Perturbative approach to the structure of a planar interface in the Landau-de Gennes model

The structure of nearly static planar interfaces is studied within the framework of the Landau-de Gennes model with the dynamics governed by the time-dependent Ginzburg-Landau equation. To account for the full elastic anisotropy the free energy expansion is extended to include a third order gradient term. The solutions corresponding to the in-plane or homeotropic director alignment at the interface are sought. For this purpose a consistent perturbative scheme is constructed which enables one to calculate successive corrections to the velocity and the order parameter of the interface. The implications of the solutions are discussed. The elastic anisotropy introduces asymmetry into the order parameter and free energy profiles, even for the high symmetry homeotropic configuration. The velocity of the interface with the homeotropic or in-plane alignment is enhanced or reduced, respectively. There is no reorientation of the optical axis in the boundary layer. For the class of nematogens with approximate splay-bend degeneracy the temperature dependence of the interface velocity is weakly affected by the remaining twist anisotropy.