A “universal" dependence of the glass transition temperatures in polymers on molecular weight?

The glass transition temperature Tg in polymers increases with molecular weight M, but the detailed Tg(M) dependence in polymers is not well understood. Evidence has accumulated that many polymers have a characteristic Tg(M) that has three regimes: (I) short oligomers which are fairly stiff near Tg; (II) oligomers with masses between roughly one and some 10s of a Rouse mass; and (III) much longer polymers, typically in the entangled and/or fully Gaussian regime. Here we present new data from a wide range of different polymers, and together with literature data demonstrate a remarkable scaling form. We show that these data are not consistent with existing theories of Tg(M). We show from primary (alpha) and secondary (beta and gamma) relaxations that this behaviour can be qualitatively understood in terms of a dynamic facilitation picture in which all of the dynamics are scaled by the molecular weight of the smallest excitation. We compare and contrast this with theories based on free volume, configurational entropy, molecular dynamics simulations, polymer-based mode coupling theories, and activated liquid-state dynamics.