Cranklike conformational transitions in polyethylene

Molecular dynamics simulations of a variety of polymeric systems provide the evidence for two different kinds of conformational transitions: independent single bond transitions and cranklike transitions (or correlated bond transitions). While single bond transitions can be rationalized according to standard theories of activated processes controlled by the saddle point crossing, a more complex description is required for the other type of transitions. In a recent work devoted to the analysis of the simplified chain model with three rotors [B. Nigro and G. J. Moro, J. Phys. Chem. B 106, 7365 (2002)], a theory has been proposed for cranklike transitions represented as a kinetic process between equilibrium states differing by two torsional angles (i.e., two bond transitions). Moreover their rate coefficients were estimated on the basis of a local expansion about the bifurcation of the separatrices departing from the potential function maximum. In the present work the same theory is applied to a model for long alkyl chains in solution, in order to rationalize the behavior of cranklike transitions in polyethylene and to recognize the molecular features controlling them. We obtain probabilities of occurrence of cranklike transitions in substantial agreement with simulation results. Furthermore, the theory is capable of explaining the dependence of the rate on the separation between the two reactive bonds, as well as the dependence on the conformational state of the starting configuration. In particular, selection rules for next-to-nearest neighbor transitions are recovered from the shape of the separatrices and the location of the corresponding bifurcations.