Liquid crystals and their computer simulations

Abstract

"There are two main approaches to the theoretical study of liquid crystals: continuum and molecular. The first, well covered in various good books (e.g. those by Chandrasekhar [1992]; de Gennes and Prost [1993]; Virga [1994]; Kleman and Lavrentovich [2003]; Stewart [2004]; Oswald and Pieranski [2005, 2006]; Barbero and Evangelista [2006]) considers anisotropic systems at macroscopic level and typically deals with optical and elastic properties as well as with many practical electrooptical applications of liquid crystals. At continuum level, liquid crystals are assumed to exist and their properties (e.g. elastic constants and viscosities) to be known, insofar as they are needed to parameterize the relevant equations. Molecules, phase transitions and spectroscopic properties are not normally taken into consideration. In this line of work computer simulations typically refer to a determination of the preferred orientation (director) or of the ordering tensor field that minimize the elastic free energy under a variety of boundary conditions, while dynamics is normally related to the solution of hydrodynamics equations for anisotropic fluids. The other main line of investigation deals"-- Cover -- Half-title -- Title page -- Copyright information -- Dedication -- Contents -- Preface -- 1 Phases and Mesophases -- 1.1 Introduction -- 1.2 Nematics -- 1.3 Polymeric Nematics -- 1.4 Chiral Nematics -- 1.5 Twist-Bend Nematic Phase -- 1.6 Biaxial Nematics -- 1.7 Orthogonal Smectics -- 1.8 Tilted Smectics -- 1.9 Smectic Liquid Crystal Polymers -- 1.10 Discotic and Columnar Phases -- 1.11 Lyotropics -- 1.12 Chromonics -- 1.13 Ionic Liquid Crystals -- 1.14 Colloidal Suspensions -- 1.15 Lyotropic Liquid Crystal Polymers -- 1.16 Liquid Crystal Elastomers -- 1.17 Active Liquid Crystals 2 Phase Transitions -- 2.1 Transitions between Phases -- 2.2 Phase Diagrams for One-Component Systems -- 2.3 Ehrenfest Classification of Phase Transitions -- 2.4 The Clausius-Clapeyron Equation -- 2.5 Empirical Order Parameters -- 2.6 Critical Exponents -- 2.7 Landau Theory -- 2.8 Lattice Models -- 2.9 The Nematic-Isotropic Transition -- 2.10 Blue Phases -- 2.11 Columnar Liquid Crystals -- 2.12 Smectic Transitions -- 2.13 Liquid Crystal Polymers -- 2.14 Lyotropics -- 2.15 Phase Diagrams for Colloidal Suspensions -- 3 Order Parameters -- 3.1 Single Particle Distributions -- 3.2 Positional Order 3.3 Orientational Order for Uniaxial Molecules -- 3.4 Experimental Determination of Orientational Order Parameters -- 3.5 Orientational Order from Computer Simulations -- 3.6 Landau-deGennes Q-Tensor Approach -- 3.7 Physical Significance of Order Parameters -- 3.8 Maximum Entropy -- 3.9 Orientational Order Parameters from X-ray Diffraction -- 3.10 Non-Cylindrical Molecules in Uniaxial Phases -- 3.11 Orientational Order in Biaxial Phases -- 3.12 Flexible Molecules -- 3.13 Order in Smectics -- 3.14 Columnar Phases -- 4 Distributions -- 4.1 Phase Space Distributions -- 4.2 Canonical Conditions 4.3 Isobaric-Isothermal Ensemble -- 4.4 Grand Canonical Ensemble -- 4.5 Microcanonical Conditions -- 4.6 Structural Properties -- 4.7 The Pair Distribution in Various Phases -- 4.8 Invariant Expansion of the Pair Distribution -- 4.9 Reduced Distributions -- 4.10 Some Thermodynamic Properties -- 4.11 Pretransitional Behaviour -- 4.12 Pair Correlations and X-ray Scattering -- 5 Particle-Particle Interactions -- 5.1 Intermolecular Interactions -- 5.2 Spherical Particles -- 5.3 Buckingham Potential -- 5.4 Atomistic Force Fields -- 5.5 Hard Anisotropic Particles (Shape Matters!) 5.6 Attractive-Repulsive Rigid Particles -- 5.7 Electrostatic Multipoles -- 5.8 Inductive and Dispersive Interactions -- 5.9 Distributed Effective Charges -- 5.10 Chiral Interactions -- 5.11 Hydrogen Bonds -- 6 Dynamics and Dynamical Properties -- 6.1 Introduction -- 6.2 Dynamic Evolution of Molecular Properties -- 6.3 Single Particle Dynamics -- 6.4 Orientational Correlation Functions -- 6.5 Orientational Joint Distributions -- 6.6 Correlations at Short and Long Times -- 6.7 Translational Diffusion -- 6.8 Time Correlation Functions from Trajectories