On the Molecular Theories of Polymer Solutions

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Abstract
This paper reports on a review of the basic molecular theories of polymer viscoelasticity and the proper extension of these theories to the continuum limit, including the effects of local changes in the submolecule friction factor. Our first concern is to show the equivalence of the hydrodynamic method of Kirkwood as exemplified by Zimm and the energetic method of Debye, Rouse, and Bueche. The discrepancy between the results of Zimm and Bueche is resolved by including the internal energy of the bead‐and‐spring model of the polymer molecule in Bueche's calculation. The dynamic viscosity and its Fourier transform, the elastic modulus, are obtained for the free‐draining and non‐free‐draining cases and the appropriate continuum expressions for these functions are given. Finally, it is shown that a natural limit exists on the allowable strength of the hydrodynamic interaction, beyond which the molecule is unstable in solution. This is a result of the assumed additivity of the hydrodynamic perturbation in the present theories.