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 μ 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 renormalisation 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 μ as a function of length at any temperature $T<T_0$, above which it is 0 macrosopically but has a finite correlation length $\xi \left(T\right)$ which diverges as $T\to T_0$. Viscosity is shown to be proportional to ${\xi }^2\left(T\right)$ and has the Vogel-Fulcher form. The specific heat is $\propto {\xi }^{-3}\left(T\right)$. 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 $T_0/\mu$.

KEYWORDS:

• Glasses
• Vogel-Fulcher law
• shear elasticity
• fragility

Acknowledgments

I thank Z. Nussinov and Clare Yu for discussions and comments on the manuscript. I also thank Frances Hellman for rekindling my interest in glasses. This work was done partially as a visiting scholar at University of California, Berkeley; I wish to thank James Analytis, Robert Birgeneau and Joel Moore for making this possible.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Some of the work and discussions about it were done at the 10.13039/100007739Aspen Center of Physics, which is supported partially by NSF grant PHY-1607611.