Excluded Volume Effects in Polymer Solutions de Lothar Schäfer

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

Lothar Schäfer

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.

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Cuprins

1. Power Laws, Scaling, Universal Crossover — a Survey of Phenomenology.- I. Basic Theoretical Techniques.- 2. From a Microscopic Description to Simple Models.- 3. The Noninteracting Gaussian Chain.- 4. The Cluster Expansion.- 5. Grand Canonical Description of Solutions at Finite Concentration.- 6. Breakdown of the Expansions in the Excluded Volume Region.- 7*. Continuous Chain Model and Naive Two Parameter Theory.- II. Renormalization Group and Scaling.- 8. The Renormalization Group: Fundamental Aspects.- 9. Scaling Theory.- 10*. More Complicated Interactions and the General Structure of the Renormalization Group.- III. Field Theoretic Formulation of the Theory.- 11. Renormalized Perturbation Theory and Field-Theoretic Renormalization Group.- 12. Dimensional Regularization and Minimal Subtraction.- 13. Quantitative Form of the Renormalization Group Mapping.- 14. The Renormalized Tree Approximation: a Simple Illustration of the Theory.- IV. One Loop Approximation: Detailed Results and Comparison to Experiment.- 15. Dilute Limit: Density Correlations, Virial Coefficients, and Interpénétration Ratio.- 16. Dilute Limit: Details on the Internal Structure of Isolated Coils.- 17. Thermodynamic Quantities for Finite Overlap.- 18. Density Autocorrelations at Finite Overlap.- 19. The Density Cumulant.- 20. Summarizing Overview.- V. Special Topics.- 21. The ?-Region.- 22. Multicomponent Solutions.

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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.