Interpretation of the glass transition temperature from the point of view of molecular mobility

Glass transition has been one of the biggest challenges in condensed matter physics during the last century: in spite of significant progress we still cannot explain the sudden solidification of undercooled liquids on the atomic scale. The liquid state itself is one of the less developed branches of condensed matter physics. The theoretical concepts of atomic mobility, diffusion and viscosity in liquids are not in good agreement with experiments. In the present paper we attempt to answer this challenge by describing the thermal motion of the native molecules of the liquid as Brownian motion. On the basis of this theory we have derived general expressions for the atomic mobility, mu, self-diffusion, D, and viscosity, eta for liquids. In dependence on a reduced temperature t, the mobility is expressed as mu = mu(0)m(t) for t >= 0 and mu = 0 for t <= 0 where mu(0) is the mobility at the jamming point of the liquid, and m(t) is defined by t = m/(1 - e(-m)). The reduced temperature t = gamma T-2/gamma T-2(c)c is determined by a quantity gamma accounting for the anharmonicity of interparticle interactions in the liquid state. At the special values gamma(c) and T-c the mobility becomes zero, i.e. the equilibrium glass transition occurs when the reduced temperature becomes equal to 1.