Some remarks on the Langmuir-Hinshelwood kinetics

This work considered the Langmuir-Hinshelwood (LH) scheme for a single reactant. In a first step, the validity of the quasi-steady state approximation (QSSA) was revised in terms of nonlinear relaxation processes. It was found that the LH equation obtained from the QSSA is not valid most of the times, except for example in the case of high reactant concentrations when the relaxation time is small enough to reduce the order of the underlying system of differential equations. Subsequently, the observability properties of the LH equations were studied in order to find that the dynamical behavior of the adsorption complex can be reconstructed from measurements of the reactant trajectory. Finally, the estimation problem of the kinetic parameters based solely on the reactant concentration behavior was considered. It is then shown that the full set of kinetic parameters can be estimated from a single reactant depletion curve by solving a least-squares problem for the complete LH scheme. Numerical results were used to illustrate the findings of this work.