Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modeling

TL;DR

This paper develops a microscopic-to-macroscopic theoretical framework for two-dimensional polar liquid crystals, incorporating three local order parameters and their couplings, to better understand phase stability and applications like microswimmers.

Contribution

It derives a phase-field-crystal model from microscopic density functional theory for 2D polar liquid crystals, linking molecular correlations to macroscopic phase behavior.

Findings

Derived free-energy density involving three order parameters.

Established coupling constants connected to molecular correlations.

Provides a basis for numerical stability analysis of polar phases.

Abstract

Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions. Starting from microscopic density functional theory, we derive a phase-field-crystal expression for the free-energy density which involves three local order-parameter fields, namely the translational density, the polarization, and the nematic order parameter. Various coupling terms between the order-parameter fields are obtained which are in line with macroscopic considerations. Since the coupling constants are brought into connection with the molecular correlations, we establish a bridge from microscopic to macroscopic modeling. Our theory provides a starting point for further numerical calculations of the stability of polar liquid-crystalline phases and is also relevant for modeling of microswimmers which are intrinsically polar.