Theory of fluidity of liquids, glass transition, and melting

Abstract

This is a presentation of a rigorous theory of fluidity of liquids, glass transition and melting of solids in the frame of an asymmetric double well potential model. Potential wells are doubled time to time by the local density fluctuations caused by the thermal longitudinal waves. The average frequency of doubling of potential wells is equal to the frequency of the most energetic waves which obey a law similar to Wein's displacement law in black body radiation. Based on the equilibrium thermodynamic theory of fluctuations and the displacement law, a law of linear pre-diffusion mean-square displacement of particles in a solid is derived: the mean-square displacement of molecules within their potential wells increases linearly with temperature. It is shown that when this is broken-down (where the mean-square displacement at a certain temperature rapidly changes its slope as a function of temperature) glass devitrifies and crystal melts, and all possible solid-liquid transitions of a substance occur at the same critical mean-square displacement: any solid (not only crystals) transforms into liquid when the mean-square displacement, as a fraction of the average intermolecular distance, acquires a certain universal critical value - the same for different substances. It is proved that molecules in a liquid perform specific Brownian motion. The average jump distance is a function of temperature and it is much smaller than the nearest intermolecular distances. At a certain temperature, shown to be the Kauzmann temperature, the average jump distance of Brownian motion becomes equal to zero: the supercooled liquid undergoes glass transition. The transition was proven to be a phase transition of the fourth order: 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. Molecular mobility, diffusion and viscosity are obtained as functions of temperature.