Introduction to the Theory of Soft Matter (eBook)

Jonathan Selinger is Professor of Chemical Physics and Ohio Eminent Scholar at Kent State's Liquid Crystal Institute. His research focuses on the theory of liquid crystals, nanoparticle suspensions, and related topics in soft materials and seeks to make connections between fundamental statistical mechanics and technological applications.Selinger studied physics at Harvard University, receiving his A.B. in 1983 and Ph.D. in 1989. He then did postdoctoral research in Los Angeles, with positions at the UCLA Department of Physics and Caltech Department of Chemical Engineering. In 1992 he moved to the Naval Research Laboratory in Washington, DC, where he worked as a Research Physicist in the Center for Bio/Molecular Science and Engineering. In 2005 he came to his current position at Kent State. In addition to these research and teaching positions, he has also served as Associate Editor of Physical Review E, responsible for the liquid-crystal section of the journal.

Preface 7
Contents 9
1 Toy Model 11
2 Ising Model for Ferromagnetism 16
2.1 Model 16
2.2 Non-interacting Spins 18
2.2.1 Standard Solution 18
2.2.2 Solution in Terms of Energy and Entropy 20
2.3 Interacting Spins 23
2.3.1 Mean-Field Theory in Terms of Energy and Entropy 23
2.3.2 Mean-Field Theory in Terms of Average Field 32
3 Gases and Liquids 34
3.1 Ideal Gas at Fixed Volume 34
3.2 Ideal Gas at Fixed Pressure 38
3.3 Ideal Gas Under Gravity 41
3.4 Gas with Interactions: van der Waals Theory 43
3.5 Gas--Liquid Transition at Fixed Pressure 46
3.6 Behavior Near Critical Point 50
3.7 Gas--Liquid Transition at Fixed Volume 53
4 Landau Theory 59
4.1 Ising Ferromagnetism 60
4.2 Gas-Liquid Transition 65
4.3 General Order Parameters 68
4.4 Beyond Mean Field: Universality Classes 70
5 First Mathematical Interlude: Variational Calculus 71
5.1 Example: Bobsled Race 72
5.2 Minimization 74
5.3 Example: Guitar String 79
6 Field Theory for Nonuniform Systems 81
6.1 What is a Field? 81
6.2 Nonuniform System in a Disordered Phase 84
6.3 Interface Between Ordered Phases 87
7 Dynamics of Phase Transitions 91
7.1 Nucleation and Growth 91
7.2 Heterogeneous Nucleation 96
8 Solids: Crystals and Glasses 98
8.1 What is a Solid? 98
8.2 Crystals 99
8.3 Close-Packed Crystals, Crystallization of Hard Spheres 105
8.4 Elasticity and Viscosity 108
8.5 Microscopic Interpretation of Viscosity 113
8.6 Glass Transition 115
9 Second Mathematical Interlude: Tensors 118
9.1 What is a Tensor? 118
9.2 Working with Tensors 121
9.3 Standard Vector and Matrix Expressions 124
9.4 Transformation Under Rotation 128
9.5 Transformation Under Inversion 131
9.5.1 Right-Hand Rule Versus Left-Hand Rule 132
9.5.2 Inversion of Coordinates 133
9.5.3 Reflection of Coordinates 133
9.6 Magnitudes, Directions, and Visualization 134
10 Liquid Crystals 138
10.1 Order and Symmetry 138
10.2 Nematic Order Parameter 141
10.3 Landau-de Gennes Theory 147
10.4 Maier-Saupe Theory 154
10.5 Onsager Theory 162
10.6 Elasticity of Nematic Order 164
10.7 Frederiks Transition 169
10.8 Defects in Nematic Phase 175
10.9 Chirality and Cholesteric Liquid Crystals 183
10.10 Other Liquid-Crystal Phases 187
Index 190