Kinetics of phase ordering of nematic liquid crystals in a confined geometry

Employing a time-dependent Ginzburg-Landau model, we investigate the phase ordering kinetics of nematic liquid crystals confined in a narrow pore. We consider various orientations of the surface field and compute domain growth laws and scaling functions. in the absence of any anchoring field we find that (and in contrast to a confined binary liquid mixture) mere confinement of the liquid crystals is insufficient to produce slow growth of the nematic domains owing to the vector nature of the order parameter. In the presence of a strong homogeneous anchoring, the system quickly reaches a nematic state. On the other hand, for homeotropic anchoring, the liquid crystal takes on an XY character and the growth law exponent crosses over from 1/2 to 1/4 as the field strength is increased.