Theory of pH changes in water desalination by capacitive deionization

In electrochemical water desalination, a large difference in pH can develop between feed and effluent water. These pH changes can affect the long-term stability of membranes and electrodes. Often Faradaic reactions are implicated to explain these pH changes. However, quantitative theory has not been developed yet to underpin these considerations. We develop a theory for electrochemical water desalination which includes not only Faradaic reactions but also the fact that all ions in the water have different mobilities (diffusion coefficients). We quantify the latter effect by microscopic physics-based modeling of pH changes in Membrane Capacitive Deionization (MCDI), a water desalination technology employing porous carbon electrodes and ion-exchange membranes. We derive a dynamic model and include the following phenomena: I) different mobilities of various ions, combined with acid-base equilibrium reactions; II) chemical surface charge groups in the micropores of the porous carbon electrodes, where electrical double layers are formed; and III) Faradaic reactions in the micropores. The theory predicts small pH changes during desalination cycles in MCDI if we only consider phenomena I) and II), but predicts that these pH changes can be much stronger if we consider phenomenon III) as well, which is in line with earlier statements in the literature on the relevance of Faradaic reactions to explain pH fluctuations.