Analysis of transients in adsorption-desorption at the surface of plasmonic sensors: Nonlinear versus linear approach

Monolayer adsorption-desorption processes at the surface of plasmonic sensors are modeled, first in an exact way, as a nonlinear second-order reaction, and then, after some approximations justified from the practical point of view, as a first order linear reaction. The time evolution of the number of adsorbed molecules from the beginning of the process to the moment in which the system reaches its equilibrium is derived in both cases. A comparative analysis of transients and steady state response is performed for a plasmon sensor with gold surface for some saturated and cyclic hydrocarbons including benzene, as well as for carbon monoxide. The results show in which practical situations the simpler linear model can be used and when the nonlinear model of adsorption-desorption must be applied instead.