Biaxiality at the Isotropic-Nematic Interface with Planar Anchoring

TL;DR

This paper refines the understanding of biaxiality at the isotropic-nematic interface using Ginzburg-Landau-de Gennes theory, providing improved analytic and numerical results that align closely with density functional data.

Contribution

It offers an improved analytic treatment of biaxiality at the interface, enhancing agreement with numerical simulations and density functional results.

Findings

Enhanced agreement between analytic and numerical profiles.

Accurate asymptotic decay results for biaxial order.

Better fits to density functional data.

Abstract

We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface and accurate fits to data from density functional approaches to this problem.