Tensorial density functional theory for non-spherical hard-body 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. 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. correction makes the latter better suited for non-isotropic particle distributions. The extended. 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.