A SIMPLE EMPIRICAL-MODEL DESCRIBING THE STEADY-STATE SHEAR AND EXTENSIONAL VISCOSITIES OF POLYMER MELTS

The purpose of the work was to find a simple equation that predicts simultaneously both shear and extensional viscosity as a function of deformation rate, as well as giving a reasonable estimate of the steady-state elastic properties. The equation chosen to work with was the White-Metzner model. The special - and highly specific - forms of the deformation rate-dependent viscosity and relaxation time we chose were: eta(s)(II(D)) = eta0/[1 + (K1II(D))n] and lambda(II(D)) = lambda0/[1 + K2II(D)] These particular forms - with a careful choice of constants - allow us to keep the value of the extensional viscosity finite, but give enough freedom to predict the expected forms of the extensional-viscosity flow curve. A collection of literature data for concurrent extensional and shear melt viscosities was assembled to test the equation. The best values for the model parameters for the data were obtained using a Simplex multivariable data-fitting method. The model gives an excellent fit to the shear viscosity rate data and a reasonable fit to extensional viscosity data, particularly in the high deformation rate range. It should be noted that the data show that at high deformation rates the experimental curves are indeed parallel -when plotted logarithmically - as predicted, a fact that as far as the authors are aware has not been pointed out before. The theory prediction here is very good, suggesting that the Trouton ratio does become constant. For simple shear experiments, the predictions are that the viscosity function can be fitted by the Cross model; the relaxation time should decrease with shear rate, eventually ending up being inversely proportional to shear rate and that at high enough shear stress there should be a linear relationship between the first normal-stress difference and the shear stress or, put another way, their ratio (twice the Recoverable Shear Strain) should become constant. All these predictions are shown to be reasonable for a range of polymer melts.