Extensional viscosity of dilute polystyrene solutions: Effect of concentration and molecular weight

Abstract

This paper reports a detailed investigation of the steady shear and extensional properties of mono-disperse polystyrene solutions for a range of molecular weights from 1.95 to 20 million and a range of concentrations from 69 ppm to 777 ppm. The steady shear and dynamic properties are reasonably well described by the Zimm model. The relaxation time and polymer viscosity evaluated using the Zimm model exhibit the expected scaling with concentration and molecular weight for theta solutions. In an extensional flow, these solutions show strain hardening and need about 5.5 to 6 strain units to reach steady state. The stress growth depends both on strain rate and strain. However, at moderate values of strain and when the Weissenberg number exceeds 6, the extensional stress growth depends only on total strain. The steady state extensional viscosity for each fluid was observed to depend on the magnitude of Weissenberg number (Wi). For Wi<6, the steady state extensional viscosity was observed to be an increasing function of the strain rate. At a Wi∼10, the steady state extensional viscosity exhibits a maximum and surprisingly, for Wi>10, the steady state extensional viscosity is a decreasing function of the strain rate. The results indicate that even dilute solutions, with concentrations as low as 0.21 times the critical concentration, do show extension thinning under certain conditions. The transient and steady state extensional viscosities are found to be proportional to molecular weight (Mw) and concentration (c). This result is rather unexpected as the Zimm model would predict a scaling with c and Mw0.5 for the transient viscosity and scaling with c and Mw1.5 for the steady state viscosity. On the other hand, the Rouse model predicts a scaling with c and Mw (for transient extensional viscosity) and with c and Mw2 (for steady state extensional viscosity). Hence the data appear to follow a Rouse-like behavior for the transient viscosity. This implies that the advent of the stretching reduces the hydrodynamic interaction and a free draining behavior is obtained. As a result, predictions using the Zimm model parameters, estimated from shear data, are unable to predict the transient extensional viscosity. The data are analyzed using a constitutive equation that incorporates an anisotropic drag coefficient along with a Rouse spectrum of relaxation time. Such a model captures the extensional behavior of the solutions.