On a self‐consistent molecular modeling of linear relaxation phenomena in polymer melts and concentrated solutions

Abstract

This paper analyzes the linear version of the theory of ‘‘relaxation interactions’’ in polymer melts and concentrated polymer solutions proposed by Pokrovskii and Volkov in 1978, and which was subsequently developed later in many of their other publications. In these papers, the Brownian dynamics of a single macromolecule surrounded by other macromolecules was considered on the basis of the bead and spring model, and the environmental macromolecules were assumed to react as a viscoelastic liquid with an unknown relaxation spectrum. The key problem in this approach is the formulation of the self‐consistency condition which delivers the equation for the unknown spectrum. Pokrovskii and Volkov assumed a simple condition of isotropy for the relaxation properties of the surrounding viscoelastic liquid and reported a good description of the relaxation properties for narrow distributed polymers with long flexible chains. However, they obtained these results using a semiempirical self‐consistency condition. The present work is focused on the derivation and analysis of the exact self‐consistency condition for the model. The condition was found in the form of a nonlinear convolution integral equation, for the complex dynamic viscosity. In the case of very long chains, an asymptotic solution was obtained for the slow part of the relaxation spectrum. In contrast with the results of Pokrovskii and Volkov, the solution describes the Rouse spectrum, which predicts a linear increase in viscosity η0 with molecular weight M, η0∼M, and is unable to explain the occurrence of the plateau on the dependence G’(ω).