Viscosity of polymer solutions

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Abstract
A cluster expansion theory is developed for the shear viscosity of solutions of linear polymers in the steady-state limit as a virial series in concentration. By assuming the chains to be rigid with respect to the translational diffusion of the centres of mass and the rotational motion of the chains, the Kirkwood-Riseman (1948) results for the translational and rotational friction coefficients are recovered at infinite dilution. The multiple scattering technique and the conventional pre-averaging approximation are utilised in the analysis. Within these approximations, there is no hydrodynamic screening at infinite dilution in contrast with the results of Freed and Edwards (1974, 1975). Every virial coefficient in the present formulation for the viscosity is convergent so that the viscosity can be directly determined to any desired order in concentration. The cluster expansion for viscosity has been converted to a set of coupled equations similar to the one obtained by Freed and Edwards but with different structure.

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