Review: Simulational Tests of the Rouse Model

TL;DR

This review critically examines literature on the Rouse model for polymer dynamics in melts, showing through simulations that its predictions do not match observed behaviors, especially regarding mode correlations and relaxation times.

Contribution

It provides a comprehensive assessment of simulation results that challenge the validity of the Rouse model in describing polymer motion in melts.

Findings

Rouse model's autocorrelation functions are stretched exponentials, not pure exponentials.

Mean-square amplitudes of Rouse modes deviate from model predictions for p > 3.

Relaxation times depend on mode index p differently than predicted.

Abstract

The file is a Chapter from my review volume "Polymer Physics: Phenomenology of Polymeric Fluid Simulations". The chapter treats literature tests of the Rouse model, which is widely invoked as a description of polymer motion in melts. In summary: The literature conclusively demonstrates that the Rouse model does not describe polymer motion in melts. Simulations find that the temporal autocorrelation function of a single Rouse amplitude is a stretched exponential in time, not the pure exponential predicted by the Rouse model. Also, the mean-square amplitude of the Rouse modes <(X_p (0) X_p (0) > deviates from the model's prediction, at least for p > 3. Furthermore, the relaxation time of <(X_p (0) X_p (t) > depends on p, but not as predicted by the Rouse model. According to the Rouse model, bead displacements are driven by independent Gaussian random processes. Accordingly, the intermediate structure factor g(q,t) is predicted to be accurately described by the Gaussian approximation. Doob's theorem then guarantees that g(q,t) decays as a single exponential in time. Simulations show that these predictions of the Rouse model are incorrect.