Super-nonlinear models of charged aerosol detectors: The physicochemical limits of linearization and quantification

Charged Aerosol Detectors (CADs) have become essential tools in modern analytical laboratories due to their near-universal applicability and ease of use. Despite their advantages, CADs exhibit a nonlinear response to analyte concentration, commonly addressed by applying power function transformations to calibration data. However, this practice can lead to overfitting. In this work, we present a theoretical model that describes the intrinsic nonlinearity of CAD peak height response as a function of analyte concentration. The model fits the empirically determined optimal power functions and reveals that CADs are not only non-linear but also cannot be globally linearized with a single power function and thus are ‘super-nonlinear’. By way of experimentation, we verify this super-nonlinear model of the CAD and assess its implications for quantitative assays undertaken using CADs. We find that the power function required to linearise calibration data varies with sample load, and that if global linearization is applied, quantification errors can be as high as 8%. However, when local linearization is used, errors drop to ~1%. This work advances the physical understanding of CAD response behavior and supports more informed calibration practices.