Surface energy of a nematic liquid crystal in contact with structured surfaces

A generalization of the functional form of the anchoring energy of a nematic liquid crystal in contact with a structured surface is proposed. The structured surface is represented by side-chain polymer, containing only aliphatic or aliphatic and mesogenic side groups, deposited as a thin alignment film onto a solid substrate. The basic assumption in the model developed in the present work is that the coupling between the polymer side groups and the nematic liquid crystal molecules is responsible for the elastic deformation and compression of the orienting groups taking place in the alignment film. We show that in the limit of small deformations, the surface energy is the same as the one given by the Rapini-Papoular approximation. In this limit, the effective anchoring strength is weak and is due to the elastic deformation of the orienting side groups, which is proportional to the inverse of the length of the aliphatic groups and the length of the linkage group of the mesogens, respectively. In the limit of large deformation, however, the term accounting the film compression is predominant which results in a nonzero torque facilitating the relaxation process of an imposed deformation when the applied electric field is switched off. Good agreement is found between the prediction of our model and the experimental data of the anchoring energy of a nematic liquid crystal aligned by means of Langmuir-Blodgett monolayers of fatty acids as a function of the length of their alkyl chains.