A sensitivity metric and software to guide the analysis of soft films measured by a quartz crystal microbalance

Abstract

This article introduces a set of mathematical and computational tools for use with a quartz crystal microbalance (QCM) to aid in experimental planning and data interpretation. The optimisation tools are based on a metric we term the total parameter matrix sensitivity (TPM-sensitivity). TPM-sensitivity is defined mathematically as the Jacobian determinant of a QCM's responses (e.g., frequency change or dissipation/bandwidth change for a given harmonic) with respect to changes in the physical properties of a soft film and surrounding solution (e.g., density or viscosity). Large TPM-sensitivity values denote conditions where the sensor responses are not only large but also allow the selected unknown physical properties to be mathematically decoupled. In some cases, the viscoelastic properties of an adlayer can be determined using only frequency responses. We validated this method using experimentally obtained data of an ageing adlayer of the enzyme bilirubin oxidase from Myrothecium verrucaria. Fits to these measurements produced more realistic film parameters when responses, including frequency-only combinations, were selected to maximise TPM sensitivity. We provide documented MATLAB code with a graphical user interface to enable other QCM users to employ this analysis. The current software can be applied to any single, homogeneous adlayer that obeys a Kelvin–Voigt viscoelastic model and sits under a semi-infinite Newtonian fluid. Only initial estimates of the film values are required, with the analysis providing guidance and predictions, allowing users to create testable hypothesis and determine the physical changes on the surface rather than have pre-existing values for them.