A THERMODYNAMIC APPROACH TO THE ANCHORING PHENOMENON IN THE NEMATIC LIQUID CRYSTAL-SUBSTRATE SYSTEM

The phenomenon of anchoring in the nematic liquid crystal-amorphous su bstrate system is considered and model independent definitions of the surface nematic director, the surface tension and the anchoring energy coefficient are proposed. Then the Landau-de Gennes model of the syst em is studied for a specific choice of the surface parameters, which l eads to a continuous homeotropic-conical anchoring transition. The fre e energy as a function of the director at a distance l from the surfac e is found. It is shown that its form is different in two regions of t he temperature-distance plane separated by the line of a Freedericksz transition. The asymptotic behaviour of the free energy for large l an d for infinitesimal deviations of the director from the anchoring dire ction is studied. It is found that the asymptotic formula holds also i n the vicinity of the anchoring transition. Finally, the results of nu merical studies of the Landau-de Gennes model are compared with the pr edictions of a simple phenomenological model.