C. Chiccoli, O.D. Lavrentovich, P. Pasini, C. Zannoni, Monte-Carlo Simulations of Stable Point Defects in Hybrid Nematic Films, Phys. Rev. Lett., 79, 4401-4404 (1997)
Monte Carlo (MC) simulations based exclusively on the Lebwohl-Lasher nearest neighbors intermolecular interactions reveal the existence of stable long-range deformations and topological defects in thin nematic films confined between two surfaces with antagonistic (normal and tangential) molecular orientations. The MC technique allows to describe a delicate balance of bulk elasticity and surface energy usually treated only with macroscopic theories.
Starting the simulations from a configuration perfectly aligned along the z axis for a 100 x100 x12 lattice at T*=0.4. the texture develops from black to a set of brushes. Each defect is marked by four brushes emerging from its core
As an example we show in Fig. 1 simulated cross- polarizer images of various evolution stages, i.e after a number of cycles equal to: 100 (top left), 6000 (top right), 50000 (bottom left), 80000 (bottom right)
The defects do not seem to appear until the lateral size L becomes much larger than thickness h (e.g. L >50 for h=10), For small thickness/are the configuration is uniform (see Fig.2)
The configuration dramatically changes for large L/h and one observes strong and stable horizontal deformations associated with topological defects of strength m= + 1. The core of the defect is located at the lower surface; the distortions vanish as one moves towards the upper plate and the molecules reorient long the z axis
Note that the results described above are specifically related to the hybrid alignment of the film.