Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces

TL;DR

This paper introduces a coupled phase-field and hydrodynamic model to simulate morphological transitions in weakly compressible smectic liquid crystals, capturing defect dynamics, flow effects, and interface curvature influences.

Contribution

The model uniquely combines non-conserved smectic order with conserved density to describe complex morphological and defect evolution in smectic-isotropic interfaces.

Findings

Pyramidal domains form at focal conics with temperature increase.

Tangential flows are observed at the surface of pyramidal domains.

Coalescence and droplet formation of smectic layers are simulated.

Abstract

A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic-isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects lead to conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.