The Isotropic-Nematic Interface with an Oblique Anchoring Condition

TL;DR

This paper investigates the isotropic-nematic interface with oblique anchoring using Ginzburg-Landau-de Gennes theory, providing analytical and numerical insights into order parameter profiles and director orientations under various boundary conditions.

Contribution

It introduces flexible variational profiles for uniaxial and biaxial order at the interface, extending previous work to oblique anchoring conditions and comparing results with numerical simulations.

Findings

Spatial order variations are confined near the interface.

Director orientation interpolates linearly between boundary conditions.

Results agree with density functional theory and molecular simulations.

Abstract

We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Gennes free energy. While spatial variations of the scalar uniaxial and biaxial order parameters are confined to the neighbourhood of the interface, nematic elasticity requires that the director orientation interpolate linearly between either planar or homoeotropic anchoring at the location of the interface and the imposed boundary condition at infinity. The selection of planar or homoeotropic anchoring at the interface is governed by the sign of the Ginzburg-Landau-de Gennes elastic coefficient L_2. Our variational calculations are in close agreement with our numerics and agree qualitatively with results from density functional theory and molecular simulations.