1208.3089 (Andrés Santos)

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

Andrés Santos

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 $\{\xi_\alpha\}$. By imposing consistency conditions, it is proven in this paper 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 scaling function which can be determined from the free-energy density of the one-component system. Extension to the inhomogeneous case is achieved by the usual replacements $\xi_0\to n_0$, $\xi_3\to n_3$, $\xi_1\xi_2\to n_1n_2-\mathbf{n}_1\cdot\mathbf{n}_2$, $\xi_2^3\to n_2(n_2^2-3\mathbf{n}_2\cdot\mathbf{n}_2)$, where $\{n_\alpha\}$ are the fundamental-measure weighted densities. Comparison with computer simulations shows the superiority of the new bulk free energy over the White Bear one.

View original: http://arxiv.org/abs/1208.3089