Lagergren kinetic model and multianalyte detection by plasmonic sensors

This work is dedicated to modeling of adsorption processes in plasmonic sensors. We give a generalization of the Lagergren first order reaction kinetic model to the situations where adsorption takes place in multianalyte environment and every analyte obeys one of the following two rules: either it has a small equilibrium constant or its initial number of particles greatly exceeds the number of corresponding binding sites on the surface. Our special concern is the influence of propagating numerical errors and peculiarities of mathematical software used to obtain the results. Complete derivations and solutions are given for an example of the temporal response of an adsorption-based plasmonic sensor in a bi- and three-analyte gaseous environment.