E3 Glass Transition: Tg and Free Volume

Topic

The glass transition of this glass is not a phase transition but a kinetic one: as the melt cools and crosses this transition without sufficient time to reorganize into its equilibrium configuration, the glass structure becomes frozen out of equilibrium, trapping excess free volume within it.

According to Cohen-Turnbull theory, this excess free volume frozen into the structure quantifies the free volume fraction; the larger this fraction, the more empty space remains available between the network atoms for them to rearrange relative to one another. A higher free volume fraction results in lower viscosity (per the Doolittle equation), while a lower fraction results in higher viscosity.

This glass transition also bears an empirical relationship to the glass's melting temperature: the "two-thirds rule" states that the glass transition temperature lies at approximately two-thirds of the melting temperature, with both values ​​expressed on the same absolute scale. Consequently, a higher melting temperature implies a higher glass transition temperature.

The structural shift occurring as the glass crosses this transition causes a discontinuity in its thermal expansion coefficient exactly at the transition temperature: below this point, the rigid glass's thermal expansion coefficient remains roughly constant, whereas above it, the coefficient rises to a different, higher value characteristic of the softened glass. Thus, regarding this model—introduced with the concepts of the glass transition and excess free volume—that very discontinuity in the thermal expansion coefficient is precisely what enables the experimental measurement of the glass transition temperature: another model in this set, which describes the glass's dilatometry, measures this discontinuity as the change in slope between the two segments of the expansion curve and determines the predicted dilatometric glass transition temperature via the intersection of those two slopes. Furthermore, the fact that this same excess free volume progressively collapses above the glass transition means that yet another model in the set incorporates this free-volume collapse into its description of the glass's viscosity across the entire temperature range.

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