Davidchack Ruslan L, Laird Brian B
School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, United Kingdom.
Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA.
J Chem Phys. 2022 Aug 21;157(7):074701. doi: 10.1063/5.0100073.
The excess chemical potential μ(σ, η) of a test hard spherical particle of diameter σ in a fluid of hard spheres of diameter σ and packing fraction η can be computed with high precision using Widom's particle insertion method [B. Widom, J. Chem. Phys. 39, 2808 (1963)] for σ between 0 and just larger than 1 and/or small η. Heyes and Santos [J. Chem. Phys. 145, 214504 (2016)] analytically showed that the only polynomial representation of μ consistent with the limits of σ at zero and infinity has a cubic form. On the other hand, through the solvation free energy relationship between μ and the surface free energy γ of hard-sphere fluids at a hard spherical wall, we can obtain precise measurements of μ for large σ, extending up to infinity (flat wall) [R. L. Davidchack and B. B. Laird, J. Chem. Phys. 149, 174706 (2018)]. Within this approach, the cubic polynomial representation is consistent with the assumptions of morphometric thermodynamics. In this work, we present the measurements of μ that combine the two methods to obtain high-precision results for the full range of σ values from zero to infinity, which show statistically significant deviations from the cubic polynomial form. We propose an empirical functional form for the μ dependence on σ and η, which better fits the measurement data while remaining consistent with the analytical limiting behavior at zero and infinite σ.
在直径为σ、堆积分数为η的硬球流体中，直径为σ的测试硬球粒子的过量化学势μ(σ, η)，对于σ在0到刚大于1之间和/或小η的情况，可使用维登粒子插入法[B. 维登，《化学物理杂志》39, 2808 (1963)]进行高精度计算。海耶斯和桑托斯[《化学物理杂志》145, 214504 (2016)]通过分析表明，与σ在零和无穷大处的极限一致的μ的唯一多项式表示具有三次形式。另一方面，通过μ与硬球流体在硬球壁处的表面自由能γ之间的溶剂化自由能关系，我们可以获得大σ时μ的精确测量值，一直延伸到无穷大（平壁）[R. L. 戴维查克和B. B. 莱尔德，《化学物理杂志》149, 174706 (2018)]。在这种方法中，三次多项式表示与形态计量热力学的假设一致。在这项工作中，我们展示了结合这两种方法对从零到无穷大的全范围σ值进行高精度测量得到的μ值，这些值显示出与三次多项式形式有统计学上的显著偏差。我们提出了一种μ对σ和η的依赖关系的经验函数形式，它能更好地拟合测量数据，同时与σ为零和无穷大时的解析极限行为保持一致。
