The isotropic-nematic interface with an oblique anchoring condition

We present numerical and analytic results for uniaxial and biaxial orders 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 homeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial orders, 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 neighborhood of the interface, nematic elasticity requires that the director orientation interpolate linearly between either planar or homeotropic anchoring at the location of the interface and the imposed boundary condition at infinity. The selection of planar or homeotropic 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.