Mechanical Properties of Substances of High Molecular Weight. IX. Non-Newtonian Flow and Stress Relaxation in Concentrated Polyisobutylene and Polystyrene Solutions

A coaxial cylinder apparatus serves to measure the apparent viscosity of a concentrated polymer solution at various shearing stresses and to follow the relaxation of stress after sudden cessation of flow. The dependence of rate of strain $\mathrm{(\gamma ̇)}$ on shearing stress $(\mathcal{T})$ can be represented by the equation ${\mathrm{\gamma ̇=k}}_1\hspace{0.17em}\sinh k_2\mathcal{T}$ . The constant k₂ is almost independent of temperature, and decreases with increasing concentration. The course of the stress relaxation depends on the steady‐state value of $\mathrm{\gamma ̇}$ preceding cessation of flow. By assuming a logarithmic distribution function Φ of elastic mechanisms which are relaxed by hyperbolic sine flow mechanisms, it can be shown that $\mathrm{\Phi \cong -(d}\mathcal{T}\mathrm{/d\hspace{0.17em}}\log {\text{t)/2.303k}}_1\text{t2\hspace{0.17em}}{\tanh }^{\text{−1}}{\mathrm{\{(\gamma ̇/k}}_1{\text{)/(1+[1+(γ̇/k}}_1{)}^2{]}^{\frac{1}{2}}\mathrm{)\}}$ , where t is the elapsed time. Values of Φ obtained from this equation are essentially independent of the rate of shear. The reduced distribution function, Φ_r=ΦT₀/Tc, plotted against the logarithm of the reduced relaxation time, τ_r=τcT/T₀η, where T is the absolute temperature, T₀=298°K, c is the concentration in g/cc, and η the viscosity at zero stress, is independent of temperature and concentration over the ranges studied for each of three polymer samples.