Simulational Tests of the Rouse Model

Abstract

An extensive review of literature simulations of polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on the mean-square amplitudes < (X_p(0))^{2} > and time correlation functions < X_p(0) X_p(t) > of the Rouse modes $X_p(t)$. Contrary to the Rouse model: (i) Mean-square Rouse mode amplitudes < (X_p(0))^2> do not scale as sin^{-2}(p \pi/2N), N being the number of beads in the polymer. For small p (say, p <= 3) < (X_p(0))^2> scales with p as p^{-2}$; for larger p it scales as p^{-3}. (ii) Rouse mode time correlation functions < X_p(t) X_p(0) > do not decay with time as exponentials; they instead decay as stretched exponentials exp(-a t^b)$. b depends on p, typically with a minimum near N/2 or N/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For p not equal to q, < X_p(t) X_{q}(0) > is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. Simulations thus conclusively demonstrate that the Rouse model is invalid in polymer melts. We also briefly consider the Kirkwood-Riseman polymer model.