fm Page i Friday, February 2, 2007 11:40 AM Title Page Physical Chemistry of Macromolecules Gary Patterson Department of Chemistry Carnegie Mellon University Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U. Government works Version Date: 20140313 International Standard Book Number-13: 978-1-4200-1450-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained.
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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.com and the CRC Press Web site at http://www.fm Page iii Friday, February 2, 2007 11:40 AM Contents Chapter one Introduction to macromolecules .1 What is a macromolecule?.2 The discovery of macromolecules.3 The structure of macromolecules in solution.4 The remarkable properties of pure bulk polymers.5 Building new materials using macromolecules.6 Suggestions for further reading.10 Chapter two Describing polymer structure .2 Geometric structure of macromolecules .3 Bond probability distributions.4 Rotational isomeric state approximation .5 Mean-squared end-to-end distance .6 Statistics of the random coil.7 Chain flexibility and the persistence length.23 Chapter three Measuring polymer structure .2 Polymer composition and sequence distribution.3 NMR spectroscopy of polymers.4 Measuring local conformations of polymers .6 Conformational statistics of n-hexane .7 Global measures of the chain structure .8 Light scattering from dilute polymer solutions.32 Chapter four The macromolecular basis of rubber elasticity .2 The thermodynamics of ideal-rubber elasticity.3 The statistical theory of rubber elasticity .4 Thermoelastic inversion point .5 The force of extension of real rubber .fm Page iv Friday, February 2, 2007 11:40 AM Chapter five Structure and properties of polymers in dilute solution.2 The structure of macromolecules in dilute solution .3 Flory theory of chain expansion.4 Thermodynamics of two component solutions .6 Flory theory of the second virial coefficient .7 Light scattering from two-component solutions .8 Flory theory of light scattering in dilute solution.9 Diffusion of particles in solution.10 Kirkwood theory of macromolecular friction .11 Concentration fluctuations and mutual diffusion.12 The viscosity of dilute polymer solutions .13 The effect of molecular-weight polydispersity .68 Chapter six Structure and properties of polymers in semidilute solution .2 The remarkable behavior of semidilute solutions.3 Microscopic theory of semidilute solutions .4 Viscosity in semidilute solutions.5 Structure near overlap.82 Chapter seven Structure and properties of polymers in concentrated solution .2 Flory-Huggins theory of concentrated solutions.3 The thermodynamics of swollen rubber: gels.4 Light scattering from concentrated solutions .5 Real solutions and the Flory–Orwoll theory.6 Diffusion in concentrated solutions.7 Viscoelasticity in concentrated polymer solutions .95 Chapter eight Structure and properties of polymers in the pure amorphous liquid state.2 Free volume and viscosity.3 Viscosity of low-molecular-weight chain liquids .4 Phenomenology of the glass transition.5 Temperature and pressure dependence of relaxation near the glass transition.fm Page v Friday, February 2, 2007 11:40 AM Chapter nine Structure and properties of rodlike polymers in solution.2 Characterization of rodlike polymers in solution .3 Second osmotic virial coefficient .4 Thermodynamics of rodlike polymer solutions. 114 Chapter ten Structure and properties of polyelectrolyte chains in solution .2 Structure of linear polyelectrolyte chains in dilute solution .3 Thermodynamics of polyelectrolyte solutions.4 Viscosity of polyelectrolyte solutions .fm Page vi Friday, February 2, 2007 11:40 AM DK2247_C000.fm Page vii Friday, February 2, 2007 11:40 AM Preface This book is the culmination of 40 years of thinking about macromolecules. It began when I considered where to attend graduate school and read Paul Flory’s15 Principles of Polymer Chemistry for the first time.
It continued at Stanford University as a member of the Flory laboratory. The application of statistical mechanics to the understanding of the properties of chain mole- cules was pursued during these years. During this time period I made the acquaintance of many polymer scientists. I learned from Robert Pecora that light scattering is a useful and informative technique for understanding molecular systems.
I was also privileged to meet Eugene Helfand while he was a visitor to Stanford in the Flory laboratory for a year. Our discussions continued at AT&T Bell Laboratories during the years from 1972 to 1984. The polymer science community at Bell Labs was large and diverse. Baker, president, would often drop by to discuss the details of my studies of the structure and dynamics of liquid polymers.
McCall, director, was a constant source of advice and encouragement. Shiro Matsuoka endeavored to teach me the importance of chemical engineering for the understanding of polymeric materials. Bovey and Field (“Stretch”) Winslow, editors of Macromolecules, opened up the full range of polymer science on a daily basis. Virtually every major figure in polymer science visited Bell Labs during my time there (1972 to 1984), and the fre- quent opportunities for travel and lecturing led to personal knowledge of most of the key contributors to the physical chemistry of macromolecules.
In addition, the large number of colleagues in polymer science provided an environment where any idea could be discussed in detail in rapid order. Good ideas could be critiqued and bad ideas could be demolished. Carnegie Mellon University is one of the important cradles of polymer science in the U. Edward Cassasa, editor of the Journal of Polymer Science, provided a vital link to the historical richness of the science of macromole- cules.
Guy Berry was an invaluable resource to everything macromolecular. The opportunity to teach courses in the physical chemistry of macromole- cules provided the motivation to create a coherent presentation of the prin- ciples of the discipline. This book was developed as a series of lectures for a graduate course in the physical chemistry of polymers. It assumes an advanced undergraduate DK2247_C000.fm Page viii Friday, February 2, 2007 11:40 AM knowledge of physical chemistry.
It contains much more than can be covered in one semester, but it is neither comprehensive nor exhaustive. It focuses on a coherent picture of polymer science inspired by pioneers like Flory, deGennes, and Ferry. Topics are developed in enough detail to inspire con- fidence in the results, and the limitations of the treatments are discussed explicitly. No attempt has been made to present the most detailed level of understanding available in the research literature.
The goal of the lectures was to make it possible to continue the development of the student to the point where the classic books and papers of the science of macromolecules could be read and understood. Nevertheless, the eventual level of the book will be a challenge to students (or scholars) with a limited knowledge of physical chemistry or polymer science. It is hoped that this book will be helpful to anyone trying to understand the science of macromolecules at a level high enough to work in this discipline. The book opens with a historical reflection on the emergence of a scien- tific discipline known as polymer science.
The influence of Herbert Morawetz on my own thinking in this area is significant. In addition, a historical project on “Paradigms in Polymer Science” is currently in progress at the Chemical Heritage Foundation. I am grateful for the award of the Charles C. Price Fellowship in Polymer History that facilitated that work and resulted in the completion of the present volume.
The concrete visualization of macromolecules necessary to formulate detailed predictions of properties provides the fundamental conceptual world that defines this book. Macromolecules are constrained by the same forces that define any molecule, and the atomic level of description is essen- tial for many problems. The inspiration for the presentation found here for the rotational isomeric state model is the classic book by Flory,19 Statistical Mechanics of Chain Molecules. When more-global properties are considered, smoothed models such as the Gaussian chain or wormlike chain model are more tractable.
The importance of selecting a model that is both empirically adequate and mathematically solvable is stressed. While this book is primarily theoretical, and the number of equations is very large, the experimental basis of polymer science is always in view. Three experimental techniques that have been important in the development of the understanding of the macromolecular paradigm are featured in Chapter 3. The ability of nuclear magnetic resonance (NMR) to distinguish the local chemical environment and the time scale for molecular motion has made this a valuable tool in the elucidation of polymer structure and dynamics.
Many of these insights are presented in a monograph by Frank A.4 The experimental basis for the rotational isomeric state model is often neglected. Actual rotational isomeric states can be experimentally visualized using vibrational spectroscopy, and R. Snyder38 has demonstrated this in detail. Another of the key experimental techniques that have contributed to our current paradigm for chain molecules is light scattering.
The historical development of this topic is rich with insights into the nature of macromol- ecules. With the invention of the laser and the publication of the classic DK2247_C000.fm Page ix Friday, February 2, 2007 11:40 AM monograph of Berne and Pecora,3 light scattering has been established as a central tool in polymer science. The phenomenon of rubber elasticity fascinated scientists of all kinds during the 19th century. The explanation of the temperature dependence of the force of retraction in terms of the Gaussian theory of chain statistics was one of the first great triumphs of the macromolecular paradigm.
One of the recurrent themes of this book is the clear explanation of actual phenomena in terms of the macromolecular nature of the system. The existence of dilute solutions of macromolecules was denied by many experts until the macromolecular hypothesis was largely accepted in the time period from 1930 to 1940. The dilute-solution state is still the basis for characterizing individual macromolecules and the interactions of pairs of macromolecules and the solvent. The structural, thermodynamic, and hydro- dynamic properties of polymer solutions are explained in terms of the ran- dom-coil model developed by Kuhn, Debye, Flory, Kirkwood, Yamakawa, and deGennes.
While this subject alone could easily be the basis for a one- semester course, the topics are developed so that the material could be presented as part of a complete development of the subject. Individual random-coil chain molecules pervade a very large volume compared with the actual chemical volume of the chain. The conceptual framework for understanding the properties of solutions concentrated enough so that the pervaded volume of the chains is comparable to the total solution volume — the so-called semidilute state — has been presented in the classic book by Pierre-Gilles deGennes,9 Scaling Concepts in Polymer Phys- ics.