From microscopic theory to macroscopic theory: a systematic study on static modeling for liquid crystals

TL;DR

This paper develops a systematic approach to connect microscopic molecular theories with macroscopic models for liquid crystals, introducing a new Q-tensor theory based on Onsager's theory that recovers classical models and characterizes different phases.

Contribution

It proposes a novel Q-tensor model derived from Onsager's molecular theory, linking microscopic and macroscopic descriptions of liquid crystals, including uniaxial and smectic-A phases.

Findings

Recovered Oseen-Frank theory from the Q-tensor model

Examined Oseen-Frank coefficients within the new framework

Characterized smectic-A phase using the derived macroscopic model

Abstract

In this paper, we propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with certain shape has been proposed. Making uniaxial assumption, we can recover the Oseen-Frank theory from the derived $Q$-tensor theory, and the Oseen-Frank model coefficients can be examined. In addition, the smectic-A phase can also be characterized by the derived macroscopic model.