Capacitive deionization (CDI) is emerging as an environment-friendly 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.

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.

Lack of potable water in communities across the globe is a serious humanitarian problem promoting the desalination of saline water (seawater and brackish water) to meet the growing demands of human civilization. Multiple ionic species can be present in natural water sources in addition to sodium chloride, and capacitive deionization (CDI) is an upcoming technology with the potential to address these challenges because of its efficacy in removing charged species from water by electro-adsorption. In this work, we have investigated the effect of device operation on the preferential removal of different ionic species. A dynamic Langmuir (DL) model has been a starting point for deriving the theory, and the model predictions have been validated using data from reports in the literature. Crucially, we derive a simple relationship between the adsorption of different ionic species for short and long adsorption periods. This is leveraged to directly predict and enhance the selective ion removal in CDI. Furthermore, we demonstrate an example of how this selectivity could reduce excess removal of ions to avoid remineralization needs. In conclusion, the method could be valuable for predicting the impact of improved device operation on capacitive deionization with multi-ion compositions prevalent in natural water sources.

Electrically driven adsorption, electroadsorption, is at the core of technologies for water desalination, energy production, and energy storage using electrolytic capacitors. Modeling can be crucial for understanding and optimizing these devices, and hence different approaches have been taken to develop multiple models, which have been applied to explain capacitive deionization (CDI) device performances for water desalination. Herein, we first discuss the underlying physics of electroadsorption and explain the fundamental similarities between the suggested models. Three CDI models, namely, the more widely used modified Donnan (mD) model, the Randles circuit model, and the recently proposed dynamic Langmuir (DL) model, are compared in terms of modeling approaches. Crucially, the common physical foundation of the models allows them to be improved by incorporating elements and simulation tools from the other models. As a proof of concept, the performance of the Randles circuit is significantly improved by incorporating a modeling element from the mD model and an implementation tool from the DL model (charge-dependent capacitance and system identification, respectively). These principles are accurately validated using data from reports in the literature showing significant prospects in combining modeling elements and tools to properly describe the results obtained in these experiments

To develop efficient and cost-effective desalination technologies is crucial for addressing the globally increasing needs for drinking water. One such desalination technology that is growing is capacitive deionization (CDI), wherein ions are electrically removed from water passing through or between two porous conducting electrodes. As the CDI field grows, design principles for scaling from small CDI cells to larger units and modules will become increasingly important. Thus, we have investigated the flow distribution in single flow-through CDI cells and interconnected modules to determine architectural principles that can feasibly reduce the pressure drop with good throughput, thus increasing energy efficiency. The most important principles found include massive parallelism, open regions to symmetrically distribute flow, and tailoring the permeability of the electrodes and spacers. Crucially, we demonstrate how simply rerouting the flow reduces the pressure drop through the cell by a factor of four in a two-cell system. Finally, we leverage the found principles to a cylindrical CDI cell well-adapted to modular up-scaling. In conclusion, implementing the design principles leads to a significant reduction in pressure drop and energy consumption of a CDI system, which is essential for upscaling to larger modular systems for practical use.

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.npj

The global need for freshwater rapidly drives the development of emerging and efficient freshwater-production methods such as capacitive deionization (CDI). To allow the CDI technique to continue to grow, simulations can be important for tractably describing, predicting, and optimizing the desalination processes. Amongst the disparate simulation tools available, the Randles-circuit model is widely used in electrochemical measurements but its simplified structure limits its use for wider CDI operations. Thus, we herein describe a systematic stepwise process for widely developing CDI models, and as a proof-of-concept, transform the core Randles circuit into an extended Randles circuit (ERaC) that is highly relevant for CDI systems. Experimental data from the literature extensively verify that the ERaC model accuracy now describes charge storage, charging rate, ion adsorption, and current leakages for a variety of structural and operational parameters, such as asymmetric electrodes, different ion concentrations, and the applied voltage. In conclusion, this developed stepwise process can systematically and effectively create, enhance, and expand CDI models. Thus, researchers will embrace this method of model development, and benefit from the broad usefulness of the proposed ERaC model for a wide range of CDI operations.

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.

The growing world population creates an ever-increasing demand for fresh drinkable water, and many researchers have discovered the emerging capacitive deionization (CDI) technique to be highly promising for desalination. Traditional modeling of CDI has focused on charge storage in electrical double layers, but recent studies have presented a dynamic Langmuir (DL) approach as a simple and stable alternative. We here demonstrate, for the first time, that a Langmuir-based approach can simulate CDI in multiple dimensions. This provides a new perspective of different physical pictures that could be used to describe the detailed CDI processes. As CDI emerges, effective modeling of large-scale and pilot CDI modules is becoming increasingly important, but such a modeling could also be especially complex. Leveraging the stability of the DL model, we propose an alternative fundamental approach based on relaxed adsorption-flow computations that can dissolve these complexity barriers. Literature data extensively validate the findings, which show how the Langmuir-based approach can simulate and predict how key changes in operational and structural conditions affect the CDI performance. Crucially, the method is tractable for simple simulations of large-scale and structurally complex systems. Put together, this work presents new avenues for approaching the challenges in modeling CDI. 

Prussian blue analogs (PBAs) form crystals with large lattice voids that are suitable for the capture, transport and storage of various interstitial ions. Recently, we introduced the concept of a ladder mechanism to describe how sodium ions inside a PBA crystal structure diffuse by climbing the frames formed by aligned cyanide groups in the host structure. The current work uses semi-empirical tight-binding density functional theory (DFTB) in a multiscale approach to investigate how differences in the size of the monovalent cation affect the qualitative and quantitative aspects of the diffusion process. The results show that the ladder mechanism represents a unified framework, from which both similarities and differences between cation types can be understood. Fundamental Coulombic interactions make all positive cations avoid the open vacant areas in the structure, while cavities surrounded by partially negatively charged cyanide groups form diffusion bottlenecks and traps for larger cations. These results provide a new and quantitative way of understanding the suppression of cesium adsorption that has previously been reported for PBAs characterized by a low vacancy density. In conclusion, this work provides a unified picture of the cation adsorption in PBAs based on the newly formulated ladder mechanism.

Clean water and affordable energy are critical worldwide challenges for which electrolytic capacitors are increasingly considered as viable alternatives. The upcoming technology of capacitive deionization (CDI) uses similar electrolytic capacitors for the desalination of water. The current work presents a new method that leverages existing support for supercapacitors in the form of current-distribution models, which enables detailed and separated descriptions of the rate-limiting resistances. Crucially, the new model blends this basis with a novel formulation centered on the adsorption of chemical species in CDI. Put together, it is adaptable to solving a wide range of problems related to chemical species in electrochemical cells. The resulting electrolytic-capacitor (ELC) model has enhanced stability and ease-of-implementation for simulations in 2D. The results demonstrate that the model accurately simulates dynamics CDI performance under a variety of operational conditions. The enhanced stability together with the adaptability further allows tractable simulations of leakage reactions and even handling multi-ion deionization in 2D. Moreover, the model naturally blends with existing interfaces in COMSOL Multiphysics, which automatically generalizes, stabilizes, and simplifies the implementation. In conclusion, the ELC model is user-friendly and tractable for standard simulations while also being especially powerful when simulating complex structures, leakage reactions, and multi-ion solutions.

Capacitive deionization (CDI) is an emerging desalination technique for which upscaling is increasingly relevant for practical applications. Recent research has suggested using bipolar stacks for fast charging and effective energy recovery, but contradicting results have been reported. In this work, we use circuit modeling and finite element (FEM) simulations to understand both the ideal and non-ideal behavior of these systems. This bottom-up approach shows that charging with the ideal bipolar connection is faster proportionally to the total number of cells in a stack. The identified reason for this gain is that the electrical resistance is mainly external, and the same current charges all cells in the stack. Better still, the maximum charge and energy consumption are the same as in the unipolar case. However, the bipolar setup will experience short-circuit if there is insufficient isolation of the solution between the cell compartments. Conversely, the improved adsorption will be nullified if there is sub-stantial resistance in the floating current collectors separating the compartments. In conclusion, bipolar con-nections have lots of potential, and developments in the internal separators between cells could be massively beneficial for future upscaled CDI devices.

Many works in capacitive deionization (CDI) use finite-element (FEM) simulations to investigate process behavior. Here, we present ELC, comprehensive software that integrates these methods with COMSOL Multiphysics. It can save significant time for common research questions in CDI operations and is well-suited for new research questions in complex and upscaled device designs. The ELC software has already been used for the simulation of time-varying desalination output, charge leakages, bipolar electrode devices, and stacks of over 100 CDI cells. Finally, we provide a video tutorial on how to use the software. In conclusion, ELC could be a strong software for aiding current and future research in electrochemical desalination.

The dangers posed by nuclear accidents necessitate developments in techniques for cesium removal. One such is the adsorption of cesium cations in Prussian blue (PB) materials, on which adsorption can be a substation process or pure physisorption. The underlying mechanism of the latter is not well understood, although a Langmuir isotherm is frequently used to model experimental results. In this work, we exploit tight-binding density-functional theory (DFTB) methods to probe the atomic interactions in the physisorption process. The results show that there is a diminishing return for the energy of adsorption as more sites are filled. This means that the adsorption sites are not independent, as stipulated by the ideal Langmuir isotherm. Instead, the results indicate that electrostatic effects need to be considered to explain the theoretical and experimental results. Therefore, an electrostatic Langmuir (EL) model is introduced, which contains an electrostatic ideality correction to the classic Langmuir isotherm. For future materials development, these physical insights indicate that shielding effects as well as the number of independent physical sites must be considered when synthesizing effective Prussian blue analogs (PBA). In conclusion, the study provides insights into the limiting mechanisms in the physisorption of cesium cations on PB.

Electrochemical deionization devices are crucial for meeting the global fresh water demands. One such is capacitive deionization (CDI), which is an emerging technology especially for brackish water desalination wherein supercapacitor devices extract salt ions from water. Here, we extend an electrolytic-capacitor (ELC)model that exploits the similarities between CDI systems and supercapacitor/battery systems. Thanks to the stability and flexibility the approach brings, the current work can present the first fully coupled and spatiotemporal 3D CDI model. This can be beneficial for investigating asymmetric CDI device structures, and the work focuses on a new generation flow-through device structure with inlet and outlet pipes at the center and corners, respectively. The results show that dead (low-flow) areas can reduce desalination rates while also raising the total leakage. However, the ionic flux in this device is still enough under normal operating conditions to ensure reasonable performance. In conclusion, researchers will now have some flexibility in designing device structures that are not perfectly symmetric (real-life case), and hence we share the model files to facilitate future research with 3D modeling of these electrochemical deionization devices.

Capacitive deionization (CDI) is a promising desalination technology based on electrosorption on the surfaces ofnanoporous electrodes. However, low total dissolved solids (TDS) in the water restricts its efficacy. In this work, we develop the theory of capacitive spacers in CDI. The investigations reveal a mechanism that we call ohmic charging; that is, the resistive losses in the spacer region drive adsorption in the capacitive spacer. As a consequence, the obtained results show that such spacers can improve desalination energy efficiency, especially at ion-starved conditions. The spacers also enhance the charging rate of the electrodes because the overall resistance is lower when the current can pass the spacer material instead of the solution, through the adsorption of anions on one side and cations on the other. Going deeper, the investigations reveal a major challenge; the spacer naturally discharges on the same timescale as the electrode charging timescale. However, only the fast timescale matters with low ionic content solutions, and under these conditions the capacitive spacers are found to be superior. Put together, capacitive spacers can make a significant difference, especially when the ion concentration is low or the cycle times are short. 

The rapidly increasing world population will dramatically expand the future global freshwater requirements, now making lots of researchers realize the fundamental importance of developing effective desalination technologies. Hence, the emerging capacitive deionization (CDI) desalination technique is increasingly grabbing the attention of researchers. Simulation of capacitive desalination brings critical value for the understanding, prediction, and optimization of the CDI process which works on the principles of charging and discharging supercapacitors. Typically, a CDI cell comprises two porous electrodes separated by a nonconducting spacer, wherein it produces freshwater by allowing an applied voltage to rapidly extract the salt ions from the steadily passing water steam (during charging of the supercapacitor).  Similarly, the electrodes are regenerated by discharging the adsorbed ions into a waste stream. Previous modeling attempts use the seminal state-of-the-art 2D-FEM method which simulates ion transport coupled with an electric-double-layer (EDL) adsorption formulation. There, the COMSOL PDE interface implements large systems of interconnected adsorption-flow PDEs, and the resulting model was usually found to be “unsteady”. In contrast, in the present work, we reinterpret the phenomena from a porous-catalyst perspective, which fundamentally breaks through the complexity wall by naturally relaxing the adsorption-flow coupling. Specifically, the Brinkman Equations simulated generalized water-flow patterns, which became the background flow in a Multiphysics-coupled Transport of Diluted Species in Porous Media. The latter thus effectively simulates both ionic transport and, through the Reactions interface, the time-dependent ion adsorption. Here, an accurate 0D Randles-circuit model pre-calculates the reaction rate to reduce simulation complexity. This approach reduces the detailed resolution but retains the ability to identify localized phenomena such as concentration shocks, and reaches the state-of-the-art performance in simulating global experimental metrics, as validated with literature data. Additionally, the decoupled Brinkman-flow calculations enable broad flow simulations and simulating the flow efficiency in complex and upscaled CDI structures. Ultimately, the approach means the new model greatly improves stability and broadly opens up research to large interconnected modules and nonlinear flow patterns. As the CDI field continues to grow, these large-scale systems will become increasingly important modeling targets, and we fundamentally believe this work will facilitate and promote future COMSOL studies in modular CDI design.

Clean water is a major global challenge. Meanwhile, capacitive deionization (CDI) is an emerging desalination technology that could help produce and reuse water. As the technology develops, the modeling of upscaled systems is becoming increasingly relevant. However, the inherent complexities in the CDI process have historically made such simulations unfeasible. In this work, we leverage the newly published electrolytic-capacitor (ECL) model to efficiently simulate parallel/serial flow modes in CDI stacks. The simulations are based on finite-element methods (FEM) that couple differential equations for describing local charging and ionic transport inside the device. The results show that both parallel and serial connections scale incredibly well with the system size. Still, parallel connections have the advantage of requiring lower pumping energy. Overall, we find that the relationship between adsorption capacity, flowrate, and compartment size is a good indicator of performance. In conclusion, the ELC model is promising for simulating upscaled CDI.