Microscopic and macroscopic theories for the dynamics of polar liquid crystals

TL;DR

This paper develops and compares microscopic and macroscopic models for the dynamics of polar liquid crystals, providing a link between molecular interactions and continuum descriptions.

Contribution

It derives dynamic equations from DDFT and compares them with Ginzburg-Landau equations, establishing a connection between microscopic and macroscopic models.

Findings

Dissipative dynamics can be derived from a dissipation function in both models.

Microscopic expressions for cross-coupling terms are obtained.

A bridge between molecular correlations and macroscopic modeling is established.

Abstract

We derive and analyze the dynamic equations for polar liquid crystals in two spatial dimensions in the framework of classical dynamical density functional theory (DDFT). Translational density variations, polarization, and quadrupolar order are used as order-parameter fields. The results are critically compared with those obtained using the macroscopic approach of time-dependent Ginzburg-Landau (GL) equations for the analogous order-parameter fields. We demonstrate that for both the microscopic DDFT and the macroscopic GL approach the resulting dissipative dynamics can be derived from a dissipation function. We obtain microscopic expressions for all diagonal contributions and for many of the cross-coupling terms emerging from a GL approach. Thus we establish a bridge between molecular correlations and macroscopic modeling for the dissipative dynamics of polar liquid crystals.