Modeling Nonlinear Dynamics of Functionalization Layers: Enhancing Gas Sensor Sensitivity for Piezoelectrically Driven Microcantilever

This article presents a parametrized response model that enhances the limit of detection (LOD) of piezoelectrically driven microcantilever (PD-MC) based gas sensors by accounting for the adsorption-induced variations in elastic properties of the functionalization layer (binder) and the nonlinear motional dynamics of the PD-MC. The developed model is demonstrated for quantifying cadaverine, a volatile biogenic diamine whose concentration is used to assess the freshness of meat. At low concentrations of cadaverine, an increase in the resonance frequency is observed, contrary to the expected reduction due to mass added by adsorption. The study explores the variations in the elastic modulus vis-à-vis the adsorbed mass of cadaverine and derives the resonance frequency to the adsorbed mass response function. We advance a blended technique involving the analysis of atomic force microscopy (AFM) force–distance (f–d) curves and fitting of the quartz crystal microbalance (QCM) impedance response spectrum to deduce the adsorption-induced changes in the viscoelastic properties of the functionalization layer. The findings obtained are subsequently employed in modeling the response function for a structurally nonhomogenous PD-MC, highlighting the significance of the functionalization layer to the global elastic properties. The structural composition of the PD-MC beam adopted herein features a trapezoidal base hosting the actuating piezoelectric stratum and a rectangular free end with a functionalization layer. The Euler–Bernoulli beam theory coupled with Hamilton's principle is used to develop the equation of motion, which is subsequently discretized into a set of nonlinear ordinary differential equations via Galerkin expansion, and the solutions to the first fundamental mode of vibration are determined using the method of multiple scales. The obtained solutions provide a basis for deducing the nonlinear response function model to the adsorbed mass. The derived model is validated by recorded resonance frequency changes resulting from exposure to known concentrations of cadaverine. We demonstrate that the increase in resonance frequency for low concentrations of cadaverine is due to the dominance of the variation of the elastic modulus of the functionalization layer originating from the initial binder–analyte interactions over damping due to added mass. It is concluded that the developed nonlinear response function model can reliably be used to quantify the cadaverine concentration at low concentrations with an elevated Limit of Detection.