Renormalization Group Treatment of the Hydrodynamics of Polymer Chains in the Rigid Body Approximation

  • Karl F. Freed
  • Shi-Qing Wang
  • Jack F. Douglas
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 9)


The Kirkwood-Riseman model is solved using renormalization group methods for the hydrodynamic radius RH through order ε2 for random walk (Gaussian) chains where ε=4−d and d is the dimensionality of space. These calculations are used, in part, to investigate the effects of the preaveraging approximation within the rigid body hydrodynamic interaction model. Our calculations produce a preaveraging correction of roughly double that found in Monte Carlo simulations, indicating the need for further higher order calculations and/or refinements of the dynamical renormalization group method. We also consider the crossover dependence of RH on the strength of hydrodynamic interactions for a Gaussian chain, showing that our results closely coincide with older classical descriptions of the hydrodynamic radius. For example, our preaveraging Kirkwood-Riseman solution is found to be identical to the Kirkwood approximation to RH to order ε2. Preaveraging affects the crossover dependence in order ε2.


Renormalization Group Hydrodynamic Interaction Perturbation Expansion Renormalization Group Method Polymer Dynamic 
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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Karl F. Freed
    • 1
  • Shi-Qing Wang
    • 1
  • Jack F. Douglas
    • 1
  1. 1.The James Franck Institute and Departments of Chemistry and PhysicsThe University of ChicagoChicagoUSA

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