Excluded Volume Effects in Polymer Solutions

1. Front Matter

   Pages I-XVII

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2. Power Laws, Scaling, Universal Crossover — a Survey of Phenomenology

   1. Power Laws, Scaling, Universal Crossover — a Survey of Phenomenology

      • Lothar Schäfer

      Pages 1-10

3. Basic Theoretical Techniques

   1. Front Matter

      Pages 11-11

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   2. From a Microscopic Description to Simple Models: Some Folk-Lore

      • Lothar Schäfer

      Pages 13-20

   3. The Noninteracting Gaussian Chain

      • Lothar Schäfer

      Pages 21-32

   4. The Cluster Expansion

      • Lothar Schäfer

      Pages 33-51

   5. Grand Canonical Description of Solutions at Finite Concentration

      • Lothar Schäfer

      Pages 53-97

   6. Breakdown of the Expansions in the Excluded Volume Region

      • Lothar Schäfer

      Pages 99-102

   7. Continuous Chain Model and Naive Two Parameter Theory

      • Lothar Schäfer

      Pages 103-123

4. Renormalization Group and Scaling

   1. Front Matter

      Pages 125-125

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   2. The Renormalization Group: Fundamental Aspects

      • Lothar Schäfer

      Pages 127-141

   3. Scaling Theory

      • Lothar Schäfer

      Pages 143-154

   4. More Complicated Interactions and the General Structure of the Renormalization Group

      • Lothar Schäfer

      Pages 155-176

5. Field Theoretic Formulation of the Theory

   1. Front Matter

      Pages 177-177

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   2. Renormalized Perturbation Theory and Field-Theoretic Renormalization Group

      • Lothar Schäfer

      Pages 179-205

   3. Dimensional Regularization and Minimal Subtraction

      • Lother Schäfer

      Pages 207-223

   4. Quantitative Form of the Renormalization Group Mapping

      • Lothar Schäfer

      Pages 225-244

   5. The Renormalized Tree Approximation: a Simple Illustration of the Theory

      • Lothar Schäfer

      Pages 245-256

6. One Loop Approximation: Detailed Results and Comparison to Experiment

   1. Front Matter

      Pages 257-257

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   2. Dilute Limit: Density Correlations, Virial Coefficients, and Interpenetration Ratio

      • Lothar Schäfer

      Pages 259-303

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.

• Critical Phenomena
• Kritische Phänomene
• Polymer Solutions
• Polymerlösungen
• Renormalization group
• Statistical Mechanics
• Theoretical Physics
• Theoretische Physik
• polymer

• Universität GH Essen, FB7 Physik, Essen, Germany

  Lothar Schäfer

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