Properties of surface Landau-de Gennes Q-tensor models

TL;DR

This paper analyzes surface Landau-de Gennes Q-tensor models for nematic liquid crystals on curved surfaces, exploring their properties, phase transitions, and how geometry influences molecular alignment.

Contribution

It derives a general thin film limit of the 3D Landau-de Gennes model, unifying various surface models and comparing their fundamental properties.

Findings

Alignment of molecules with principal curvature lines

Order parameter symmetry varies among models

Different phase transition behaviors identified

Abstract

Uniaxial nematic liquid crystals whose molecular orientation is subjected to a tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of freedom. We consider a general thin film limit of a Landau-de Gennes Q-tensor model which retains the characteristics of the 3D model. From this, previously proposed surface models follow as special cases. We compare fundamental properties, such as alignment of the orientational degrees of freedom with principle curvature lines, order parameter symmetry and phase transition type for these models, and suggest experiments to identify proper model assumptions.