Nonlocal tensor order parameter of the deformed state of liquid crystals

TL;DR

This paper introduces a nonlocal tensor order parameter for liquid crystals, improving modeling of their deformed states and phase transitions by addressing limitations of local models.

Contribution

It proposes a generalized nonlocal tensor order parameter framework that enhances the description of liquid crystal deformations and phase behavior.

Findings

Eliminates the drawback of local tensor models.

Demonstrates the model's effectiveness for small-scale structures.

Provides solutions for steady states and phase transitions.

Abstract

A generalized notion of a nonlocal tensor order parameter is introduced within the framework of the phenomenological approach. This parameter has the form of a traceless tensor correlation function or a tensor integral operator. Based on this form, the governing relations are written, which determine the steady states and phase transitions of the deformed liquid crystal. Linear relations for eigenfunctions of the introduced operator are derived. A principal drawback of currently available models of liquid crystals based on the local presentation of the tensor order parameter (equality of two Frank constants in the case of a quadratic form of the strain part of the free energy) is eliminated. Particular examples are considered, which demonstrate the model workability and the absence of contradictions in the model as well as its adequacy when describing small-scale structures.