Abstract

An empirical partition function, $f,$ for polyethylene (PE) was determined based on a pressure (P_V)-volume (V)-temperature (T_V)-entropy (S_V) isochoric equation of state where the variables of P_V, T_V and S_V were evaluated by using the experimental P-V-T data and the isochoric heat capacity for PE . The empirical partition function is expressed by summation of the terms of $T^{-1\mathrm{}},\mathrm{}T,\mathrm{}{T}^3$ and $a(V)e^{-\frac{{\theta }_i}{T}}$ with i = 1 to 6 where the ${\theta }_i\mathrm{}$ temperatures in the Boltzmann factors were in the range of${\mathrm{}\theta }_i\mathrm{}$= 70.5 to 423 K. The thermodynamic derivatives, such as bulk modulus, ${\kappa }_T,$ and isochoric heat capacity, C_V, over a wide range of pressure were evaluated based on the two types of the partition functions derived from the isochoric equation of state and the reformed Debye partition function with ${\theta }_i=i{\theta }_1$ and ${\theta }_1=70.5K.$ The reliability of the reformed Debye partition function was checked by the partition function calculated from the empirical isochoric equation of state.

摘要

经验配分函数， $F,$聚乙烯 ( PE ) 是根据压力 ( P _V )-体积 ( V )-温度 ( T _V )-熵 ( S _V ) 等容状态方程确定的，其中评估了P _V、T _V和S _V的变量通过使用实验PVT数据和PE的等容热容。经验配分函数由以下各项的总和表示${吨}^{-1\mathrm{}},\mathrm{}吨,\mathrm{}{吨}^3$ 和 $\mathrm{一个}(五)e^{-\frac{{\theta }_{\mathrm{一世}}}{吨}}$ i = 1 到 6 其中 ${\theta }_{\mathrm{一世}}\mathrm{}$ 玻尔兹曼因子的温度范围为${\mathrm{}\theta }_{\mathrm{一世}}\mathrm{}$= 70.5 至 423 K. 热力学导数，例如体积模量， ${\kappa }_{吨},$和等容热容，C _V，在很宽的压力范围内，基于从等容状态方程导出的两种类型的配分函数和改良的德拜配分函数${\theta }_{\mathrm{一世}}=\mathrm{一世}{\theta }_1$ 和 ${\theta }_1=70.5ķ.$ 通过根据经验等容状态方程计算的配分函数检查了改进的德拜配分函数的可靠性。