Abstract. In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.

Using the Gauss-Bonnet theorem we deconvolute exactly the Mayer f-function for arbitrarily shaped convex hard bodies in a series of tensorial weight functions, each depending only on the shape of a single particle. This geometric result allows the derivation of a free energy density functional for inhomogeneous hard-body fluids which reduces to Rosenfeld's fundamental measure theory [Phys. Rev. Lett. 63, 980 (1989)10.1103/PhysRevLett.63.980] when applied to hard spheres. The functional captures the isotropic-nematic transition for the hard-spherocylinder fluid in contrast with previous attempts. Comparing with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall, we show that the new functional also improves upon previous functionals in the description of inhomogeneous isotropic fluids.

In a recent publication (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) we constructed a free energy functional for the inhomogeneous hard-body fluid, which reduces to Rosenfeld's fundamental measure theory (Rosenfeld 1989 Phys. Rev. Lett. 63 980) when applied to hard spheres. The new functional is able to yield the isotropic-nematic transition for the hard-spherocylinder fluid in contrast to Rosenfeld's fundamental measure theory for non-spherical particles (Rosenfeld 1994 Phys. Rev. E 50 R3318). The description of inhomogeneous isotropic fluids is also improved when compared with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall. However, the new functional for the inhomogeneous fluid in general does not comply with the exact second order virial expansion. We introduced the ζ correction in order to minimize the deviation from Onsager's exact result in the isotropic bulk fluid. In this article we give a detailed account of the construction of the new functional. An extension of the ζ correction makes the latter better suited for non-isotropic particle distributions. The extended ζ correction is shown to improve the description of the isotropic-nematic bulk phase diagram while it has little effect on the results for the isotropic but inhomogeneous hard-spherocylinder fluid. We argue that the gain from using higher order tensorial weighted densities in the theory is likely to be inferior to the associated increase in complexity.

We calculate the solvation free energy of proteins in the tube model of Banavar and Maritan [Rev. Mod. Phys. 75, 23 (2003)10.1103/RevModPhys.75.23] using morphological thermodynamics which is based on Hadwiger's theorem of integral geometry. Thereby we extend recent results by Snir and Kamien [Science 307, 1067 (2005)10.1126/science.1106243] to hard-sphere solvents at finite packing fractions and obtain new conclusions. Depending on the solvent properties, parameter regions are identified where the beta sheet, the optimal helix, or neither is favored.