Relative Contributions of Coupled Rotations and Small-Amplitude Torsions to Conformational Relaxation in Polymers

Local dynamics of polyethylene and 1,4-trans-polybutadiene chains are analyzed by the cooperative kinematics approach. The method includes the effects of environmental friction and the conformational energy changes involved in bond rotational motions. A given bond is rotated by 120° and the response of the surrounding bonds along the chain, which are necessary for localizing the motion, are analyzed. The conformational responses are classified into two sets, one exhibiting a coupled rotation of another bond, i.e. involving a rotational barrier crossing, and the other accommodated by collective small-amplitude torsions (librational) of several bonds in the neighborhood of the rotating bond. Coupled rotations are shown to increase significantly with increasing environmental frictional resistance. Conversely, librational motions are dominant for localization in less viscous environments. An important finding is that, for polyethylene, the subset of transitions in which the relaxation is achieved by torsional librations only has the same mechanism as that of the complete set of transitions. Thus, cooperative torsional librations may localize a motion as efficiently as coupled rotational jumps in polyethylene, although their proportion may be low in highly viscous environments. This is in support of the postulate advanced recently by Moe and Ediger [Moe, N. E.; Ediger, M. D.Macromolecules 1996, 29, 5484] on local dynamics of polyisoprene, in the sense that libration alone can dissipate local disturbances in the conformations. However, for 1,4-trans-polybutadiene, the set of motions including librations only exhibit some departure from that of the overall set of transitions. The size of the correlated sequence of bonds responding to the isomerization of the central bond by libration is about eight bonds and is symmetrically distributed on both sides of the central bond for polyethylene and slightly biased for one side in poly 1,4-trans-polybutadiene. Coupled barrier crossing rotations, on the other hand, take place either on one side of the central bond only in the former or absolutely in one side in the latter and hence involve a shorter correlation length along the chain.