Probe Diffusion in Sodium Polystyrene Sulfonate−Water:  Experimental Determination of Sphere−Chain Binary Hydrodynamic Interactions

Phillies, George D. J.; Lacroix, and Mickey; Yambert, Jennifer E.

doi:10.1021/jp970534v

Cited by 10 publications

(11 citation statements)

References 17 publications

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“…with the solvent viscosity η 0 and the thermal energy k B T . As demonstrated, e.g., for the case of a tracer sphere in solution of polymers [8,9,10,11], the naive approach to replace the pure solvent viscosity with the macroscopic shear viscosity η macro of the polymer solution (as measured in a viscosimeter) in general fails. The polymer solution in the vicinity of the moving sphere is not homogeneous.…”

Section: Introductionmentioning

confidence: 99%

Diffusion of a sphere in a dilute solution of polymer coils

Krüger

Rauscher

2009

The Journal of Chemical Physics

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We calculate the short time and the long time diffusion coefficients of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized Einstein relation (fluctuation dissipation theorem). The tracer particle as well as the polymer coils are idealized as hard spheres with a no-slip boundary condition for the solvent but the hydrodynamic radius of the polymer coils is allowed to be smaller than the direct-interaction radius. We take hydrodynamic interactions up to 11th order in the particle distance into account. For the limit of small polymers, the expected generalized Stokes-Einstein relation is found. The long time diffusion coefficient also roughly obeys the generalized Stokes-Einstein relation for larger polymers whereas the short time coefficient does not. We find good qualitative and quantitative agreement to experiments.

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Section: Introductionmentioning

confidence: 99%

Diffusion of a sphere in a dilute solution of polymer coils

Krüger

Rauscher

2009

The Journal of Chemical Physics

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“…Phillies, et al's [24] paper Probe Diffusion in Sodium Polystyrene Sulfonate -Water: Experimental Determination of Sphere-Chain Binary Hydrodynamic Interactions made a quantitative test of the hydrodynamic model used here. D c of three sizes of polystyrene sphere was determined in solutions of seven different monodisperse polystyrene sulphonates (1.5 ≤ M ≤ 1188 kDa), each at ten or more concentrations up to 20 g/L.…”

Section: Brief Description Of Individual Historical Papersmentioning

confidence: 99%

“…Is the extended Kirkwood-Riseman model accurate? Phillies, Lacroix, and Yambert [24] made a quantitative experimental test of the model of Section 3. The test was successful.…”

Section: Phenomenological Evidencementioning

confidence: 99%

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The Hydrodynamic Scaling Model for the Dynamics of Non-Dilute Polymer Solutions: A Comprehensive Review

Phillies¹

2016

Preprint

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This article presents a comprehensive review of the Hydrodynamic Scaling Model for the dynamics of polymers in dilute and nondilute solutions. The Hydrodynamic Scaling Model differs from some other treatments of non-dilute polymer solutions in that it takes polymer dynamics up to high concentrations to be dominated by solvent-mediated hydrodynamic interactions, with chain crossing constraints presumed to create at most secondary corrections. Many other models take the contrary stand, namely that chain crossing constraints dominate the dynamics of nondilute polymer solutions, while hydrodynamic interactions only create secondary corrections. This article begins with a historical review. We then consider single-chain behavior, in particular the Kirkwood-Riseman model; contradictions between the Kirkwood-Riseman and more familiar Rouse-Zimm models are emphasized. An extended Kirkwood-Riseman model that gives interchain hydrodynamic interactions is developed and applied to generate pseudovirial series for the self-diffusion coefficient and the low-shear viscosity. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler Positive-Function Renormalization Group are developed and applied to the pseudovirial series for Ds and η. Based on the renormalization group method, a two-parameter temporal scaling ansatz is invoked as a path to determining the frequency dependences of the storage and loss moduli. A short description is given for each of the individual papers that developed the Hydrodynamic Scaling Model. Phenomenological evidence supporting aspects of the model is noted. Finally, directions for future development of the Hydrodynamic Scaling Model are presented.

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“…That is, via the fluctuation-dissipation theorem we can extend the Kirkwood-Riseman model from treating a single isolated polymer molecule to treat the hydrodynamic interactions between polymer molecules. Indeed, there is a substantial development of polymer dynamics in non-dilute solutions based on computing the hydrodynamic interactions between polymer coils[16][17][18][19][20][21][22][23][24].…”

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confidence: 99%

The Kirkwood-Riseman Polymer Model of Polymer Dynamics is Qualitatively Correct

Phillies¹

2018

Preprint

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We use Brownian dynamics to show: For an isolated polymer coil, the Kirkwood-Riseman model for chain motion is qualitatively correct. The Rouse model for chain motion is qualitatively incorrect. The models are qualitatively different. Kirkwood and Riseman say polymer coils in a shear field perform wholebody rotation; in the Rouse model rotation does not occur. Our simulations demonstrate that in shear flow:Polymer coils rotate. Rouse modes are cross-correlated. The amplitudes and relaxation rates of Rouse modes depend on the shear rate. Rouse's calculation only refers to a polymer coil in a quiescent fluid, its application to a polymer coil undergoing shear being invalid.

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Probe Diffusion in Sodium Polystyrene Sulfonate−Water: Experimental Determination of Sphere−Chain Binary Hydrodynamic Interactions

Cited by 10 publications

References 17 publications

Diffusion of a sphere in a dilute solution of polymer coils

Diffusion of a sphere in a dilute solution of polymer coils

The Hydrodynamic Scaling Model for the Dynamics of Non-Dilute Polymer Solutions: A Comprehensive Review

The Kirkwood-Riseman Polymer Model of Polymer Dynamics is Qualitatively Correct

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