Evaluation of Osmotic Virial Coefficients via Restricted Gibbs Ensemble Simulations, with Support from Gas-Phase Mixture Coefficients

We present a method for computing
osmotic virial coefficients in
explicit solvent via simulation in a restricted Gibbs ensemble. Two
equivalent phases are simulated at once, each in a separate box at
constant volume and temperature and each in equilibrium with a solvent
reservoir. For osmotic coefficient BN, a
total of N solutes
are individually exchanged back and forth between the boxes, and the
average distribution of solute numbers between the boxes provides
the key information needed to compute BN. Separately,
expressions are developed
for BN as a series in solvent reservoir density
ρ1, with the coefficients of the series expressed
in terms of the usual gas-phase mixture coefficients Bij. Normally, the Bij are defined for an infinite volume, but
we suggest that the observed dependence of Bij on system size L can be
used to estimate L dependence of the BN, allowing
them to be computed accurately
at L → ∞ while simulating much smaller system sizes than
otherwise possible. The methods for N = 2 and 3 are
demonstrated for two-component mixtures of size-asymmetric additive
hard spheres. The proposed methods are demonstrated to have greater
precision than established techniques, for a given amount of computational
effort. The ρ1 series for BN when
applied by itself is (for this noncondensing
model) found to be the most efficient in computing accurate osmotic
coefficients for the solvent densities considered here.