Non hard sphere thermodynamic perturbation theory over a wide range of temperatures
Non hard sphere thermodynamic perturbation theory over a wide range of temperatures
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DOI：
10.1088/1742-5468/2011/09/p09001
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发表时间：
2011-09
期刊：
影响因子：
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通讯作者：
Shiqi Zhou
中科院分区：
文献类型：
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作者：
Shiqi Zhou
近期提出了一种非硬球（HS）耦合参数展开（CPE）热力学微扰理论（TPT），本文对其在广泛温度范围内的性能进行了评估，尤其关注它对所谓低温问题的处理能力。即传统的高温级数展开TPT的性能会随着温度降低而逐渐变差，最终在定性上出现错误。因此，我们针对蜂窝模型势在正则系综中进行了蒙特卡罗模拟，获取了流体相在较宽密度和温度范围内的压力、超额内能、超额亥姆霍兹自由能、超额化学势以及超额焓。这些新的模拟数据，结合已发表的极低温下硬球+方阱流体的模拟数据，被用于检验非硬球CPE三阶TPT的性能。本文提出了一种通用方案，将所考虑势函数的部分尾项纳入参考体系，这确保了非硬球微扰程序在亚临界温度下能正常运行，且当所考虑温度无限升高时能平稳过渡到常用的硬球微扰方案。研究发现，对于传统茨万齐格（Zwanzig）型TPT在定性上出现错误、甚至硬球CPE三阶TPT在某些情况下也严重失效的极低温情况，非硬球CPE三阶TPT的表现非常令人满意，甚至极为精确。在所考虑的热力学量中，理论上最难预测的是定容超额热容，而对于这一物理量，非硬球CPE三阶TPT也明显优于其他理论。
A recently proposed non hard sphere (HS) coupling parameter expansion (CPE) thermodynamic perturbation theory (TPT) is evaluated for its performance over a wide range of temperatures, particularly in tackling a so-called low temperature problem, i.e. the traditional high temperature series expansion TPT performance becomes progressively less satisfactory as the temperature drops, and finally becomes qualitatively incorrect. Accordingly, we have performed Monte Carlo simulations in the canonical ensemble for a honeycomb model potential, and the pressure, excess internal energy, excess Helmholtz free energy, excess chemical potential, and excess enthalpy have been obtained over wide density and temperature ranges for the fluid phase. These new simulation data, together with published simulation data for an HS + square well fluid at very low temperatures, have been used to test the performance of the non HS CPE third-order TPT. A general scheme for assimilating part of the tail term of the potential function considered into a reference system is proposed, which ensures running normality of the non HS perturbation code at subcritical temperatures and smooth transition into a commonly used HS perturbation scheme when the temperatures considered rise infinitely. It is found that the non HS CPE third-order TPT is very satisfactory or even very accurate for these extremely low temperatures for which traditional Zwanzig type TPT is qualitatively incorrect and even an HS CPE third-order TPT also seriously fails in some cases. Among the thermodynamic quantities considered the most difficult one to predict theoretically is the constant volume excess heat capacity, and for this quantity the non HS CPE third-order TPT is also obviously superior to its competitors.