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

Abstract

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., θ = dTg/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 θ. 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 θ, 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.

Influence of cooling rate on pVT‐data of semicrystalline polymers

“…Many models, like the Tait equation [23], assume that the specific volume only depends on pressure and temperature. Modifying the Tait equation for cooling rate effects was done by Chang [2]. The resulting set of equations only holds for amorphous polymers at a maximum cooling rate of approximately 0.167[Ks −1 ] and it was shown by Zoller [22] that, on the one hand, the Tait equation does not yield a good representation of the compressibility behavior of solid semi-crystalline polymers like polypropylene but, on the other hand, semi-crystalline polymer melts are represented well.…”

“…Other problems are the possible leakage between the piston and the die, and the formation of voids in the sample when solidifying. The technique was, for instance, applied by Chang [2] who used a pVT-100 apparatus from SWO Germany [5].…”

Analysis of equations of state for polymers

“…In these equations, v is the specific volume of the polymeric material; the coefficient C is a constant equal to 0.0894; o v is the specific volume at zero pressure; t ν is the specific volume corresponding to crystalline phase; B is the sensitivity to pressure of material; 1 9 b are particular parameters of semicrystalline polymers that describe the form of the state transition [24] .…”

Equations of State and Free‐Volume Content

“…Thus, at least four empirical parameters are needed, but since often, the simple exponential is insufficient, expressions that are more complex had to be used. Several modifications of the Tait dependence have been published [Sun et al, 1992;Chang et al, 1996]. This concludes our short review of empirical and semi-empirical equations of state.…”