Strain criterion in nonlinear creep and recovery in concentrated polymer solutions

Abstract

AbstractTransient and steady‐state rheological data are reported for several anionic polystyrene solutions in tritolylphosphate (1. 6 < cM/ρMc < 7). Here c is the concentration of the solution, M is the molecular weight, ρ the density of the undiluted polymer, and Mc the molecular weight between entanglements as determined from zero‐shear viscosity. The polystyrene used had Mw = 410,000 and Mw/Mn < 1.06. Data are also given for solutions of polyisobutylene and poly(vinyl acetate) with larger Mw/Mn. The results give a critical strain γ′ ∝ c−1 such that linear viscoelastic behavior was obtained in a simple shear deformation with shear less than γ′. A simplified version of the constitutive equation of Bernstein, Kearsley, and Zapas is used with an empirical strain function F (γ) which contains γ′ as a parameter to discuss transient and steady‐state behavior in terms of the distribution of relaxation (or retardation) times determined for linear viscoelastic responce. Features of the dependence of the steady‐state viscosity ηk, recoverable compliance Rk, the first‐normal stress function Nk(1) on shear rate k are discussed in terms of F (γ) and the distribution of relaxation times to conclude that the latter plays a dominant role in the behavior observed in the range of k usually studied. The results predict that the reduced functions ηk/η0, Rk/R0, and Nk(1)/N0(1) should depend on η0R0k, and that the functional form depends markedly on the distribution of relaxation times, at least in the range η0R0k < 102. Comparison with the mechanistic model of Doi and Edwards shows a similar F (γ) but substantial differences in the reduced functions caused by a very narrow distribution of relaxation times in the model.