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

• Published in: Journal of applied physics 1951-06, Vol.22 (6), p.711-717
• Main Authors: Schremp, Frederic W., Ferry, John D., Evans, Warren W.
• Format: Article
• Language: English
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.1700036

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 (γ̇) on shearing stress (T) can be represented by the equation γ̇=k1 sinhk2T. 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 γ̇ 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 Φ≅−(dT/d logt)/2.303k1t2 tanh−1{(γ̇/k1)/(1+[1+(γ̇/k1)2]12)}, 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, Φr=ΦT0/Tc, plotted against the logarithm of the reduced relaxation time, τr=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.