Density functional theory for two-dimensional hard rods

Despite their simplicity, (non-spherical) hard particles became a standard model for colloidal systems. Fundamental measure theory (FMT) and its recent generalizations allow to predict the phase behavior of such a fluid solely from the shape of the individual particles. Such density functionals, which are exact in the low-density limit have been successfully applied to hard spherocylinders in three dimensions. However, the implementation of the most general framework, fundamental mixed measure theory (FMMT), usually requires systematic approximations of the comprised two-body term.

In this presentation, we demonstrate that the free numerical minimization of the FMMT functional is feasible in two dimensions, even for highly inhomogeneous systems. Applying the theory to a fluid of hard diskorectangles, we map out a full phase diagram including stable isotropic, nematic, smectic and crystalline phases. The theory predicts the transition between the inhomogeneous phases very accurately when compared to our new computer simulations, which also resolve the smectic-to-crystal transition. Finally, we present an analytic formula for the second-order isotropic-to-nematic transition line.