Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid

Abstract

The contact values $g(\sigma ,{\sigma }^{\prime })$ of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution $f(\sigma )$ are considered. A ``universality'' assumption is introduced, according to which, at a given packing fraction $\eta$, $g(\sigma ,{\sigma }^{\prime })=G(z(\sigma ,{\sigma }^{\prime }))$, where $G$ is a common function independent of the number of components (either finite or infinite) and $z(\sigma ,{\sigma }^{\prime })=[2\sigma {\sigma }^{\prime }/(\sigma +{\sigma }^{\prime })]{\mu }_2/{\mu }_3$ is a dimensionless parameter, ${\mu }_n$ being the $n$-th moment of the diameter distribution. A cubic form proposal for the $z$-dependence of $G$ is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express $G(z)$ in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations.

9 pages, 7 figures

References in corpus (3)

• Equilibrium phase behavior of polydisperse hard spheres
• Molecular dynamics and theory for the contact values of the radial distribution functions of hard-disk fluid mixtures
• On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids

Cited by in corpus (6)

• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids
• Coarse-Grained Molecular Dynamics Simulations of Depletion-Induced Interactions for Soft Matter Systems
• Multicomponent fluid of hard spheres near a wall
• Test of a universality ansatz for the contact values of the radial distribution functions of hard-sphere mixtures near a hard wall
• Contact values for disparate-size hard-sphere mixtures