-and-plate rheometer is another rheological instrument widely utilized in polymer industry [69]. As schematically presented in Fig. 8.24, a cone with small vertical angle (θ0) is placed on a horizontal flat plate. The fluid is squeezed in the wedge-like space between a plate and a cone, and the shear stress is identical at any region of the filled liquid. The shear rate in the liquid can be calculated by γ_ ¼ Ω1 =θ0 ,

FIG. 8.24

(8.20)

The cone and plate rheometer. Modified based on Figure 3.16, Chapter 3.2.3 The Cone-and-Plate Rheometer, T.A. Osswald, Understanding Polymer Processing: Processes and Governing Equations, Hanser Publishers, 2011.

I. Polymer science

176

8. Polymer processing and rheology

where Ω1 is the angular velocity of the rotating cone, the shear rate is independent of the rheological properties of the filled liquids. The measurement of shear stress by combining the couple C applied on the cone and radius of the cone a can be given by τ¼

3C : 2πa3

(8.21)

Thus, the corresponding viscosity can be obtained by dividing the pairs of shear stress and shear rate: η¼

3Cθ0 2πa3 Ω1

(8.22)

References [1] C.A. Harper, Handbook of Plastics Technologies: The Complete Guide to Properties and Performance, second ed., McGraw Hill Professional, New York, 2006. [2] T.P. Hunt, Polymer additives: supercritical fluid chromatography, in: Encyclopedia of Separation Science, Elsevier Science Ltd, San Diego, 2000, pp. 3901–3906. [3] R. Gensler, C.J.G. Plummer, H.H. Kausch, E. Kramer, J.R. Pauquet, H. Zweifel, Thermo-oxidative degradation of isotactic polypropylene at high temperatures: phenolic antioxidants versus HAS, Polym. Degrad. Stab. 67 (2) (2000) 195–208. [4] E. Yousif, R. Haddad, Photodegradation and photostabilization of polymers, especially polystyrene, Springerplus 2 (1) (2013) 398. [5] M. Rahman, C.S. Brazel, The plasticizer market: an assessment of traditional plasticizers and research trends to meet new challenges, Prog. Polym. Sci. 29 (12) (2004) 1223–1248. [6] V. Marturano, P. Cerruti, V. Ambrogi, Polymer additives, Phys. Sci. Rev. 2 (6) (2017) 20160130. [7] I. Van der Veen, J. de Boer, Phosphorus flame retardants: properties, production, environmental occurrence, toxicity and analysis, Chemosphere 88 (10) (2012) 1119–1153. [8] K.M. Cantor, P. Watts, Plastics processing, in: Applied Plastics Engineering Handbook, Elsevier, 2011, pp. 195–203. [9] M.M. Rueda, M.C. Auscher, R. Fulchiron, T. Perie, G. Martin, P. Sonntag, P. Cassagnau, Rheology and applications of highly filled polymers: a review of current understanding, Prog. Polym. Sci. 66 (2017) 22–53. [10] J. Ottino, R. Chella, Laminar mixing of polymeric liquids; a brief review and recent theoretical developments, Polym. Eng. Sci. 23 (7) (1983) 357–379. [11] A.L. Moore, Fluoroelastomers Handbook: The Definitive User’s Guide and Databook, William Andrew Inc, Norwich, 2006. [12] C. Rauwendaal, Mixing in single-screw extruders, in: Mixing in Polymer Processing, New York, Marcel Dekker, Inc, 1991, pp. 129–240. [13] M. Kutz, Applied Plastics Engineering Handbook: Processing and Materials, first ed., William Andrew, Waltham, 2011. [14] J. Shapiro, A. Halmos, J. Pearson, Melting in single screw extruders, Polymer 17 (10) (1976) 905–918. [15] H.F. Giles Jr., E.M. Mount III, J.R. Wagner Jr., Extrusion: The Definitive Processing Guide and Handbook, William Andrew, Inc, Norwich, 2004. [16] C.I. Chung, Extrusion of Polymers: Theory and Practice, second ed., Hanser Publishers, Munich, 2000. [17] C. Tzoganakis, Reactive extrusion of polymers: a review, Adv. Polym. Technol.: J. Polym. Process. Inst. 9 (4) (1989) 321–330. [18] T. Villmow, B. Kretzschmar, P. P€ otschke, Influence of screw configuration, residence time, and specific mechanical energy in twin-screw extrusion of polycaprolactone/multi-walled carbon nanotube composites, Compos. Sci. Technol. 70 (14) (2010) 2045–2055.

I. Polymer science

References

177

[19] W. Szydlowski, R. Brzoskowski, J. White, Modelling flow in an intermeshing co-rotating twin screw extruder: flow in kneading discs, Int. Polym. Process. 1 (4) (1987) 207–214. [20] J. Covas, O. Carneiro, A. Brito, Designing extrusion dies for thermoplastics, J. Elastomers Plast. 23 (3) (1991) 218–238. [21] T. Whelan, J. Goff, Injection molding of thermoplastics, in: Injection Molding of Thermoplastics Materials—1, Springer, Boston, 1990, pp. 10–48. [22] H.W. Cox, C.C. Mentzer, R.C. Custer, The flow of thermoplastic melts: experimental and predicted, Polym. Eng. Sci. 24 (7) (1984) 501–510. [23] D.M. Bryce, Plastic Injection Molding: Mold Design and Construction Fundamentals, Society of Manufacturing Engineers, Dearborn, 1998. [24] H. Zhou, Computer Modeling for Injection Molding: Simulation, Optimization, and Control, John Wiley & Sons, Inc., Hoboken, 2013 [25] C. Park, W. Lee, Compression molding in polymer matrix composites, in: Manufacturing Techniques for Polymer Matrix Composites (PMCs), Woodhead Publishing Limited, Sawston, 2012, pp. 47–94. [26] S. Newman, D.G. Fesko, Recent developments in sheet molding compound technology, Polym. Compos. 5 (1) (1984) 88–96. [27] B.A. Davis, P.J. Gramann, A.C. Rios, T.A. Osswald, Compression Molding, Hanser Publisher, Munich, 2003. [28] R.A. Pethrick, Polymer Science and Technology for Scientists and Engineers, Whittles Publishing, Dunbeath, 2010. [29] N.C. Lee, Blow Molding Design Guide, Hanser, Munich, 2008. [30] G. Menary, C. Tan, E. Harkin-Jones, C. Armstrong, P. Martin, Biaxial deformation and experimental study of PET at conditions applicable to stretch blow molding, Polym. Eng. Sci. 52 (3) (2012) 671–688. [31] M. Kontopoulou, M. Bisaria, J. Vlachopoulos, An experimental study of rotational molding of polypropylene/ polyethylene copolymers, Int. Polym. Process. 12 (2) (1997) 165–173. [32] R.J. Crawford, R.J. Crawford, J.L. Throne, Rotational Molding Technology, William Andrew, Norwich, 2001. [33] A. Spence, R. Crawford, Removal of pinholes and bubbles from rotationally moulded products, Proc. Inst. Mech. Eng. Pt. B: J. Eng. Manuf. 210 (6) (1996) 521–533. [34] G. Capelle, Calendering technology, in: Rubber Products Manufacturing Technology, Routledge, 2018, pp. 179–265. [35] N.P. Cheremisinoff, Introduction to Polymer Rheology and Processing, CRC Press, 2018. [36] A.K. Sen, Coated Textiles: Principles and Applications, CRC Press, Boca Raton, 2001. [37] H.A. Barnes, J.F. Hutton, K. Walters, An Introduction to Rheology, Elsevier, Amsterdam, 1989. [38] T.G. Mezger, The Rheology Handbook, second ed., Vincentz, Coatings Compendia, 2006. [39] J.M. Brader, Nonlinear rheology of colloidal dispersions, J. Phys. Condens. Matter 22 (2010) 363101. [40] J.J. Stickel, R.L. Powell, Fluid mechanics and rheology of dense suspensions, Annu. Rev. Fluid Mech. 37 (2005) 129. [41] M.C. Williams, Molecular rheology of polymer solutions: interpretation and utility, AICHE J. 21 (1) (1975) 1–25. [42] G. Schramm, A Practical Approach to Rheology and Rheometry, second ed., Gebrueder Haake, Germany, 2000. [43] A.J. Poslinski, M.E. Ryan, R.K. Gupta, S.G. Seshadri, F.J. Frechette, Rheological behavior of filled polymeric systems I. Yield stress and shear-thinning effects, J. Rheol. 32 (1988) 703. [44] X. Cheng, J.H. McCoy, J.N. Israelachvili, I. Cohen, Imaging the microscopic structure of shear thinning and thickening colloidal suspensions, Science 333 (6047) (2011) 1276–1279. [45] N.J. Wagner, J.F. Brady, Shear thickening in colloidal dispersions, Phys. Today 62 (2009) 27. [46] A.K. Doufas, L. Rice, W. Thurston, Shear and extensional rheology of polypropylene melts: experimental and modeling studies, J. Rheol. 55 (1) (2011) 95–126. [47] R.G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press, New York, 1999. [48] D. Rajagopalan, R.C. Armstrong, R.A. Brown, Finite element methods for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity, J. Non-Newtonian Fluid Mech. 36 (1990) 159–192. [49] J.M. Piau, J.F. Agassant, Rheology for Polymer Melt Processing, Elsevier, Amsterdam, 1996. [50] T.A. Osswald, Understanding Polymer Processing: Processes and Governing Equations, Hanser Publishers, 2011. [51] A.J. Giacomin, T. Samurkas, J.M. Dealy, A novel sliding plate rheometer for molten plastics, Polym. Eng. Sci. 29 (1989) 499–503. [52] C. Clasen, Determining the true slip of a yield stress material with a sliding plate rheometer, Rheol. Acta 51 (2012) 883–890.

I. Polymer science

178

8. Polymer processing and rheology

[53] J.M. Dealy, R.G. Larson, Structure and Rheology of Molten Polymers: From Structure to Flow Behaviour and Back Again, Hanser Publishers, Munich, 2006. [54] M. Rubinstein, R.H. Colby, Polymer Physics, Oxford University Press, New York, 2003. [55] I. Newton, Philosophiae naturalis principiaa mathematica (“principia”), London(1687). [56] A. De Waele, Viscometry and plastometry, Oil Color Chem. Assoc. J. 6 (1923) 33–88. [57] E.C. Bingham, An investigation of the laws of plastic flow, U.S. Bureau Stand. Bull. 13 (1916) 309–353. [58] W.H. Herschel, R. Buckley, Measurement of consistency as applied to rubber benzene solutions, Proc. Am. Soc. Test Mater. 26 (1926) 621. [59] S.G. Hatzikiriakos, J.M. Dealy, Wall slip of molten high density polyethylenes. II. Capillary rheometer studies, J. Rheol. 36 (4) (1992) 703–741. [60] H. Ozoe, S.W. Churchill, Hydrodynamic stability and natural convection in Ostwald-de Waele and Ellis fluids: the development of a numerical solution, AICHE J. 18 (6) (1972) 1196–1207. [61] S.R. Hong, N.M. Wereley, Y.T. Choi, S.B. Choi, Analytical and experimental validation of a nondimensional Bingham model for mixed-mode magnetorheological dampers, J. Sound Vib. 312 (3) (2008) 399–417. [62] T.A. Osswald, N. Rudolph, Polymer Rheology: Fundamentals and Applications, Hanser Publishers, 2015. [63] C. Han, Rheology and Processing of Polymeric Materials, Oxford University Press, Oxford, UK, 2007. [64] E.B. Bagley, End corrections in the capillary flow of polyethylene, J. Appl. Phys. 28 (1957) 193–209. [65] D.J. Highgate, R.W. Whorlow, End effects and particle migration effects in concentric cylinder rheometry, Rheol. Acta 8 (2) (1969) 142. € [66] B. Rabinowitsch, Uber die Viskosit€at und Elastizit€at von Solen, Z. Physik. Chem. A 145 (1929) 1–26. [67] J.M. Dealy, Weissenberg and Deborah numbers – their definition and use, Rheol. Bull. 79 (2) (2010) 14–18. [68] J.M. Dealy, J.F. Petersen, T.-T. Tee, A concentric-cylinder rheometer for polymer melts, Rheol. Acta 12 (1973) 550–558. [69] A. Magnin, J.M. Piau, Cone-and-plate rheometry of yield stress fluids. Study of an aqueous gel, J. NonNewtonian Fluid Mech. 36 (1990) 85–108.

I. Polymer science

C H A P T E R

9

Thermal, mechanical, and electrical properties Yi-Yang Peng, Diana Diaz Dussan, Ravin Narain Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

9.1 Thermal analysis of polymers Thermal analysis encompasses a series of techniques that measure a material’s response to changes with temperature. The goal is to establish a connection between temperature and the specific physical properties of the materials. The most popular techniques are differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), thermomechanical analysis (TMA), dynamic mechanical analysis (DMA), dielectric analysis (DEA), and micro/ nanothermal analysis (μ/n-TA) [1]. Three of the most important physical properties of a material that are needed for heattransfer calculations are thermal conductivity, thermal diffusivity, and specific heat and are routinely used in laboratories and industries for the thermal and mechanical characterization of the polymers, design of manufacturing processes, and for estimating their lifetimes in various environments. The properties that we will discussed are key elements required for the proper characterization of a polymeric material and its application [2].

9.1.1 The melting temperature of polymers The melting point refers to the temperature at which a polymer changes from the crystalline state into a viscous amorphous state. In the case of polymers, this change is observed in a temperature range due to the polydispersity of the polymeric chains, their branching, and imperfection of the crystallites formed. The melting point Tm is a physical characteristic and is extremely difficult to calculate. There are some calculation methods based on the chemical structure of the repeating unit of the polymer (monomer). The estimation is founded on the relation between the glass transition temperature Tg and the melting point Tm according to the Beaman rule, where

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00009-1

179

# 2020 Elsevier Inc. All rights reserved.

180

9. Thermal, mechanical, and electrical properties

Tg/Tm
2/3 (this is only valid for temperature in Kelvin). Nonetheless, detailed analysis of a large range of polymers has indicated that this relation varies in a wide range, although for a broad group of polymeric systems, it is 2/3. For more complex systems, the relation for Tg/Tm is presented in the following form: 2 31 X ΔV Tg 4 i i X  A5 ¼ X (9.1) Tm ð δ ΔV Þ + γ i i j i j Here, δi ¼ (k0  kg)/ki (ki is the partial coefficient of packing of the ith atom); γ j are the constants taking into calculation the contribution of strong intermolecular interactions; k

g ¼ 10:418. Values of δi and γ j are shown in Table 9.1. A ¼ k0 k g

Adjusted and experimental values of δi and γ j for certain groups and corrections to Eq. (9.1) are used to calculate copolymers melting values [3]. Measurements of Tm and melting range are conveniently made by thermal analysis techniques like DSC. The value of Tm is usually taken to be the temperature at which the highest melting crystallites disappear [4].

9.1.2 Glass transition temperature of polymers The glass transition is the property of only the amorphous portion of a semicrystalline solid. When an amorphous polymer is heated, the temperature at which it changes from a glass to the rubbery form is named the glass transition temperature, Tg. A given polymer sample has multiple values of Tg because the glass phase is not at equilibrium. The measured value of Tg will depend upon the relative molecular mass of the polymer, on its thermal history and age, on the measurement method, and on the speed of heating or cooling [5].

TABLE 9.1 Values of parameters of δi and γ j of various atoms and types of intermolecular interactions. Atom or type of intermolecular interaction

Designation

δi

˚ 3) γ i (A

Silicon

δSi

0.0840

–

Carbon

δc

0.08685

–

Hydrogen

δH

0.0740

–

Oxygen in the backbone

δO,

0.0621

–

Dipole-dipole interaction

δd

0.0212

–

Hydrogen bond

γh

–

0.0188

p-Substitution

–

–

0.100

b

Adapted from A.A. Askadskiı˘, A. Andreı˘. Computational Materials Science of Polymers. Cambridge International Science Publication, p. 696, 2003.

I. Polymer science

9.1 Thermal analysis of polymers

181

In the highly viscous region above the Tg, polymeric materials are soft and rubbery, whereas below the Tg, polymers are hard and brittle. Tg is unique from polymer to polymer depending on the polymer chain structure and whether the polymer is amorphous or semicrystalline. For amorphous polymers, it is a transitional temperature of polymer chain stiffness or mobility from glassy state to flexible state. The glass transition temperature, often called Tg, is a crucial property when considering polymers for a specific end use. Some polymers are used above their glass transition temperatures, and some are used below the Tg depending on the application. Sometimes, we want to tune the Tg of a polymer for a particular use. For example if we have a polymer with a high Tg, we can add a small molecule which will get in between the polymer chains and space them out from each other called plasticizer to lower the Tg (Fig. 9.1). We call this increment the free volume. When this happens, they will slide past one another more easily. When they slide past one another more easily, they will move around at lower temperatures than they might without the plasticizer. In this way, the Tg of a polymer can be lowered, to make a polymer more flexible, and easier to work with. Depending on how easily the chains move, the Tg changes. A polymer chain which can move around fairly easily will have a really low Tg, while one that does not move so well will have a high one. The more easily a polymer can move, the less heat it takes for the chains to commence wiggling and escape of the rigid glassy state and into the soft rubbery state. There are several things that affect the mobility of a polymer chain like the backbone flexibility and the pendant groups it has. The more flexible the backbone chain is, the better the polymer will move, and the lower its Tg will be, silicones are a good example. Polydimethylsiloxane has a very flexible backbone and has a Tg at 127°C. This chain is so flexible that it is a liquid at room temperature, and it is used to thicken shampoos and conditioners. On the other hand, poly(phenylene sulfone) is very rigid and stiff. This polymer does not have a Tg. It can be heated to over 500°C and it will still stay in the glassy state. In order to make a polymer that is processable, flexible groups need to be added in the backbone chain, like ether groups. This are called poly(ether sulfones), and those flexible ether groups bring the Tg down to 190°C (Fig. 9.2). The structural order of a polymer also affects its Tg. Syndiotactic polymers are highly regular and pack into crystalline structures (crystalline) rather than atactic polymers which are irregular and cannot crystallize (amorphous). Pendant groups have also a huge effect on chain mobility (Fig. 9.3). Even a small pendant group can act as a fish hook that will catch

FIG. 9.1 Examples of common plasticizers.

I. Polymer science

182

9. Thermal, mechanical, and electrical properties

FIG. 9.2 The introduction of ether linkages to poly(phenylene sulfone) increases the flexibility of the polymer chain and the Tg is reduced to 190°C.

FIG. 9.3 Series of methacrylate polymers. Adding a pendant alkyl chain changes the Tg. We start out at 120°C for poly(methyl methacrylate), but by the time we get to poly(butyl methacrylate), the Tg has dropped to only 20°C.

on any nearby molecules when the polymer chain tries to move. Pendant groups also catch on one another when chains attempt to slither past one another. One pendant group for getting a high Tg is the adamantyl group. A big group like this does act like a hook that catches on nearby molecules and keeps the polymer from moving. But big bulky pendant groups can lower the Tg, too. The big pendant groups limit how closely the polymer chains can compress. The further they are from each other, the more easily they can move around. This lowers the Tg, within the same way a plasticizer does. There is more free volume in the polymer. The more free volume, the lower the Tg generally. Chemical cross-linking greatly limits chain mobility. Cross-linked polymers often do not exhibit Tg. Polycarbonate (PC), for instance, is used below its Tg of 150°C which is well above room temperature. Note that due to its unique chemical bond, PC is both a stiff and tough polymer providing great impact resistance below its Tg. If PC is exposed to above 150°C, it will become flexible due to polymer chain mobility. Polyisoprene or natural rubber, on the

I. Polymer science

183

9.1 Thermal analysis of polymers

other hand, is used above its Tg of 75°C which is well below room temperature. If natural rubber is exposed to less than 75°C, it will be in the glassy state. If the polymer is used as a load-bearing structural element, Tg defines an upper boundary for its use temperature. For example, if a certain polymer is employed as a part of the body of an airplane, one must make sure that the polymer would not be exposed to a temperature higher than its glass transition to stay in its rigid state, since above Tg the polymer will soften. On the other hand, if the polymer is being employed as a flexible rubber, then Tg represents a lower bound on its use temperature [6]. Approximate glass transition temperatures of a few polymers are shown in Table 9.2. For copolymers, the Flory-Fox equation is a simple empirical formula that relates molecular weight to the Tg of a polymer system. The Flory-Fox equation relates the number-average relative molecular mass, Mn, to the glass transition temperature, Tg as shown in the following equation: Tg ¼ Tg, ∞ 

K Mn

(9.2)

where Tg,∞ is the maximum glass transition temperature that can be achieved at a theoretical infinite molecular weight and K is an empirical parameter that is related to the free volume present in the polymer sample. This equation serves the purpose of providing a model for TABLE 9.2

Glass transition temperature of some polymers. Tg (°C)

Polymer Poly(chlorotrifluoroethylene)

87

Poly(vinyl chloride), PVC

83

Poly(vinyl fluoride), PVF

52

Poly(vinylidene chloride), PVDC

17

Poly(vinylidene fluoride), PVDF

34

Teflon, PTFE

119

Polychloroprene, neoprene

36

Poly(acrylamide)

165

Poly(N,N-dimethylacrylamide)

106

Poly(2-cyanobutyl acrylate)

111

Poly(2-cyanoethyl acrylate)

4

Poly(2-ethylhexyl acrylate)

53

Poly(ethylene)

80

Poly(isobutene)

70

Poly(propylene)

10

Poly[1-(tert-butyl)ethene]

64

I. Polymer science

184

9. Thermal, mechanical, and electrical properties

how glass transition temperature changes over a given molecular weight range. Another method to modify the glass transition temperature as we have mentioned is to add plasticizers, to the polymer. The presence of a low molecular weight additive increases the free volume of the system and subsequently lowers Tg, thus allowing for rubbery properties at lower temperatures. This effect is described by the Fox equation: 1 ω1 ω2 ¼ + Tg Tg,1 Tg,2

(9.3)

where ω1 and ω2 are weight fractions of components 1 and 2, respectively. In general, the accuracy of the Fox equation is extremely good and it is commonly also applied to predict the glass transition temperature in (miscible) polymer blends and statistical copolymers.

9.1.3 Thermal conductivity of polymers Thermal conductivity is the property that determines the working temperature levels of a material. The thermal conductivity of bulk polymers is usually very low, on the order of 0.1–0.5 W/m K, which is due to the complex morphology of polymer chains. The thermal conductivity of a polymer depends greatly on its morphology. When amorphous domains are dominant, vibrational modes in the polymer tend to be localized, resulting in a low thermal conductivity. It is therefore natural to expect that the thermal conductivity can be enhanced by improving the alignment of the polymer chains by using mechanical stretching, nanoscale templating, and electrospinning. In addition to engineering the morphology of the polymer chains, another common method to enhance the thermal conductivity of polymers is to blend polymers with highly thermal conductive fillers. In Fig. 9.4, we summarize the main mechanism that affect the thermal conductivity of polymers. The low thermal conductivity of polymers is often one among the main technological barriers for the polymer-based flexible electronics thanks to the limited heat-spreading

FIG. 9.4 Physical mechanisms affecting the thermal conductivity of (A) polymers and (B) polymer nanocomposites [7]. Copyright 2019, Elsevier.

I. Polymer science

9.1 Thermal analysis of polymers

185

capability. If a polymer can be engineered with high thermal conductivity, it could find many applications in electronics, water, and the energy industry [7]. The progress of nanotechnology over the last two decades has provided diverse high thermal conductivity fillers of different material types and topological shapes [7]. One example is shown in Fig. 9.5A, where the thermal conductivity of π-conjugated polyacetylene is higher than that of PE. Conjugated π-bond is also found in aromatic rings as shown in Fig. 9.5B, where the thermal conductivity of chains with aromatic-backbone structures is much higher than that with aliphatic-backbone structures. In addition, the type of carbon-carbon bonding, the thermal conductivity of polymer chains can also be tuned by replacing the hydrocarbon functional groups in the backbone with other atomic species. Fig. 9.5C shows the effect of replacing dCH2d groups in the backbone with O atoms. Because the dCH2dOd bonding energy (335 kJ/mol) is lower than dCH2dCH2d (350 kJ/mol) and O atom is heavier than dCH2d group, the thermal conductivity of poly(ethylene oxide) is much lower than that of both PE and poly(methylene oxide). Cross-linking a polymer also can form efficient heat conduction pathways and networks by connecting polymer chains with strong covalent bonds, so increasing the amount of

FIG. 9.5 The thermal conductivity dependence of bond strength: (A) effect of double bonds, (B) effect of aromatic backbone, and (C) effect of bond-strength disorder. Copyright 2019, Elsevier.

I. Polymer science

186

9. Thermal, mechanical, and electrical properties

cross-links within the polymer network increases the thermal conductivity. However, recent simulations have shown that the enhanced thermal conductivity with cross-links cannot be explained completely by only considering covalent bonds. In addition to the covalent bonds connecting different chains, another effect of the cross-links is to bring the polymer chains closer to each other. As a result, the nonbonding coupling (vdw, Coulombic or H-bonds) becomes stronger when there are more cross-links in the polymer, which in turn significantly enhances the thermal conductivity. In summary, (1) improving crystallinity or chain alignment of polymers usually enhances polymer thermal conductivity by selecting appropriate polymer species with special chain structures. (2) The thermal conductivity of pristine polymers could be increased by enhancing interchain coupling, such as through H-bonds and covalent cross-links. The enhancement of the intrinsic thermal conductivity of polymers is only experimentally realized by enhancing chain alignment and interchain coupling with polymer blends. Blending polymers could only obtain a slightly enhanced thermal conductivity which is usually lower than 0.5 W/m K and this method is difficult to be adopted because of complex synthesis conditions. To further enhance the thermal conductivity, appropriate polymer species should be selected based on the theoretical studies before carrying out the chain [7].

9.1.4 Thermal diffusivity Thermal diffusivity is the measurement of speed of the heat propagation through a material. It is an important property in all problems involving nonsteady-state heat conduction. In the extrusion process, knowledge of the precise value of the thermal diffusivity and its temperature dependence is essential. Nowadays, several different techniques for the determination of the thermal diffusivity and thermal conductivity may be found in the literature, and they can be divided into two classes: direct and indirect methods. Direct methods are those with which the desired property is measured directly from the experimental results. Indirect methods are those, where the desired property is derived from a previous property determined from the experimental results. The laser flash technique is a direct method in the determination of the thermal diffusivity, while this is an indirect method in the determination of the thermal conductivity. In this case, the thermal conductivity is derived from the thermal diffusivity, with the additional acknowledge of the specific heat and bulk density [2]. These parameters are related by the following equation: α¼

k ρcp

(9.4)

where α is the thermal diffusivity (m2/s), k is the thermal conductivity (W/m K), ρ is the bulk density (kg/m3), and cp specific heat (J/kg K). The thermal diffusivities α of two samples of PBT with different crystallinity (X ¼ 0.12 and 0.34) are shown in Fig. 9.6A. For the sample with X ¼ 0.12, an abrupt drop in α is observed near the glass transition (Tg ¼320 K), consistent with the behavior of amorphous polymers such as poly(ethylene terephthalate). However, for the sample with higher crystallinity (X ¼ 0.34), the transition is more diffused and hence not so noticeable. It is also apparent that

I. Polymer science

187

9.2 Differential scanning calorimeter

10

HDPE

8 6

2.5

∝ (cm2 s–1)

∝ x 103 (cm2 s–1)

3

2

LDPE

4 i-PP

2

1.5

P4MP1

1 100

(A)

Tg 200 T (K)

300

a-PP

PB-1

1

(B)

100

200 T (K)

300

FIG. 9.6

(A) Temperature dependence of thermal diffusivity of two samples of PBT with different degrees of crystallinity X: (●) X ¼ 0.12; (►) X ¼ 0.34. Tg denotes the glass transition. (B) Temperature dependence of thermal diffusivity of various polyolefins. HDPE and LDPE denote high- and low-density polyethylene, respectively, and i-PP and a-PP represent isotactic and atactic polypropylene, respectively [8]. Copyright from 2019, John Wiley and Sons.

α is weakly dependent on crystallinity X and increases by only 10%–15% as X increases from 0.12 to 0.34. The thermal diffusivities of PB-1, P4MP1, nylon 6, and PET are shown in Fig. 9.6B, together with the data for other polymers obtained in previous studies. It is clear that the thermal diffusivity of amorphous polymers decreases with rising temperature [8].

9.1.5 Techniques The thermal, electrical, and mechanical testing of polymers is a vital part of the product development and production process. This characterization allows the developers to better understand their product and introduce stronger quality control. Physical and mechanical testing of polymers ensures that the composition complies with industry specifications. This applies to aerospace, automotive, consumer, medical, and defense industries, among others. With the vast array of product types and additives available, understanding the capabilities and limitations of a material may be a key concern to suppliers, manufacturers, and merchandise developers on every level of the polymer industry supply chain.

9.2 Differential scanning calorimeter The first differential scanning calorimeter (DSC) was introduced by Watson et al. (1964). Differential thermal analysis (DTA) measures the difference in temperature (dt/T) between sample and reference, but it is possible to convert dt/T into absorbed or evolved heat via a mathematical procedure. The conversion factor is temperature-dependent. However, a DTA which accurately measures calorimetric properties is referred to as a DSC. In practice, a

I. Polymer science

188

9. Thermal, mechanical, and electrical properties

sample is placed within a sample pan which is then placed within the sample holder block. A similar empty pan is placed in the reference holder block. The instrument then allows T, the common temperature of the two holders, to be changed at a constant rate dT/dt ¼ Τ , while the two holders are ideally maintained at the same temperature by a feedback loop. Extra energy Q must be supplied to the sample holder at a rate dQ/dt to take care of its temperature an equivalent as that of the reference holder; this rate is registered by the instrument and plotted either against T or against time t. It is generally possible to assume that away from any transitions in the sample, the sample and the sample pan are at the same temperature and that the sample and reference pans are identical. It then follows that dQ/dt ¼ mCp, where m is the mass of the sample and Cp is the specific heat per unit mass. The DSC thermogram (Fig. 9.7) of an undercooled, potentially semicrystalline polymer shows that at low temperatures, the sample and the reference are at the same temperature (balance). When the glass transition is reached, an increase in the (endothermal) heat flow to the sample is required in order to maintain the two at the same temperature. The change in level of the scanning curve is thus proportional to L/Cp. The polymer crystallizes at a higher temperature and exothermal energy is evolved. The heat flow to the sample should in this temperature region be less than the heat flow to the reference. The integrated difference between the two, i.e., the area under the exothermal peak, is thus equal to the crystallization [9, 10].

9.2.1 Differential thermal analysis In this method, sample and reference are heated by a single source and temperatures are measured by thermocouples embedded in the sample and reference or attached to their pans.

FIG. 9.7 DSC thermogram exhibiting the detection of transitions such as melting, glass transitions, phase changes,

and cross-linking. Specific heat capacity versus temperature for an initially amorphous PEEK sample. Tg, glass transition; Tcc, cold crystallization; Tm, final melting. Copyright from Springer Nature.

I. Polymer science

9.2 Differential scanning calorimeter

189

FIG. 9.8 Differential thermal analysis (DTA): (A) classical apparatus (S ¼ sample; R ¼ reference), (B) heat-flux, and (C) typical DTA curve. (Note the DTA convention that endothermic responses are represented as negative, i.e., downward peaks.) [11]. Copyright from Springer Nature.

The key features of a DTA kit are as follows (Fig. 9.8): sample holder comprising thermocouples, sample containers and a ceramic or metallic block, a furnace, a temperature programmer, and a logging system. Because heat is now supplied to the two holders at the same rate, a difference in temperature between the sample and the reference develops, which is recorded by the instrument. The difference in temperature depends, among other things, on the value of κ (the thermal conductance between the sample holder and the sample), which needs to be low to obtain large enough differences in temperature to measure accurately. The area under a transition peak now depends on κ and it is difficult to work out this accurately or to take care of it at a constant [12]. The accuracy in the determination of transition temperatures by DSC/DTA is dependent on several factors: • Standardized sample geometry and mass. The sample should be flat and have good thermal contact with the sample pan. Heat-conductive, “thermally inert” liquid media may be used to improve the thermal contact. • The purge gas and the sample pan material should be “inert.” • Thermal lag (difference) between sample and thermometer may be corrected for by using the slope of the leading edge of the melting of highly pure indium (or similar metal). • Parallel processes should be inhibited. Melting of polymer crystals is accompanied by crystal thickening (parallel process) [13].

I. Polymer science

190

9. Thermal, mechanical, and electrical properties

9.2.2 Thermomechanical analysis These instruments not only measure volume and linear thermal expansion coefficients but also modulus as a function of temperature. When thermal expansion or penetration (modulus) is being measured, the sample is placed on a platform of a quartz sample tube (Fig. 9.9). The thermal expansion coefficient of quartz is small (about 0.6  106 K1) compared to the polymer materials. The quartz tube is connected to the armature of a linear variable differential transformer (LVDT) and any change in the position of the core of the LVDT, which floats frictionless within the transformer coil, results in a linear change in the output voltage. The upper temperature limit for the currently available commercial instruments is about 725°C [15]. The coefficient of linear thermal expansion, α, can be determined from the slope of the expansion curve, since ΔL dL ¼ ¼ L1 α ΔT dT

(9.5)

FIG. 9.9 Thermomechanical analysis (TMA): (A) penetration, (B) extension, (C) flexure, and (D) torsional measurements [14]. Copyright from Springer Nature.

I. Polymer science

9.2 Differential scanning calorimeter

191

Alternatively, the time derivative of the dilation may be recorded, using electronic differ  entiation, and    dL dt dL dT ¼ L1 α or ¼ L1 αϕ where ϕ ¼ ¼ heating rate dt dT dt dt

9.2.3 Thermogravimetry Thermogravimetry (TG) is carried out in a so-called thermobalance which is an instrument permitting the continuous measurement of sample weight as a function of temperature/time. It should be noted that the sample size and form affect the shape of the TG curve. A large sample may develop thermal gradients within the sample, a temperature deviation from the set temperature due to endo- or exothermal reactions and a delay in mass loss due to diffusion obstacles. Finely ground samples are preferred in quantitative analysis for the aforementioned reasons. TG can provide information about physical phenomena, such like second-order phase transitions, including vaporization, sublimation, absorption, adsorption, and desorption. Likewise, TG can provide information about chemical phenomena including chemisorptions, desolvation (especially dehydration), decomposition, and solid-gas reactions (e.g., oxidation or reduction). TG is usually determines selected characteristics of materials that exhibit either mass loss or gain thanks to decomposition, oxidation, or loss of volatiles (such as moisture). Common applications of TG are (1) materials characterization through analysis of characteristic decomposition patterns, (2) studies of degradation mechanisms and reaction kinetics, (3) determination of organic content in a sample, and (4) determination of inorganic content in a sample, which can be useful for corroborating predicted material structures or just used as a qualitative analysis. TG is often combined with various techniques to analyze the evolved gas. Infrared (IR) spectroscopy and gas chromatography, the latter often combined with mass spectrometry or IR, are used for the identification of the volatile products [15]. TG can be used to evaluate the thermal stability of a material (Fig. 9.10). In a desired temperature range, if a FIG. 9.10 TGA thermograms of polymer/ AgNPs nanocomposites using MWI and in situ method. PMMA, Polymethyl methacrylate [16].

I. Polymer science

192

9. Thermal, mechanical, and electrical properties

species is thermally stable, there will be no observed mass change. Negligible mass loss corresponds to little or no slope in the TG trace. TG also gives the upper use temperature of a material. Beyond this temperature, the material will begin to degrade [16].

9.2.4 Density measurements Polymer samples usually are irregular in shape, making it difficult to quantify their volume directly. Many polymers can be partially crystalline and the degree of crystallinity can have a noticeable effect on their density. Conversely, a knowledge of the density can be useful in assessing the degree of crystallinity. One of the most important ways that densities of polymers are determined is by the use of a density-gradient column, or density column. A varying mixture of two miscible liquids of different densities injected into the bottom of a vertical tube. The liquids must be compatible with the samples to be studied, i.e., the liquids must not attack or penetrate the polymer. The column must be calibrated to give the densityversus-distance relationship, which is done by carefully inserting specially calibrated floats into it, each of which has a known effective density. Other methods of determining density can be used, such as the specific gravity bottle or pycnometer. In a pycnometer, the volume of the polymer is calculated by the displacement of a liquid or gas. A special container, made from soda glass to avoid static charges, typically is employed for the experiment. However, the density-column method is usually far simpler and of greater accuracy [12].

9.3 Mechanical properties of polymers The mechanical property indicates the physical alteration of material upon exposure to an external force. The measurements of mechanical properties include modulus, strength, toughness, ductility, elongation, etc. Modulus indicates the capability of polymer in resisting deformation, and Young’s modulus represents this characteristic of material when Hooke’s law is obeyed. Strength/Toughness indicates the amount of force/energy required to break the material. Toughness calculation is shown in Eq. (9.6); σ is the stress and ε is the strain. The value of toughness indicates the amount of energy that a material can absorb up to the point of failure. Ductility is a measure of energy absorption during plastic deformation before fracture. In the following section, general concepts of stress and strain, stress-strain curve, DMA (the instrument used to characterize the mechanical properties), viscoelastic behavior of polymer, and factors that influence the polymeric mechanical properties will be introduced. Z Toughness ¼ σdε (9.6)

9.3.1 Basic concepts of stress and strain When considering mechanical property of the polymers, the stress, strain, and their relationship are the first thing that needs to be understood. Stress (σ) is the force per unit of area I. Polymer science

9.3 Mechanical properties of polymers

193

and its SI unit is N/m2 or Pa (Eq. 9.7), and strain (ε) is the relative elongation of a deformation material in comparison to its original shape (Eq. 9.8) and is unitless. F A0

(9.7)

li  l0 Δl ¼ l0 l0

(9.8)

Stress σ ¼ Strain ε ¼

Stress can be divided into two subcategories: normal stress (σ) and shear stress (τ). More specifically, the material becomes shorter/longer when exposes to compression/tensile stress. Longitudinal strain and volumetric strain are the two subcategories of strain; the first one indicates the change in length alone and the second one is changed in volume only.

9.3.2 Stress-strain curve Stress-strain curve is a plot that describes the stress as a function of strain of a material. Fig. 9.11 is an example of a stress-strain curve. Some important points describe the important feature of the material and they are explained below: • Proportionality limit: The maximum amount of stress that material can have with the linear stress-strain curve. • Elastic limit: The largest amount stress that allows material return to original shape after the withdrawing of the load. After the elastic limit, the deformation becomes irreversible. • Yield point (Sty): The point where the plastic deformation starts. • Ultimate strength (Stu): The maximum value of stress that material has on its stress-strain curve. • Fracture point: The point where the fracture breaks into two pieces. • Strain hardening: The strain value increases quickly with a small increase in stress, and the material will be strengthening by plastic deformation. • Necking: Cross-sectional area of deformation is decreased.

FIG. 9.11 Illustration of stress-strain curve and point of interest.

I. Polymer science

194

9. Thermal, mechanical, and electrical properties

Before the proportionality limit, the stress-strain of the material has linear relationship and in the linear region. In this linear region, the material follows the general Hooke’s law (Eq. 9.9) and Young’s modulus (E) can be derived by calculating the slope of this region. The toughness of a material, amount of energy that a sample can withstand before fracture, can be obtained by calculating the area under the stress-strain curve. σ ¼ E∗ε

(9.9)

Generally, when considering the mechanical property, the polymer can be categorized into three different kinds of polymers: brittle, plastic, and elastomer polymer. The examples of stress-strain curve of each type of polymer are shown in Fig. 9.12. The brittle polymer is strong but not tough as they deform elastically and break easily with slight elongation. Examples of brittle polymers include polystyrene, poly(methyl methacrylate), and PC. The plastic polymer is strong, but not as strong as brittle polymer, and tough as it has a large area under the curve. Plastic polymers possess high modulus which allows them resist deformation initially and deform plastically deformation after achieving the yield point and break eventually. Polyethylene and polypropylene are in this category. Lastly, the elastomer polymers, such as polyisoprene, polybutadiene, and polyisobutylene, are neither strong nor tough as the polymers do not resist deformation, and the area under the curve is small. Table 9.3 summarizes the characteristic features of stress-strain behavior of various kinds of polymers.

9.3.3 Dynamic mechanical analysis DMA is an instrument that is widely utilized to measure the modulus (stiffness) and damping (energy dissipation characteristics of the material in the process of deformation), which was exposed to oscillatory stress. The mechanical properties of a material can also be determined under various temperature, time, and frequency, and it can also be used to determine the glass transition temperature of polymers. Fig. 9.13 illustrates the basic components of DMA. Drive motor is used to provide the sinusoidal deformation force to the sample that is held by a clamp, and deformation of material is measured by the displacement sensor, FIG. 9.12

Mechanical property of polymers: stress-strain curve. Reprint from W.D. Callister, D.G. Rethwisch, Chapter 7: Mechanical Properties. Fundamentals of Materials Science and Engineering: An Integrated Approach, fifth ed., John Wiley & Sons, Inc., Hoboken, NJ, 2016 with Permission from John Wiley & Sons, Inc.

I. Polymer science

195

9.3 Mechanical properties of polymers

TABLE 9.3

The mechanical property of stress-strain behavior of various kinds of polymer.

Material stress-strain behavior

Elastic modulus

Yield point

Tensile strength

Elongation at break

Soft and weak (polymer gels)

Low

Low

Low

Moderate

Hard and brittle (polystyrene)

High

Practically nonexistent

High

Low

Hard and strong (polyvinyl chloride)

High

High

High

Moderate

Soft and tough (rubbers and plasticized PVC)

Low

Low

Moderate

High

Hard and tough (cellulose acetate, nylon)

High

High

High

High

Reproduced from U.W. Gedde. Polymer physics. J. Chem. Inf. Model. 53 (2013) 1689–1699.

FIG. 9.13 Illustration of DMA components [14].

LVDT. Free resonance analyzers and forced resonance analyzers are the two common types of DMA analyzers used. The first one is suitable for rod or rectangular-shaped material and measures the free oscillations of damping of the sample via suspending and swinging the sample. The second one makes the sample to oscillate at a specific frequency under various temperature. Test modes for DMA include temperature sweep, frequency sweep, and I. Polymer science

196

9. Thermal, mechanical, and electrical properties

dynamic stress-strain studies. Temperature sweep involves the measurement of the complex modulus at low constant frequency while varying the temperature of the sample. For frequency sweep, the complex modulus of the sample is measured at various frequency under a constant temperature. Lastly, dynamic stress-strain studies conduct by gradually elevating the amplitude of oscillations. Sinusoidal oscillatory test is one kind of dynamic mechanical test. The test records the strain response while applying low frequency stress to the test subject.

9.3.4 Viscoelastic behavior of polymers Viscoelastic materials possess both viscous and elastic characteristics in the process of deformation. Combining behavior can be illustrated in Fig. 9.14, where the strain response of viscoelastic material is the summation of elastic and viscous component. Viscous means the flow resistance of fluid, and materials that tend to recover to original shape after the disappearance of external force are the elastic material. Strain rate as a function of time is observed for viscous material. However, unlike elastic material, in a cycle of applying and withdrawing of load, loss of energy is observed as hysteresis. Viscoelastic material possesses the following properties: • Hysteresis (Fig. 9.15) can be seen in the stress-strain curve. • Decreasing of stress is observed while step constant strain applies: stress relaxation. • Elevation of strain is triggered by step constant stress: creep. In order to describe viscoelastic behavior, Maxwell model, the Kelvin-Voigt model, and the standard linear model are used for various loading conditions. Springs and dashpots are used to model the elastic and viscous components of viscoelastic behavior, respectively. The elastic components are modeled as a spring by the Eq. (9.10) where E is elastic modulus of the material. For viscous components, dashpots are used which give the stress-strain rate relationship that is shown in Eq. (9.9) where η is the viscosity of the material and dε/dt is the time derivative of strain. σ ¼ Eε

FIG. 9.14

Combination of viscous and elastic behavior for viscoelastic deformation [19].

I. Polymer science

(9.10)

9.3 Mechanical properties of polymers

197

FIG. 9.15 Stress-strain curve of elastic material (A) and viscoelastic material (B). The red area is a hysteresis loop which indicates the amount of energy loss (heat) during a loading and unloading cycle [17].

σ¼η

dε dt

(9.11)

Maxwell model connects a purely viscous damper and a purely elastic spring in series (Fig. 9.16A) and can be described by Eq. (9.11) where stress plus stress rate influences the strain rate. Inaccurate prediction of creep of the material is the disadvantage of this model σ+

η dσ dε ¼η E dt dt

(9.12)

Kelvin-Voigt model or Voigt model connects a Newtonian damper and Hookean elastic spring in parallel (Fig. 9.16B), and the relationship is illustrated by Eq. (9.12). The model is accurate in describing creep behavior of materials, but it is bad in prediction of relaxation. σ ¼ Eε + η

dε dt

(9.13)

The standard linear solid model or Zener model has a dashpot and two springs, and the model properly model creep and stress relaxation behavior of a viscoelastic polymer. The model contains two representations: Maxwell (Fig. 9.16C) and Kelvin (Fig. 9.16D); the relationship is illustrated in Eqs. (9.14) and (9.15), respectively. η dσ ηðE1 + E2 Þ dε ¼ E1 ε + E2 dt E2 dt

(9.14)

η dσ E1 E 2 E1 dε ¼ ε+ η E1 + E2 dt E1 + E2 dt E1 + E2

(9.15)

σ+ σ+

FIG. 9.16

Models for describing viscoelastic behavior: Maxwell model (A), Kelvin-Voigt model (B), and standard linear solid model with Maxwell (C), and Kelvin (D) representation.

I. Polymer science

198

9. Thermal, mechanical, and electrical properties

Overall, the standard linear solid model is better than the Maxwell and Kelvin models in describing the behavior of the material. Two tests are used to evaluate the mechanical property of the viscoelastic polymer: creep test and stress relaxation test. For the creep test, the elongation of the material is recorded as a function of time while a constant weight is applied to the material. Creep compliance, J, is the ratio of the creep strain to the applied stress, as shown in Eq. (9.16): J ¼ ε=σ

(9.16)

Materials, with small values of J, indicate that material hardly creeps and vice versa. When doing the creep test, constant load is applied while recording the response of strain. An example of creep curves is shown in Fig. 9.17. For stress relaxation test, the material was suddenly deformed to a set amount; then, the stress that needs to keep the deformation constant is recorded as a function of time. An example of stress relaxation curves is shown in Fig. 9.18.

9.3.5 Effects of structure and composition on mechanical properties Molecular weight (Mw), cross-linking, molecular configuration, and composition (side chain) are the main factors that influence the mechanical properties of the polymers.

FIG. 9.17 Creep curves for a viscoelastic material [18].

FIG. 9.18 Stress relaxation curve for viscoelastic material [18].

I. Polymer science

9.4 Electrical properties of polymers

199

9.3.5.1 Molecular weight The strength of polymers can be improved by increasing the molecular weight of the polymer and the relationship can be described by the following equation: σ ¼ σ∞ 

A Mw

(9.17)

σ ∞ represents the tensile strength of the polymer with infinity value of Mw, and A is some constant. The influence of constant A is reduced as the Mw of the polymer is larger. Strength of low Mw polymer is lower as the van der Waals force is weaker with short chain and the chains free more freely in comparison to high Mw polymer. Furthermore, the long-chain movement of the high Mw polymer is more restricted as they are more likely to be tangled [19]. 9.3.5.2 Cross-linking As mentioned above, the movement restriction of polymeric chains increases the strength of polymers. Cross-linking makes more chains aligned, resulting in more van der Waals bonds thus elevate the strength of the polymer. 9.3.5.3 Molecular configuration The presence of crystallinity in the polymer provides the strength for the polymers; thus, the tacticity of a polymer chain can have a major influence on its properties. Atactic polymers lead to more disordered arrangement, thus no crystallization and lower the strength. 9.3.5.4 Composition If the pendant group among the polymer can interact with each and form crystallinity, the strength of the polymer can also be enhanced. Fig. 9.19 introduces several inter- and intramolecular interactions that can increase the strength of the polymers.

9.4 Electrical properties of polymers Most polymers are considered as dielectrics or insulators as they resist the flow of a current, which attributes to its saturated hydrocarbon structure, that lead to termination of electric flow. Dielectric material can be induced to dipole structure and lead to a flow of electron.

FIG. 9.19 Inter- and intramolecular interactions [18].

I. Polymer science

200

9. Thermal, mechanical, and electrical properties

Dielectric polymer can also be divided into two groups: polar and nonpolar. The polarity of polymer, which origins from the imbalance of electronic charge distribution among the polymers, aligned dipoles with the applied electric field and facilitated the movement of electrons. Examples of polar polymers include poly(methyl methacrylate), polyvinyl chloride, and Nylon. Nonpolar polymers do not have presence of dipole when exposed to electric field and have high resistivity and low dielectric constants. PTFE is a nonpolar polymer. Conductivity inverse of resistivity is described in Eq. (9.18). Conductivity ¼

length of the object Cross  sectional area∗intrinsic resistivity of material

(9.18)

To characterize the electrical property of the polymer, the relative dielectric coefficient (εr), a dimensionless coefficient, is used, and it represents ratio of the absolute value of permittivity of a material to the vacuum permittivity of the material. The accumulated charge (Q) that passed through a circuit has linear relationship with consumed voltage (U) as shown in Eq. (9.18). C is the capacitance and it indicates the ability of a system to store an electric charge. Q ¼ CU C ¼ εr ε0

(9.19)

A d

(9.20)

Capacitance can be obtained by vacuum’s dielectric coefficient (ε0) and εr. A is the disk’s area of the condenser circuit for measure capacitance and d is the distance between plates. With higher εr, more capacitance and accumulated charge of the material will have. Table 9.4 shows examples of εr of several polymers.

9.4.1 Conductive polymers Thanks to the advancing of technology, the unsaturated polymeric backbone can be synthesized which results in preparation of conductive polymers. Henry Letheby was the first scientist to introduce the usage of polyaniline (PANI) in electricity conduction in 1862. Polyacetylene, polyphenylene vinylene, polypyrrole, and polypyrrole are examples of conductive polymers (Fig. 9.20). For conductive polymers, the polymer backbone composes of many sp2 hybridized carbon centers, which provide high mobility to the electrons and resulting in conductivity. TABLE 9.4 Relative dielectric coefficient of various polymers at 23°C under 1 kHz. Polymer

εr

PTFE

2.1

Polyethylene

2.25

Polyimide

3.4

Polystyrene

2.2–2.36

I. Polymer science

References

201

FIG. 9.20

Examples of conductive polymers: polyphenylene vinylene (A), polyacetylene (B), polypyrrole (C), and polyaniline (D).

References [1] J.D. Menczel, R.B. Prime, P.K. Gallagher, Thermal analysis of polymers: fundamentals and applications, J. Therm. Anal. 5 (2009) 698. [2] W.N. Dos Santos, P. Mummery, A. Wallwork, Thermal diffusivity of polymers by the laser flash technique, Polym. Test. 24 (5) (2005) 628–634. [3] M.A. Kashfipour, N. Mehra, J. Zhu, A review on the role of interface in mechanical, thermal, and electrical properties of polymer composites, Adv. Compos.Hybrid Mater. 1 (2018) 415–439. [4] A. Rudin, P. Choi, Properties of polymer solids and liquids, Elem. Polym. Sci. Eng. (2012) 149–229. [5] A.D. Padsalgikar, Introduction to plastics, in: Plastics in Medical Devices for Cardiovascular Applications, Elsevier Inc., 2017, pp. 1–29. Available from: https://doi.org/10.1016/B978-0-323-47358-3.00017-X. [6] A. Hale, Chapter 9 thermosets, in: Handbook of Thermal Analysis and Calorimetry, vol. 3, Elsevier, 2002, pp. 295–354. [7] C. Huang, X. Qian, R. Yang, Thermal conductivity of polymers and polymer nanocomposites, Mater. Sci. Eng. R. Rep. 132 (May) (2018) 1–22. Available from: https://doi.org/10.1016/j.mser.2018.06.002. [8] C.L. Choy, E.L. Ong, F.C. Chen, Thermal diffusivity and conductivity of crystalline polymers, J. Appl. Polym. Sci. 26 (7) (1981) 2325–2335. [9] P. Gill, T.T. Moghadam, B. Ranjbar, Differential scanning calorimetry techniques: applications in biology and nanoscience, J. Biomol. Tech. 21 (2010) 167–193. [10] I.B. Durowoju, K.S. Bhandal, J. Hu, B. Carpick, M. Kirkitadze, Differential scanning calorimetry—a method for assessing the thermal stability and conformation of protein antigen, J. Vis. Exp. (2017) 55262. [11] P.J. Haines, F.W. Wilburn, Differential thermal analysis and differential scanning calorimetry, Therm. Methods Anal. i (1995) 63–122. [12] D.I. Bower, D.I. Bower, Some physical techniques for studying polymers, in: An Introduction to Polymer Physics, Cambridge University Press, 2012. [13] J.F. Johson, P.S. Gill, Analytical Calorimetry, Springer Nature, 1984. [14] K. Menard, Thermomechanical analysis, in: Dynamic Mechanical Analysis, CRC Press, 2008, pp. 57–69. [15] U.W. Gedde, Polymer physics, J. Chem. Inf. Model. 53 (2013) 1689–1699. [16] E.H. Alsharaeh, Polystyrene-poly(methyl methacrylate) silver nanocomposites: significant modification of the thermal and electrical properties by microwave irradiation, Materials 9 (2016) 458. [17] M.A. Meyers, K.K. Chawla, Mechanical Behavior of Materials, Cambridge University Press, 2009. [18] M.L. Cerrada, Introduction to the viscoelastic response in polymers, in: Thermal Analysis Fundamentals and Applications to Material Characterization, Universidade da Corun˜a, Servizo de Publicacio´ns, 2005, pp. 167–182. [cited 2019 Dec 5]. Available from: https://ruc.udc.es/dspace/handle/2183/11487. [19] K. Balani, V. Verma, A. Agarwal, R. Narayan, Physical, thermal, and mechanical properties of polymers, in: Biosurfaces, John Wiley & Sons, Inc., 2015, pp. 329–344.

I. Polymer science

C H A P T E R

10

Hydrogels Wenda Wang, Ravin Narain, Hongbo Zeng Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

10.1 Introduction Hydrogels are three-dimensional (3D) cross-linked polymer networks, which can absorb and retain large amount of water. The first hydrogel material appeared in literature in 1960. Wichterle and Lim reported a biocompatible polyhydroxyethylmethacrylate (PHEMA) hydrogel, which was used for permanent contact applications with human tissues (e.g., contact lenses, arteries, etc.) [1]. Over the past decades, advanced hydrogel materials have received great research interests. Due to their tunable properties and functionalities as well as their simple preparation methods, hydrogels play important roles in numerous biomedical and engineering applications, ranging from tissue-engineering scaffolds, drug-delivery systems, soft contact lenses, and antifouling coatings, to sensors, actuators, soft robotics, and wastewater treatment [2–9]. The formation of hydrogels involves a cross-linking process of polymer chains. Such process is also known as the “gelation” process. Based on different gelation mechanisms, gelation can take place either by physical cross-linking (physical gelation) or by chemical cross-linking (chemical gelation) of polymer chains. In the case of physically cross-linked hydrogels, the formation of hydrogel network results from various strong/weak intermolecular interactions between the polymer chains (e.g., hydrogen bonds [10, 11], electrostatic interactions [12], hydrophobic interactions [13, 14], crystallization [15, 16], etc.). In the case of chemically crosslinked hydrogels, polymer chains are cross-linked by covalent bonds, which are formed either by chemical reactions of complementary functional groups (between polymers or between polymers and cross-linkers) or by free radical polymerization of vinyl monomers in the presence of cross-linking agents. In order to meet the requirements and standards in various biomedical and engineering applications, different properties of the hydrogel need to be carefully characterized. Generally, the properties of the hydrogel can be characterized from five aspects, including physical (e.g., swelling ratio, degradability, thermal stability, porosity, etc.), chemical (e.g., chemical

Polymer Science and Nanotechnology https://doi.org/10.1016/B978-0-12-816806-6.00010-8

203

# 2020 Elsevier Inc. All rights reserved.

204

10. Hydrogels

composition, etc.), mechanical (e.g., tensile/compressive strength, Young’s modulus, toughness, etc.), rheological (e.g., loss/storage modulus, viscosity, etc.), and biological (e.g., biocompatibility, etc.) properties. It is important to be familiar with the commonly used characterization methods of hydrogels. “Self-healing” refers to the ability of a material to heal the damage autonomously and regain its original properties. Developing advanced self-healing hydrogels has attracted much research interests since the self-healing property could not only prolong the lifespan but also improve the reliability and durability of the hydrogels in various biomedical and engineering applications. Based on the self-healing mechanisms, the self-healing hydrogels can be divided into physically and chemically self-healing hydrogels. Physically self-healing hydrogels reform the networks through reversible noncovalent interactions (e.g., hydrogen bonds [17, 18], hydrophobic interactions [19], metal-ligand coordination [20, 21], host-guest interactions [22, 23], a combination of multiple intermolecular interactions [5, 24], etc.). Chemically self-healing hydrogels restore the structure through dynamic covalent chemistry (e.g., phenylboronic ester complexation [3, 25], Schiff base [26, 27], acylhydrazone bonds [28, 29], disulfide bonds [30], reversible radical reactions [31, 32], Diels-Alder reactions [33], etc.). It is critical to understand the self-healing mechanisms fundamentally so that one can adopt the appropriate design strategies to fabricate self-healing hydrogels. Conventional hydrogels are considered to be mechanically weak with low toughness and fracture energy (