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

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