Critical exponent equations: Their relation with free volumes at Tgand TRand with the macromolecular domain concept

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Abstract
Packing density and activation energy considerations reveal that the fractional free volume of a fully amorphous linear polymer at Tg, (FFV)Tg, is about 0.037. Tg is shown to be the temperature at which sufficient free volume and segmental flexibility combine to redistribute the free volume, changing from the uniform distribution below Tg into effective-hole distribution above Tg. The same considerations indicate that at the reference temperature TR, (FFV)TR ≌ 0.113. TR and the exact value of (FFV)TR are determined through a critical exponent equation, with the exponent β = 1/3. It is shown that TR is the temperature at which the number of nearest neighbors of each segment is one less than their number at Tg. TR is the temperature at which the extrapolated mechanical strength is essentially zero, and at which the activation energy for flow asymptotically becomes vanishingly small and temperature-independent. It is further shown that nonpolymeric glass-formers behave in these respects the same as polymers. Finally, it is shown that the macromolecular domain character of amorphous polymers is describable through the utilization of physical cluster concepts, and that the density variations associated with the domain and its cavity follow critical exponent equations essentially the same as those describing density changes of the bulk polymers.

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