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Geometry And Phase Transitions In Colloids And Polymers [Kõva köide]

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(Northwestern Univ, Usa)
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Geometry And Phase Transitions In Colloids And PolymersSuurem pilt
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Püsilink: https://www.kriso.ee/db/9789812834966.html
Märksõnad:
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.
Preface vii
List of Figures xv
List of Tables xxii
The Big Picture 1
1. Modern Physics at a Glance
3
Geometry and Phase Transitions, in General 15
2. Phase Transitions and Critical Phenomena
17
2.1 Introduction
17
2.1.1 Evolution of the Universe: Decoupling of the Four Fundamental Forces
18
2.1.2 Three States of Water
19
2.1.3 Spins and Magnetism
21
2.2 Modern Classification of Phase Transitions
23
2.3 First-Order Phase Transitions: Solid-Liquid Transition
24
2.4 Second-Order Phase Transitions: Scaling and Universality
25
2.5 Renormalization Group
26
2.5.1 Kadanoff Picture: Coarse-Graining of Spin Blocks
26
2.5.2 General Formulation
28
2.5.3 Critical Exponents
31
2.5.4 Origin of Universality Class
32
2.5.5 Wilsonian Picture: Momentum-Space Renormalization Group
33
2.6 Mathematical Miscellanies: Semi-Group Structure and Fixed-Point Theorems
34
2.6.1 Semi-groups
34
2.6.2 Miscellany on Fixed-Points
35
2.7 Conclusion
35
3. Overview of Density-Functional Theory
38
3.1 Introduction
38
3.2 Electronic Density-Functional Theory
38
3.3 Classical Density-Functional Theory
42
3.4 Conclusion
46
4. Survey of Solid Geometry and Topology
49
4.1 Introduction
49
4.2 Lattice Symmetry Groups
50
4.3 Two-Dimensional Space Groups
53
4.3.1 Hermann-Mauguin Crystallographic Notation
55
4.3.2 Orbifold notation
57
4.3.3 Why Are There Exactly 17 Wallpaper Groups?
78
4.3.4 Other Aspects of Topology in Physics
84
4.4 Three-Dimensional Point Groups
85
4.4.1 Face-centered Cubic (FCC) Lattices
85
4.4.2 Body-Centered Cubic (BCC) Lattices
88
4.4.3 A15 Lattices
89
4.5 Conceptual Framework of the Foam Model
90
4.6 The Kelvin Problem and the Kepler Conjecture
92
4.7 Conclusion
97
Geometry and Phase Transitions, in Colloidal Crystals 101
5. Lattice Free Energy via the Foam Model
103
5.1 Introduction
103
5.2 Bulk Free Energy
104
5.3 Interfacial Free Energy
109
5.3.1 Charged Colloidal Crystals
109
5.3.2 Fuzzy Colloidal Crystals
111
5.4 Conclusion
112
6. Phases of Charged Colloidal Crystals
115
6.1 Introduction
115
6.2 Phase Transitions of Charged Colloids
117
6.3 Foam Analogy and Charged Colloids
119
6.4 Conclusion
120
7. Elasticity of Colloidal Crystals
122
7.1 Introduction
122
7.2 Foam Analogy and Cubic Elastic Constants
124
7.3 Elasticity of Charged Colloidal Crystals
129
7.4 Elasticity of Fuzzy Colloids
137
7.5 Conclusion
143
Geometry and Phase Transitions, in Topologically Constrained Polymers 145
8. Topologically-Constrained Polymers in Theta Solution
147
8.1 Introduction
147
8.2 O(N)-Symmetric φ6-Theory
148
8.3 Chern-Simons Theory and Writhe
154
8.4 One-Loop Scaling of Closed Polymers
159
8.5 Two-Loop Results
163
8.6 Conclusion
170
Summary 175
9. Final Thoughts
177
Index 179