On finding the zero‐shear‐rate viscosity of polymer melts

Abstract

A significant fraction of the experimental works on the rheology of polymer melts include an attempt to find the zero‐shear‐rate viscosity η0. This is done for good reasons, because η0 is a limiting property that depends only on thermodynamic variables and, importantly, the molecular and supermolecular structure of the melt. As with all limiting properties, η0 is impossible to measure directly. Fortunately with many melts, it can be estimated from viscosity measurements at very low shear rates or frequencies, but still remains one of those properties that becomes in the limit very prone to error. The common approach is to use a set of frequency‐ or shear‐rate‐dependent data and extrapolate to find η0. As with any extrapolation, the major question is the function used for the extrapolation. This question is addressed in some detail in this article. The question of which function to use was discarded in favor of using a large sample of 20 equations of many functional forms. This sample of randomly chosen equations was used to generate a set of η0 values, and the statistics of this distribution were examined, in the usual fashion, by description with an analytical probability density function that gives a high probability of being a likely generator of the data. In addition, a weighted average was proposed, where the weighting factor takes into account the quality of the fit. For testing these ideas, the room temperature melts of poly(vinyl isobutyl ether), poly(isobutylene), and poly(dimethyl siloxane) were used. The η0 of the latter was reachable; for the other resins, a falling ball technique was attempted.

Application and Optimization of the Rheological Model for a Hydrophobically Associating Dendrimer Polymer

“…At this time, the measured viscosity is zero-shear viscosity. Under very small shear stress, as in Newtonian fluids, the solution viscosity remains high [16]. (3) The limit shear section (C) occurs for the following reasons: Once the shear rate increases to a certain extent, the molecular orientation reaches the limit state, and the orientation no longer changes with the shear rate.…”

Falling ball method for determining zero shear and shear‐dependent viscosity of polymeric systems: Solutions, melts, and composites

“…[3,4] It is thus always desirable to establish its value independently rather than by treating it as a disposable parameter. Shaw [5] has recently evaluated the relative performance of scores of viscosity models to determine the values of zero-shear viscosity (η 0 ) for polypropylene melts and indeed, it was not at all possible to prescribe a single viscosity equation, which yielded reliable values of the zero-shear viscosity, η 0 under all conditions. The shear rate range corresponding to the constant zero-shear viscosity region shifts to the increasingly lower values of shear rate with the increasing molecular weight, loading of additives and concentration of the polymer in the solution which are either not always accessible through rotational viscometers like cone-plate, couette and parallel plate configurations or the resulting torque values are too small to be measured accurately and/or close to the lower limit of measurement.…”