Direct correlation functions in two-dimensional anisotropic fluids

A geometrical approximation for the direct correlation of two-dimensional multicomponent fluids is introduced herein. This approximation is semianalytical and involves the knowledge of elementary geometrical properties of a single particle. The formalism is applied to anisotropic two-dimensional fluids of various particle shapes such as hard ellipses, diskorectangles, and cut disks of various size ratios. The particular case of the hard needles fluid is also investigated. The accuracy of the approximation is tested by comparing the equation of state and the correlation functions to those obtained by integral equation techniques and Monte Carlo simulations. In almost all cases these comparisons are found to be quite satisfactory and even excellent in the case of moderate size ratios. Both the isotropic and orientationally ordered phases are investigated and particular attention is paid to the orientational stability of the isotropic phase. The cut disk fluid has a particularly interesting long-range order for thicknesses around 0.3, which is very much reminiscent of the cubatic order observed in the corresponding three-dimensional case of cut spheres. This feature observable by both the simulations and the hypernetted chain integral equation is also predicted by the present geometrical theory, but at larger thicknesses.