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

TL;DR

This paper numerically investigates the stability of various liquid crystalline phases within a phase-field-crystal model, revealing complex topological defect patterns and phase diagrams consistent with simpler models.

Contribution

It introduces a detailed phase-field-crystal model with multiple order parameters to analyze liquid crystal phase stability and topological defect structures.

Findings

Identified stable isotropic, nematic, columnar, smectic A, and plastic crystalline phases.

Found complex topological defect patterns in plastic crystals.

Phase diagrams align qualitatively with simpler one-mode approximations.

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.