Comparison between some empirical equations of state for polymers

Some commonly used empirical equations of state for polymers are considered: the Spencer-Gilmore equation with two and three adjustable parameters, the Whitaker-Griskey equation, and the Rehage-Breuer equation. Also, a new equation is proposed: the Inverse Volume equation. These equations are evaluated with regard to fitting experimental P-V-T data and agreement with experimental data on isothermal compressibility and thermal expansion coefficient. The adjustable parameters for each equation are determined with the help of Rosenbrock's optimum-seeking technique. Analysis of the residuals on specific volume for a variety of materials suggests that the Spencer-Gilmore equation with three adjustable parameters, the Rehage-Breuer and the Inverse Volume equations yield the smallest and most random residuals and thus the least systematic error. The same three equations mentioned above yield results in good agreement with experimental isothermal compressibility data. However, among all the equations considered in this study, the Inverse Volume equation yields the best agreement with experimental thermal expansion coefficient data. Furthermore, it is the only equation to correctly predict the rise in thermal expansion coefficient with increasing temperature.