| Abstract
| - We present a new quantitative development of the reptation picture of de Gennes−Doi−Edwards. It is well-known that the original reptation theory is unable to fit linear relaxation spectra (G‘and G‘ ‘) as it misses several important physical processes: (1) contour length fluctuations, (2) constraintrelease, and (3) longitudinal stress relaxation along the tube. All of these processes were treatedtheoretically before; however, the treatment used either uncontrolled approximations or failed to includeall of them at the same time. The aim of this work is to combine self-consistent theories for contourlength fluctuations and constraint release with reptation theory. First, we improve the treatment of contourlength fluctuations using a combined theoretical and stochastic simulation approach. This allows us toobtain an expression for the single chain relaxation function μ(t) without any adjustable parameters andapproximations. To include constraint release, we use the scheme proposed by Rubinstein and Colby,which provides an algorithm for calculating the full relaxation function G(t) from the single chainrelaxation μ(t). Then longitudinal modes are added, and a detailed comparison with different experimentaldata is given. One of the conclusions is that polystyrene is described by theory very well, but polybutadieneshows problems, which may be a first indication of nonuniversality of polymer dynamics.
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