Dynamic Heterogeneity In Polymers – How Many Chain Segments Must Move So That One Can Move?

Molecules and chain segments exert reciprocal influences as they move, so that motion of one entails motion of many. These many-body correlations underlie dynamic heterogeneity, in which different segments reorient at different rates. Essential to understanding this phenomenon is determination of the number of dynamically correlated segments, Nc. The issue is increasingly important because of the burgeoning interest in nanoscale devices and the nano-confinement of polymers. A central question is whether the substantial changes in properties of nano-confined polymers occur because confinement intrudes on the cooperative length scale.

We examine various methods to determine Nc from calorimetry and dielectric spectroscopy, both of which involve approximations, and from molecular dynamic simulations, which give exact results. Our main finding is that Nc depends only on the timescale of the motions, independent of temperature or pressure. This discovery is relevant to developing a theory of polymer dynamics, since relaxation times and Nc cannot be derived separately and be expected to exhibit such correlation by coincidence.

 Experiments on 1,4-polyisoprene will be described, in which motion of the entire chain is measured, to serve as a “molecular ruler” of the cooperative length scale. One finding is that Nc decreases with decreasing molecular weight of the polyisoprene, a consequence of the configurational freedom conferred by the chain ends.