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We review simulations of polymeric fluids that report mean-square displacements g(t) of polymer beads, segments, and chains. By means of careful numerical analysis, but contrary to some models of polymer dynamics, we show that hypothesized power-law regimes g(t)∼tα are almost never present. In most but not quite all cases, plots of log(g(t)) against log(t) show smooth curves whose slopes vary continuously with time. We infer that models that predict power-law regimes for g(t) are invalid for melts of linear polymers.

We apply numerical analysis to interpret reported simulations of polymer blend melts, in particular simulational determinations of mean-square displacements g(t) of polymer beads and polymer centers of mass. Our interest is a quantitative comparison of g(t) with theoretical models that predict g(t). Many models predict that g(t) can be described as a sequence of power-law regimes g(t)∼tα. In each regime, α has a model-predicted value. We find that these models are not consistent with simulations of blend melts. Instead, g(t) generally has a single power-law regime and (when those times are reached) a long-time diffusive (α≈1) regime. Outside these two regions, if one writes g(t)∼tα, then α is a smoothly-changing function of time.

The time-dependencies of polymer mean-square displacements g(t) provide significant tests of some modern theories of polymer dynamics. Familiar models propose that g(t) is described by a series of power-law regimes g(t)∼tα, the models predicting values of α and time regimes within which those values will be found. g(t) has been obtained quantitatively over a wide range of times by means of computer simulations, permitting comparison of simulation measurements with these models. Here, we demonstrate a path for quantitatively analyzing g(t). We show that we can readily distinguish between regimes in which g(t) actually follows a power law in time, does not follow a power law in time, or has an inflection point. The method accurately determines local values of the exponent, without imposing any a priori assumption as to the exponent’s value.

Presenting a completely new approach to examining how polymers move in non-dilute solution, this book focuses on experimental facts, not theoretical speculations, and concentrates on polymer solutions, not dilute solutions or polymer melts. From centrifugation and solvent dynamics to viscosity and diffusion, experimental measurements and their quantitative representations are the core of the discussion. The book reveals several experiments never before recognized as revealing polymer solution properties. A novel approach to relaxation phenomena accurately describes viscoelasticity and dielectric relaxation and how they depend on polymer size and concentration. Ideal for graduate students and researchers interested in the properties of polymer solutions, the book covers real measurements on practical systems, including the very latest results. Every significant experimental method is presented in considerable detail, giving unprecedented coverage of polymers in solution.

Recently, there has been interest in determining the viscoelastic properties of polymeric liquids and other complex fluids by means of Diffusing Wave Spectroscopy (DWS). In this technique, light-scattering spectroscopy is applied to highly turbid fluids containing optical probe particles. The DWS spectrum is used to infer the time-dependent mean-square displacement and time-dependent diffusion coefficient \\(D\\) of the probes. From \\(D\\), values for the storage modulus \\(G'(\\omega)\\) and the loss modulus \\(G''(\\omega)\\) are obtained. This paper is primarily concerned with the inference of the mean-square displacement from a DWS spectrum. However, in much of the literature, central to the inference that is said to yield \\(D\\) is an invocation \\(g^{(1)}(t) = \\exp(- 2 q^{2} \\overline{X(t)^{2}})\\) of the Gaussian Approximation for the field correlation function \\(g^{(1)}(t)\\) of the scattered light in terms of the mean-square displacement \\(\\overline{X(t)^{2}}\\) of a probe particle during time \\(t\\). Experiment and simulation both show that the Gaussian approximation is invalid for probes in polymeric liquids and other complex fluids. In this paper, we obtain corrections to the Gaussian approximation that will assist in interpreting DWS spectra of probes in polymeric liquids. The corrections reveal that these DWS spectra receive contributions from higher moments \\(\\overline{X(t)^{2n}}\\), \\(n >1\\), of the probe displacement distribution function.

We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes \\(g(t) \\equiv \\langle (\\Delta x(t))^{2} \\rangle\\) for all times at which \\(g(t)\\) was measured, and that gives values for the logarithmic derivative of \\(g(t)\\) for the same times. By these means we can readily distinguish between regimes in which \\(g(t)\\) follows a power law in time, does not follow a power law in time, or has an inflection point. In a power-law regime, the method accurately determines the exponent, without imposing any assumption as to the exponent's value.

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.

Dielectric relaxation spectra of block polymers containing sequential type-A dipoles are considered. Spectra of a specific set of block copolymers can be combined to isolate the dynamic cross-correlation between the motions of two distinct parts of the same polymer chain. Unlike past treatments of this problem, no model is assumed for the underlying polymer dynamics.

Polymer Physics: Phenomenology of Polymeric Fluid Simulations is a review volume that I am writing. I anticipate it will take a while to complete, so I am supplying individual chapters when each is more-or-less completed. This Chapter considers collective coordinates and collective models for isolated polymer chains. Collective coordinates can be effective tools for isolating aspects of polymer motion that are less obvious if only the Cartesian coordinates of the individual atoms or monomers are viewed. I treat Fourier, Rouse, and Haar wavelets as suppliers of collective coordinates. One of the sets of collective coordinates that i consider, the Rouse coordinates, follows naturally from the Rouse model of polymer dynamics. We therefore consider the Rouse model as well as its more important predecessor, the Kirkwood-Riseman model. Haar wavelets are noteworthy because they allow one to isolate individual regions of a polymer

Contrary to some expectations, an experimental finding for a polymer that the solution intrinsic viscosity \\([\\eta]\\) or the melt viscosity is linear in the polymer molecular weight \\(M\\) does not indicate that polymer dynamics are Rouselike. Why? The other major polymer dynamic model, due to Kirkwood and Riseman [\\emph{J. Chem.\\ Phys.\\ } \\textbf{16}, 565-573 (1948)], leads in its free-draining form to a prediction \\([\\eta] \\sim M\\), even though the polymer motions in this model are totally unlike the polymer motions in the Rouse model. In the Rouse model, the chain motions are linear translation and internal ('Rouse') modes. In the Kirkwood-Riseman model (and its free-draining form, derived here), the chain motions are translation and whole-body rotation. The difference arises because Rouse's calculation implicitly refers only to chains subject to zero external shear force (And, as an aside, Rouse's construction of \\([\\eta]\\) is invalid, because it concludes that there is viscous dissipation in a system that Rouse implicitly assumed to have no applied shear).