(Georgia Institute of Technology, 1982-12-01)
Helfand, Eugene; Skolnick, Jeffrey
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.
(Georgia Institute of Technology, 1981-11-01)
Helfand, Eugene; Wasserman, Z. R.; Weber, Thomas A.; Skolnick, Jeffrey; Runnels, John H.
Conformational transitions in chain molecules have been shown to proceed via a reaction coordinate which is a localized mode involving rotations about bonds, and also bond angle bending and bond stretching. By investigating the kinetics as a function of the force constants (flexibility) for bond angle bending and bond stretching, the role of the localized mode is probed. The study reported here consists of computer simulations of the Brownian dynamics of chain motions, and of kinetic calculations of rates and reaction modes. The theory accurately predicts the relative effects of force constant variations on transition rates determined by simulation.
(Georgia Institute of Technology, 1980-05-15)
Skolnick, Jeffrey; Helfand, Eugene
A theory is developed for the rate of conformational transitions (transgauche) of bonds in chain molecules, such as alkanes and polymers. This is a multidimensional extension of Kramers' reaction rate theory. Central to the understanding of how changes in the chain's geometry affect transition rate is the determination and examination of the reaction coordinate. The reaction coordinate is a localized mode; i.e., the rotational motion of the transforming bond is accompanied by motion in neighboring bonds, but this motion diminishes with distance. Comparison is made between the calculated rates and those determined by Brownian molecular dynamics simulations.