Theoretical direct correlation function for two-dimensional fluids of monodisperse hard spheres

The direct correlation function plays an important role in describing the effects of the structure of particle systems with respect to light diffraction, x-ray diffraction as well as transmission and transmission fluctuations of radiation through a dense suspension. In this paper, the direct correlation function for a monolayer of monodisperse hard spheres or disks is derived theoretically. Based on the approximation of Baus and Colot [Phys. Rev. A 36, 3912 (1987)] and the equation of state for a fluid of hard disks by Santos et al. [J. Chem. Phys. 103, 4622 (1995)], we propose a new direct correlation function, which compares well to the approximate analytical expressions and gives a good prediction of the structure factor in a wide range of monolayer density or suspension concentration. The resulting radial distribution function also agrees well with Monte Carlo computer simulation data. The corresponding contact values of the radial distribution function compare well with the results of analytic approximations, numerical solutions, and computer simulations. Our proposed direct correlation function is applied to the transmission fluctuation spectrometric study. Experimental results show good agreement with the theory.