Molecular Weight and Concentration Dependences of the Terminal Relaxation Time and Viscosity of Entangled Polymer Solutions

R. W. Rendell, K. L. Ngai, G. B. McKenna

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Abstract

A new model is presented for entangled polymer solutions which accounts for the observed molecular weight and concentration dependences of the zero-shear viscosity ή0and the terminal relaxation time λd. Our development, based upon the coupling model of relaxation, quantitatively describes how relaxation of a primitive mode is modified by coupling through entanglements to its environment. The primitive mode is represented by a Rouse chain of Gaussian submolecules, each of root mean square length σ equal to the entanglement distance and each characterized by an entanglement friction coefficient f0. By extending the analyses developed previously for polymer melts, the model predicts thatή0αM2/(1-n)φγ[φ(α(1-v)]2/(1-n) where φ is the polymer volume fraction. Here n is the coupling parameter describing the terminal relaxation and γ, α, and v are given by GN° φ γ, Me α φ, and σ φ-vα. Numerical examples are shown to agree with experiment; e.g., for n = 0.41, γ = 2, α = 1, v = 0.6, ή0 α f⋆M3.4φ3.4. Comparison of the present results is also made to the reptation and scaling theory predictions.

Original languageEnglish
Pages (from-to)2250-2256
Number of pages7
JournalMacromolecules
Volume20
Issue number9
DOIs
StatePublished - Sep 1 1987

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