# Introduction to the Theory of Soft Matter

## From Ideal Gases to Liquid Crystals

• Jonathan V. Selinger
Book

Part of the Soft and Biological Matter book series (SOBIMA)

1. Front Matter
Pages i-x
2. Jonathan V. Selinger
Pages 1-5
3. Jonathan V. Selinger
Pages 7-24
4. Jonathan V. Selinger
Pages 25-49
5. Jonathan V. Selinger
Pages 51-62
6. Jonathan V. Selinger
Pages 63-72
7. Jonathan V. Selinger
Pages 73-82
8. Jonathan V. Selinger
Pages 83-89
9. Jonathan V. Selinger
Pages 91-110
10. Jonathan V. Selinger
Pages 111-130
11. Jonathan V. Selinger
Pages 131-182
12. Back Matter
Pages 183-185

### Introduction

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 by a set of “interactive figures,” which allow online readers to change parameters and see what happens to a graph, some allow users 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.

### Keywords

Dynamics of phase transitions Gas-liquid transition Glass transition Mathematical and theoretical methods for soft matter Order transitions in liquid crystals Order, disorder and symmetry in soft matter Soft condensed matter textbook Theory of phase transitions

#### Authors and affiliations

• Jonathan V. Selinger
• 1
1. 1.Liquid Crystal Inst, Kent State UniversiChemical Physics Interdisciplinary ProgrKentUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-21054-4
• Copyright Information Springer International Publishing Switzerland 2016
• Publisher Name Springer, Cham
• eBook Packages Physics and Astronomy
• Print ISBN 978-3-319-21053-7
• Online ISBN 978-3-319-21054-4
• Series Print ISSN 2213-1736
• Series Online ISSN 2213-1744
• Buy this book on publisher's site
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