Ashton Douglas J, Wilding Nigel B, Roth Roland, Evans Robert
Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061136. doi: 10.1103/PhysRevE.84.061136. Epub 2011 Dec 20.
We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q ≡ σ(s)/σ(b). Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir η(s)(r). Two Monte Carlo simulation schemes--the geometrical cluster algorithm, and staged particle insertion--are deployed to obtain accurate depletion potentials for a number of combinations of q ≤ 0.1 and η(s)(r). After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, η(s)(r) = 0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this η(s)(r). The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient B(2) as a function of η(s)(r). Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with q ≤ 0.1. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size-asymmetric mixtures.
我们报告了一项详细研究，该研究使用最先进的模拟和理论方法，研究了浸没在小得多的硬球储库中的一对大硬球之间的有效（排空）势，尺寸差异由直径比(q\equiv\sigma(s)/\sigma(b))衡量。小颗粒采用巨正则系综处理，其影响通过储库中它们的填充分数(\eta(s)(r))进行参数化。部署了两种蒙特卡罗模拟方案——几何团簇算法和分步粒子插入法——以获得(q\leq0.1)和(\eta(s)(r))多种组合下的精确排空势。在对模拟有限尺寸效应进行校正后，将排空势与基于使用罗森菲尔德泛函及后续几种修正的插入技巧的新密度泛函理论（DFT）计算预测进行比较。虽然DFT与模拟之间的一致性总体良好，但在我们模拟方法可达到的最大储库填充分数，即(\eta(s)(r)=0.35)时，明显存在显著差异。然而，与在该(\eta(s)(r))下模拟与德亚金近似的差得多的预测之间的差异相比，这些差异较小。最近提出的形态计量近似比德亚金近似表现更好，但对于我们考虑的尺寸比和小球填充分数，比DFT稍差。来自模拟、DFT和形态计量近似的有效势用于计算作为(\eta(s)(r))函数的第二维里系数(B(2))。结果比较能够评估DFT在(q\leq0.1)的加性二元硬球混合物中正确预测流体 - 流体相分离倾向的程度。总之，新的模拟结果为评估计算高度尺寸不对称混合物中排空势的理论方法的相对准确性提供了一个完全定量的基准。
