Stability of liquid crystalline phases in the phase-field-crystal model

Abstract

The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order parameter, and the mean local direction of the orientations. The equilibrium free-energy functional involves local powers of the order parameters up to fourth order, gradients of the order parameters up to fourth order, and different couplings between the order parameters. The stable phases of the equilibrium free-energy functional are calculated for various coupling parameters. Among the stable liquid-crystalline states are the isotropic, nematic, columnar, smectic A, and plastic crystalline phases. The plastic crystals can have triangular, square, and honeycomb lattices and exhibit orientational patterns with a complex topology involving a sublattice with topological defects. Phase diagrams were obtained by numerical minimization of the free-energy functional. Their main features are qualitatively in line with much simpler one-mode approximations for the order parameters.

Submitted to Physical Review E

References in corpus (8)

• Dynamics of a Brownian circle swimmer
• Derivation of the phase field crystal model for colloidal solidification
• Derivation of a three-dimensional phase-field-crystal model for liquid crystals from density functional theory
• Phase-field-crystal model for liquid crystals
• Liquid crystals in two dimensions: First-order phase transitions and nonuniversal critical behavior
• Glassy Dislocation Dynamics in 2-D Colloidal Dimer Crystals
• Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
• Local order and orientational correlations in liquid and crystalline phases of carbon tetrabromide from neutron powder diffraction measurements

Cited by in corpus (12)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Classical dynamical density functional theory: from fundamentals to applications
• Active crystals on a sphere
• Differently Shaped Hard Body Colloids in Confinement: From passive to active particles
• Microscopic and macroscopic theories for the dynamics of polar liquid crystals
• Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
• Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Structure and dynamics of interfaces between two coexisting liquid crystalline phases
• Active smectics on a sphere
• Liquid crystalline growth within a phase-field crystal model
• Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions