Modeling of adatom vibrational populations and recombination rates in exoergic reactions

The steady-state vibrational populations of adatoms, during the exoergic recombination of gas atoms at catalytic surfaces, are computed in closed form by a kinetic approach. The vibrational distributions are found to be non-Boltzmann and this is needed, under steady-state conditions, to ensure the number conservation of vibrational quanta. The shape of the distribution depends upon recombination rate, vibrational frequency of adatoms in the adsorption potential well and on the rate constants for vibrational quantum exchanges among adatoms and between the adatoms and the solid lattice. For the model case of a four-levels vibrational ladder, the analytical solution is in good agreement with the numerical solutions of the master equations previously discussed in the literature [M. Tomellini, Surf. Sci. 556 (2–3) (2004) 184]. The theoretical approach has also been applied to describe vibrational populations and reaction rates in case of multi-level vibrational ladders and for the model case of single reaction channels. It is shown that the adlayer can undergo a kinetic transition, from equilibrium to non-equilibrium states, which is characterized by an enhancement of the reaction rate. This transition is governed by the ratio between the rate constants for recombination and for dissipation of the adatom vibrational quanta in the solid.