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

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

2012-02-04

arxiv.org/abs/1202.0918v1

Physics

Condensed Matter

Statistical Mechanics

21 pages

Scientific paper

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.

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