Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see http://dx.doi.org/10.1063/1.2390712

Rescaled density expansions and demixing in hard-sphere binary mixtures

The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid separates into two phases of different composition with a lower consolute critical point. By successively incorporating the third, fourth, and fifth virial coefficients, the critical consolute point moves to higher values of the pressure and to lower values of the partial number fraction of the large spheres. When the exact low-density expansion of the pressure is rescaled to higher densities as in the Percus-Yevick theory, by adding more exact virial coefficients a different qualitative movement of the critical consolute point in the phase diagram is found. It is argued that the Percus-Yevick factor appearing in many empirical equations of state for the mixture has a deep influence on the location of the critical consolute point, so that the resulting phase diagram for a prescribed equation has to be taken with caution.Comment: 5 pages, 1 figure; to be published in The Journal of Chemical Physic

Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.Comment: 3 pages, 1 figur

On the radial distribution function of a hard-sphere fluid

Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.Comment: 3 pages, 1 figure; v2: slightly shortened, figure changed, to be published in JC