Surface energy of the biaxial nematic liquid crystal

Abstract

In this paper, two forms of surface energy of the biaxial nematic liquid crystal are derived. One is related to the deviation of surface directors with respect to the easy axes０,０ and０in the surface. The other is related to the surface order parameter matrix Q. The relations between the two forms are derived. In the former one, four independent coefficients are involved while in the latter one, only two independent coefficients are involved. In order to inspect the physical meaning of these coefficients, a simple model of molecular interaction between liquid crystal and boundary plate is proposed. In the model, the biaxial orientation of molecules along０and 0 is assumed to arise from two perpendicular mean fields along 0,０competing with each other. In three geometric features of Freedericksz transition where and rotate around 0， [WTHX][AKb^][WTBZ] and [WTHX][AKc^D][WTBZ] around [WTHX][AKa^D][WTBZ]0,[WTHX][AKc^D][WTBZ] and [WTHX][AKa^D][WTBZ] around [WTHX][AKb^][WTBZ]０ respectively, possible experimental measurements of surface anchoring coefficients [WTBX]Wa,Wb[WTBZ] and [WTBX]Wc[WTBZ] involved in the distortions are explored.