The effect of surfaces on molecular ordering in thin liquid-crystal systems

A theoretical method for analyzing the interplay between pair long-range intermolecular forces and nonlocal, relatively short-range, surface interactions in liquid crystals, confined between plates of thin planar cells, is developed. It is shown that this method, as involving the concept of local orientational and translational order parameters, enables detailed investigations of the emergence of smectic A, nematic, and isotopic phases, as well as yields an insight into phase transitions between them, in cases of systems strongly affected by surfaces. The evidence of various surface effects, including the coexistence of different phases and the inward propagation of surface melting under the increase of temperature, is also given. The underlying numerical procedure, based on the algorithm of self-consistent calculations of local order parameters, is found to be very effective, allowing one to consider model systems of rather large thicknesses, corresponding to thicknesses of real sample cells.