Free energy model for the inhomogeneous hard-body fluid: application of the Gauss-Bonnet theorem

Abstract

By capturing the correct geometrical features, the fundamental-measure free energy density functional (Rosenfeld, Y., 1989, Phys. Rev. Lett., 63, 980; 1993, J. chem. Phys., 98, 8126; 1994, Phys. Rev. Lett., 72, 3831) leads to an accurate description of the general inhomogeneous simple (atomic) fluid. The key to its derivation is the convolution decomposition of the excluded volume for a pair of spheres in terms of characteristic functions for the geometry of the two individual spheres. The extension of this functional to molecular (complex) fluids is now made possible by uncovering the relation between the convolution decomposition for spheres and the Gauss-Bonnet theorem for the geometry of convex bodies (Rosenfeld, Y., 1994, Phys. Rev. E, 50, R3318). This provides (i) a free energy functional for hard particles, for which the accurate fundamental-measure functional for hard spheres is just a special case, and (ii) a simple geometrical test for its expected accuracy; also (iii) it constitutes a powerful new general method in density functional theory applicable to ‘complex’ fluids of asymmetric molecules.