Dynamical field theories for biaxial liquid crystals

Abstract

Phase field crystal (PFC) models constitute central tools for a microscopic understanding of the dynamics of complex systems in soft matter physics. They have found widespread application in the modeling of the uniaxial orientational ordering of liquid crystals. However, only very limited progress has been made in applying them to the more complex cases of biaxial phases and biaxial particles. Here, we discuss the microscopic derivation of PFC models for biaxial liquid crystals. We illustrate it by presenting two models, one involving four scalar orientational order parameters relevant for the dynamics of biaxial particles, and one involving two scalar order parameters and a director field to describe biaxial phases in a three-dimensional uniaxial nematic liquid crystal. These models allow for an efficient simulation of spatially inhomogeneous biaxial orientational ordering dynamics. We also combine a microscopic and macroscopic approach to extract model coefficients for a full biaxial model from the microscopic derivation for a simple special case. This universal method also enables to perform derivations for other low-symmetry particles where, due to the complexity of the general case, this has not been previously attempted.

References in corpus (12)

• Derivation of the phase field crystal model for colloidal solidification
• Superscreening and polarization control in confined ferroelectric nematic liquids
• On the origin of diverse time scales in the protein hydration layer solvation dynamics: A molecular dynamics simulation study
• Machine learning of a density functional for anisotropic patchy particles
• Perspective: New directions in dynamical density functional theory
• Stationary broken parity states in active matter models
• First-principles superadiabatic theory for the dynamics of inhomogeneous fluids
• Complex-tensor theory of simple smectics
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Defect dynamics in active smectics induced by confining geometry and topology
• Broken living layers: dislocations in active smectics
• Biaxial nematic order in fundamental measure theory