Theory of the Nematic-Isotropic Transition in a Restricted Geometry

We discuss, using a Landaude Gennes formalism, the nematic-isotropic transition temperature for a system placed between two parallel plates, subject to identical homeotropic or homogeneous boundary conditions at each plate. The temperature at the phase transition may increase or decrease as the inverse sample thickness, D^-1, increases, depending on the nature of the boundary conditions. In all cases the transition terminates at a critical point for sufficiently large D^-1, beyond which the nematic and isotropic phases are no longer distinct. The phase transition temperature is well described by a liquid crystal analogy of the Kelvin equation which can be generalized to give an exact Clausius-Clapeyron relation. Under many circumstances the system behaves from a thermodynamic point of view as though it were in a bulk ordering field. The finite geometry restricts the growth of nematic or isotropic wetting films. We discuss the disjoining pressure experiment of Horn, Israelachvili and Perez 15]. Finally we place our work in the context of recent progress in the statistical mechanics of surfaces and systems in restricted geometries.