Correlation between the equation of state and the pressure dependence of glass transition and melting temperatures in polymers and rare-gas solids

Abstract

A correlation between the equation of state and the pressure dependence of the glass transition temperature T g in polymers such as polystyrene (PS) and poly (methyl methacrylate) (PMMA) and the pressure dependence of the melting temperature T m in polymers such as polyethylene (PE), in rare-gas solids such as argon (Ar) and in hydrogen (H 2) has been examined based on the experimental data by Simha, Zoller and Rehage for polymers and Cheng, Mills and Zha for rare-gas solids and an equation of state derived in a previous work. The volume-pressure relation at constant temperature for solid and liquid states is expressed by: V x(P 0, T)/V x(P, T)= A x(P + P x) m x where V x ( P 0, T) is the volume at constant pressure P 0 and temperature T, V x ( P, T) is the volume at P and T, P x is a function of temperature, m x is a constant and the subscript x means a state such as x = 1 for liquid and x = s for solid. It is found that values of P x change discontinuously with increasing temperature in the vicinity of T g, while m x changes discontinuously at T m where P x is continuous with respect to temperature. Values of F m,s defined by F m,s = 1 − V s (P m , 0) V s (P m , T m ) for a rare-gas solid such as Ar are calculated based on the experimental data and are around 0.09 for Ar, independent of pressure, where V s( P m, T m) is the volume of solid phase at T m. Values of F g defined by F g = 1 − V s (P g , T 0) V(P g ), T g ) at T g are 0.036-0.055 for PS and 0.018–0.036 for PMMA. A three dimensional P- V- T surface over the temperature region including T g and T m is established based on the experimental data.