Orientational ordering in fluids with partially constrained molecule orientations

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Molecular orientations in anisotropic fluids can be partially constrained as a result of electric or magnetic fields or interface influences. A statistical approach for the investigation of the orientational ordering in such systems is proposed. The long-range correlations are taken into account consistently. The method is illustrated for the well-known thermotropic nematic model in an infinite disorienting field W, when the molecules are constrained to orient perpendicularly to the field direction. For this problem the analytical solution of the anisotropic Ornstein-Zernike equation is obtained, and the asymptotic expression for the long-range correlations on large distances is given. The phase diagram and elastic constants are calculated for W-->infinity and are compared with the usual case of a uniaxial nematic ordering at W=0. In the case W-->infinity when the temperature decreases the orientational phase transition of the second order becomes the one of the first order at a tricritical point. The disorienting field W increases much the region of an ordered fluid. It is shown that at a given pressure the orientational ordering temperature for W-->infinity is higher about 1.2-1.5 times than the one at W=0. The orientational ordering pressure is less about 4-5 times than the pressure of the uniaxial nematic ordering (W=0) at the same temperature. The disorienting field increases elastic properties of the model under consideration.