Introduction to the Theory of Soft Matter (eBook)

From Ideal Gases to Liquid Crystals

Jonathan V. Selinger (Autor)

eBook Download: PDF

2015 | 1st ed. 2016
X, 185 Seiten
Springer International Publishing (Verlag)
978-3-319-21054-4 (ISBN)

Infos

This book presents the theory of soft matter to students at the advanced undergraduate or beginning graduate level. It provides a basic introduction to theoretical physics as applied to soft matter, explaining the concepts of symmetry, broken symmetry, and order parameters; phases and phase transitions; mean-field theory; and the mathematics of variational calculus and tensors. It is written in an informal, conversational style, which is accessible to students from a diverse range of backgrounds. The book begins with a simple 'toy model' to demonstrate the physical significance of free energy. It then introduces two standard theories of phase transitions-the Ising model for ferromagnetism and van der Waals theory of gases and liquids-and uses them to illustrate principles of statistical mechanics. From those examples, it moves on to discuss order, disorder, and broken symmetry in many states of matter, and to explain the theoretical methods that are used to model the phenomena. It concludes with a chapter on liquid crystals, which brings together all of these physical and mathematical concepts. The book is accompanied online by a set of 'interactive figures'-some allow readers to change parameters and see what happens to a graph, some allow readers to rotate a plot or other graphics in 3D, and some do both. These interactive figures help students to develop their intuition for the physical meaning of equations. This book will prepare advanced undergraduate or early graduate students to go into more advanced theoretical studies. It will also equip students going into experimental soft matter science to be fully conversant with the theoretical aspects and have effective collaborations with theorists.

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 19.8.2015
• Reihe/Serie: Soft and Biological Matter
• Reihe/Serie: Soft and Biological Matter
• Zusatzinfo: X, 185 p. 78 illus., 69 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik ► Bauwesen
• Schlagworte: Dynamics of phase transitions • Gas-liquid transition • Glass transition • Mathematical and theoretical methods for soft matter • Order, disorder and symmetry in soft matter • Order transitions in liquid crystals • Soft condensed matter textbook • Theory of phase transitions
• ISBN-10: 3-319-21054-8 / 3319210548
• ISBN-13: 978-3-319-21054-4 / 9783319210544