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 Moving forward, research into new electrode materials and chemistries, modification and optimization of existing materials, investigation of parameters in selectivity operation, modeling of selectivity at the system and molecular level, and finally, techno-economic analysis into the viability of selective ion separation via CDI will be crucial for fully realizing the potential of ion-selectivity via CDI. M. A. Lilga, R. J. Orth, J. P. H. Sukamto, S. M. Haight and D. T. Schwartz, Sep. Purif. Technol., 1997, 11, 147–158 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. T. Rijnaarts, D. M. Reurink, F. Radmanesh, W. M. de Vos and K. Nijmeijer, J. Membr. Sci., 2019, 570–571, 513–521 CrossRef CAS. R. Zhao, M. van Soestbergen, H. H. M. Rijnaarts, A. van der Wal, M. Z. Bazant and P. M. Biesheuvel, J. Colloid Interface Sci., 2012, 384, 38–44 CrossRef CAS. Z. Sun, L. Chai, M. Liu, Y. Shu, Q. Li, Y. Wang and D. Qiu, Chemosphere, 2018, 195, 282–290 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.An ability to predict ion-selectivity will help streamline the efforts being made in this field of CDI, enhancing the strength of the technology to remove ions selectively. Our work takes a step in this direction by putting forward a theory, at the system level, for prediction of ion-selectivity of a class of intercalation electrodes. A logical next step is the investigation of the molecular origins for the preference of electrode materials towards different ions. Further insight into the mechanism of preferential electrosorption of ions can help to tune the selectivity-inducing properties of the electrode material. Hawks et al. 41 carried out molecular dynamics (MD) simulations to elucidate the selective adsorption of NO 3 − over Cl − and SO 4 2− in carbon electrodes. This simulation assisted the authors to understand how hydration of the ions influenced the anion selectivity in very narrow micropores. According to the MD simulations, nitrate and chloride have similar hydration energies, much lower than sulfate, which suggests that sulfate is less prone to rearrange its solvation shell to fit inside of the micropores. At the same time, the higher selectivity of nitrate over chloride is explained by the higher distribution of the water molecules on the equatorial region rather than the perpendicular region of nitrate, suggesting that water molecules are weakly bound on the axial region of nitrate. Since NO 3 − has a delocalized water shell, 41 as predicted by MD simulations, the ion is more prone to fit inside of the slit micropores of the investigated activated carbon. For porous carbon materials, the use of MD simulations can be extended to several other ions, which allows one to predict the ion selectivity based on the surface characteristics of the electrode material. The selectivity of anions was further investigated by Gabelich et al. taking into account ionic properties such as the ionic mass, radius, and valence. 45 Compared to the work of Eliad et al., the authors used an electrode with pore size distribution large enough to prevent ion sieving by the electrode (lowest average pore size of 4 nm). A strong correlation was observed between the valence of the ionic species, and its preferential electrosorption into the carbon micropores using single-salt solutions. No statistical difference was observed for the electrosorption of anions of different radii and mass. S. Ren, M. Li, J. Sun, Y. Bian, K. Zuo, X. Zhang, P. Liang and X. Huang, Front. Environ. Sci. Eng., 2017, 11, 17 CrossRef. L. Eliad, G. Salitra, A. Soffer and D. Aurbach, J. Phys. Chem. B, 2001, 105, 6880–6887 CrossRef CAS. Dr Rafael Linzmeyer Zornitta is a postdoctoral researcher in the Organic Chemistry group at the Wageningen University & Research, The Netherlands. He received his BSc in Chemical Engineering from State University of Maringa (Brazil), MSc and PhD from Federal University of Sao Carlos (Brazil), with internships at the Malaga University (Spain), and Leibniz Institute for New Materials (Germany). His research interests include the development of new electrode materials, ion-selective membranes, and optimization of cell design for water desalination and selective ion recovery using electrochemical technologies.

C. Erinmwingbovo, M. S. Palagonia, D. Brogioli and F. La Mantia, ChemPhysChem, 2017, 18, 917–925 CrossRef CAS. X. Zhang, K. Zuo, X. Zhang, C. Zhang and P. Liang, Environ. Sci.: Water Res. Technol., 2020, 6, 243–257 RSC.P. Ratajczak, M. E. Suss, F. Kaasik and F. Béguin, Energy Storage Mater., 2019, 16, 126–145 CrossRef. S. Porada, A. Shrivastava, P. Bukowska, P. M. Biesheuvel and K. C. Smith, Electrochim. Acta, 2017, 255, 369–378 CrossRef CAS. N. Pugazhenthiran, S. Sen Gupta, A. Prabhath, M. Manikandan, J. R. Swathy, V. K. Raman and T. Pradeep, ACS Appl. Mater. Interfaces, 2015, 7, 20156–20163 CrossRef CAS. Similar to the work of Tang et al., Xing et al. investigated the selectivity towards ClO 4 − over Cl − by adapting the one-dimensional EDL model for carbon electrodes. 73 The authors showed that bare carbon electrodes prefer ClO 4 − over Cl − reaching a selectivity ( ρ) of about 11 even for lower concentrations of ClO 4 −. Based on the model, the authors ascribed this high selectivity value to the higher diffusivity of ClO 4 − (9 × 10 −10 m 2 s −1) compared to Cl − (1 × 10 −10 m 2 s −1) inside the pores of the carbon ( Fig. 6C). L. Gan, Y. Wu, H. Song, S. Zhang, C. Lu, S. Yang, Z. Wang, B. Jiang, C. Wang and A. Li, Sep. Purif. Technol., 2019, 212, 728–736 CrossRef CAS.

E. Avraham, B. Yaniv, A. Soffer and D. Aurbach, J. Phys. Chem. C, 2008, 112, 7385–7389 CrossRef CAS. Selective removal of Pb 2+ over Ca 2+ and Mg 2+ was studied by Dong et al. by using activated carbon electrodes in an asymmetric CDI setup. This setup only contained an AEM (hence asymmetric), as the Pb 2+ desorption was reported inefficient when a CEM was used as well, thus hindering its selectivity. 64 The asymmetric system was selective towards Pb 2+ over Ca 2+ and Mg 2+. The selectivity mechanism was hypothesized to be a swapping process where Ca 2+ and Mg 2+ are initially adsorbed due to their higher mobilities, but later replaced by Pb 2+ owing to its higher affinity towards the native functional groups ( e.g., carboxyl groups) present on the electrode.which is set up and solved at each coordinate twice, first for i = Na + with j = K + and second for the reverse situation. In this equation, parameter V T is the thermal voltage given by V T = RT/ F which at room temperature is around 25.6 mV. All other parameter values are given in ESI (Section 7) of Porada et al. 78 For CDI, the capacity to store ions is of paramount importance, and is important to study by electrosorption experiments at different values of the charging and discharging voltages that define a CDI cycle. In addition, we can use methods to measure the charge stored in the EDLs in the CDI electrodes, using the GITT method (galvanostatic intermittent titration technique). The charge that can be stored is often formulated as a capacity in C per gram electrode material which is typically defined by total mass of both electrodes 38 (also reported as mA h g −1 in some literature) while the change of capacity with voltage is the capacitance, expressed in F g −1. Additional information can possibly be inferred from electrochemical methods such as cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). Data for charge (capacity) provide valuable information for electrodes used for desalination since it can indicate whether an electrode is feasible as a CDI electrode. Although the storage capacity cannot be directly translated into desalination capacity, good correlations between capacitance and salt adsorption capacity have been reported. 39 In terms of selectivity, the storage capacity values in different single-salt solutions is a simple and fast way to compare whether an electrode has preference for a target ion or not. Comparisons between capacitance values were used by different research groups to explore the preference of one ion over another. 40–42 In case of intercalation materials, CV can provide information about the preference of the active materials towards different ions. Higher cathodic peak potential associated with intercalation of an ion indicate a higher preference for intercalation of the electrode towards that ion. This technique of determination has been used in CDI literature for selective separation from cationic mixtures. 43,44 A heavy metal (Pb 2+) and salt (Na +) recovery method from wastewater using 3D graphene-based electrodes was proposed by Liu et al. 63 They used 3D graphene electrodes modified with ethylenediamine triacetic acid (EDTA) and 3-aminopropyltriethoxysilane (APTES) as the cathode and the anode, respectively. Two different mechanisms were presented for Pb 2+ and Na + removal. Pb 2+ is adsorbed via a chelation reaction with EDTA ( Fig. 6E), whereas Na + is adsorbed via electrosorption in the pores. Based on these mechanisms, the separation of ions was achieved during the desorption stage. First, Na + was desorbed by applying an inverse potential, followed by a short circuit potential. Afterwards Pb 2+ was desorbed in a separate step using nitric acid as an eluent. For the term, γα′, γ is a constant, namely γ = 0.0725, while α′ = d i/ h p. Here, d i is the (hydrated) ion size and h p is the ratio of pore volume over pore wall area. For a slit-shaped pore, h p is equal to the pore width divided by 2, and for a cylindrical pore it is equal to pore size ( i.e., pore diameter) divided by 4. Thus h p is a characteristic pore size, but because we typically do not know these values exactly, neither the ion size in the pore, nor the factor h p, α′ is typically an empirical factor. S. Samatya, N. Kabay, Ü. Yüksel, M. Arda and M. Yüksel, React. Funct. Polym., 2006, 66, 1206–1214 CrossRef CAS.

Flow-electrode CDI. In a recent addition to the set of CDI systems, flow-electrode capacitive deionization (FCDI) was invented to solve the persistent issue of the finite adsorption capacity of standard CDI cell designs. 81 In FCDI, a carbon slurry flows through channels between the current collector and IEM, continuously replenishing the capacitive material and eliminating the need for the regeneration step that pauses desalination ( Fig. 3b). Various closed-systems, in which the slurry is continuously discharged and re-used without pausing the desalting step, have been demonstrated. 82,83 Because the electrode material is continuously regenerated at a rate set by the electrode flow speed, performance metrics such as electrode capacity become less important; the limiting factor for FCDI, as shown in recent studies, is instead electrode conductivity. K. Singh, H. J. M. Bouwmeester, L. C. P. M. De Smet, M. Z. Bazant and P. M. Biesheuvel, Phys. Rev. Appl., 2018, 9, 064036 CrossRef CAS. S. Kim, J. Lee, J. S. Kang, K. Jo, S. Kim, Y. E. Sung and J. Yoon, Chemosphere, 2015, 125, 50–56 CrossRef CAS. P. Srimuk, J. Lee, A. Tolosa, C. Kim, M. Aslan and V. Presser, Chem. Mater., 2017, 29, 9964–9973 CrossRef CAS. T. M. Mubita, J. E. Dykstra, P. M. Biesheuvel, A. van der Wal and S. Porada, Water Res., 2019, 164, 114885 CrossRef CAS.A. Hassanvand, G. Q. Chen, P. A. Webley and S. E. Kentish, Water Res., 2018, 131, 100–109 CrossRef CAS. S. A. Hawks, A. Ramachandran, S. Porada, P. G. Campbell, M. E. Suss, P. M. Biesheuvel, J. G. Santiago and M. Stadermann, Water Res., 2019, 152, 126–137 CrossRef CAS.