In the mean field approximation, it was assumed that each molecule is subjected to an average internal field which is independent of any local variations or short-range ordering. The orientational energy of a molecule may be postulated as where q is the angle which the molecular axis makes with the preferred axis, and S is the order parameter. The thermodynamic properties of an ordered system relative to those of the disordered to this relation the variation of the order parameter S versus temperature may be evaluated to get the clear points of liquid crystals under mean field approximation. The Gay-Berne potential was proved to be of considerable value in computer simulation studies of liquid crystals. The potential function g(q) was tried to form by using Gay-Berne functional. According to our experimental studies for the triphenylene derivatives with vinyloxy peripheral chains, which are abbreviated as C18H6(OC5H11)6-n(OC2H4OCH=CH2)n (n=0~3), the more unsaturated chain the molecule contains, the higher the clear point is. These molecules have been studied with an ONIOM(MP2/6-31G*(0.25):UFF) method. The interaction energies between two molecules in four configurations have been evaluated. Then the parameters in the Gay-Berne potential have been determined by comparison with these interaction energies. The clear point data obtained from the mean field approximation are in agreement with the experimental results.

Key words: iscotic liquid crystal, clear point, mean field, Gay-Berne potential, ONIOM method