Instrument stiffness artifacts: avoiding bad data with operational limit lines of \(G_{\max }\) and \(E_{\max }\)

Abstract

We derive an operating limit line for the non-ideal artifacts caused by machine stiffness (instrument compliance) which causes measured apparent viscoelastic moduli to be systematically lower than the true values. The limit is represented as a maximum measurable apparent shear modulus \(G_{\max }\), or tensile modulus \(E_{\max }\), which can be shown explicitly on plots of viscoelastic moduli independent of the applied displacement, load, or frequency. Uncorrected data should be much lower than these limits. Corrected data can be above these limits and credible. These interpretations are supported by studying how correction equations can be re-written in terms of \(G_{\max }\) or \(E_{\max }\) and how error propagates in the corrections. We also show how the dynamic compliance representation leads to simpler corrections and how machine stiffness can be calibrated from apparent dynamic compliance measurements of a single sample at two different geometry conditions. Equations are provided for rotational rheometers as well as linear displacement dynamic mechanical analyzers. Used as an operational limit line, \(G_{\max }\) or \(E_{\max }\), the method can assess the credibility of data from others—even without access to their primary data of displacement, force, torque, or amount of correction, which are rarely reported. The method can also anticipate future issues before data are taken, e.g., to understand operational limits when selecting instruments and test geometries.