Modeling the isotropic/smectic-C tilted lamellar liquid crystalline transition

TL;DR

This paper extends a Landau-de Gennes model to describe the transition from isotropic to smectic-C liquid crystals, comparing two proposed models and analyzing their physical and computational viability.

Contribution

It introduces and evaluates two new extensions of the Landau-de Gennes model for the isotropic/smectic-C transition, focusing on physical accuracy and computational feasibility.

Findings

Neither model allows deterministic phase diagram computation.

Recommendations are made for model inclusion based on physics and computational considerations.

The study clarifies limitations of existing modeling approaches for smectic-C transitions.

Abstract

Extensions of a previously presented Landau-de Gennes type liquid crystalline phase transition model for the direct isotropic/smectic-A (lamellar) a phase transition to the direct isotropic/smectic-C (tilted lamellar) transition are studied. Two different proposed extensions to the model are studied both in the context of ideal ordering (point volume) and full three-dimensional uniaxial scalar/vector decomposition. Recommendations based upon the inclusion of essential physics and computational feasibility are made, distinguishing each of the two proposed extensions based upon these criteria. Additionally, it is found that the approach used for the isotropic/smectic-A model to deterministically compute phase diagram data is not possible for either of the two proposed isotropic/smectic-C models.