Structural order parameters, the Prigogine–Defay ratio and the behavior of the entropy in vitrification

The glass transition is theoretically described in terms of a generic approach employing de Donder’s structural order parameter method, appropriate expressions for the relaxation behavior of glass-forming systems and an order parameter related to the free volume of the system. Employing this approach the behavior of a variety of thermodynamic quantities describing glass-forming systems in vitrification and devitrification processes is interpreted theoretically. Particular attention is devoted here to the estimation of the value of the Prigogine–Defay ratio Π and the analysis of the behavior of the entropy in vitrification. In contrast to previous findings it is shown that treating vitrification correctly as proceeding in some interval of temperature and/or pressure the use of only one structural order parameter is sufficient to explain the generally obtained experimentally results Π > 1. In addition, an analysis of some alternative approaches of introduction of different order parameters is performed and relationships between different structural order parameters are analyzed. It is shown how the concept of an internal (fictive) pressure can be introduced straightforwardly in terms of the generic approach described. Finally, within the framework of the generic approach utilized here, a general model-independent definition of internal (fictive) pressure and fictive temperature is given for the case that an arbitrary number of structural order parameters is required for the description and some further consequences are discussed briefly.