第四、第五维里系数的关联

A METHOD TO FIT THE FOURTH AND THE FIFTH VIRIAL COEFFICIENTS

对于Lennard-Jone势,目前只求出了第四、第五维里系数在特定温度下的数值解,而且求解过程极其繁复,不便于实际应用。本文发现,当温度趋于无穷大时,各级维里系数之比趋于α·T^(0.25～0.50),据此提出了一组关联第四、第五维里系数的经验式,它在形式上和第二、第三维里系数的解析式十分相似,能很好地拟合已知的数值解。和其它经验式相比,该方法的优点是简单、准确、所有的维里系数计算具有统一的形式。

For the Lennard-Jones potential, only numerical solution of the fourth and the fifth virial coefficients has been obtained at specific temperature, and the calculation process is so complex that it is hard to use them in practical research work. In this paper, it is found that the ration between Virial coefficients tends to α·T^(0.25～0.50) as the temperature tends to infinite, and a set of empirical formulas are proposed to calculate the fourth and the fifth Virial coefficients. These formulas, which look like the theoretical forms of the second and the third ones, can be used conveniently to fit the values obtained by numerical solution. Comparing with the other empirical formulas, this method is charactrized by its simplicity, accuracy, and common calculation form for all Virial coefficients.