Local relaxation of polymers in dense media: Cooperative kinematics theory and applications

Cooperative kinematics (CK) theory and its recent applications are presented. CK theory has been developed as an efficient approach for predicting the mechanism of segmental relaxation processes in bulk polymers. The theory aims at determining the most probable changes in atomic coordinates, occurring collectively in response to a given, external or localized, structural perturbation. The basic postulate is the minimization of the energy change involved in the overall conformational motion, which naturally yields the optimal pathway of cooperative relaxation. Attention has been confined here to the collective motions accompanying the rotational transitions of backbone bonds in polyethylene (PE) and polybutadiene (PB). The strong dependence of the mechanism of motions on the geometry of the repeat unit and on chain connectivity is emphasized. The differences in the types of correlated transitions operating in different structures, the effective conformational energy changes triggered by bond rotational jumps, and the correlation lengths for particular bond isomerizations are analyzed. The reorientations of C-H bond vectors in cis- and trans-PB are also examined to explain the shorter correlation time of cia units, compared to trans, detected by NMR. A good agreement between various CK predictions and results from molecular dynamics (MD) simulations is obtained. The fact that CK calculations are at least two orders of magnitude faster than MD simulations invites attention to the utility of the CK method as an efficient tool for elucidating the pathway of motion in complex systems.