Kinetic criteria of glass-formation, pressure dependence of the glass-transition temperature, and the Prigogine-Defay ratio

An analysis of some current topics of discussion in the theoretical modeling of the glass transition and of glass properties is given. In the first part, a general model-independent kinetic criterion of glass-formation is formulated. Its interrelation with other attempts of formulation of such criteria is discussed and some consequences not studied so far in detail are analyzed. It is shown that the value of the glass transition temperature depends not only on system properties and rates of change of external control parameters but, as a rule, also on the property of the system measured for its specification. In addition, systems described by several structural order-parameters may exhibit multiple glass transitions. The respective glass transition temperatures are shown to depend on the spectrum of relaxation times of the respective structural order-parameter and the degree of deviation of the system from the thermodynamic equilibrium state. Employing mentioned kinetic criteria, further on general equations for the pressure dependence of the glass transition temperature and the value of the viscosity at the glass transition temperature in dependence on cooling rate are formulated. In the second part, existing different approaches to the theoretical determination of the Prigogine-Defay (PD) ratio in glass transition are critically reviewed. As shown, following the kinetic approach to the determination of the glass transition temperature Tg, the analysis of the pressure dependence of Tg does not lead to any generally valid predictions for the value of the PD-ratio. It is demonstrated further that some recent attempts to question it do not affect the basic result of earlier analysis (J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511/1-11 (2006)) concerning the possibility to predict theoretically values of the PD-ratio larger than one when only one structural order-parameter is employed to describe kinetic freeze-in at glass transition.