Fundamental Measure Theory for Inhomogeneous Fluids of Nonspherical Hard Particles

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)] 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.

Figure 1

The isotropic-nematic transition of hard spherocylinders (length $L$, diameter $D$, packing fraction $\eta$) as obtained from the FMT excess free energy density $\Phi$, Eqs. (5, 10), with $\zeta =\frac{5}{4}$ and $\zeta =1.6$. For comparison we show simulation data obtained by Bolhuis and Frenkel [15]. The lower (upper) line or symbol indicates the density of the isotropic (nematic) phase at coexistence. At moderate aspect ratios the density gap is too small to be resolved in the simulations. For elongated rods the FMT underestimates the difference between coexisting densities.

Figure 2

Density profiles ${\rho }_{\vartheta }(z)$ from Monte Carlo simulations (open circles) and from minimization of the density functionals ($\zeta =0$, dashed-dotted lines; $\zeta =1.6$, dashed lines; $\zeta =\frac{5}{4}$, solid lines) for a fluid of hard spherocylinders at a hard planar wall located at $z=0$. The length-to-diameter ratio and bulk packing fraction are (a) $L/D=2.5$, $\eta \simeq 0.346$ and (b) $L/D=10.0$, $\eta \simeq 0.127$.