We consider a nematic liquid crystal confined by two parallel planar interfaces, one being laterally homogeneous and the other provided by a substrate endowed with a periodic chemical stripe pattern. Based on continuum theory we analyze the influence of the lateral pattern on the liquid-crystalline Casimir force acting on the interfaces of the nematic cell at distance d due to the thermal fluctuations of the nematic director. For d much larger than the pattern periodicity, the influence of the patterned substrate can be described by a homogeneous, effective anchoring energy. By tuning this parameter we recover previous results for the liquid-crystalline Casimir force. For the general case, i.e., smaller separations, we present new numerical results.
@article{arxiv.cond-mat/0405668,
title = {Liquid-crystalline Casimir effect in the presence of a patterned substrate},
author = {F. Karimi Pour Haddadan and F. Schlesener and S. Dietrich},
journal= {arXiv preprint arXiv:cond-mat/0405668},
year = {2009}
}