Class of consistent fundamental-measure free energies for hard-sphere mixtures

Abstract

In fundamental-measure theories the bulk excess free-energy density of a hard-sphere fluid mixture is assumed to depend on the partial number densities ${\rho }_i$ only through the four scaled-particle-theory variables ${\xi }_{\alpha }$, i.e., $\Phi ({\rho }_i)\to \Phi ({\xi }_{\alpha })$. By imposing consistency conditions, it is proven here that such a dependence must necessarily have the form $\Phi ({\xi }_{\alpha })=-{\xi }_0\ln (1-{\xi }_3)+\Psi (y){\xi }_1{\xi }_2/(1-{\xi }_3)$, where $y\equiv {\xi }_2^2/12\pi {\xi }_1(1-{\xi }_3)$ is a scaled variable and $\Psi (y)$ is an arbitrary dimensionless scaling function which can be determined from the free-energy density of the one-component system. Extension to the inhomogeneous case is achieved by standard replacements of the variables ${\xi }_{\alpha }$ by the fundamental-measure (scalar, vector, and tensor) weighted densities $n_{\alpha }(\mathbf{r})$. Comparison with computer simulations shows the superiority of this bulk free energy over the White Bear one.

arXiv comment5 pages; v2: substantial additions

References in corpus (4)

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• Predicting phase equilibria in polydisperse systems
• Close to the edge of Fundamental Measure Theory: density functional for hard sphere mixtures
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