1202.0918 (Hiroshi Matsuoka)

Molar excess entropy and viscosity of a deeply supercooled liquid: a
thermodynamic model for the glass transition    [PDF]

Hiroshi Matsuoka

For a deeply supercooled liquid just above its glass transition temperature
Tg, we present a simple thermodynamic model, where the deeply supercooled
liquid is assumed to be a mixture of solid-like and liquid-like micro regions.
Without referring to a specific microscopic origin of these micro regions, we
assume that the solid-like micro regions have, on average, a slightly higher
density and a slightly lower potential energy than the liquid micro regions. We
also assume that the mole fraction x of the liquid-like micro regions vanishes
at Tg and decreases as the temperature of the supercooled liquid is decreased
toward Tg. With these assumptions, we can show that x controls the
thermodynamic properties of the supercooled liquid, especially, its molar
excess heat capacity at constant pressure, which is directly related to the
molar excess entropy of the supercooled liquid. Using the universal temperature
dependence of the molar excess entropy, we then obtain the temperature
dependence of x. Assuming that the mole fraction, 1-x, of the solid-like micro
regions controls the relaxation time or the viscosity of the supercooled
liquid, we obtain the universal temperature dependence of the relaxation time
or the viscosity. These two universal properties are thus connected through the
temperature dependence of x. A parameter that controls the temperature
dependence of x is shown to be a measure for the fragility of a supercooled
liquid. We also suggest a way to test our assumptions about the solid-like and
liquid-like micro regions by means of molecular dynamics simulations of model
liquids.

View original: http://arxiv.org/abs/1202.0918