In a combined experimental and theoretical study we show that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. This effect is found in experiments on capacitive deionization of water containing NaCl/CaCl 2 mixtures, when the concentration of Na + ions in the water is 5 times higher than the Ca 2+ -ion concentration. In this experiment, after applying a voltage difference between two porous carbon electrodes, first the majority monovalent Na + cations are preferentially adsorbed in the EDLs, and later they are gradually replaced by the minority, divalent Ca 2+ cations. In a process where this ion adsorption step is followed by washing the electrode with freshwater under open-circuit conditions, and subsequent release of the ions while the cell is shortcircuited, a product stream is obtained which is significantly enriched in divalent ions. Repeating this process three times by taking the product concentrations of one run as the feed concentrations for the next, a final increase in the Ca 2+ /Na + -ratio of a factor of 300 is achieved. The phenomenon of timedependent ion selectivity of EDLs cannot be explained by linear response theory. Therefore, a nonlinear time-dependent analysis of capacitive charging is performed for both porous and flat electrodes. Both models attribute time-dependent ion selectivity to the interplay of the transport resistance for the ions in the aqueous solution outside the EDL, and the voltage-dependent ion adsorption capacity of the EDLs. Exact analytical expressions are presented for the excess ion adsorption in planar EDLs (Gouy-Chapman theory) for mixtures containing both monovalent and divalent cations.key-words: water desalination; porous electrode theory; capacitive (non-faradaic) electrochemical cells; electrostatic double layer theory.2

Abstract-An accurate mathematical description of the charge transfer rate at electrodes due to an electro chemical reaction is an indispensable component of any electrochemical model. In the current work we use the generalized Frumkin Butler-Volmer (gFBV) equation to describe electrochemical reactions, an equa tion which, contrary to the classical Butler-Volmer approach, includes the effect of the double layer compo sition on the charge transfer rate. The gFBV theory is transparently coupled to the Poisson-Nernst-Planck ion transport theory to describe mass transfer in an electrochemical cell that consists of two parallel plate electrodes which sandwich a monovalent electrolyte. Based on this theoretical approach we present analytical relations that describe the complete transient response of the cell potential to a current step, from the first initial capacitive charging of the bulk electrolyte and the double layers all the way up to the steady state of the system. We show that the transient response is characterized by three distinct time scales, namely; the capac itive charging of the bulk electrolyte at the fastest Debye time scale, and the formation of the double layers and the subsequent redistribution of ions in the bulk electrolyte at the longer harmonic and diffusion time scales, respectively.

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The removal of salt from porous building materials under the influence of an applied voltage gradient normally results in high pH gradients due to the formation of protons and hydroxyl ions at the electrodes. The formed acidic and alkaline regions not only lead to disintegration of the porous material, but also affect the salt transport. In this work we use ion exchange membranes between the electrodes and the porous material to prevent the protons and hydroxyl ions from intruding into the material. The porous material used in this study is fired clay brick, which has been saturated with a 4 mol/l sodium chloride solution prior to the desalination treatment. In order to experimentally determine the salt removal, we monitored the sodium ion concentration profiles across the material with nuclear magnetic resonance (NMR). In addition, we present theoretical predictions for the salt removal according to a model based on the Poisson-Nernst-Planck theory for ion transport. From the work reported here, we can conclude that the use of ion exchange membranes to desalinate porous building materials is not useful since it reduces the salt removal rate to such an extent that desalination with poultices, which is driven by diffusion only, is more efficient. The reason behind this is twofold. First, the ion exchange membranes provide a penalty for the ions to leave the material. Second, in the absence of acidic and alkaline regions, the salt concentration at the edges of the porous material will reduce to almost zero, which leads to a locally increased electrical resistance, and thus a reduction of the electrical field in the bulk of the material. Due to this reduction the effect of the applied voltage gradient across the material vanishes, and the salt removal is limited by diffusion.

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