Role of internal viscosity in polymer viscoelasticity

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Abstract
A new theory of the internal viscosity in polymer chains is proposed. Although some of the conclusions are in agreement with the Kuhn‐Cerf‐Peterlin theories, the present approach is based on more rigorous statistical‐mechanical grounds. However, the theory is unable to predict the exact value of the effective Arrhenius factor (A) related to the gauche⇄trans transitions between rotational states on the chain bonds. The internal viscosity force turns out to be a nonlinear effect of the chain motion. Confining our attention to the linear component, and assuming an oscillatory applied force, the diffusion equation is obtained as a modification of the corresponding equation formerly proposed by Zimm. For infinitely long chains the eigenvalue problem is exactly solved and, with reference to the free‐draining model, the dynamic intrinsic viscosity of a polymer solution as well as the tensile and dielectric relaxation effects are calculated.