A Cost-effective Determination of Pressure - and Temperature-Dependent Viscosity of Polymers by Linking Conventional Viscosity Data to PVT Data

Abstract

The viscosity of polymer melts is dependent on various factors such as shear rate, temperature, pressure and molecular structure. High-pressure capillary rheometery (HPCR) can be used to determine viscosity as a function of shear rate and temperature in the shear rate range relevant for injection molding and extrusion processing. Conventional HPCR measurements cannot determine the pressure dependence of viscosity so that it is typically neglected. Particularly at high pressures and low shear rates, the viscosity is therefore underestimated. However, it is possible to determine the pressure dependency using a counter pressure chamber or actively controlled counter pressure viscometer. Nevertheless, these devices are rarely available, and the measuring effort is high compared to conventional measurements. In order to be able to represent the pressure-dependent material behavior and thus improve the accuracy of process simulations in a cost-effective way, the aim of this paper is to use the free volume approach via the coupled equations of state according to Simha and Somcynsky¹ to link the temperature and pressure dependence of the melt density to the viscosity. The model was extended according to Utracki and Sedlacek^2–4 and applied to true viscosity data at constant shear stresses in the process relevant apparent shear rate range from 1 to 5000 1/s. The necessary viscosity data for the investigated PP and PC at different temperatures in the typical processing range were determined using a conventional HPCR, and a pvT measuring device was used to determine the melt density. The hole fraction as a measure for the free volume is calculated at each shear stress through the coupled equations of state and linked to the true viscosity through error square minimization at the mean pressure in the capillary. This allows for the recalculation of an isobaric viscosity curve at different pressure and temperature levels. For validation of the model viscosities were also measured at various pressure levels using a counter pressure chamber to determine an experimental pressure coefficient. The model results for the investigated materials show a high agreement with the experimentally determined pressure coefficients