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.