Mitigation strategies to avoid climate change impacts rely on direct air capture (DAC) of CO 2 . We demonstrate absorption of CO 2 at 400 ppm, and its desorption, by using solid proton-intercalation electrodes to swing the pH of an alkaline electrolyte. 1.76±0.16 GJ tonne -1 of electrical energy is used when enriching CO 2 two-fold, extrapolating to 25.3±0.16 GJ tonne -1 to include water condensation and compression energy. Twenty-fold enrichment requires 5.81±2.42 GJ tonne -1 of electrical energy, extrapolating to 7.81±2.42 GJ tonne -1 . Here, symmetric potassium-stabilized alpha-phase manganese dioxide electrodes are used to (de)intercalate protons from two separate electrolyte streams, thereby swinging dissolved inorganic carbon (DIC) solubility in an asynchronous cycle wherein electrochemical steps occur in sequence with CO 2 transfer steps. Mixing among aqueous streams is shown by theory to reduce CO 2 transfer, where the retention of DIC concentration during alkalizing/dealkalizing steps is affected by mixing more so than alkali-ion concentration swing. Energy use further reduces by pre-mixing post-absorption and post-desorption electrolytes. Theory predicts that alkali-ion concentration swing increases with increasing electrode specific capacity and decreasing mixing volume, motivating the co-design of active materials and their electrode microstructures to enhance efficiency, productivity, and enrichment. The present DAC cycle may also be implemented using other electrochemical architectures.

Ion-exchange membranes (IEMs) that separate cation-intercalation electrodes in symmetric Faradaic deionization (SFDI) increase the capital cost of desalination. We experimentally test SFDI cells that use nanofiltration (NF) membranes instead. Theory is first used to contrast the rate-dependent salt depletion in IEM-free SFDI with IEM-based SFDI. Theory reveals that salt removal scales directly with the intercalation-induced cation-depletion rate relative to the membrane's cation diffusion flux by including the following effects: a current efficiency λ for parasitic electrode processes and a permeance Pm,+ and transference number tm,+ for membrane cation transport. Fitting to experiments indicates that bulk-electrolyte ion transport in the NF membrane's support layer (250 μm) dominates over active-layer ion transport (∼100 nm). An IEM-free SFDI flow cell using embedded, microinterdigitated flow fields was shown to desalinate feeds using 85 mM NaCl or 3.2 g/L of Instant Ocean synthetic salt. The cell produced either freshwater or drinkable water using 1.4-2.2 kWh/m3 at parity with reverse osmosis, electrodialysis, and membrane capacitive deionization. Water recovery was shown in IEM-free SFDI to increase with the charge transferred during batch-type experiments, contrasting its usual decrease with IEMs. Theory further suggests that NF membranes minimize concentration polarization relative to IEMs, decreasing mineral-scaling potential.

Interdigitated flow fields using optimally tapered channels promise to uniformize flow through porous electrodes for desalination using intercalative Faradaic deionization, energy storage using flow batteries, and other flow-based electrochemical processes. 3D Darcy-Brinkman simulations show here that optimally tapered embedded channels produce uniformly spaced streamlines through porous electrode material in comparison with straight and linearly tapered channels that respectively produce dead zones in the central and peripheral electrode material between channels, consistent with quasi-1D theory [Rahman, Loud, Do, Hamid, and Smith, Electrochim. Acta, 514, 145632 (2025)]. Quasi-1D theory and 3D simulations predict apparent permeability enhancements greater than a hundred-fold relative to porous electrode material alone, as determined by a dimensionless hydraulic-resistance parameter Xi . 3D convective mass-transport simulations further reveal the emergence at low flow rates of reaction hot spots that exacerbate electrochemical polarization. Quasi-1D theory introduced here shows reaction distributions that agree with 3D simulations, confirming that hot spots are caused by the back-diffusion of active species from electrode material into channels. Quasi-1D theory further shows that hot spots are eliminated by using a residence time that produces a P & egrave;clet number exceeding a critical value which increases with a Damk & ouml;hler number that depends on overpotential.

Interdigitated flow fields (IDFFs) stand out among flow fields used in electrochemical energy storage and conversion for their modest pressure drop through electrodes. While recent efforts have sought to optimize flow-field topologies and channel shapes, we present a bottom-up strategy to taper channel cross-sections in IDFFs to maximize flow uniformity, eliminating the dead zones that plague straight channels. A linear variation in channel hydraulic conductance is shown to produce constant inter-channel velocity with minimal pressure drop, and mapping between conductance and cross-section geometry with appropriate Poiseuille flow relations enables their implementation. Using a micro-engraving process, we design and manufacture tapered channels having piecewise-constant cross-sections chosen from a library with different nominal widths and depths. The spacing between channels is then optimized to simultaneously minimize material removal and maximize apparent hydraulic permeability. Such tapered-channel IDFFs are embedded in porous, cation-intercalating electrodes for use in desalination by symmetric Faradaic deionization (FDI), where an increase in hydraulic permeability of tapered channels greater than two-fold compared to straight channels is shown to reduce pumping energy by 62% when desalinating seawater-salinity feeds. Energy efficiency doubles at 50% salt removal as a result, motivating hybridization of FDI with conventional desalination processes. Total energy consumption levels of 7.3 kWh/m3 and 0.69 kWh/m3 to produce freshwater respectively from seawater-salinity and brackish feeds is lower than smallscale reverse osmosis and thermal distillation. Low-pressure, high-efficiency operation enabled by IDFFs designed with optimally tapered channels motivates their broad use in flow-based electrochemical separations, energy storage, and energy conversion.

Manifolds that distribute fluid into or that collect fluid from a multiplicity of streams are ubiquitous. We introduce a new theory for manifold design to produce uniform flow among their streams. By constructing a tapered header region that feeds uniformly spaced diffuser channels (constraint A), flow uniformity can be achieved with less than a quarter of the footprint of bifurcating manifolds, provided that diffuser channels are arrayed in triangular form (constraint B) with a design-specific angle that satisfies a compatibility condition between its header and diffuser (constraint C). The associated theory harnesses creeping-flow hydraulics to induce a constant header pressure-gradient, in contrast with past theory that relied on the interplay between kinetic energy, pressure, and viscous losses to uniformize header pressure at finite Reynolds number. Experiments using dye-based flow visualization from manifolds incorporating these three design constraints are shown to produce uniform flows, while designs that violate any of the three constraints produce flow that is biased toward the manifold's ends or its center. Our experiments and three-dimensional simulations of such uniformizing manifolds show maximum deviations from uniformity of ∼10% for Reynolds number as high as ∼10. As expected from creeping-flow theory, simulations confirm that such flow uniformity is facilitated by a uniform header-pressure gradient. Finally, the associated uniformizing manifold is shown to produce lower hydraulic resistance than a rectangular manifold circumscribed around it. In addition to the theory's embodiment in the specific form tested here, it is readily applicable to a variety of header and diffuser-channel cross-sectional types.

Interdigitated microchannels embedded in porous electrodes containing nickel hexacyanoferrate enable flow-through electrochemical desalination with low energy input when used with aqueous feeds having either seawater, brackish-water, or hypersaline-brine salinity.

Renewable power sources have drawn interest due to scarcity of fossil fuels and associated pollution during their combustion-based power production. Renewables are projected to produce approximately 60% of US electricity generation by 2050, with an expected contribution of 2000 TW-h from wind power alone. To overcome the mismatch between electricity demand and intermittent supply, such power plants require large-scale energy-storage device integrated with them. In contrast to other technologies, redox flow batteries (RFBs) offer independently scalable power and energy capacity that is demanded for such applications. Despite significant achievement in their designs through experimentation and modeling, limited understanding has been established to date concerning their transient response while operating under irregular charge/discharge scenarios in renewable-powered grids and micro-grids. Under such conditions pore-scale mass transport physics and different mechanisms of concentration polarization can occur, but the conventional film law of mass transfer (FLoMT) using a constant Sherwood number cannot capture time-varying diffusion layer thickness near electrode surfaces. Further, the mean solute advection rate through porous RFB electrodes can deviate from the value expected from product of superficial velocity and average concentration inside the electrode if pore-scale concentration polarization is substantial. Consideration of these effects in the present bottom-up theory makes it applicable to over-limiting conditions, while predicting concentration polarization in agreement with experimental observations. We accomplish this by creating theory with similarity to the theory of Ralph White and co-workers for solid-state, particle-scale diffusion in Li-ion batteries [ J. Power Sources , 2012, Vols. 214 and 218], while our theory is instead applied to an arbitrary representative volume element of flowing liquid electrolyte inside electrode pores. Here, we present a theory to incorporate these transient effects into a bottom-up transient model (B-UTM) by using frequency-dependent transfer functions (TFs) that are derived from the Fourier transformed pore-scale mass conservation equations (MCEs). These TFs preserve pore-scale mass transfer physics during their embedding into an up-scaled model. One of these TFs is the spectral Sherwood number that extends the film law of mass transfer to transient conditions and that correlates reactive flux with concentration polarization through an output-input relationship in the frequency domain. Another TF named the advective-flux transfer function captures the acceleration/suppression of solute advection rate that arises from the inhomogeneity in pore-scale concentration distributions. We first present validation of this theory using transient RFB experiments where the introduced B-UTM predicts the time evolution of concentration polarization in good agreement. Meanwhile the conventional FLoMT model that uses time-independent Sherwood number and neglects the solute acceleration/suppression effect shows systematically larger polarization (up to 400%), which restricts such models from simulating charging/discharging with applied current near and above the limiting current. The utility of the introduced bottom-up theory is demonstrated by incorporating it into a multi-scale RFB model in which redox-active electrolyte flows through a porous electrode comprised of an array of circular cylinders in crossflow that mimics commonly used carbon felt. The frequency dependence of the introduced TFs obtained from numerical solution of pore-scale MCEs are analyzed for different electrode porosity and Péclet number, where both the TFs reach a non-zero finite value in the limit of vanishing frequency. The non-zero value of the spectral Sherwood number in this limit is identical to the Sherwood number obtained in the pseudo-steady limit (PSL) where transient effects are negligible. With increasing frequency both the TFs show a transition from lagless response to semi-infinite Warburg response with orders higher values compared to that of the PSL. Finally, these TFs are embedded into an up-scaled model to obtain the time-domain response of RFBs operating under a step impulse applied current with different step durations. Numerically obtained concentration polarization and the average reactant concentration inside electrodes is used to construct non-dimensional regime maps showing a regime of over-limiting current. The results show that fast current fluctuations are sustained even when current exceeds the limiting current, which provides a means to increase the utilization of charge capacity of existing flow-based electrochemical devices that are operated under transient conditions. The theory introduced here can find applicability in other flow-based electrochemical devices including electrochemical separations and CO 2 capture. Figure 1

New theory is presented for the dynamic response of redox-active electrolyte flowing through porous electrodes under time-dependent applied current. This is done by introducing certain frequency-dependent transfer functions (TFs) that incorporate pore-scale transport physics. One TF – dubbed the spectral Sherwood number – extends the film law of mass transfer (FLoMT) to transient conditions. Another TF captures the acceleration/suppression of solute advection that results from pore-scale velocity/concentration gradients. Numerical results are shown for the frequency-dependent TFs of solid cylinders in crossflow to represent porous electrodes commonly used in flow batteries (FBs). Spectral regions are observed where a transition from lagless response to semi-infinite Warburg response occurs with increasing frequency. The embedding of these TFs into an up-scaled model is also formulated to obtain the time-domain response of FBs. Without adjustable parameters this model predicts polarization in agreement with transient FB experiments, despite systematic overprediction by the conventional FLoMT model. Analysis of concentration polarization and reactant concentration is also used to construct non-dimensional maps of operational space. These predictions show that fast current fluctuations are sustained even when current exceeds the limiting current expected from the time-invariant FLoMT without solute advection suppression/acceleration, suggesting implications for electrochemical conversion and separations devices in addition.

NASICON (sodium superionic conductor) materials are promising host compounds for the reversible capture of Na+ ions, finding prior application in batteries as solid-state electrolytes and cathodes/anodes. Given their affinity for Na+ ions, these materials can be used in Faradaic deionization (FDI) for the selective removal of sodium over other competing ions. Here, we investigate the selective removal of sodium over other alkali and alkaline-earth metal cations from aqueous electrolytes when using a NASICON-based mixed Ti-V phase as an intercalation electrode, namely, sodium titanium vanadium phosphate (NTVP). Galvanostatic cycling experiments in three-electrode cells with electrolytes containing Na+, K+, Mg2+, Ca2+, and Li+ reveal that only Na+ and Li+ can intercalate into the NTVP crystal structure, while other cations show capacitive response, leading to a material-intrinsic selectivity factor of 56 for Na+ over K+, Mg2+, and Ca2+. Furthermore, electrochemical titration experiments together with modeling show that an intercalation mechanism with a limited miscibility gap for Na+ in NTVP mitigates the state-of-charge gradients to which phase-separating intercalation electrodes are prone when operated under electrolyte flow. NTVP electrodes are then incorporated into an FDI cell with automated fluid recirculation to demonstrate up to 94% removal of sodium in streams with competing alkali/alkaline-earth cations with 10-fold higher concentration, showing process selectivity factors of 3-6 for Na+ over cations other than Li+. Decreasing the current density can improve selectivity up to 25% and reduce energy consumption by as much as ∼50%, depending on the competing ion. The results also indicate the utility of NTVP for selective lithium recovery.

Prussian blue analogs (PBAs) are an important material class for aqueous electrochemical separations and energy storage owing to their ability to reversibly intercalate monovalent cations. However, incorporating interstitial H2O molecules in the ab initio study of PBAs is technically challenging, though essential to understanding the interactions between interstitial water, interstitial cations, and the framework lattice that affect intercalation potential and cation intercalation selectivity. Accordingly, we introduce and use a method that combines the efficiency of machine-learning models with the accuracy of ab initio calculations to elucidate mechanisms of (1) lattice expansion upon intercalation of cations of different sizes, (2) selectivity bias toward intercalating hydrophobic cations of large size, and (3) semiconductor–conductor transitions from anhydrous to hydrated lattices. We analyze the PBA nickel hexacyanoferrate [NiFe(CN)6] due to its structural stability and electrochemical activity in aqueous electrolytes. Here, grand potential analysis is used to determine the equilibrium degree of hydration for a given intercalated cation (Na+, K+, or Cs+) and NiFe(CN)6 oxidation state based on pressure-equilibrated structures determined with the aid of machine learning and simulated annealing. The results imply new directions for the rational design of future cation-intercalation electrode materials that optimize performance in various electrochemical applications, and they demonstrate the importance of choosing an appropriate calculation framework to predict the properties of PBA lattices accurately.

Prussian blue analogues (PBAs) containing metal centers bridged by cyanide ligands exhibit one of the simplest structures among metal organic frameworks, which lends them to facile and reversible insertion of monovalent cations. Such a property has motivated their use in aqueous electrochemical separations, including our most recent demonstration of brackish water desalination with only 25% more energy consumption than thermodynamic minimum. 1 Despite their selectivity bias toward cations of small hydrated radius being known for 36 years, 2 the microscopic mechanisms responsible for such bias that could be used to inform the rational design of future materials are not well understood. Accordingly, we report on our recent efforts 3,4 to uncover the interactions between inserted cations, interstitial water, and PBA lattices that produce selectivity bias. To understand the interplay between structural distortion, bonding, and water uptake from contacting electrolyte we use a first-principles approach that combines machine learning with density functional theory and grand potential analysis to explore the potential energy landscapes of disordered arrangements of interstitial species in nickel hexacyanoferrate PBA. Here, a competition for dative bonds of acidic interstitial cations between basic oxygen in interstitial water and basic cyanide ligands is shown to result in complexation between cations and water that deviate fundamentally from bulk hydration in pure water, despite the common attribution of PBA selectivity to purely steric effects of cation hydration. Van der Waals interactions are further shown to enhance the formation of water clusters and extended hydrogen-bonded networks within the PBA host, depending on the bare ionic radius of inserted cations. Grand potential analysis is performed to ultimately produce previously observed selectivity bias (Cs + > K + > Na + ) and to determine the equilibrium hydration degree of the PBA in both reduced and oxidized forms. This analysis shows that small (Na + ) and moderately sized (K + ) cations require two to four water molecules per formula unit in both reduced and oxidized forms of the PBA, while large cations (Cs + ) exhibit much smaller hydration levels in oxidized form and exhibit no hydration in reduced form. References Reale, E. R., Regenwetter, L., Agrawal, A., Dardón, B., Dicola, N., Sanagala, S. & Smith, K. C. Low porosity, high areal-capacity Prussian blue analogue electrodes enhance salt removal and thermodynamic efficiency in symmetric Faradaic deionization with automated fluid control. Water Res. X 13, 100116 (2021). Ikeshoji, T. Separation of Alkali Metal Ions by Intercalation into a Prussian Blue Electrode. J. Electrochem. Soc. 133, 2108 (1986). Liu, S. & Smith, K. C. Linking the polyatomic structure of interstitial H2O and cations to bonding within Prussian blue analogues ab initio using gradient-boosted machine learning. Phys. Rev. Mater. 5, 035003 (2021). Liu, S. & Smith, K. C. Effects of interstitial water and alkali cations on the expansion, intercalation potential, and orbital coupling of nickel hexacyanoferrate from first principles. J. Appl. Phys. 131, 105101 (2022).

Prussian blue analogues (PBAs) show great potential for low-energy Faradaic deionization (FDI) with reversible Na-ion capacity approaching 5 M in the solid-state. However, past continuous-flow demonstrations using PBAs in FDI were unable to desalinate brackish water to potable levels using single-pass architectures. Here, we show that recirculation of effluent from a symmetric cation intercalation desalination cell into brine/diluate reservoirs enables salt removal exceeding 80% at thermodynamic efficiency as high as 80% when cycled with 100 mM NaCl influent and when controlled by a low-volume, automated fluid circuit. This exceptional performance is achieved using a novel heated, alkaline wet phase inversion process that modulates colloidal forces to increase carbon black aggregation within electrode slurries to solidify crack-free, high areal-capacity PBA electrodes that are calendered to minimize cell impedance and electrode porosity. The results obtained demonstrate the need for co-design of auxiliary fluid-control systems together with electrode materials to advance FDI beyond brackish salinity.

Prussian blue analogues (PBAs) are model host compounds for the intercalation of monovalent cations for electrochemical energy storage and separations. However, the interactions among interstitial species and their effects on atomic arrangements therein are understood mainly at a phenomenological level. Analyzing correlations between electronic interactions and polyatomic arrangements in hydrated Prussian blue analogues is complicated by the nonlocal hydrogen-bonding interactions between zeolitic water and framework lattices. Here, we train machine-learning (ML) models to learn DFT-calculated energy landscapes of nickel hexacyanoferrate PBA lattices with various lattice hydration degrees, oxidation states, and types of intercalated alkali cations based on various three-particle feature parameters. This ML approach is enabled by using gradient-boosted regression trees with features that are rotationally invariant geometric parameters. ML model accuracy is shown to be a cation-specific indicator of correlations between energy and polyatomic arrangements. Overlap population analysis among correlated atoms further confirms that such correlations are caused by the competition for dative bonding between Lewis-acid intercalated cations and Lewis bases (cyanide and oxygen in ${\mathrm{H}}_{2}\mathrm{O}$). Examination of lowest-energy structures reveals that cation hydrophilicity and bare ionic radius determine dative-bonding strength, resulting in cation-${\mathrm{H}}_{2}\mathrm{O}$ ordering in interstitial space. The projected energy landscapes of hydrated PBA lattices is also explored in subspaces spanned by certain many-particle feature parameters inspired by ML analysis. The downhill traces in such landscapes indicate that lattice distortion is accompanied by two kinds of collective movements: (1) rearrangements in the hydration shells around small and hydrophilic cations and (2) collective attack of ${\mathrm{H}}_{2}\mathrm{O}$ molecules on nickel-cyanide bonds promoted by large, hydrophobic cations.

While many practically important electrolytes contain lithium ions, interactions of these ions are particularly difficult to probe experimentally because of their small X-ray and neutron scattering cross sections and large neutron absorption cross sections. Molecular dynamics (MD) is a powerful tool for understanding the properties of nonaqueous electrolyte solutions from the atomic level, but the accuracy of this computational method crucially depends on the physics built into the classical force field. Here, we demonstrate that several force fields for lithium bistriflimide (LiTFSI) in acetonitrile yield a solution structure that is consistent with the neutron scattering experiments, yet these models produce dramatically different ion dynamics in solution. Such glaring discrepancies indicate that inadequate representation of long-range interactions leads to excessive ionic association and ion-pair clustering. We show that reasonable agreement with the experimental observations can be achieved by renormalization of the ion charges using a "titration" method suggested herewith. This simple modification produces realistic concentration dependencies for ionic diffusion and conductivity in <2 M solutions, without loss in quality for simulation of the structure.

Theoretical models have recently been used to simulate deionization technology by capturing electrochemical processes at atomistic, electrode, and plant length scales in electrodialysis, capacitive deionization using electric double layers, and Faradaic deionization using intercalation materials and redox-active polymers. We review the salient features of such models, identifying their major accomplishments in quantifying energy consumption and ion removal, analyzing the feasibility of large-scale systems, and discovering new electrode materials and understanding their deionization mechanisms. After summarizing strengths and weaknesses of recent modeling strategies, we identify research directions to expand modeling capabilities that can be used to inform electrode material/microstructure design, to assign energy losses to electrode-scale mechanisms, to bridge length scales, and to capture Faradaic kinetic/diffusion processes.

Redox flow batteries (RFBs) are attractive energy storage solutions for the grid, the simulation of which enables system and material optimization. In this article, we introduce tailored numerical schemes to model coupling between the transport of dissolved species, electrons, and fluid with redox reaction kinetics within RFBs in a robust way. The macro-scale transport of species (including advection, migration, and hydrodynamic dispersion) is coupled with the volume-averaged pore-scale processes of reaction kinetics, and mass transport, while the Poisson equation is used to model Donnan exclusion across ion exchange membranes that limit capacity fade due to the crossover of redox-active species. The governing equations are discretized using the finite volume method with a Newton-Raphson iteration scheme to resolve non-linearity. We introduce several numerical schemes to increase solver robustness, including reaction rate damping and logarithmic transform of concentration fields. Based on fixed-point iteration convergence criteria we also show that the mechanistic Marcus-Hush-Chidsey (MHC) redox kinetics model can tolerate larger time steps than the empirical Butler-Volmer (BV) kinetics model. The numerical schemes presented in this article can also find application in other electrochemical systems, including desalination devices, fuel cells, and electrodialysis.

Life in a tight spot: Transport and collective behavior of bacteria in

Various microscopic processes are responsible for the inefficiencies with which redox flow batteries (RFBs) operate. We introduce theory presently to enable the systematic analysis of energy losses in RFBs using exergy destruction rates derived from irreversible thermodynamics. We apply this analysis to RFBs for the first time by performing simulations with a transient, 2D model using a homogenized Poisson-Nernst-Planck formulation including multicomponent hydrodynamic dispersion, Donnan exclusion in ion exchange membranes, and Marcus-Hush-Chidsey kinetics. In the limit of low Wagner number, we map charge capacity utilization and cell polarization in the space of pore-scale Damköhler number (a non-dimensional parameter for characteristic pore-scale mass transfer resistance) and salt Damköhler number (a non-dimensional parameter for characteristic ohmic polarization) by varying the applied current density and electrode fiber diameter. Exergy destruction rates are analyzed from (1) pore-scale mass transfer, (2) reaction kinetics, (3) irreversible tank mixing, (4) bulk species transport, and (5) electronic conduction. For high coulombic efficiencies the sum of these exergy destruction contributions balances with the energy lost during a given cycle. This method of energy loss assignment to specific mechanisms at specific instants in time and locations in space provides guidance for the development of energy-efficient, high-rate RFBs in the future.

We report the exploitation of spectroplasmonics for innovations in optical transducer development, specifically in the well-established application of labeled fluorescent analytes known as fluorescence spectroscopy. Presented herein are comprehensive analyses of nanoscale plasmonic lattice feature geometries using finite-difference time-domain software to determine the largest surface electric ($E$E) field enhancement resulting from localized surface plasmon resonance for reducing the limit of detection of plasmon-enhanced fluorescence. This parametric optimization of the critical dimensions of the plasmon resonance of noble metal nanostructures will enable improved excitation and emission enhancement of fluorophores used in visible wavelength fluorescence spectroscopy.