The Glass Transition and Free Volume

In Chapters 1 and 2, the glass transition was described as the point, or narrow region, on the temperature scale where the thermal expansion coefficient a 

Schematic variation of total specific volume, occupied volume, and free volume (relative to specific volume at Tg) with temperature for a supercooled liquid. (After Kovacs.)  

We picture the total volume per gram, u, as the sum of u/ and an occupied volume Vo, which includes not only the volume of the molecules as represented by their van der Waals radii but also the volume associated with vibrational motions. 

The occupied volume also increases with temperature, but its magnitude and thermal expansion coefficient Uo. as drawn schematically in Fig. 11-6,-remain a matter of conjecture and can be estimated only indirectly. It cannot be identified with the van der Waals covolume. In Fig. 11-6, the specific volumes are normalized by the volume Og at the glass transition temperature. Thus the fractional free volume,/, a dimensionless number, is oj/og. (Alternatively,/may be defined as Vf/o, which is nearly equivalent since d varies by only a few per cent in a temperature range of interest.) 

Values of Tg of poly(vinyl acetate) quoted in the literature range from 25 to 

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Tg as an Iso-Free-Volume State In 1950 Fox and Flory (74) studied the glass transition and free volume of polystyrene as a function of molecular weight and relaxation time. For infinite molecular weight, they found that the specific free volume, V/, could be expressed above Tg as... 

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