Excluded Volume Effects in Polymer Solutions: As Explained by the Renormalization Group

ISBN-13: 9783642642548 / Angielski / Miękka / 2011 / 554 str.

Lothar Sch Fer

Opis

Schafer 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."

Spis treści

Power Laws, Scaling, Universal Crossover.- Part I: Basic Theoretical Techniques: From a Microscopic Description to Simple Models.- The Noninteracting Gaussian Chain.- The Cluster Expansion.- Grand Canonical Description of Solutions at Finite Concentration.- Breakdown of the Expansions in the Excluded Volume Region.- Continuous Chain Model and Naive Two Parameter Theory. Part II: Renormalization Group and Scaling: The Renormalization Group.- Scaling Theory.- More Complicated Interactions. Part III: Field Theoretic Formulation of the Theory: Renormalized Perrturbation Theory.- Dimensional Regularization and Minimal Subtraction.- Quantitative Form of the Renormalization Ground Mapping.- The Renormalized Tree Approximation. Part IV: One Loop Approximation: Detailed Results and Comparison to Experiment: Dilute Limit.- Details on Internal Structure of Isolated Coils.- Thermodynamic Quantities for Finite Overlap.- Density Autocorrelation at Finite Overlap.- The Density Cumulant.- Summarizing Overview. Part V: Special Topics: The Theta-Region.- Multicomponent Solutions.

Blurb

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. 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.