Pressure effects in polymer melt rheology

Wide ranges of pressure and temperature are encountered in many polymer processing operations. In addition, the pressures and temperatures often change rapidly with time, as, for example, in injection molding. While varying thermal histories have been explored in some detail, little work has been done on the corresponding pressure problem. The data which do exist for high pressures often show a dramatic increase in viscosity but the magnitude of the increase varies greatly, depending on the type of experiment and the experimental conditions.

The present work is largely concerned with the measurement and analysis of the viscosity of an amorphous polymer (polystyrene) in its melt state under high pressures. The measurements were made in a standard capillary rheometer plus a specially constructed downstream chamber, with the downstream chamber being held at a high pressure by forcing the material through a needle valve constriction. The data were analyzed in a general framework that includes not only high shear rate data from the present work, but also low shear rate data from the literature. A modified form of the so-called Bogue-White model was used to predict viscosity over all shear rate ranges. The model makes use of an important fact from rheological theory: viscosity can be expressed as the product of elastic moduli and time constants (in the present case, by one modulus and one time constant).

The pressure (and temperature) dependence of the time constant was motivated by the Simha-Somcynsky equation of state, which contains an explicit parameter related to the free volume. Utracki first noted the usefulness of this theory for correlating the viscosities of both low molecular weight liquids and polymers. Although the Simha-Somcynsky equation is useful conceptually because it provides a free volume prediction for each pressure and temperature combination, it is concluded in the present work that several empirical adjustments are needed to use it quantitatively.

The experimental results at high pressure and high shear rates show substantial viscosity increases, although not nearly so high as expected from zero shear data. However, these two asymptotes can be understood within the framework of the rheological model used: at low shear rates, the magnitude of both the modulus and the time are important factors in determining viscosity, whereas at high shear rates, the modulus becomes the dominating factor.