The molecular weight dependence of Tg in polymers

The polymer glass transition temperature Tg(M) decreases with decreasing molecular weight M. Early theories related this to the increasing free volume (Fox Flory), to configurational entropy for short chains and/or to chain flexibility (Gibbs-DiMarzio, Generalized Entropy Theory). A more recent theory combined ideas from Mode Coupling Theory with activated behaviour, accounting for polymer flexibility and packing to provide precise predictions (Schweizer et al.). Here we review and evaluate these theories in the context of experiments on Tg(M) on many polymer chemistries, from monomer to the "infinite" chain limit; these data show a general M-dependence that can be simply related to measures of chain bulkiness and flexibility, and are a challenge to existing theories.