Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Phases and Mesophases
- 2 Phase Transitions
- 3 Order Parameters
- 4 Distributions
- 5 Particle–Particle Interactions
- 6 Dynamics and Dynamical Properties
- 7 Molecular Theories
- 8 Monte Carlo Methods
- 9 The Molecular Dynamics Method
- 10 Lattice Models
- 11 Molecular Simulations
- 12 Atomistic Simulations
- Appendix A A Modicum of Linear Algebra
- Appendix B Tensors and Rotations
- Appendix C Taylor Series
- Appendix D The Dirac Delta Function
- Appendix E Fourier Series and Transforms
- Appendix F Wigner Rotation Matrices and Angular Momentum
- Appendix G Molecular and Mesophase Symmetry
- Appendix H Quaternions and Rotations
- Appendix I Nuclear Magnetic Resonance
- Appendix J X-ray Diffraction
- Appendix K Stochastic Processes
- Appendix L Simulating Polarized Optical Microscopy Textures
- Appendix M Units and Conversion Factors
- Appendix N Acronyms and Symbols
- References
- Index
7 - Molecular Theories
Published online by Cambridge University Press: 21 July 2022
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Phases and Mesophases
- 2 Phase Transitions
- 3 Order Parameters
- 4 Distributions
- 5 Particle–Particle Interactions
- 6 Dynamics and Dynamical Properties
- 7 Molecular Theories
- 8 Monte Carlo Methods
- 9 The Molecular Dynamics Method
- 10 Lattice Models
- 11 Molecular Simulations
- 12 Atomistic Simulations
- Appendix A A Modicum of Linear Algebra
- Appendix B Tensors and Rotations
- Appendix C Taylor Series
- Appendix D The Dirac Delta Function
- Appendix E Fourier Series and Transforms
- Appendix F Wigner Rotation Matrices and Angular Momentum
- Appendix G Molecular and Mesophase Symmetry
- Appendix H Quaternions and Rotations
- Appendix I Nuclear Magnetic Resonance
- Appendix J X-ray Diffraction
- Appendix K Stochastic Processes
- Appendix L Simulating Polarized Optical Microscopy Textures
- Appendix M Units and Conversion Factors
- Appendix N Acronyms and Symbols
- References
- Index
Summary
This chapter develops the essentials of the two main types of approximate molecular theories for liquid crystals, originating from various modifications and extensions of the original theories of Maier and Saupe and of Onsager. Even though quite different, both theories are essentially of the Mean Field type, and obtain the anisotropic potential acting on a single particle by the effect of all the others in the system. A selection of results for the two approaches is presented.
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- Liquid Crystals and their Computer Simulations , pp. 332 - 358Publisher: Cambridge University PressPrint publication year: 2022