Dynamics of the proton exchange process in benzoic acid, interacting with the substrate of lithium niobate crystal

Abstract

This paper is devoted to numerical analysis of the behavior of ion boundary layer, forming in the process of proton exchange during the interaction of the benzoic acid melt and lithium niobate wafer. This interaction leads to the dissociation of acid molecules and absorption of released protons by the crystal with following injection of benzoate-ions and lithium ions back into the acid. Mathematical model, offered in the article, implies that it is possible to use continuous media approximation to describe this phenomenon. Statement of current problem includes diffusion and electrostatic mechanisms of mass transfer. In addition, the ions recombination is taken into account in our description. Numerical scheme, based on the two-field finite differences method, shows formation of the steady state, which is characterized by exponential-like profiles of concentration and appearance of induced nonuniform electric field. It is important to note, that full charge of the system remains be equal to zero. Results of numerical simulation demonstrate the formation of boundary layer for benzoate-ion. At the same time, nonuniformities, appearing in the layer, don’t induce instabilities, breaking mechanical equilibrium, and don’t lead to high scale concentration convection.