Degradation in cone-plate rheometry

We analyze quantitatively the oxidative degradation of a sample in a cone-plate rheometer, as oxygen diffuses inward, radially, from the free boundary. We examine rheometer error mitigation by means of nitrogen blanketing, and also, of cone-plate partitioning. We arrive at exact analytical expressions for the oxygen concentration, and thus, for the degradation rate. We then integrate this rate over time to get the amount of oxygen reacted as a function of radial position and time in the degrading sample. To illustrate the usefulness of our analytical expressions, we provide two worked examples investigating the effect of nitrogen blanketing and cone-plate partitioning. We find that, though nitrogen blanketing always produces less degradation, its benefits are limited for short times. Additionally, cone-plate partitioning provides a simpler solution and allows samples to be run for longer times without degradation compromising measurement, even in samples initially saturated with oxygen. We close by considering the effect of antioxidants.