The Excluded Volume Problem For Dilute Polymer Solutions

Schäfer gives a concise overview of the static equilibrium properties of polymer solutions. In the first part diagrammatic perturbation theory is derived from scratch. The second part illustrates the basic ideas of the renormalization group (RG). The crucial role of dilation invariance is stressed. The more efficient method of dimensional regularization and minimal subtractions is worked out in part three. The fourth part contains a unified evaluation of the theory to the one loop level. All the important experimental quantities are discussed in detail, and the results are compared extensively to experiment. Empirical methods of data analysis are critically discussed. The final (fifth) part is devoted to extensions of theory. The first three parts of this book may serve as the basis of a course. Parts four and five are hoped to be useful for detailed quantitative evaluations of experiments.

The effect of excluded volume on the coil size of dilute linear polymers was investigated by off-lattice Monte Carlo simulations. The radius of gyration R{sub g} was evaluated for a wide range of chain lengths at several temperatures and at the athermal condition. The theta temperature and the corresponding theta chain dimensions were established for the system, and the dependence of the size expansion factor, a{sub s} = R{sub g} /(R{sub g}){sub {theta}}, on chain length N and temperature T was examined. For long chains and at high temperatures, a{sub s} is a function of N/N{sub s}2 alone, where the length scale N{sub s}2 depends only on T. The form of this simulations-based master function compares favorably with [alpha]{sub s}(M/M{sub s}2), an experimental master curve for linear polymers in good solvents, where M{sub s}2 depends only on polymer-solvent system. Comparisons when N{sub s}2(T) and M{sub s}2(system) are reduced to common units, numbers of Kuhn steps, strongly indicate that coil expansion in even the best of good solvents is small relative to that expected for truly athermal solutions. An explanation for this behavior is proposed, based on what would appear to be an inherent difference in the equation of state properties for polymeric and monomeric liquids.

A 7090 IBM digital computer program was developed to verify certain results and contribute to the excluded volume problem. The distribution of the mean square length of all possible walks of n steps was computed for walks of up to and including sixteen steps in the two dimensional, 90 degrees, three-choice lattice. The values of u sub n, non-intersecting closed walks of n steps, were also computed and the computed values of nonintersecting walks of n steps and u sub n agree perfectly with the values given by Fisher and Sykes (Phys. Rev. 14:45-48,1959). (Author).

Written by a chemical physicist specializing in macromolecular physics, this book brings to life the definitive work of celebrated scientists who combined multidisciplinary perspectives to pioneer the field of polymer science. The author relates firsthand the unique environment that fostered the experimental breakthroughs underlying some of today's

The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This volume explores topics from Thermodynamic Properties of Polyelectrolyte Solutions to ion-binding of polyelectrolytes. The book features: The only series of volumes available that presents the cutting edge of research in chemical physics Contributions from experts in this field of research Representative cross-section of research that questions established thinking on chemical solutions An editorial framework that makes the book an excellent supplement to an advanced graduate class in physical chemistry or chemical physics