Continuum description of the interfacial layer of nematic liquid crystals in contact with solid surfaces

We investigate when it is possible to introduce surface physical parameters characterizing the nematic/substrate interface. The analysis is performed by solving the problem assuming that the presence of the surface introduces a spatial variation, mainly localized close to the limiting surfaces, of the bulk properties of the nematic (delocalized model). The results of the calculation are compared to the prediction of a model in which the presence of the surface is taken into account by means of new physical parameters, localized to the surface (localized model). We show that if the viscous dissipative effects or the surface alignment effects are considered, the two models predict the same relaxation times and the same threshold for the Freedericksz transition is obtained. From these results we deduce that the localized models are equivalent to the delocalized ones. A continuum description of the interfacial layer of nematic liquid crystals in contact with solid surface in terms of surface properties is then correct, which makes the solution of this kind of problems simpler. Also a softening of the elastic constants near the surfaces can be represented by a localized surface energy term.