On a molecular based Q-tensor model for liquid crystals with density variations

TL;DR

This paper explores a new Q-tensor model for liquid crystals that incorporates density variations, demonstrating its effectiveness through numerical simulations of phase transitions and interfaces, and connecting it with classical models.

Contribution

The paper introduces a new Q-tensor model that includes density as an order parameter, bridging classical models and capturing complex phase behaviors efficiently.

Findings

Successfully modeled phase transitions including smectic phases.

Effectively captured density variations at interfaces.

Connected the new model with classical liquid crystal theories.

Abstract

In this article, we study the new Q-tensor model previously derived from Onsager's molecular theory by Han \textit{et al.} [Arch. Rational Mech. Anal., 215.3 (2014), pp. 741-809] for static liquid crystal modeling. Taking density and Q-tensor as order parameters, the new Q-tensor model not only characterizes important phases while capturing density variation effects, but also remains computationally tractable and efficient. We report the results of two numerical applications of the model, namely the isotropic--nematic--smectic-A--smectic-C phase transitions and the isotropic--nematic interface problem, in which density variations are indispensable. Meanwhile, we show the connections of the new Q-tensor model with classical models including generalized Landau-de Gennes models, generalized McMillan models, and the Chen-Lubensky model. The new Q-tensor model is the pivot and an appropriate trade-off between the classical models in three scales.