Density functional theory for colloidal mixtures of hard platelets, rods, and spheres

摘要

A geometry-based density functional theory is presented for mixtures of hardspheres, hard needles and hard platelets; both the needles and the plateletsare taken to be of vanishing thickness. Geometrical weight functions that arecharacteristic for each species are given and it is shown how convolutions ofpairs of weight functions recover each Mayer bond of the ternary mixture andhence ensure the correct second virial expansion of the excess free energyfunctional. The case of sphere-platelet overlap relies on the sameapproximation as does Rosenfeld's functional for strictly two-dimensional harddisks. We explicitly control contributions to the excess free energy that areof third order in density. Analytic expressions relevant for the application ofthe theory to states with planar translational and cylindrical rotationalsymmetry, e.g. to describe behavior at planar smooth walls, are given. Forbinary sphere-platelet mixtures, in the appropriate limit of small plateletdensities, the theory differs from that used in a recent treatment [L. Harnauand S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of ourapproach we consider the isotropic-nematic bulk transition of pure hardplatelets, which we find to be weakly first order, with values for thecoexistence densities and the nematic order parameter that compare well withsimulation results.