Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain.
J Chem Phys. 2016 Dec 7;145(21):214504. doi: 10.1063/1.4968039.
The Labík and Smith Monte Carlo simulation technique to implement the Widom particle insertion method is applied using Molecular Dynamics (MD) instead to calculate numerically the insertion probability, P(η,σ), of tracer hard-sphere (HS) particles of different diameters, σ, in a host HS fluid of diameter σ and packing fraction, η, up to 0.5. It is shown analytically that the only polynomial representation of -lnP(η,σ) consistent with the limits σ→0 and σ→∞ has necessarily a cubic form, c(η)+c(η)σ/σ+c(η)(σ/σ)+c(η)(σ/σ). Our MD data for -lnP(η,σ) are fitted to such a cubic polynomial and the functions c(η) and c(η) are found to be statistically indistinguishable from their exact solution forms. Similarly, c(η) and c(η) agree very well with the Boublík-Mansoori-Carnahan-Starling-Leland and Boublík-Carnahan-Starling-Kolafa formulas. The cubic polynomial is extrapolated (high density) or interpolated (low density) to obtain the chemical potential of the host fluid, or σ→σ, as βμ=c+c+c+c. Excellent agreement between the Carnahan-Starling and Carnahan-Starling-Kolafa theories with our MD data is evident.
拉比克和史密斯的蒙特卡罗模拟技术用于实现 Widom 粒子插入法，使用分子动力学 (MD) 代替数值计算不同直径 σ 的示踪硬球 (HS) 粒子在直径 σ 和堆积分数 η 的宿主 HS 流体中的插入概率 P(η,σ)，高达 0.5。从分析上可以看出，与 σ→0 和 σ→∞ 极限一致的 -lnP(η,σ)的唯一多项式表示必然具有三次形式，c(η)+c(η)σ/σ+c(η)(σ/σ)+c(η)(σ/σ)。我们对 -lnP(η,σ)的 MD 数据进行拟合，得到这样的三次多项式，并且发现 c(η) 和 c(η) 在统计学上与它们的精确解形式没有区别。同样，c(η) 和 c(η) 与 Boublík-Mansoori-Carnahan-Starling-Leland 和 Boublík-Carnahan-Starling-Kolafa 公式非常吻合。通过三次多项式进行外推（高密度）或内插（低密度），得到宿主流体的化学势，或 σ→σ，其中 βμ=c+c+c+c。可以明显看出，卡纳汉-斯塔林理论和卡纳汉-斯塔林-科拉法理论与我们的 MD 数据之间具有极好的一致性。
