Fundamental mixed measure theory for non-spherical colloids

Abstract

Accurate predictions for the collective behavior of non-spherical colloids and nano-particles can guide the search for novel self-assembled materials. We derive a new type of density functional theory for mixtures of arbitrarily shaped convex hard bodies using integral geometry's translative integral formula and a scaling argument. Our fundamental mixed measure theory is exact in the low-density limit and does not require truncation or empirical parameters unlike previous functionals. Quantitatively correct results for hard spherocylinders validate our general approach. In particular, we present the phase diagram, including a qualitatively and quantitatively accurate smectic phase, and the isotropic-nematic interfacial tension.