Derivation of a three-dimensional phase-field-crystal model for liquid crystals from density functional theory

TL;DR

This paper derives a three-dimensional phase-field-crystal model for liquid crystals from density functional theory, incorporating both translational and orientational order parameters, providing a microscopic basis for studying phase transitions.

Contribution

It introduces a generalized phase-field-crystal model for liquid crystals with microscopic expressions for all parameters, extending the conventional model to include orientational degrees of freedom.

Findings

Provides a microscopic derivation of the free energy functional.

Includes both translational density and orientational order parameters.

Offers a basis for exploring phase transitions and interfaces in liquid crystals.

Abstract

Using a generalized order parameter gradient expansion within density functional theory, we derive a phase-field-crystal model for liquid crystals composed by apolar particles in three spatial dimensions. Both the translational density and the orientational direction and ordering are included as order parameters. Different terms involving gradients in the order parameters in the resulting free energy functional are compared to the macroscopic Ginzburg-Landau approach as well as to the hydrodynamic description for liquid crystals. Our approach provides microscopic expressions for all prefactors in terms of the particle interactions. Our phase-field-crystal model generalizes the conventional phase-field-crystal model of spherical particles to orientational degrees of freedom and can be used as a starting point to explore phase transitions and interfaces for various liquid-crystalline phases.