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.

本研究提出了一种基于受限吉布斯系综（restricted Gibbs ensemble）模拟的方法，可在显式溶剂体系中计算渗透维里系数（osmotic virial coefficients）。该方法可同时模拟两个等价相：两相分别置于独立的恒容恒温模拟盒中，且均与溶剂储库（solvent reservoir）保持平衡。针对第N阶渗透维里系数B_N，我们将总计N个溶质（solute）在两个模拟盒之间逐一往复交换，通过两相中溶质数目的平均分布，即可获取计算B_N所需的核心信息。此外，本研究还推导了以溶剂储库密度ρ₁为变量的B_N级数展开式，该级数的各项系数可通过常规气相混合维里系数B_ij表示。通常，B_ij的定义基于无限大体积体系，但本研究提出，可利用已观测到的B_ij随体系尺度L的变化关系，来估算B_N的尺度依赖性，从而在模拟远小于实际尺度的体系时，仍能精准计算L趋近于无穷大时的B_N值。本研究针对尺寸不对称的双组分加和性硬球混合体系，验证了N=2与N=3时的计算方法。在相同计算量的前提下，所提出的方法相较于已有技术，展现出更高的计算精度。针对本文所考察的溶剂密度范围，单独使用B_N的ρ₁级数展开式（针对该非凝聚模型（noncondensing model）），被证实是获取精准渗透维里系数的最高效方案。