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In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood–Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood–Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient $Ds$ and the low-shear viscosity $\eta$. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger–Dahler positive-function renormalization group are presented. The rationales correctly predict how $D_s$ and $\eta$ depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted. Full article

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 $⟨{\left(X_p\left(0\right)\right)}^2⟩$ and time correlation functions $⟨X_p\left(0\right)X_p\left(t\right)⟩$ of the Rouse mode $X_p\left(t\right)$. 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 $⟨{\left(X_p\left(0\right)\right)}^2⟩$ do not scale as ${sin}^{-2}(p\pi /2N)$, N being the number of beads in the polymer. For small p (say, $p\le 3$) $⟨{\left(X_p\left(0\right)\right)}^2⟩$ scales with p as $p^{-2}$; for larger p, it scales as $p^{-3}$. (ii) Rouse mode time correlation functions $⟨X_p\left(t\right)X_p\left(0\right)⟩$ do not decay with time as exponentials; they instead decay as stretched exponentials $exp(-\alpha t^{\beta })$. $\beta$ 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 $p\ne q$, $⟨X_p\left(t\right)X_q\left(0\right)⟩$ 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. Full article

The Rouse model is the foundational basis of much of modern polymer physics. The period alternative, the Kirkwood–Riseman model, is rarely mentioned in modern monographs. The models are qualitatively different. The models do not agree as to how many internal modes a polymer molecule has. In the Kirkwood–Riseman model, polymers in a shear field perform whole-body rotation; in the Rouse model, polymers respond to shear with an affine deformation. We use Brownian dynamics to show that the Kirkwood–Riseman model for chain motion is qualitatively correct. Contrary to the Rouse model, in shear flow, polymer coils rotate. Rouse modes are cross-correlated. The amplitudes and relaxation rates of Rouse modes depend on the shear rate. Several alternatives to Rouse modes as collective coordinates are discussed. Full article