The glass transition of amorphous polymers: About a continuous equation of state and its derivatives

Abstract

Describing the pressure-volume-temperature (PVT) behavior of polymers is often hindered due to limitations of models and theories. In this work, we propose the logistic function to derive a phenomenological equation of state (EOS) that overcomes these limitations. Without dividing the temperature domain into several intervals, this continuous EOS describes the PVT behavior of amorphous polymers in the equilibrium state, the vitreous state and at glass transition. Discontinuities at glass transition are inherently eliminated. The EOS is continuously differentiable with respect to temperature and pressure. The thermal expansion coefficient and compression modulus thus can be determined at any valid reference state. The EOS linearly depends on temperature both in the equilibrium state and vitreous state. Furthermore, a parameter of the EOS is interpreted as the pressure-dependent glass transition temperature. Using PVT data of polyethersulfone (PES), measured in the temperature range of 20 − 360 ° C and pressure range of 10 − 200 MPa in both the isobaric and standard isothermal mode, the validity of the EOS is discussed. Polymer processing simulation and solid mechanics benefit from the EOS and its derivatives, respectively. In addition, the EOS can be used to determine the glass transition temperature from PVT data.