Surface anchoring energy and the first order Fréedericksz transition of a NLC cell

Many authors have suggested new forms to describe the surface anchoring energy of the liquid crystal-wall interface, replacing the Rapini-Papoular (RP) formula g s = (1/2) A sin2 theta. If the RP function is considered as the primary approximation, and a lowest order modification is included, then the surface anchoring energy can be represented by g s = (1/2) A sin2 theta(1 + zeta sin2 theta). zeta characterizes the modification to the RP formula and varies for the different energy forms. It is well known that the RP formula predicts a second order Freedericksz transition. This paper points out that the transition can be first order if the modification is taken into account, in which case at the threshold point the tilt angle of the director at the middle layer of the cell, thetam, is finite. The conditions for the existence of the first order transition are obtained; zeta < 0 is required for a first order transition. The approximate expression of the threshold field is also given.