Fluctuation theory of the liquid-glass transition

Abstract

The glassy state and the character of the liquid-glass transition from undercooled liquid to amorphous solid is one of the biggest challenges of our time. In spite of significant progress we still cannot explain accurately the sudden solidification of undercooled liquids on the atomic scale. In the present paper we present an analytical theory of the dependence of the glass transition temperature on the rate of cooling: the glass transition temperature increases with increasing cooling rate but does not exceed some upper limit. At almost zero cooling rates (hypothetical reversible transformation of the liquid into glass) the glass transition temperature reduces to a critical temperature, similar to a phase transition temperature.