Complex-tensor Theory of Simple Smectics

Dr Tyler Shendruk (University of Edinburgh)

Thursday 13th October, 2022 14:00-15:00 Maths 311B / ZOOM (ID: 878 5223 3360)

Abstract

Many important biological and industrial substances have complex materials properties that arise from their internal structure and partial ordering, making them intermediate mesophases between pure liquids and solids. The smectic liquid crystal phase is a quintessential example that possesses lamellar structure — stacking along one direction while maintaining liquid-like disorder within layers. They are excellent systems for exploring self-assembly and topology in confining geometries because smectic layering allows both dislocation defects and disclinations. However, these very same properties that make smectic phases such interesting materials contrive to make them challenging to model. We present a novel complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation. We then construct a phenomenological Landau theory that employs the complex tensor in bulk, compression and curvature free energies, which is analogous to the Landau-de Gennes theory for nematic liquid crystals. This theory has the capacity to account for both parallel and perpendicular elastic contributions but can also reduce to previous employed models of simple smectics. We demonstrate its capability in describing both dislocations and disclinations, as well as arrested configurations and colloid-induced local ordering. Furthermore, we argue that this framework can be easily coupled to existing nematic descriptions. Though versatile, this theory considerably simplifies numerics, facilitating new studies of smectic phases and their topological defects under large deformations in non-trivial geometries.

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