The liquid–glass transition – is it a fourth order phase transition?

Abstract

The liquid–glass transition is analyzed using a theory of Brownian motion in liquids recently developed by the author. It is shown that if a liquid could be cooled in quasi-static process and still avoids crystallization it would transform into a stable non-crystalline solid, which would be a normal thermodynamic phase. This hypothetical phase transition is neither first nor second order. At equilibrium transition temperature the free energy of the system and its first, second and third derivatives are all continuous functions, but its fourth derivative with respect to temperature is discontinuous. Therefore, the equilibrium liquid to non-crystalline solid transition may be considered a fourth order phase transition. The temperature of this phase transition, T K, which coincides approximately with the Kauzmann temperature, is below the standard glass transition temperature T g. (When the temperature decreases below T g, the viscosity increases above 10 13 dPa s.) When the temperature decreases below T K, the system becomes an ideal solid because the molecular mobility becomes zero and the viscosity becomes infinite if we neglect vacancy-like mechanisms of mobility. This hypothetical quasi-static transition is physically unobservable because the real liquid–glass transition must be done at a cooling rate high enough to suppress the growth of nanocrystals, which makes the liquid–glass transformation a non-equilibrium complicated phenomenon. Understanding this ideal phase transition is a first step towards describing the real liquid–glass transition from first principles.