Concentrated polymer solution: Part II. Dependence of viscosity and relaxation time on concentration and molecular weight

A previouly presented molecular theory for non‐Newtonian viscosity in moderately concentrated polymer solutions is extended here to a specific consideration of the influence of solute concentration c and molecular weight M on the limiting viscosity ηo and the relaxation time λ. Estimates of the M,c dependence of several intermediate functions are necessary including that of Kirkwood's friction coefficient. The prediction ηo ∼ (cM0.625)2 is in good agreement with the empirical observation that ηo is a function of the parameter cM0.68, but is inadequate for extremes of M and c. Plausibility arguments are advanced to suggest λ ∼ ηoc−2 rather than λdil. ∼ Mηoc−1 predicted by dilute solution theory and widely accepted. This would explain the utility of the factor c2 used in recent rheological correlations, and would reconcile some conflicting reports of λ(M) measurements.