Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex bodies

Entropy-driven demixing in spherocylinder binary mixtures

The stability of binary fluid mixtures, with respect to a demixing transition, is examined within the framework of the geometrical approximation of the direct correlation for hard nonspherical particles. In this theory, the direct correlation function is essentially written in terms of the geometrical properties of the individual molecules, and those of the overlap region between two different molecules, taken at fixed separation and orientations. Within the present theory, the demixing spinodal line in the (rho(1),rho(2)) concentration plane is obtained analytically, and shown to be a quadratic function of the total packing fraction and the compositions. The theory is applied herein to binary mixtures of hard spherocylinders in the isotropic phase. Isotropic fluid-fluid demixing can be predicted for a large variety of sizes and aspect ratios, and the necessary condition for entropic demixing is a sufficiently large thickness difference between the two particles that belong to each of the fluids in the mixture. As the theory reduces exactly to the Percus-Yevick approximation for a hard sphere mixture, accordingly it will not predict fluid-fluid demixing for this particular case. Demixing is also forbidden in two other cases; for a mixture of spherocylinders and small spheres, and for mixtures of equally thin spherocylinders. The influence and competition of an ordering instability on the demixing is also examined. The ordering of a fluid will always be displaced toward higher packing fractions by the addition of a nonordering fluid, and in some cases the entropic demixing can dominate the entire fluid range. Although the present theory merges exactly with the correct Onsager limit, it is shown that, for intermediate cases, the results can be significantly different from predictions of Onsager type approaches. These discrepancies are analyzed in particular for the needle plus spherocylinder mixture. Finally, in view of the nature of the theory, it is conjectured that the predicted demixing densities values are rather upper bounds to what should be expected.

Integral equation theory for fluids ordered by an external field: separable interactions

The structural and thermodynamical properties of classical fluids orientationally ordered by an external field are investigated by means of integral equation theories. A general theoretical framework for handling these theories is developed and detailed for the particular case of separable interactions between fluid particles. This approach is then illustrated for the case of two (off lattice) models: the ferromagnetic Heisenberg model and a simple liquid crystal model, for which the numerical solution of integral equations such as the Percus-Yevick, the hypernetted chain, and the reference hypernetted chain closure equations are presented and compared with Monte Carlo simulation results and the analytical solution of the mean spherical approximation. The zero-field case is also examined, and the spontaneous ordering is analyzed in detail, mainly in what concerns the appearance of infinite wavelength singularity in the Ornstein-Zernike equation and the relation with the one-body closure equations and the long range orientational ordering that occurs. In particular, it is shown that the Wertheim one-body closure equation appears as a sum rule compatible with the Ornstein-Zernike equation. The relation between the elastic constant and the long range tail of the pair correlation function is made explicit. In particular, the long range behavior of the various terms in the expansion of the pair correlation function is depicted. The numerical investigation of the two models shows that it is not possible to discriminate between the four integral equations, as to which one would be the most accurate in all cases. The general trends in the thermodynamical and structural properties seem to indicate that the Percus-Yevick approximation is generally better in the strong ordering case, whereas the reference hypernetted chain approximation might be better suited to the study of the isotropic phase and the low ordering regimes.