Virial Coefficients and Equations of State for Hard Polyhedron Fluids

Hard polyhedra are
a natural extension of the hard sphere model
for simple fluids, but there is no general scheme for predicting the
effect of shape on thermodynamic properties, even in moderate-density
fluids. Only the second virial coefficient is known analytically for
general convex shapes, so higher-order equations of state have been
elusive. Here we investigate high-precision state functions in the
fluid phase of 14 representative polyhedra with different assembly
behaviors. We discuss historic efforts in analytically approximating
virial coefficients up to B4 and numerically
evaluating them to B8. Using virial coefficients
as inputs, we show the convergence properties for four equations of
state for hard convex bodies. In particular, the exponential approximant
of Barlow et al. (J. Chem. Phys. 2012, 137, 204102) is found to be useful up to the first
ordering transition for most polyhedra. The convergence behavior we
explore can guide choices in expending additional resources for improved
estimates. Fluids of arbitrary hard convex bodies are too complicated
to be described in a general way at high densities, so the high-precision
state data we provide can serve as a reference for future work in
calculating state data or as a basis for thermodynamic integration.