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
6 - Dynamics and Dynamical Properties
Published online by Cambridge University Press: 21 July 2022
- 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
The dynamic evolution of a classic molecular system is first introduced formally via Liouville equation. Then, single-particle time correlation functions and their general properties (like short and long time limits) for orientational correlation functions (OCF) in liquid crystals are discussed and translational and orientational diffusion coefficients are introduced. The link between OCFs, obtainable from computer simulations, and experiments is established with Linear Response theory and examples from dielectric relaxation, ionic and thermal conductivity, viscosities are presented, with reference to the literature. The rotational diffusion equation in an anisotropic fluid, normally employed to analyze experiments is also introduced, with explicit expressions derived for Fluorescence Depolarization.
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- Liquid Crystals and their Computer Simulations , pp. 288 - 331Publisher: Cambridge University PressPrint publication year: 2022