School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China.
J Chem Phys. 2013 Sep 28;139(12):124111. doi: 10.1063/1.4821762.
By appealing to the coupling parameter series expansion to calculate the first seven perturbation coefficients of the high temperature series expansion (HTSE) of the free energy, analysis of convergence and low temperature adaptability of the HTSE in calculating fluid thermodynamic properties is performed for the first time; the fluid thermodynamic properties considered include critical parameters, vapor-liquid coexistence curve, thermodynamic characteristic functions, chemical potential, pressure, and constant volume excess heat capacity. To proceed with the analysis, a well known square well model is used as sample; the well widths considered range over a wide interval, and the relevant temperatures amenable to simulation calculations (used as "exact" results to analyze the HTSE) can be both very high and very low. The main discoveries reached are summarized as follows: (1) The HTSE usually converges at the 4th-order truncation, but with decrease of the temperature considered, the lowest truncation order, which makes the HTSE to converge, tends to rise. As a conservative estimate, it is considered that the HTSE always converges for reduced temperature T* higher than 0.25, whereas for T* < 0.25 there appear signs indicating that the HTSE may diverge from the 7th-order truncation. (2) Within the temperature interval with T* ≥ 0.5, the HTSE converges approximately to the correct solution, and the HTSE can be reliably used to calculate the fluid thermodynamic properties, and within this temperature interval, the 4th-order truncation is enough; whereas for T* < 0.5, such as within the temperature interval with 0.275 ≤ T* ≤ 0.355, although the HTSE does converge, it does not converge to the correct solution, and the deviations between the HTSE calculations and MC simulations become an ever-prominent issue with the rising of the density, and the slopes of the thermodynamic properties over density are not satisfactorily represented. As a result, the HTSE is not suited for calculations for temperature interval T* < 0.5.
通过调用耦合参数级数展开式，计算自由能的高温级数展开式（HTSE）的前七个微扰系数，首次对 HTSE 计算流体热力学性质的收敛性和低温适应性进行了分析；所考虑的流体热力学性质包括临界参数、汽液共存曲线、热力学特征函数、化学势、压力和定容超额热容。为了进行分析，使用了一个众所周知的方阱模型作为样本；所考虑的阱宽范围很广，相关温度适用于模拟计算（用作分析 HTSE 的“精确”结果），可以非常高也可以非常低。主要发现总结如下：（1）HTSE 通常在四阶截断时收敛，但随着所考虑温度的降低，使 HTSE 收敛的最低截断阶数趋于上升。作为保守估计，认为对于还原温度 T高于 0.25，HTSE 总是收敛的，而对于 T<0.25，则出现 HTSE 可能从七阶截断发散的迹象。（2）在 T*≥0.5 的温度区间内，HTSE 近似收敛于正确解，HTSE 可可靠地用于计算流体热力学性质，并且在该温度区间内，四阶截断就足够了；而对于 T*<0.5，例如在 0.275≤T*≤0.355 的温度区间内，虽然 HTSE 确实收敛，但它并不收敛于正确解，HTSE 计算与 MC 模拟之间的偏差随着密度的升高而变得越来越明显，并且热力学性质随密度的斜率不能令人满意地表示。因此，HTSE 不适用于 T*<0.5 的温度区间的计算。
