Theory of melting of glasses

Abstract

Glassy matter like crystals resists change in shape. Therefore a theory for their continuous melting should show how the shear elastic constant $\mu$ goes to zero. Since viscosity is the long wave-length low frequency limit of shear correlations, the same theory should give phenomena like the Volger-Fulcher dependence of the viscosity on temperature near the transition. A continuum model interrupted randomly by asymmetric rigid defects with orientational degrees of freedom is considered. Such defects are orthogonal to the continuum excitations, and are required to be imprisoned by rotational motion of the nearby atoms of the continuum. The defects interact with an angle dependent $\mu/r^3$ potential. A renormalization group for the elastic constants, and the fugacity of the defects in 3D is constructed. The principal results are that there is a scale-invariant reduction of $\mu$ as a function of length at any temperature $T < T_0$, above which it is 0 macrosopically but has a finite correlation length $\xi(T)$ which diverges as $T \to T_0$. Viscosity is shown to be proportional to $\xi^2(T)$ and has the Vogel-Fulcher form. The specific heat is $\propto \xi^{-3}(T)$. As $T \to T_0$, the Kauzman temperature from above, the configuration entropy of the liquid is exhausted. The theory also gives the ``fragility" of glasses in terms of their $T_0/\mu$.