DC electric field effects on Ehrenfest-like relations at the glass transition

There have been numerous studies on the effects of dc and alternating electric fields on phase transitions in small-molecule mixtures and high-molecular weight polymers. Furthermore, textbook examples discuss modifications in the melting temperature of pure materials that are subjected to uniform dc fields. This thermodynamic analysis extends some of these predictions to second-order phase transitions. Upon invoking both volume and entropy continuity via the integral approach to phase equilibrium at second-order transitions, electric field effects on the glass transition are developed that parallel the Ehrenfest equations for the pressure dependence of Tg. Both Tg-field equations predict small changes in the glass transition temperature that scale as the square of the electric field strength. If one equates the dependence of Tg on the magnitude of the electric field via (i) volume continuity and (ii) entropy continuity, it is possible to obtain the electric-field analog of the Prigogine-Defay equality, in which thermophysical properties and discontinuous observables at the zero-field and field-dependent second-order phase transition temperatures are related. When the temperature and pressure dependencies of the relative electric permittivity (i.e., dielectric constant) are neglected in the absence of external fields, one recovers the classic Prigogine-Defay equality (i.e., the lower limit of the Prigogine-Defay ratio) that was developed from a consideration of volume and entropy continuity for the pressure dependence of Tg, by invoking the differential approach to phase equilibrium.