Relationships between Low and High Concentration Regimes

Let us suppose that the experimental contribution of polymer to solution viscosity at low concentration, rj0 — t]s, can be represented to a sufficient approximation by the Martin equation [Eq.(5.9)]. An alternative which is presumably always available to the solution is free draining behavior [Eq.(4.16)]. As concentration is increased, then, according to the minimum dissipation principle, the behavior would be expected to change from the Martin form to the free draining form in the range where the two expressions for rj0 — rjs become equal  

If [ /] in the front factor on the right side of Eq.(5.11) is replaced by its value according to the Zimm theory [Eq.(5.1)], and if 0 is replaced by the Stokes formula for spheres, 0 = 6nt]sR0, in which R0 is the effective Stokes radius of a main chain atom, Eq.(5.11) becomes  

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