The effect of confinement on the isotropic-nematic transition

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Abstract
The Lebwohl-Lasher model of a liquid crystal is examined in a slab geometry, with free top and bottom surfaces, using standard molecular-field and a new Bethe-type approximation that includes some effects of correlations. The results are compared with computer simulations for a range of slab widths L. We find that the approximate treatments, while predicting a nematic-isotropic transition that is too strongly first-order, are in semiquantitative agreement with the simulation results. The results of the approximate treatments show that the Kelvin equation for the shift in transition temperature due to confinement is accurate for L ≥ 64 layers. For large L a wetting film of the disordered, isotropic phase intrudes between each surface and the nematic phase. The film thickness, evaluated at the transition in the slab, increases as ln L in accord with the theory of complete wetting for systems with short-ranged forces.