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.

arXiv comment9 pages, 7 figures

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• Coarse-Grained Molecular Dynamics Simulations of Depletion-Induced Interactions for Soft Matter Systems
• Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions
• Depletion potential in the infinite dilution limit
• Multicomponent fluid of hard spheres near a wall
• Transport properties of highly asymmetric hard sphere mixtures
• Note: An exact scaling relation for truncatable free energies of polydisperse hard-sphere mixtures
• Communication: Inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities
• Test of a universality ansatz for the contact values of the radial distribution functions of hard-sphere mixtures near a hard wall
• Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures
• Contact values for disparate-size hard-sphere mixtures
• Direct correlation function from the consistent fundamental-measure free energies for hard-sphere mixtures