P. Ratajczak, M. E. Suss, F. Kaasik and F. Béguin, Energy Storage Mater., 2019, 16, 126–145 CrossRef. Fig. 4 (A) GCS model – EDL formation on a charged surface, and (B) mD model – EDL formation inside a charged carbon pore. J. Pan, Y. Zheng, J. Ding, C. Gao, B. van der Bruggen and J. Shen, Ind. Eng. Chem. Res., 2018, 57, 7048–7053 CrossRef CAS. The most accurate approach in describing the ion transport in combination with adsorption has been the porous electrode theory, put forward in 2010. 140 It was further developed by Biesheuvel and co-workers when they used this framework in a model that combined faradaic reactions and capacitive electrode charging for a mixture of a monovalent anion, a monovalent cation, and divalent cations, making use of the mD model to describe ion adsorption ( μ att = 0). 141 The same porous electrode theory was also used by Zhao et al. for a purely capacitive electrode, and extended by Dykstra et al. 48 for a solution with two types of monovalent cations and a monovalent anion. Here for the first time, a full cell with two electrodes is considered. Furthermore, the simple mD model with μ att = 0 is replaced by the improved mD model which considers a salt-concentration dependent ion adsorption energy. In Dykstra et al., the only mechanism causing a difference in adsorption between different monovalent cations was the diffusion coefficient of the ions leading to a selectivity for K + over Na + of up to S ≈ 1.4, in close agreement with detailed experiments. Theoretical calculations predict this selectivity to be at a maximum at intermediate cycle times, a result that was not fully corroborated by the experiments. Recently, Guyes et al. presented a theory which predicted an enhancement of size-based selectivity towards K + over Li + and Na +, with increasing chemical charges in the micropore added by surface modification. 142 In CDI experiments using a CMX membrane, selectivity towards divalent over monovalent cations was reported. 119,120 Although the CMX membrane was not designed to differentiate between different cations, its negatively charged outermost layer attracts divalent more than the monovalent cations. 121 Hassanvand et al. stated that the implementation of CMX in CDI leads to sharper desorption peaks of divalent cations since larger amounts of di-over monovalent cations are temporarily stored within the CMX membrane. 53 On the other hand, the CIMS membrane resulted in preferential transport of monovalent over divalent cations. 122 Similarly, Choi et al. used a CIMS membrane and obtained monovalent cation selectivity ( R) of 1.8 for sodium over calcium ions. 121 By selectively removing Na +, a Ca 2+-rich solution was obtained. In addition, the selectivity attained its maximum value at higher cell voltages, pH, and lower TDS (total dissolved solids) concentration.

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L. Han, K. G. Karthikeyan, M. A. Anderson and K. B. Gregory, J. Colloid Interface Sci., 2014, 430, 93–99 CrossRef CAS. Mr Jayaruwan Gunathilake Gamaethiralalage is currently a PhD candidate in the Department of Organic Chemistry at Wageningen University & Research, The Netherlands. He received his BSc in chemistry from Kutztown University of Pennsylvania in the United States of America, joint MSc degrees in analytical chemistry from University of Tartu in Estonia, and Åbo Akademi University in Finland. His research interests include development of new material for ion separation and sensing, wastewater treatment, and electrodriven systems for circular water economy. P. M. Biesheuvel, R. Zhao, S. Porada and A. van der Wal, J. Colloid Interface Sci., 2011, 360, 239–248 CrossRef CAS. D. I. Oyarzun, A. Hemmatifar, J. W. Palko, M. Stadermann and J. G. Santiago, Water Res.: X, 2018, 1, 100008 Search PubMed.

C. Hou, P. Taboada-serrano, S. Yiacoumi and C. Tsouris, J. Chem. Phys., 2008, 129, 224703 CrossRef. For an ionic mixture with ions of all possible valencies z, typically ranging between −2 and +2, an overall micropore charge balance is Q. Dong, X. Guo, X. Huang, L. Liu, R. Tallon, B. Taylor and J. Chen, Chem. Eng. J., 2019, 361, 1535–1542 CrossRef CAS.B. Giera, N. Henson, E. M. Kober, M. S. Shell and T. M. Squires, Langmuir, 2015, 31, 3553–3562 CrossRef CAS. Adsorption and ion transport dynamics in intercalation materials. Theory for ion transport in CDI electrodes with ion mixtures has until now focused on electrodes based on porous carbons. Here, we extend the state-of-the-art and present the first model calculations for CDI with porous electrodes made from an intercalation material (such as NiHCF, a Prussian blue analogue). Our calculation results illustrate the general observation of ion selectivity studies that the ideal, or maximum attainable, or “thermodynamic”, separation factor (selectivity), is not easily reached in a practical process. This is because mass transfer limitations and mixing of ions lead to a lower selectivity value in the actual desalination process than the ideal value. This is also the case in the example calculation of CDI with intercalation materials presented below. Therefore, this example calculation serves to underscore the point that careful design of an electrochemical desalination cell and the operational conditions, thereby reducing transfer resistances and avoiding mixing, is crucial in increasing the actual selectivity to values as close as possible to the ideal, thermodynamic selectivity. D. I. Kim, R. R. Gonzales, P. Dorji, G. Gwak, S. Phuntsho, S. Hong and H. Shon, Desalination, 2020, 484, 114425 CrossRef CAS.

J. E. Dykstra, J. Dijkstra, A. Van der Wal, H. V. M. Hamelers and S. Porada, Desalination, 2016, 390, 47–52 CrossRef CAS. where subscript j indicates the phase, either the electrolyte outside the micropore, ∞, or the micropore region (the subscript j is dropped). Note that all potential terms are without dimension, and can be multiplied by a factor RT to obtain a potential in J mol −1. The parameter μ ref, i is the reference chemical potential of ion i, the second term relates to ion entropy, z i ϕ j is the electrostatic term, while μ exc, i, j represents a contribution due to excess or volumetric interactions, and μ aff, i, j relates to chemical interactions, the interaction of the ion with the environment, not described by volume or charge. The simplest relevant situation is when all ions are ideal point charges, and there are no affinity effects. Then ions are subject to entropic effects, given by ln c i, j, and the electrostatic field, given by z i ϕ j. Potential ϕ j refers to the electric potential of phase j, and ϕ − ϕ ∞ is the dimensionless Donnan potential, ϕ D. This potential can be multiplied by V T = RT/ F to obtain a voltage with unit volt. At phase equilibrium, the chemical potential of ion i is balanced between the micropore and bulk electrolyte, yielding Recently, Zhang et al. used activated carbon in flow CDI to selectively remove Cu 2+ from a solution which also contained Na +. 65 A higher affinity towards Cu 2+ was obtained in the system. This was attributed to the preferential adsorption of Cu 2+ on the carbon particles and was also reduced to Cu. The preference of carbon towards divalent over monovalent cations, as shown in Fig. 6A was also reported here. The Na + removed from the feed remained in the electrolyte of the flow electrode. Fig. 2 A graphical timeline depicting the evolution of ion selectivity in CDI and MCDI. The works employing membranes are denoted in italics.

Abstract

X. Su, H. J. Kulik, T. F. Jamison and T. A. Hatton, Adv. Funct. Mater., 2016, 26, 3394–3404 CrossRef CAS. Within the last decade, in addition to water desalination, capacitive deionization (CDI) has been used for resource recovery and selective separation of target ions in multicomponent solutions. In this review, we summarize the mechanisms of selective ion removal utilizing different electrode materials, carbon and non-carbon together with or without membranes, from a mixture of salt solutions, by a detailed review of the literature from the beginning until the state-of-the-art. In this venture, we review the advances made in the preparation, theoretical understanding, and the role of electrodes and membranes. We also describe how ion selectivity has been defined and used in literature. Finally, we present a theory of selective ion removal for intercalation materials that, for the first time, considers mixtures of different cations, evidencing the time-dependent selectivity of these electrodes. Here we develop eqn (5) for another situation, that when we have a mixture of cations with varying valence. If cations were to have the same valence and Φ i, eqn (5) shows that the ratio of cation concentrations in the micropore is the same as that in solution: c 1/ c 2 = c 1,∞/ c 2,∞. However, for a mixture of divalent and monovalent cations, the ratio of concentrations in the micropore is strongly favoured towards the divalent ion. To demonstrate this result, we evaluate eqn (5) neglecting the anions, as micropore anion concentration approaches zero for the case where the dilution, β = | σ 0|/ c ∞ ≫ 1, where c ∞ is the total concentration of the anions in the bulk solution. For charge versus potential, we then arrive at

c School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Daehak-dong, Gwanak-gu, Seoul 151-742, Republic of Korea Y. Bian, X. Chen, L. Lu, P. Liang and Z. J. Ren, ACS Sustainable Chem. Eng., 2019, 7, 7844–7850 CrossRef CAS.In 2013, Zafra et al. evaluated the electrosorption capacity of high surface area electrodes using single-salt solutions consisting of nutrients (Cl −, NO 3 −, and H 2PO 4 −/HPO 4 2−). 40 The authors found a lower phosphate electrosorption compared to nitrate or chloride. It was suggested that this reduced capacity was caused by the sieving effect of the prepared activated carbon (average pore size of 0.855 nm) towards to the smaller ions (Cl − and NO 3 −) compared to the large phosphate species (H 2PO 4 −/HPO 4 2−). This investigation agrees well with the report about the sieving effect of the porous carbon described by former authors ( Fig. 6B). In the same line of nutrient recovery, Ge et al. investigated the competition between physical adsorption and electrosorption of phosphate anions. 69 The authors suggested that electrosorption could only overcome the effect of physical adsorption at very high cell voltages. Therefore, to improve phosphate electrosorption the authors applied a cell voltage as high as 3.0 V, which also cause faradaic reactions. Although the authors suggest that some species formed during the faradaic reactions could also promote a disinfection of the treated water, there is an expressive reduction of the charge efficiency. Nevertheless, this work is important in understanding the lower electrosorption capacity of phosphate at neutral pH compared to other ions.