A second-order nonlinear model of monolayer adsorption in refractometric chemical sensors and biosensors case of equilibrium fluctuations

Abstract

In adsorption-based chemical and biological refractometric sensors the dependence of the refractive index of the sensing area on the number of adsorbed particles is used for detection and quantification of analytes. We perform stochastic analysis of equilibrium fluctuations of the adsorbed particles number for monolayer adsorption using a nonlinear second-order model. We derive an analytical expression for the power spectral density (PSD) of the refractive index change fluctuations. Our theory is applicable to sensors operating in closed volume systems with spatially uniform analyte concentration. Our analysis of fluctuations in a benzene sensor shows a significant difference between the PSD according to the derived expression and the PSD obtained by the linear adsorption model, especially for very low amounts of analyte. The developed theory is valid in a wider range of pressures and temperatures. Since signal fluctuations determine the detection limit, the presented theoretical model is applicable as a tool for the design, optimization and characterization of practical adsorption-based refractometric sensors.