Director reorientation in a nematic liquid crystal with a photosensitive layer

We use a molecular-motor model previously proposed for a nematic cell with an azo-dye monolayer to calculate the director orientation when light is normally impinged on the cell. We consider an initial planar configuration for which one of the surrounding plates, which we call the reference plate, is submitted to a hard-anchoring boundary condition. The other confining plate has a coating monolayer of azo-dye molecules such that the change of the orientation of azo-dye isomers, due to light, causes changes in the nematic director. The boundary conditions on both plates along with the optical field determine the director configuration in the bulk. The existence of periodic solutions for the density of isomers in trans and cis states, corresponding to weak optical fields, has been discussed in the literature. Using a similar approach, we find an approximate expression for the density of isomers, written in terms of the director angle, which allows us to close the equation for the director configuration on the boundary having a photosensitive plate. We decouple the director's angle and the isomer densities by assuming extremely different temporal time scales between them. We show for a given sample that switching times inversely depend on the trans-cis transition rate of photoexcitation whereas relaxation times do not depend on it. On the other hand, switching and relaxation times linearly depend on effective surface viscosity values. Our model allows us to estimate surface viscosity values.