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arXiv 1609.06905cond-mat.softcond-mat.stat-mechphysics.chem-ph
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变尺寸硬球在硬球流体中的化学势

Chemical potential of a test hard sphere of variable size in a hard-sphere fluid

David M. Heyes, Andrés Santos

摘要:

应用Labik和Smith Monte Carlo模拟技术实现Widom粒子插入方法,并使用分子动力学(MD)来数值计算不同直径的示踪硬球(HS)粒子的插入概率$P_0(η,σ_0)$,$σ_0$,在直径为$σ$和填充分数为$η$的主体HS流体中,直至$0.5$。分析表明,唯一的多项式表示的$-\ln P_0(η,σ_0)$符合的限制$σ_0\to 0$和$σ_0\to\infty$必然有一个三次形式,$c_0(η)+c_1(η)σ_0/σ+c_2(η)(σ_0/σ)^2+c_3(η)(σ_0/σ)^3$。我们的MD数据$-\ln P_0(η,σ_0)$适合这样一个三次多项式和功能$c_0(η)$和$c_1(η)$被发现是统计上无法区分从他们的精确的解决方案的形式。同样地,$c_2(η)$和$c_3(η)$与Boublík-Mansoori-Carnahan-Starling-Leland和Boublík-Carnahan-Starling-Kolafa公式非常吻合。三次多项式被外推(高密度)或内插(低密度)以获得主体流体的化学势或$σ_{0}\toσ$,作为$βμ^{\text{ex}}=c_0+c_1+c_2+c_3$。Carnahan-Starling和Carnahan-Starling-Kolafa理论与我们的MD数据之间的良好一致性是显而易见的。

英文摘要:

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, $P_0(η,σ_0)$, of tracer hard-sphere (HS) particles of different diameters, $σ_0$, 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 $-\ln P_0(η,σ_0)$ consistent with the limits $σ_0\to 0$ and $σ_0\to\infty$ has necessarily a cubic form, $c_0(η)+c_1(η)σ_0/σ+c_2(η)(σ_0/σ)^2+c_3(η)(σ_0/σ)^3$. Our MD data for $-\ln P_0(η,σ_0)$ are fitted to such a cubic polynomial and the functions $c_0(η)$ and $c_1(η)$ are found to be statistically indistinguishable from their exact solution forms. Similarly, $c_2(η)$ and $c_3(η)$ 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 $σ_{0}\toσ$, as $βμ^{\text{ex}}=c_0+c_1+c_2+c_3$. Excellent agreement between the Carnahan-Starling and Carnahan-Starling-Kolafa theories with our MD data is evident.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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