Simulational Tests of the Rouse Model

Abstract

An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes ⟨(Xp(0))2⟩ and time correlation functions ⟨Xp(0)Xp(t)⟩ of the Rouse mode Xp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes ⟨(Xp(0))2⟩ do not scale as sin−2(pπ/2N), N being the number of beads in the polymer. For small p (say, p≤3) ⟨(Xp(0))2⟩ scales with p as p−2; for larger p, it scales as p−3. (ii) Rouse mode time correlation functions ⟨Xp(t)Xp(0)⟩ do not decay with time as exponentials; they instead decay as stretched exponentials exp(−αtβ). β 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≠q, ⟨Xp(t)Xq(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. We also briefly consider the Kirkwood–Riseman polymer model.

Review: Kirkwood–Riseman Model in Non-Dilute Polymeric Fluids

“…In many of these models, polymer motion over short time periods, and polymer motion ('reptation') through the hypothesized tubes in entangled polymeric fluids, were assumed to be described by Rouseian dynamics. However, as we previously found [1,2], simulations show that the Rouse model does not describe polymer motions in the melt.…”

“…Section 5 uses the model to calculate the concentration dependence of the viscosity. Section 5.1 calculates the flow field u (1) created by the scattering of a shear field u (0) by a polymer chain, and the additional flow field u (2) created by the scattering of flow field u (1) by a second polymer. Section 5.2 calculates the power dissipated by various polymer chains exposed to flow fields u (0) , u (1) , and u (2) .…”

“…Section 5.1 calculates the flow field u (1) created by the scattering of a shear field u (0) by a polymer chain, and the additional flow field u (2) created by the scattering of flow field u (1) by a second polymer. Section 5.2 calculates the power dissipated by various polymer chains exposed to flow fields u (0) , u (1) , and u (2) . Section 5.3 calculates the total shear field that would be experimentally determined as a result of these flow fields, leading to a determination in Section 5.4 of the intrinsic viscosity and the Huggins coefficient for the extended Kirkwood-Riseman model.…”

“…The hydrodynamic scaling model is based on extensions of the Kirkwood-Riseman model, while in contrast, many tube/reptation models reference the original Rouse treatment. I have previously discussed [1,2] the Rouse model in detail and will not repeat that discussion here. A major emphasis of this Section is therefore to alert readers familiar with Rouse and Zimm models as to the very different way in which Kirkwood and Riseman described the movements of an individual polymer coil.…”

“…In two prior articles [1,2], we considered the simulational tests of the Rouse-Zimm [3,4] and Kirkwood-Riseman [5] models for chain dynamics in polymeric fluids. We demonstrated that the behavior of model polymer chains in simulated melts and simulated dilute solutions under shear was entirely inconsistent with the Rouse model.…”