A New Approach to the Glass Transition

Abstract

Transitions of disordered systems usually involve the cessation of a degree of freedom, a notable example being the cessation of electron mobility in a disordered potential. A classical problem related to this is the cessation of diffusion in a glass which occurs at the glass transition. Since the phenomenon appears to be universal, a particular model is studied i n this paper. It i s argued that as the variable x characterizing the transition (x could be (density)^-1 or temperature, etc.) the diffusion constant D behaves like

$$D = {D_0}(1 - \frac{X}{{{X_c}}})$$

in mean field treatment

$$D = {D_0}{e^{\frac{A}{{{x_c}}}}}e - (\frac{A}{{{X_C} - X}})$$

when complex rearrangements are taken inot account but finally right at the point x=x_c

$$D = {D_0}{(1 - X/{X_C})^\alpha } where \alpha = 7/6$$