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17 - Afterword: hydrodynamic scaling model for polymer dynamics

Published online by Cambridge University Press:  05 August 2012

George D. J. Phillies
George D. J. Phillies
Affiliation:
Worcester Polytechnic Institute, Massachusetts
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Summary

This very short chapter sketches a theoretical scheme – the hydrodynamic scaling model – that is consistent with the results in the previous chapter, and that predicts aspects of the observed behavior of polymers in nondilute solution. The model is incomplete; it does not predict everything. However, where it has been applied, its predictions agree with experiment. Here the model and its developments as of date of writing are described qualitatively, the reader being referred to the literature for extended calculations.

The hydrodynamic scaling model is an extension of the Kirkwood-Riseman model for polymer dynamics(1). The original model considered a single polymer molecule. It effectively treats a polymer coil as a bag of beads. For their collective coordinates, the beads have three center-of-mass translations, three rotations around the center of mass, and unspecified other coordinates. The use of rotation coordinates causes the Kirkwood-Riseman model to differ from the Rouse and Zimm models(2, 3). The other collective coordinates of the Kirkwood–Riseman model are lumped as “internal coordinates” whose fluctuations are in first approximation ignored. The beads are linked end-to-end, the links serving to establish and maintain the coil's bead density and radius of gyration. However, the spring constant of the links only affects the time evolution of the internal coordinates; it has no effect on translation or rotation of the coil as a whole.

When a coil moves with respect to the solvent, each bead sets up a wake, a fluid flow described in first approximation by the Oseen tensor.

Type
Chapter
Information
Phenomenology of Polymer Solution Dynamics , pp. 494 - 498
Publisher: Cambridge University Press
Print publication year: 2011

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References

[1] J. G., Kirkwood and J., Riseman. The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J. Chem. Phys., 16 (1948), 565–573.Google Scholar
[2] P. E., Rouse Jr., A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys., 21 (1953), 1272–1280.Google Scholar
[3] B. H., Zimm. Dynamics of polymer molecules in dilute solution: Viscosity, flow birefringence and dielectric loss. J. Chem. Phys., 24 (1956), 269–278.Google Scholar
[4] G. D. J., Phillies. Quantitative prediction of α in the scaling law for self-diffusion. Macromolecules, 21 (1988), 3101–3106.Google Scholar
[5] A. R., Altenberger and J. S., Dahler. Application of a new renormalization group to the equation of state of a hard-sphere fluid. Phys. Rev. E, 54 (1996), 6242–6252.Google Scholar
[6] G. D. J., Phillies. Derivation of the universal scaling equation of the hydrodynamic scaling model via renormalization group analysis. Macromolecules, 31 (1998), 2317– 2327.Google Scholar
[7] S. C., Merriam and G. D. J., Phillies. Fourth-order hydrodynamic contribution to the polymer self-diffusion coefficient. J. Polym. Sci. B: Physics, 42 (2004), 1663–1670.Google Scholar
[8] G. D. J., Phillies. Quantitative experimental confirmation of the chain contraction assumption of the hydrodynamic scaling model. J. Phys. Chem., 101 (1997), 4226–4231.Google Scholar
[9] G. D. J., Phillies and P. C., Kirkitelos, Higher-order hydrodynamic interactions in the calculation of polymer transport properties. J. Polymer Sci. B: Polymer Physics, 31 (1993), 1785–1797.Google Scholar
[10] G. J., Kynch. The slow motion of two or more spheres through a viscous fluid. J. Fluid Mech., 5 (1959), 193–208.Google Scholar
[11] G. D. J., Phillies, M., Lacroix, and J., Yambert. Probe diffusion in sodium polystyrene sulfonate–water: experimental determination of sphere–chain binary hydrodynamic interactions. J. Phys. Chem., 101 (1997), 5124–5130.Google Scholar
[12] G. D. J., Phillies. Low-shear viscosity of nondilute polymer solutions from a generalized Kirkwood–Riseman model. J. Chem. Phys., 116 (2002), 5857–5866.Google Scholar
[13] G. D. J., Phillies. Self-consistency of hydrodynamic models for the zero-shear viscosity and the self-diffusion coefficient. Macromolecules, 35 (2002), 7414–7418.Google Scholar
[14] G. D. J., Phillies. Polymer solution viscoelasticity from two-parameter temporal scaling. J. Chem. Phys., 110 (1999), 5989–5992.Google Scholar
[15] G. D. J., Phillies. Temporal scaling analysis: Linear and crosslinked polymers. J. Polym. Sci. B, 40 (2002), 375–386.Google Scholar
[16] G. D. J., Phillies. Temporal scaling analysis: Viscoelastic properties of star polymers. J. Chem. Phys., 111 (1999), 8144–8150.Google Scholar
[17] G. D. J., Phillies. Viscosity of hard sphere suspensions. J. Coll. Interface Sci., 248 (2002), 528–529.Google Scholar

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