Geometry and phase transitions in colloids and polymers / William Kung.

Includes bibliographical references and index.

The big picture. 1. Modern physics at a glance -- Geometry and phase transitions, in general. 2. Phase transitions and critical phenomena. 2.1. Introduction. 2.2. Modern classification of phase transitions. 2.3. First-order phase transitions: solid-liquid transition. 2.4. Second-order phase transitions: scaling and universality. 2.5. Renormalization group. 2.6. Mathematical miscellanies: semi-group structure and fixed-point theorems. 2.7. Conclusion. 3. Overview of density-functional theory. 3.1. Introduction. 3.2. Electronic density-functional theory. 3.3. Classical density-functional theory. 3.4. Conclusion. 4. Survey of solid geometry and topology. 4.1. Introduction. 4.2. Lattice symmetry groups. 4.3. Two-dimensional space groups. 4.4. Three-dimensional point groups. 4.5. Conceptual framework of the foam model. 4.6. The Kelvin Problem and the Kepler conjecture. 4.7. Conclusion -- Geometry and phase transitions, in colloidal crystals. 5. Lattice free energy via the foam model. 5.1. Introduction. 5.2. Bulk free energy. 5.3. Interfacial free energy. 5.4. Conclusion. 6. Phases of charged colloidal crystals. 6.1. Introduction. 6.2. Phase transitions of charged colloids. 6.3. Foam analogy and charged colloids. 6.4. Conclusion. 7. Elasticity of colloidal crystals. 7.1. Introduction. 7.2. Foam analogy and cubic elastic constants. 7.3. Elasticity of charged colloidal crystals. 7.4. Elasticity of fuzzy colloids. 7.5. Conclusion -- Geometry and phase transitions, in topologically constrained polymers. 8. Topologically-constrained polymers in theta solution. 8.1. Introduction. 8.2. O(N)-symmetric ø[symbol]-theory. 8.3. Chern-Simons theory and Writhe. 8.4. One-loop scaling of closed polymers. 8.5. Two-loop results. 8.6. Conclusion -- Summary. 9. Final thoughts.

This monograph represents an extension of the author's original PhD thesis and includes a more thorough discussion on the concepts and mathematics behind his research works on the foam model, as applied to studying issues of phase stability and elasticity for various non-closed packed structures found in fuzzy and colloidal crystals, as well as on a renormalization-group analysis regarding the critical behavior of loop polymers upon which topological constraints are imposed. The common thread behind these two research works is their demonstration of the importance and effectiveness of utilizing geometrical and topological concepts for modeling and understanding soft systems undergoing phase transitions.

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