On finding the zero‐shear‐rate viscosity of polymer melts. Issue 4 (14th February 2021) - Shaw, Montgomery T.
Abstract: A significant fraction of the experimental works on the rheology of polymer melts include an attempt to find the zero‐shear‐rate viscosity η 0 . This is done for good reasons, because η 0 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, η 0 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 η 0 . 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 η 0 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 η 0 of the latter was reachable; for the other resins, a falling ball technique was attempted. Abstract : The zero‐shear‐rate viscosity, η 0, is a limiting material property that depends on thermodynamic variables and composition of a polymer. As with all limiting properties, η 0 is impossible to measure directly. It can be estimated from viscosity measurements at very low shear rates or frequencies, but becomes in the limit very prone to error. The common approach is to extrapolate frequency‐ or shear‐rate‐dependent data to find η 0 . The major question is the function used for the extrapolation; this is addressed in some detail in this article, but was discarded in favor of using a sample of 20 equations of many functional forms. These randomly chosen equations were used to generate a set of η 0 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 η 0 of the latter was reachable; for the other resins, a falling ball technique was attempted.