Capacitive deionization (CDI) is emerging as an environmentfriendly and energy-efficient water desalination option for meeting the growing global demand for drinking water. It is important to develop models that can predict and optimize the performance of CDI systems with respect to key operational parameters in a simple way. Such models could open up modeling studies to a wider audience by making modeling more accessible to researchers. We have developed the dynamic Langmuir model that can describe CDI in terms of a few fundamental macroscopic properties. Through extensive comparisons with data from the literature, it is shown that the model could describe and predict charge storage, ion adsorption, and charge efficiency for varying input ion concentrations, applied voltages, electrolyte compositions, electrode asymmetries, and electrode precharges in the equilibrium state. We conclude that the model could accurately describe a wide range of key features while being a simpler approach than the commonly applied theories for modeling CDI. Article pubs.acs.org/JPCC

Capacitive deionization is an emerging method of desalinating brackish water that has been presented as an alternative to the widely applied technologies such as reverse osmosis. However, for the technology to find more widespread use, it is important not only to improve its efficiency but also to make its modeling more accessible for researchers. In this work, a program has been developed and provided as an open-source with which a user can simulate the performance of a capacitive deionization system by simply entering the basic experimental conditions. The usefulness of this program was demonstrated by predicting how the effluent concentration in a continuous-mode constant-voltage operation varies with time, as well as how it depends on the flow rate, applied voltage, and inlet ion concentration. Finally, the generality of the program has been demonstrated using data from reports in the literature wherein various electrode materials, cell structures, and operational modes were used. Thus, we conclude that the model, termed the dynamic Langmuir model, could be an effective and simple tool for modeling the dynamics of capacitive deionization.

Capacitive deionization (CDI) is an upcoming desalination technology being increasingly considered to be a simple and cost-effective solution for brackish water, where electrosorption leads to the removal of charged species from water. Real-world water samples typically contain a multitude of ions that must be considered apart from sodium−chloride salt. In this work, we have developed a method to quantify the competitive adsorption of different ionic species during CDI processes. The method is straightforward, requiring a single calibrating experiment to extract a 'periodic table' of competitiveness scores for all ions present in the experiment. Using a dynamic Langmuir model that was developed by our group, it is shown that these scores could subsequently be used to predict the adsorption of any ion species in a multi-ion solution. Excellent agreement with data from the literature could be achieved with this model, and the method is especially well-suited for trace ions as these can be predicted directly. The derived method is simple and accurate for quantifying and predicting adsorption in multi-ion solutions and could be valuable for predicting the effect when applying CDI to real-world water samples.

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While black-box models such as neural networks have been powerful in many applications, direct physical modeling (white box) remains crucial in many fields where experimental data are difficult or time-consuming to obtain. Here, we demonstrate with an example from desalination by capacitive deionization (CDI), how an existing physical model could be strengthened by combining a general modeling framework with physical insights (gray box). Thus, a dynamic Langmuir (DL) model is extended to a linear-state-space DL model (LDL). Results obtained show the new LDL model could incorporate general structural and operational modes, including membrane CDI and constant-current operation. The formulation removes the need for direct measurements of detailed device properties without adding model complexity, and MATLAB code for automatically implementing the model is provided in the Supplementary Information. We conclude the new LDL model is widely applicable, offering great flexibility in calibration data, and enabling prediction over general operating modes.

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Prussian blue (PB) and its analogues (PBAs) are drawing attention as promising materials for sodium-ion batteries and other applications, such as desalination of water. Because of the possibilities to explore many analogous materials with engineered, defect-rich environments, computational optimization of ion-transport mechanisms that are key to the device performance could facilitate real-world applications. In this work, we have applied a multiscale approach involving quantum chemistry, self-consistent mean-field theory, and finite-element modeling to investigate ion transport in PBAs. We identify a cyanide-mediated ladder mechanism as the primary process of ion transport. Defects are found to be impermissible to diffusion, and a random distribution model accurately predicts the impact of defect concentrations. Notably, the inclusion of intermediary local minima in the models is key for predicting a realistic diffusion constant. Furthermore, the intermediary landscape is found to be an essential difference between both the intercalating species and the type of cation doping in PBAs. We also show that the ladder mechanism, when employed in multiscale computations, properly predicts the macroscopic charging performance based on atomistic results. In conclusion, the findings in this work may suggest the guiding principles for the design of new and effective PBAs for different applications.

The massive need for freshwater is driving new desalination technologies such as capacitive deionization (CDI), wherein an applied electric field between porous electrodes removes salt ions from water. In this work, we present substantial advances in numerical approaches to 2D finite‐element models that make it possible to tractably and accurately simulate the local transport, charge‐transfer, and ion‐adsorption processes. This is achieved by introducing a new numerical approach that improves the stability of the method (SmD), which further allows precise and effective modeling that was previously too unstable for use in the state‐of‐the‐art 2D models. The results show that the model now accurately and reliably simulates CDI processes while being effectively applicable to a wider range of structural (device level) and operational conditions (like flow). Crucially, this opens up new opportunities that allow us to provide novel insights into the CDI processes, especially relating to ion‐starved conditions. Finally, novel algorithms support fully automatic implementation with simultaneous fit to multiple data sets and we openly provide all software code to increase accessibility. Thus, we fundamentally believe that the developed model will provide a solid foundation for 2D spatiotemporal simulations of capacitive deionization and aid the future development of CDI technology.