Nonlinear viscoelasticity of polystyrene solutions. II. Non‐Newtonian viscosity

Abstract

Abstract The steady shear viscosity η( k ) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10 5 to 7.62 × 10 6 and 0.112–0.329 g/cm 3 , respectively. Measurements were performed with a rheometer of the cone‐and‐plate type in the range 10 −4 < k < 1 sec −1 . The Cox–Merz relation η( k ) = |η * (ω)| ω= k was tested with the experimental result (| * (ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η( k ) began to decrease at a lower rate of shear than |η * (ω)| ω= k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ 1 > τ 2 > …, and the values of τ 1 , τ 2 η 1 and η 2 were determined for some solutions. The relaxation times τ 1 and τ 2 were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η 1 and η 2 were approximately 60 and 20–30%, respectively, of η and the non‐Newtonian behavior was due to large decreases of η 1 and η 2 with increasing k . It was shown that η 1 ( k ) may be evaluated from the relaxation strength G 1 (s) for the longest relaxation time of the strain‐dependent relaxation modulus with a constitutive model for relatively high c – M systems as well as for low c – M systems.