DIRECT CORRELATION-FUNCTIONS IN 2-DIMENSIONAL ANISOTROPIC FLUIDS

A geometrical approximation for the direct correlation of two-dimensio nal multicomponent fluids is introduced herein. This approximation is semianalytical and involves the knowledge of elementary geometrical pr operties of a single particle. The formalism is applied to anisotropic two-dimensional fluids of various particle shapes such as hard ellips es, diskorectangles, and cut disks of various size ratios. The particu lar 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 techn iques and Monte Carlo simulations. In almost all cases these compariso ns are found to be quite satisfactory and even excellent in the case o f moderate size ratios. Both the isotropic and orientationally ordered phases are investigated and particular attention is paid to the orien tational stability of the isotropic phase. The cut disk fluid has a pa rticularly interesting long-range order for thicknesses around 0.3, wh ich is very much reminiscent of the cubatic order observed in the corr esponding three-dimensional case of cut spheres. This feature observab le by both the simulations and the hypernetted chain integral equation is also predicted by the present geometrical theory, but at larger th icknesses.