Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: comparison of simulation results with theory.
Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: comparison of simulation results with theory.
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DOI：
10.1103/physreve.84.061136
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发表时间：
2011-08
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影响因子：
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通讯作者：
Douglas J. Ashton;N. Wilding;R. Roth;R. Evans
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文献类型：
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作者：
Douglas J. Ashton;N. Wilding;R. Roth;R. Evans
我们报告了一个详细的研究，使用国家的最先进的模拟和理论方法，有效（耗尽）之间的潜力一对大的硬球浸没在一个水库的小得多的硬球，大小的差距是衡量的比直径q <$σ（s）/σ（B）。小颗粒被处理为宏观正则，它们的影响被参数化为它们在储层中的填充分数η（s）（r）。采用两种蒙特卡罗模拟方案--几何簇算法和分阶段粒子插入--来获得q ≤ 0.1和η（s）（r）的多种组合的精确耗尽势。应用模拟有限尺寸效应的校正后，耗尽电位进行了比较与预测的新的密度泛函理论（DFT）计算的基础上使用Rosenfeld功能和随后的几个修改的插入技巧。虽然DFT和模拟之间的一致性通常良好，但在我们的模拟方法可获得的最大储层填充分数处，即η（s）（r）= 0.35，明显存在显著差异。然而，这些差异与模拟和在此η（s）（r）处的Derjaguin近似的差得多的预测之间的差异相比是小的。最近提出的形态近似比Derjaguin，但有点穷比DFT的尺寸比和小球包装分数，我们认为。使用模拟、DFT和形态近似的有效势计算第二维里系数B（2）作为η（s）（r）的函数。结果的比较使得能够评估DFT可以预期正确预测q ≤ 0.1的添加剂二元硬球混合物中的流体-流体相分离倾向的程度。总之，新的模拟结果提供了一个完全定量的基准，用于评估计算高度尺寸不对称混合物中耗尽电位的理论方法的相对准确性。
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.