Chain-Length-Dependent Correlated Molecular Motion in Polymers

We show how dynamic heterogeneities (DHs), a hallmark of glass-forming materials, depend on chain flexibility and chain length in polymers. For highly flexible polymers, a relatively large number of monomers ( N c ∼ 500 ) undergo correlated motion at the glass transition temperature ( T g ), independent of molecular weight ( M ). In contrast, less flexible polymers show a complex N c ( M ) behavior divided into three regimes, consistent with observations in both T g ( M ) and chain conformational structure. For short oligomers ( ≲ 2 Kuhn steps), a transition from mainly intermolecular correlations and N c ∼ 200 to strongly intramolecular correlations and N c < 50 (roughly the molecular size) is observed; for longer chains, N c increases weakly, before saturating. For poly(methyl methacrylate), a remarkable similarity is found between N c ( M ) and the M -dependent ratio of the activation barriers of the structural ( α ) and secondary ( β ) relaxations; we present evidence that this relationship is a general feature of glass-forming polymers. Our results suggest a direct link between the DH length scale and the number of β relaxation events jointly activated to facilitate the α relaxation.