Phase transitions in finite-thickness nematogenic materials bounded by two planar surfaces and characterized by identical surface interactions linearly proportional to the order parameter have been studied theoretically by solving the coupled nonlinear Euler-Lagrange equations. The surface interaction was assumed to favor molecular orientation in the surface plane with no rubbed or preferred direction. The related problem of a semi-infinite film having a single surface has been studied previously at temperatures above the bulk nematic-isotropic phase transition point T-NI. For that geometry and physically relevant elastic constants, it was shown that, in addition to the bulk transition, there is a second transition at higher temperatures between biaxial and uniaxial ordering of the surface layer when the strength of the surface coupling is not too weak. It is shown here that this double phase transition reduces to a single one for sufficiently thin layers.
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