Glass transition temperatures (Tgs) of polymers have been correlated with the concept of free volume so that the relationship between Tg and the molecular mass M (7.1) where T; is the glass transItIon temperature for infinite molecular weight, K is a constant and M is the molecular weight. This relation is understandable if one considers that the fractional free volume due to the chain ends decreases as the molecular weight increases. Assuming that molecular motion of a chain end is greater than for an internal part of the chain, a low molecular weight polymer will have a Tg lower than a corresponding high molecular weight polymer. The constant K is the contribution of the end-groups (7.2) where p is the polymer density, N A is Avogadro's number, e is the contribution of a chain end to the free volume and a[ is the thermal expansion coefficient of the free volume.A few long branches on a polymer backbone decrease Tg by increasing the number of chain ends, while regular short branching along the chain increases both the stiffness and Tg and decreases chain mobility. Crosslinking reduces the specific volume so that Tg rises as a consequence of the reduction in molecular motion. l For homo cyclic and heterocyclic aromatic polymers, structure-property relationships have been reviewed mainly for polyimides and some general features have been pointed out. In the case of aromatic substitution, meta-versus para-catenation decreases Tg and flexible bridging groups such as oxygen or methylene decrease Tg more than do highly dipolar groups such as carbonyl and sulfone. Bulky substituents or substituents which restrict free rotation between two phenyl rings also increase Tg• 2 ,3 Aromatic and heterocyclic high performance polymers are very often amorphous and the variation in properties is governed by Tg•
J. R. Ebdon et al. (eds.), New Methods of Polymer Synthesis