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A simplified model of the nano-structured polymeric surface was proposed,characterized by a one-dimensional periodic stripe patterned surface with alternate planar and homeotropic anchoring.This paper investigated the effect of both the coupling of nematic liquid crystals with alignment layer polymers and the coupling of the polymers with the substrate surface,on the anchoring of nematic liquid crystals at such a surface,using the extended anisotropic surface energy form proposed by Alexe-Ionescu et al.In our theoretical treatment,the equal anchoring strength of the two anchoring regions was assumed.The results show that the coupling of the polymer with the surface will affect the director field of the nematic,and reduce the relaxation distance as well as the total free energy of the system.

With Monte Carlo simulation,this paper investigated Freedericksz transitions of biaxial nematics induced by an external magnetic field.In the simulation process,the pair potential in London's dispersion forces approximation was used.With three different orientations,nine different Freedericksz transitions were discussed by changing the molecular magnetic susceptibility and the directions of magnetic field.The transition of two short axes u and v,the transition of long axis w and short axis u,and the transition of long axis w and short axis v were all simulated.With the result of simulations,relations of the nine elastic constants can be discussed and they are fit with one elastic constant approximation.The result is practical in the sense that it works as a theoretical basis for developing biaxial display device.