A possible scenario for the fragile-to-strong dynamic crossover predicted by the extendedmode-coupling theory for glass transition

Abstract

It is argued that the extended mode-coupling theory for glass transition predicts a dynamic crossover inthe α-relaxation time and in the self-diffusion constant as a general implication of the structureof its equations of motion. This crossover occurs near the critical temperatureTc of the idealized version of the theory, and is caused by the change in the dynamics from the onedetermined by the cage effect to that dominated by hopping processes. When combined with amodel for the hopping kernel deduced from the dynamical theory for diffusion–jump processes,the dynamic crossover can be identified as the fragile-to-strong crossover (FSC) in which theα-relaxation time and the self-diffusion constant cross over from a non-Arrhenius to anArrhenius behavior. Since the present theory does not resort to the existence of theso-called Widom line, to which the FSC in confined water has been attributed, it provides apossible explanation of the FSC observed in a variety of glass-forming systems in which theexistence of the Widom line is unlikely. In addition, the present theory predicts that theStokes–Einstein relation (SER) breaks down in different ways on the fragile and strongsides of the FSC, in agreement with the experimental observation in confined water. It isalso demonstrated that the violation of the SER in both the fragile and strong regions canbe fitted reasonably well by a single fractional relation with an empirical exponent of 0.85.