Statistical approach to the orienting photopolymer-nematic-liquid-crystal anchoring energy

A statistical approach for the nematic order on an orienting photopolymer, also taking into account the surface anisotropy, has been formulated in the framework of mean field theory. This approach gives a Boltzmann-type orientational distribution function depending on both nematic-nematic and nematic-polymer interaction energies. The azimuthal anchoring energy coefficient has been evaluated from the extra Helmholtz free energy within an interface of thickness xi that may be interpreted as the length over which the density changes from pure polymer to pure liquid crystal or, generally speaking, as the typical length over which the interaction between polymer and liquid crystal takes place. In the case of surface anisotropy given by linearly polarized UV photopolymerization, the anchoring energy coefficient depends on the exposure time and on xi.