Mechanism and rates of conformational transitions in heterogeneous polymers

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Abstract
A general expression is presented for the rate of a trans to gauche conformational transition of a bond in a polymer backbone. The polymer is composed of nonidentical atoms, i.e., centers of differing friction constants and masses. The rate is obtained from a multidimensional extension of Kramers’ steady state solution to the Fokker–Planck equation for flux over a reaction barrier of a system in a frictional medium. Langer’s formulation is used. Results are appropriate for all but extremely small friction, with simplification occurring in the high friction limit. One also determines the reaction coordinate, an examination of which gives insight into the kinetic mechanism. Explicit results are obtained for six and 32 vertex chains, and the influence of chain conformation and relative friction constants are discussed.