Concentration Dependence of the Frictional Coefficient of Polymers in Solution

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Abstract
The frictional coefficient of chain polymers at finite concentrations is calculated on the basis of the Kirkwood—Riseman approach taking into account the intramolecular and intermolecular hydrodynamic interactions. The intermolecular potential energy of Flory and Krigbaum is employed for the calculation of the perturbation velocity produced in the neighborhood of one molecule by the presence of another. Difficulties arising from an improper integral encountered in the intermolecular treatment of the viscosity to the Stokes approximation do not occur in the present problem. Evaluation is carried out up to the term linear in concentration, and the final expression is rewritten in terms of the molecular parameters familiar in the recent dilute polymer solution theories. The results show that the frictional coefficient is initially independent of concentration at the theta temperature, and that the ratio of the coefficient of the linear term to the intrinsic viscosity takes a value of about 1.7 for good solvent systems. These conclusions are in agreement with the experimental observations. A detailed comparison with experiment is made for several systems.