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

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.

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Sch?fer 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.

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Sch?fer 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.
Content:
Front Matter....Pages I-XVII
Power Laws, Scaling, Universal Crossover — a Survey of Phenomenology....Pages 1-10
Front Matter....Pages 11-11
From a Microscopic Description to Simple Models: Some Folk-Lore....Pages 13-20
The Noninteracting Gaussian Chain....Pages 21-32
The Cluster Expansion....Pages 33-51
Grand Canonical Description of Solutions at Finite Concentration....Pages 53-97
Breakdown of the Expansions in the Excluded Volume Region....Pages 99-102
Continuous Chain Model and Naive Two Parameter Theory....Pages 103-123
Front Matter....Pages 125-125
The Renormalization Group: Fundamental Aspects....Pages 127-141
Scaling Theory....Pages 143-154
More Complicated Interactions and the General Structure of the Renormalization Group....Pages 155-176
Front Matter....Pages 177-177
Renormalized Perturbation Theory and Field-Theoretic Renormalization Group....Pages 179-205
Dimensional Regularization and Minimal Subtraction....Pages 207-223
Quantitative Form of the Renormalization Group Mapping....Pages 225-244
The Renormalized Tree Approximation: a Simple Illustration of the Theory....Pages 245-256
Front Matter....Pages 257-257
Dilute Limit: Density Correlations, Virial Coefficients, and Interpenetration Ratio....Pages 259-303
Dilute Limit: Details on the Internal Structure of Isolated Coils....Pages 305-343
Thermodynamic Quantities for Finite Overlap....Pages 345-379
Density Autocorrelations at Finite Overlap....Pages 381-400
The Density Cumulant....Pages 401-430
Summarizing Overview....Pages 431-433
Front Matter....Pages 435-435
The ?-Region....Pages 437-477
Multicomponent Solutions....Pages 479-539
Back Matter....Pages 541-554

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Sch?fer 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.
Content:
Front Matter....Pages I-XVII
Power Laws, Scaling, Universal Crossover — a Survey of Phenomenology....Pages 1-10
Front Matter....Pages 11-11
From a Microscopic Description to Simple Models: Some Folk-Lore....Pages 13-20
The Noninteracting Gaussian Chain....Pages 21-32
The Cluster Expansion....Pages 33-51
Grand Canonical Description of Solutions at Finite Concentration....Pages 53-97
Breakdown of the Expansions in the Excluded Volume Region....Pages 99-102
Continuous Chain Model and Naive Two Parameter Theory....Pages 103-123
Front Matter....Pages 125-125
The Renormalization Group: Fundamental Aspects....Pages 127-141
Scaling Theory....Pages 143-154
More Complicated Interactions and the General Structure of the Renormalization Group....Pages 155-176
Front Matter....Pages 177-177
Renormalized Perturbation Theory and Field-Theoretic Renormalization Group....Pages 179-205
Dimensional Regularization and Minimal Subtraction....Pages 207-223
Quantitative Form of the Renormalization Group Mapping....Pages 225-244
The Renormalized Tree Approximation: a Simple Illustration of the Theory....Pages 245-256
Front Matter....Pages 257-257
Dilute Limit: Density Correlations, Virial Coefficients, and Interpenetration Ratio....Pages 259-303
Dilute Limit: Details on the Internal Structure of Isolated Coils....Pages 305-343
Thermodynamic Quantities for Finite Overlap....Pages 345-379
Density Autocorrelations at Finite Overlap....Pages 381-400
The Density Cumulant....Pages 401-430
Summarizing Overview....Pages 431-433
Front Matter....Pages 435-435
The ?-Region....Pages 437-477
Multicomponent Solutions....Pages 479-539
Back Matter....Pages 541-554
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