Quantitative Theory for Linear Dynamics of Linear Entangled Polymers

TLDR

Reptation theory fails to reproduce linear relaxation spectra because it omits contour‑length fluctuations, constraint release, and longitudinal stress relaxation, and prior treatments either used uncontrolled approximations or omitted some of these processes. The authors aim to construct a quantitative theory that unifies self‑consistent treatments of contour‑length fluctuations and constraint release with the reptation framework. They achieve this by combining a theoretical–stochastic simulation approach for contour‑length fluctuations, the Rubinstein–Colby algorithm for constraint release, and longitudinal mode contributions to compute the full relaxation function G(t) from the single‑chain μ(t). The resulting parameter‑free μ(t) accurately describes polystyrene relaxation but fails for polybutadiene, suggesting a possible nonuniversality of polymer dynamics.

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) constraint release, and (3) longitudinal stress relaxation along the tube. All of these processes were treated theoretically before; however, the treatment used either uncontrolled approximations or failed to include all of them at the same time. The aim of this work is to combine self-consistent theories for contour length fluctuations and constraint release with reptation theory. First, we improve the treatment of contour length fluctuations using a combined theoretical and stochastic simulation approach. This allows us to obtain an expression for the single chain relaxation function μ(t) without any adjustable parameters and approximations. 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 chain relaxation μ(t). Then longitudinal modes are added, and a detailed comparison with different experimental data is given. One of the conclusions is that polystyrene is described by theory very well, but polybutadiene shows problems, which may be a first indication of nonuniversality of polymer dynamics.