Kinetic criteria of glass formation and the pressure dependence of the glass transition temperature.

An overview on different attempts of formulation of kinetic criteria of glass formation is given. It is analyzed which of the characteristic time scales-time of observation, time of relaxation, and time of change of external parameters-have to be employed to appropriately develop such criteria. Based on this analysis, a general model-independent kinetic criterion for glass formation is formulated. As a first consequence, it is shown that it is not-as often claimed-the Deborah number which governs glass formation. Based on this general kinetic criterion for glass formation, general expressions for the dependence of the glass transition temperature on pressure (and vice versa) are obtained being essentially ratios of the partial derivatives of the appropriate relaxation times with respect to pressure and temperature, respectively. Employing, as examples, further two different (free volume and entropy based) models for the description of viscous flow and relaxation, respectively, relations similar but, in general, not identical to the classical Ehrenfest relations describing second-order equilibrium phase transitions are obtained. In this way, it can be explained why one of the Ehrenfest's relations is usually fulfilled in glass transition and the other not and why the Prigogine-Defay ratio in glass transition is not equal to one as this is the case with Ehrenfest's ratio in second-order equilibrium phase transitions.