Modifying the Tait equation with cooling-rate effects to predict the pressure-volume-temperature behaviors of amorphous polymers: Modeling and experiments

Cooling-rate effects play an important role in polymer processing because the materials experience rapid cooling when transferring from melt states to solid states. The traditional Tait equation has been used widely in representing the volumetric behaviors of polymers as a function of temperature and pressure, but not of cooling rate. Based on the dependence of glass-transition temperature on cooling rate (i.e., theta = dT(g)/d log \q\), the volumetric dependence on cooling rate is employed in this work to modify the traditional Tait P-V-T equation to become a time-dependent P-V-T model. The physical meanings of the traditional Tait equation parameters are interpreted and, thereby, parameters in the new model are derived according to the material constant theta. The controlled cooling-rate measurements of polymeric volumetric data have been performed in this work to verify the validity of the proposed model. Additionally, the material parameter theta, calculated from the measured data of polystyrene (PS) (Chi-Mei PG-33) in this work, equals 2.85 K, which is close to 2.86 K calculated from the Greiner-Schwarzl work. Furthermore, a comparison of the predicted results with the experimental data both in this work and from literature is discussed under different pressures and various cooling rates. The results have indicated that the proposed non-equilibrium P-V-T model closely correlates with experimental data.