Kinematics of Polymer Chains in Dense Medium. 4. Effect of Backbone Geometry and Application to Polybutadiene

The present study is an extension of the cooperative kinematics (CK) approach (Bahar, I.; Erman, B.; Monnerie, L.Macromolecules 1992, 25, 6309), which has been demonstrated to give an efficient and realistic account of the mechanism of local relaxational processes in polyethylene (PE). In the present work, the effects of (i) departure from tetrahedral backbone geometry and (ii) differences in torsional potentials of backbone bonds are addressed by considering cisand trans-polybutadiene (PBD) chains. The method is based on the minimization of the atomic displacements of chain units and the torsional energy changes, succeeding the isomerization of a given bond. In contrast to the highly localized response of PE to bond rotational jumps, in which the strongest coupling between rotational motions was observed between second neighboring bonds, the coupling in PBD is shown to involve longer chain segments, embodying the strongly correlated torsions of third or fourth neighboring bonds along the chain. The mechanism of motion is unique for each type of rotating bond for cis and trans structures: In trans-PBD, strong counterrotations are encountered at the second neighboring bonds separated by a double bond, whereas in cis-PBD, the same pair of bonds undergoes coupled corotations. Orientational and translational motions of chain units located between successive double bonds are significantly affected by nonbonded intramolecular interactions in cis-PBD, while this effect is not seen in the trans structure. Changes in environmental conditions do not affect the mechanism of localization phenomena, but rather modulate the amplitudes of motion. Under the same frictional environment, cis-PBD atomic displacements are larger than those in trans-PBD by a factor of ∼1.5. The predictions of the theory are in good agreement with the results from recent molecular dynamics (MD) simulations of PBD (Kim, E.-G.; Mattice, W. L. J. Chem. Phys. 1994, 101, 6242; Gee, R. H.; Boyd, R. H. J. Chem. Phys. 1994, 101, 8028). More interestingly, good agreement between the results obtained for cis-PBD and those from the bulk state MD simulations of cis-polyisoprene (Moe, N. E.; Ediger, M. D. Polymer, submitted) is found, confirming that backbone geometry has the major role in determining the mechanism of local conformational relaxations. An advantage of the present approach is that the computational time required is at least 2 orders of magnitude less than that of conventional MD simulations.