Monolayer gas adsorption in plasmonic sensors: Comparative analysis of kinetic models

The analysis of adsorption kinetics is given, assuming no dissociative adsorption takes place and no multiple binding sites exist. The phenomenological nonlinear model and the simple linear model are considered from the point of view of surface plasmon resonance (SPR) chemical sensors. A simple method for analytical calculation of the necessary rate constants is proposed. A comparative analysis of the described models is performed. Two conditions that affect the validity of the linear model are found. First one, referring to the ratio between the overall number of particles and the number of binding sites, and the second one, that guarantees the validity of linear model in much broader spectrum of practical situations, referring to the ratio of rate constants. A method for avoiding the accumulation of numerical errors in calculus is also proposed. The presented approach is general and can be used in various applications, including other types of chemical sensors, membranes for filtering, different catalytic systems, resonant micro or nano-electro-mechanical structures.