Dynamics of the Proton Exchange Process in Benzoic Acid Interacting with Lithium Niobate Crystals

This paper provides a numerical analysis of the behavior of the ion boundary layer formed during proton exchange. Thermal dissociation of benzoic acid melt molecules leads to the formation of benzoate ions and hydrogen ions. The latter can be absorbed by a lithium niobate wafer, with subsequent diffusion of lithium ions in the acid. The mathematical model proposed in the article implies that it is possible to use continuous media approximation to describe this phenomenon. The statement of the current problem includes both diffusion and electrostatic mechanisms of mass transfer and the recombination mechanism of ion interaction. The numerical scheme, based on a two-field method, has shown a steady-state formation, characterized by exponential-like profiles of concentration in the presence of an induced nonuniform electric field. It is important to note that the net charge of the system remains zero. The results of numerical simulation have demonstrated the formation of a boundary layer of benzoate ions. At the same time, nonuniformities that appear in the layer do not create instability that breaks mechanical equilibrium, and they do not lead to a high-scale concentration convection.