Nonlinear dynamics of capacitive charging and desalination by porous electrodes

Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors

Supercapacitors store energy due to the formation of an electric double layer (EDL) at the interface of the electrodes and electrolyte. The present article deals with the finite element study of equilibrium electric double layer capacitance (EDLC) in the mixed morphology electrodes comprising all three fundamental crystal structures, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic morphologies (FCC). Mesoporous-activated carbon forms the electrode in the supercapacitor with (C2H5)4NBF4/propylene carbonate organic electrolyte. Electrochemical interference is clearly demonstrated in the supercapacitors with the formation of the potential bands, as in the case of interference theory due to the increasing packing factor. The effects of electrode thickness varying from a wide range of 50 nm to 0.04 mm on specific EDLC have been discussed in detail. The interfacial geometry of the unit cell in contact with the electrolyte is the most important parameter determining the properties of the EDL. The critical thickness of the electrodes is 1.71 μm in all the morphologies. Polarization increases the interfacial potential and leads to EDL formation. The Stern layer specific capacitance is 167.6 μF cm-2 in all the morphologies. The maximum capacitance is in the decreasing order of interfacial geometry, as FCC > BCC > SC, dependent on the packing factor. The minimum transmittance in all the morphologies is 98.35%, with the constant figure of merit at higher electrode thickness having applications in the chip interconnects. The transient analysis shows that the interfacial current decreases with increasing polarization in the EDL. The capacitance also decreases with the increase of the scan rate.

A network model to predict ionic transport in porous materials

Understanding the dynamics of electric-double-layer (EDL) charging in porous media is essential for advancements in next-generation energy storage devices. Due to the high computational demands of direct numerical simulations and a lack of interfacial boundary conditions for reduced-order models, the current understanding of EDL charging is limited to simple geometries. Here, we present a network model to predict EDL charging in arbitrary networks of long pores in the Debye-Hückel limit without restrictions on EDL thickness and pore radii. We demonstrate that electrolyte transport is described by Kirchhoff's laws in terms of the electrochemical potential of charge (the valence-weighted average of the ion electrochemical potentials) instead of the electric potential. By employing the equivalent circuit representation suggested by these modified Kirchhoff's laws, our methodology accurately captures the spatial and temporal dependencies of charge density and electric potential, matching results obtained from computationally intensive direct numerical simulations. Our network model provides results up to six orders of magnitude faster, enabling the efficient simulation of a triangular lattice of five thousand pores in 6 min. We employ the framework to study the impact of pore connectivity and polydispersity on electrode charging dynamics for pore networks and discuss how these factors affect the time scale, energy density, and power density of capacitive charging. The scalability and versatility of our methodology make it a rational tool for designing 3D-printed electrodes and for interpreting geometric effects on electrode impedance spectroscopy measurements.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Tracking Ion Transport in Nanochannels via Transient Single-Particle Imaging

The transport behavior of ions in the nanopores has an important impact on the performance of the electrochemical devices. Although the classical Transmission-Line (TL) model has long been used to describe ion transport in pores, the boundary conditions for the applicability of the TL model remain controversial. Here, we investigated the transport kinetics of different ions, within nanochannels of different lengths, by using transient single-particle imaging with temporal resolution up to microseconds. We found that the ion transport kinetics within short nanochannels may deviate significantly from the TL model. The reason is that the ion transport under nanoconfinement is composed of multi basic stages, and the kinetics differ much under different stage domination. With the shortening of nanochannels, the electrical double layer (EDL) formation would become the "rate-determining step" and dominate the apparent ion kinetics. Our results imply that using the TL model directly and treating the in-pore mobility as an unchanged parameter to estimate the ion transport kinetics in short nanopores/nanochannels may lead to orders of magnitude bias. These findings may advance the understanding of the nanoconfined ion transport and promote the related applications.

Molecular Understanding of Charging Dynamics in Supercapacitors with Porous Electrodes and Ionic Liquids

Porous electrodes and ionic liquids could significantly enhance the energy storage of supercapacitors. However, they may reduce the charging dynamics and power density due to the nanoconfinement of porous electrodes and the high viscosity of ionic liquids. A comprehensive understanding of the charging mechanism in porous supercapacitors with ionic liquids provides a crucial theoretical foundation for their design optimization. Here, we review the progress of molecular simulations of the charging dynamics in supercapacitors consisting of porous electrodes and ionic liquids. We highlight and delve into the breakthroughs in the ion transport and charging mechanism for electrodes with subnanometer pores and realistic porous structures. We also discuss future directions for the charging dynamics of supercapacitors.

Real-time visualisation of ion exchange in molecularly confined spaces where electric double layers overlap

Ion interactions with interfaces and transport in confined spaces, where electric double layers overlap, are essential in many areas, ranging from crevice corrosion to understanding and creating nano-fluidic devices at the sub 10 nm scale. Tracking the spatial and temporal evolution of ion exchange, as well as local surface potentials, in such extreme confinement situations is both experimentally and theoretically challenging. Here, we track in real-time the transport processes of ionic species (LiClO4) confined between a negatively charged mica surface and an electrochemically modulated gold surface using a high-speed in situ sensing Surface Forces Apparatus. With millisecond temporal and sub-micrometer spatial resolution we capture the force and distance equilibration of ions in the confinement of D ≈ 2-3 nm in an overlapping electric double layer (EDL) during ion exchange. Our data indicate that an equilibrated ion concentration front progresses with a velocity of 100-200 μm s-1 into a confined nano-slit. This is in the same order of magnitude and in agreement with continuum estimates from diffusive mass transport calculations. We also compare the ion structuring using high resolution imaging, molecular dynamics simulations, and calculations based on a continuum model for the EDL. With this data we can predict the amount of ion exchange, as well as the force between the two surfaces due to overlapping EDLs, and critically discuss experimental and theoretical limitations and possibilities.

Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers

Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.

Unraveling the effect of CDI electrode characteristics on Cs removal from the perspective of ion transfer and energy composition

Capacitive deionization (CDI) is surprisingly efficient to remove the aqueous Cs ion due to its small hydrated size and low hydration energy. But current experimental techniques fail in investigating deeply into the influence of some key electrode characteristics due to the difficulty in experimentally fabricating the electrodes as desired. This work presents a dynamic transport model of salt ions in a flow-by CDI cell. By using this model, the electrode thickness, macro- and micro-porosity are investigated to evaluate Cs ion removal efficiency and energy efficiency particularly from the aspect of ion transfer by the approach of decomposing energy contribution. The results indicate that the thick electrode coupled with the high current could greatly improve the effluent quality, but reduce the salt adsorption capacity (SAC). The increasement of the current density from 3 A/m² to 6 A/m² greatly decreases the SAC from 4.0 mg/g to 0.8 mg/g. Lower current could prolong the charging period, leading to more ions stored in the micropore. Not all the electrical energy is consumed for separating ions from the feed as desired, but some are used for driving ions diffusing in the electrodes. Consequently charging efficiency will be reduced especially when the electrodes are characterized with high porosity. It is highlighted that future work is required to further consider the complex details of porous structure and pore connectivity.

Theory and Simulations of Ionic Liquids in Nanoconfinement

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Frequency-Dependent Impedance of Nanocapacitors from Electrode Charge Fluctuations as a Probe of Electrolyte Dynamics

The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation relation for the capacitance recovered in the low-frequency limit and provide an illustration on water-gold nanocapacitors. This Letter opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent circuit models as in experiments.

Unlocking the potential of polymeric desalination membranes by understanding molecular-level interactions and transport mechanisms

Polyamide reverse osmosis (PA-RO) membranes achieve remarkably high water permeability and salt rejection, making them a key technology for addressing water shortages through processes including seawater desalination and wastewater reuse. However, current state-of-the-art membranes suffer from challenges related to inadequate selectivity, fouling, and a poor ability of existing models to predict performance. In this Perspective, we assert that a molecular understanding of the mechanisms that govern selectivity and transport of PA-RO and other polymer membranes is crucial to both guide future membrane development efforts and improve the predictive capability of transport models. We summarize the current understanding of ion, water, and polymer interactions in PA-RO membranes, drawing insights from nanofiltration and ion exchange membranes. Building on this knowledge, we explore how these interactions impact the transport properties of membranes, highlighting assumptions of transport models that warrant further investigation to improve predictive capabilities and elucidate underlying transport mechanisms. We then underscore recent advances in in situ characterization techniques that allow for direct measurements of previously difficult-to-obtain information on hydrated polymer membrane properties, hydrated ion properties, and ion-water-membrane interactions as well as powerful computational and electrochemical methods that facilitate systematic studies of transport phenomena.

Fully 3D Modeling of Electrochemical Deionization

Electrochemical deionization devices are crucial for meeting global freshwater demands. One such is capacitive deionization (CDI), which is an emerging technology especially suited for brackish water desalination. In this work, we extend an electrolytic capacitor (ELC) model that exploits the similarities between CDI systems and supercapacitor/battery systems. Compared to the previous work, we introduce new implementational strategies for enhanced stability, a more detailed method of describing charge efficiency, layered integration of leakage reactions, and theory extensions to new material and operational conditions. Thanks to the stability and flexibility the approach brings, the current work can present the first fully coupled and spatiotemporal three-dimensional (3D) CDI model. We hope that this can pave the way toward generalized and full-scale modeling of CDI units under varying conditions. A 3D model can be beneficial for investigating asymmetric CDI device structures, and the work investigates a 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.

2D metal-organic frameworks for ultraflexible electrochemical transistors with high transconductance and fast response speeds

Electrochemical transistors (ECTs) have shown broad applications in bioelectronics and neuromorphic devices due to their high transconductance, low working voltage, and versatile device design. To further improve the device performance, semiconductor materials with both high carrier mobilities and large capacitances in electrolytes are needed. Here, we demonstrate ECTs based on highly oriented two-dimensional conjugated metal-organic frameworks (2D c-MOFs). The ion-conductive vertical nanopores formed within the 2D c-MOFs films lead to the most convenient ion transfer in the bulk and high volumetric capacitance, endowing the devices with fast speeds and ultrahigh transconductance. Ultraflexible device arrays are successfully used for wearable on-skin recording of electrocardiogram (ECG) signals along different directions, which can provide various waveforms comparable with those of multilead ECG measurement systems for monitoring heart conditions. These results indicate that 2D c-MOFs are excellent semiconductor materials for high-performance ECTs with promising applications in flexible and wearable electronics.

A review of transport models in charged porous electrodes

There is increased interest in many different processes based upon interactions between a charged solid surface and a liquid electrolyte. Energy storage in capacitive porous materials, ionic membranes, capacitive deionization (CDI) for water desalination, capacitive energy generation, removal of heavy ions from wastewater streams, and geophysical applications are some examples of these processes. Process development is driven by the production of porous materials with increasing surface area. Understanding of the physical phenomena occurring at the charged solid-electrolyte interface will significantly improve the design and development of more effective applied processes. The goal of this work is to critically review the current knowledge in the field. The focus is on concepts behind different models. We start by briefly presenting the classical electrical double layer (EDL) models in flat surfaces. Then, we discuss models for porous materials containing macro-, meso-, and micro-pores. Some of the current models for systems comprising two different pore sizes are also included. Finally, we discuss the concepts behind the most common models used for ionic transport and Faradaic processes in porous media. The latter models are used for simulation of electrosorption processes in porous media.

Predictive Molecular Models for Charged Materials Systems: From Energy Materials to Biomacromolecules

Electrostatic interactions play a dominant role in charged materials systems. Understanding the complex correlation between macroscopic properties with microscopic structures is of critical importance to develop rational design strategies for advanced materials. But the complexity of this challenging task is augmented by interfaces present in the charged materials systems, such as electrode-electrolyte interfaces or biological membranes. Over the last decades, predictive molecular simulations that are founded in fundamental physics and optimized for charged interfacial systems have proven their value in providing molecular understanding of physicochemical properties and functional mechanisms for diverse materials. Novel design strategies utilizing predictive models have been suggested as promising route for the rational design of materials with tailored properties. Here, an overview of recent advances in the understanding of charged interfacial systems aided by predictive molecular simulations is presented. Focusing on three types of charged interfaces found in energy materials and biomacromolecules, how the molecular models characterize ion structure, charge transport, morphology relation to the environment, and the thermodynamics/kinetics of molecular binding at the interfaces is discussed. The critical analysis brings two prominent field of energy materials and biological science under common perspective, to stimulate crossover in both research field that have been largely separated.

Probing Nanoconfined Ion Transport in Electrified 2D Laminate Membranes with Electrochemical Impedance Spectroscopy

The recent emergence of electrically conductive nanoporous membranes based on graphene and other 2D materials opens up new opportunities to revisit some longstanding nanoconfined ion transport problems under electrification. This work probes the ionic resistance in electrified multilayered graphene membranes with electrochemical impedance spectroscopy. This study demonstrates that the combination of additive-free feature and tunable slit pore sizes in the sub-10 nm range in graphene-based membranes has made it possible to deconvolute the different ionic processes from the impedance obtained and examine the exclusive influence of pore size on the ionic resistance in a quantitative manner. The trends revealed for the ionic resistance at the pore entrance and inside the pores under severe nanoconfinement (<2 nm) are found to be generally consistent with the microscale theoretical simulations previously reported. It also allows a quantitative analysis of the relative effects of the external polarization potential and ion identity under nanoconfinement. The results suggest that the classic electrochemical impedance spectroscopy technique, when applied to appropriate nanoporous electrode materials, can provide rich information about nanoconfined ion transport phenomena under electrification for fundamental understanding and application development.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Microscopic Simulations of Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference $2\Phi$ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements.We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers.Next to the dimensionless applied potential $\Phi$, we consider the ratio $R/R_b$ of the pore's resistance $R$ to the bulk reservoir resistance $R_b$ and the ratio $r_{p}/\ld$ of the pore radius $r_p$ to the Debye length $\ld$.We compare our data to theoretical predictions by Aslyamov and Janssen ($\Phi$), Posey and Morozumi ($R/R_b$), and Henrique, Zuk, and Gupta ($r_{p}/\ld$).Through our numerical approach, we delineate the validity of these theories and the assumptions on which they were based.

Electroconvective instability near an ion-selective surface: A mesoscopic lattice Boltzmann study

Direct numerical simulations of electroconvection instability near an ion-selective surface are conducted using a mesoscopic lattice Boltzmann method (LBM). An electrohydrodynamic model of ion transport and fluid flow is presented. We numerically solve the Poisson-Nernst-Planck equations for the electric field and the Navier-Stokes equations for the flow field. The results cover Ohmic, limiting, and overlimiting current regimes, and they are in good agreement with the asymptotic analytical solution for the relationship between current and voltage. The influences of different ion transport mechanisms on the voltage-current relationship are discussed. The results reveal that the electroconvection mechanism is as important as other ion transport mechanisms in electrohydrodynamic flow. By comparing the contribution of different regions in the numerical domain, we find that the flow in the extended space charge layer is dominated by electroconvection. We also study the influences of multiple driving parameters, and the electrohydrodynamic coupling constant plays a dominant role in triggering convective instability. The flow pattern and ion concentration distribution are described in detail. Moreover, the route of flow from steady state to periodic oscillation and then to chaos is discussed.

Knowledge and Technology Used in Capacitive Deionization of Water

The demand for water and energy in today’s developing world is enormous and has become the key to the progress of societies. Many methods have been developed to desalinate water, but energy and environmental constraints have slowed or stopped the growth of many. Capacitive Deionization (CDI) is a very new method that uses porous carbon electrodes with significant potential for low energy desalination. This process is known as deionization by applying a very low voltage of 1.2 volts and removing charged ions and molecules. Using capacitive principles in this method, the absorption phenomenon is facilitated, which is known as capacitive deionization. In the capacitive deionization method, unlike other methods in which water is separated from salt, in this technology, salt, which is a smaller part of this compound, is separated from water and salt solution, which in turn causes less energy consumption. With the advancement of science and the introduction of new porous materials, the use of this method of deionization has increased greatly. Due to the limitations of other methods of desalination, this method has been very popular among researchers and the water desalination industry and needs more scientific research to become more commercial.

Electrical image potential and solvation energies for an ion in a pore in a metallic electrode or in a nanotube

Electrical image potentials can be important in small spaces, such as nanoscale pores in porous electrodes, which are used in capacitive desalination and in supercapacitors, as argued by Bazant's group at Massachusetts Institute of Technology. It will be shown here that inside pores in porous metallic materials the image potentials can be considerably larger than near flat walls, as a result of the fact that the dielectric constant for an electric field perpendicular to a wall is much smaller than the bulk dielectric constant of water. Calculations will be presented for the image potential in spherical and cylindrically shaped pores. The calculations for cylindrical pores can also be applied to nanotubes. It was believed for a long time, on the basis of molecular dynamics simulations, that in order to push a salt solution through a small radius nanotube, work must be done against the solvation energy of the ions, which is larger inside a narrow nanotube than it is in the bulk. The relatively large image charge potential energy in narrow nanotubes, however, tends to oppose this increase in the solvation energy. The degree to which the image potential facilitates the flow of the salt ions into nanotubes will be discussed.

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

An optimal combination of power and energy characteristics is beneficial for the further progress of supercapacitors-based technologies. We develop a nanoscale dynamic electrolyte model, which describes both static capacitance and the time-dependent charging process, including the initial square-root dependency and two subsequent exponential trends. The observed charging time corresponds to one of the relaxation times of the exponential regimes and significantly depends on the pore size. Additionally, we find analytical expressions providing relations of the time scales to the electrode's parameters, applied potential, and the final state of the confined electrolyte. Our numerical results for the charging regimes agree with published computer simulations, and estimations of the charging times coincide with the experimental values.

Charging dynamics of electrical double layers inside a cylindrical pore: predicting the effects of arbitrary pore size

Porous electrodes are found in energy storage devices such as supercapacitors and pseudocapacitors. However, the effect of electrode-pore-size distribution on their energy storage properties remains unclear. Here, we develop a model for the charging of electrical double layers inside a cylindrical pore for arbitrary pore size. We assume small applied potentials and perform a regular perturbation analysis to predict the evolution of electrical potential and ion concentrations in both the radial and axial directions. We validate our perturbation model with direct numerical simulations of the Poisson-Nernst-Planck equations, and obtain quantitative agreement between the two approaches for small and moderate potentials. Our analysis yields two main characteristic features of arbitrary pore size: (i) a monotonic decrease of the charging timescale with an increase in relative pore size (pore size relative to Debye length); (ii) large potential changes for overlapping double layers in a thin transition region, which we approximate mathematically by a jump discontinuity. We quantify the contributions of electromigration and charge diffusion fluxes, which provide mechanistic insights into the dependence of charging timescale and capacitance on pore size. We develop a modified transmission circuit model that captures the effect of arbitrary pore size and demonstrate that a time-dependent transition-region resistor needs to be included in the circuit. We also derive phenomenological expressions for average effective capacitance and charging timescale as a function of pore-size distribution. We show that the capacitance and charging timescale increase with smaller average pore sizes and with smaller polydispersity, resulting in a gain of energy density at a constant power density. Overall, our results advance the mechanistic understanding of electrical-double-layer charging.

Applicability of Different Double-Layer Models for the Performance Assessment of the Capacitive Energy Extraction Based on Double Layer Expansion (CDLE) Technique

Capacitive energy extraction based on double layer expansion (CDLE) is a renewable method of harvesting energy from the salinity difference between seawater and freshwater. It is based on the change in properties of the electric double layer (EDL) formed at the electrode surface when the concentration of the solution is changed. Many theoretical models have been developed to describe the structural and thermodynamic properties of the EDL at equilibrium, e.g., the Gouy–Chapman–Stern (GCS), Modified Poisson–Boltzmann–Stern (MPBS), modified Donnan (mD) and improved modified Donnan (i-mD) models. To evaluate the applicability of these models, especially the rationality and the physical interpretation of the parameters that were used in these models, a series of single-pass and full-cycle experiments were performed. The experimental results were compared with the numerical simulations of different EDL models. The analysis suggested that, with optimized parameters, all the EDL models we examined can well explain the equilibrium charge–voltage relation of the single-pass experiment. The GCS and MPBS models involve, however, the use of physically unreasonable parameter values. By comparison, the i-mD model is the most recommended one because of its accuracy in the results and the meaning of the parameters. Nonetheless, the i-mD model alone failed to simulate the energy production of the full-cycle CDLE experiments. Future research regarding the i-mD model is required to understand the process of the CDLE technique better.

A Combined Chemical-Electrochemical Process to Capture CO2 and Produce Hydrogen and Electricity

Several carbon sequestration technologies have been proposed to utilize carbon dioxide (CO2) to produce energy and chemical compounds. However, feasible technologies have not been adopted due to the low efficiency conversion rate and high-energy requirements. Process intensification increases the process productivity and efficiency by combining chemical reactions and separation operations. In this work, we present a model of a chemical-electrochemical cyclical process that can capture carbon dioxide as a bicarbonate salt. The proposed process also produces hydrogen and electrical energy. Carbon capture is enhanced by the reaction at the cathode that displaces the equilibrium into bicarbonate production. Literature data show that the cyclic process can produce stable operation for long times by preserving ionic balance using a suitable ionic membrane that regulates ionic flows between the two half-cells. Numerical simulations have validated the proof of concept. The proposed process could serve as a novel CO2 sequestration technology while producing electrical energy and hydrogen.

Transmission Line Circuit and Equation for an Electrolyte-Filled Pore of Finite Length

I discuss the strong link between the transmission line (TL) equation and the TL circuit model for the charging of an electrolyte-filled pore of finite length. In particular, I show how Robin and Neumann boundary conditions to the TL equation, proposed by others on physical grounds, also emerge in the TL circuit subject to a stepwise potential. The pore relaxes with a timescale τ, an expression for which consistently follows from the TL circuit, TL equation, and from the pore's known impedance. An approximation to τ explains the numerically determined relaxation time of the stack-electrode model of Lian et al. [Phys. Rev. Lett. 124, 076001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.076001].

Modulating Interfacial Energy Dissipation via Potential-Controlled Ion Trapping

As a metal (gold) surface at a given, but variable potential slides past a dielectric (mica) surface at a fixed charge, across aqueous salt solutions, two distinct dissipation regimes may be identified. In regime I, when the gold potential is such that counterions are expelled from between the surfaces, which then come to adhesive contact, the frictional dissipation is high, with coefficient of friction μ ≈ 0.8-0.9. In regime II, when hydrated counterions are trapped between the compressed surfaces, hydration lubrication is active and friction is much lower, μ = 0.05 ± 0.03. Moreover, the dissipation regime as the surfaces contact is largely retained even when the metal potential changes to the other regime, attributed to the slow kinetics of counterion expulsion from or penetration into the subnanometer intersurface gap. Our results indicate how frictional dissipation between such a conducting/nonconducting couple may be modulated by the potential applied to the metal.

Dynamics and Model Research on the Electrosorption by Activated Carbon Fiber Electrodes

Electrosorption is a new emerging technology for micro-polluted water treatment. To gain a more accurate understanding of the mass and charge transfer process of electrosorption, the electrosorption performance of activated carbon fiber (ACF) electrodes with various concentrations was studied. In this paper, quasi-first-order and quasi-second-order dynamic equations, and an intra-particle diffusion equation were used to describe the electrosorption behaviors. It is believed that the electrosorption process is dominated by physical adsorption for ACF material, and the most important rate control steps in this process are intra-diffusion and electromigration steps. Based on the experimental results and modified Donnan model theory, a considerable electrosorption dynamic model which considered the influence of physical adsorption and the intra-diffusion resistance was proposed. This model quantitatively described the salt adsorption and charge storage in the ACF electrode and can fit the experimental data well.

Ionic Layering and Overcharging in Electrical Double Layers in a Poisson-Boltzmann Model

Electrical double layers (EDLs) play a significant role in a broad range of physical phenomena related to colloidal stability, diffuse-charge dynamics, electrokinetics, and energy storage applications. Recently, it has been suggested that for large ion sizes or multivalent electrolytes, ions can arrange in a layered structure inside the EDLs. However, the widely used Poisson-Boltzmann models for EDLs are unable to capture the details of ion concentration oscillations and the effect of electrolyte valence on such oscillations. Here, by treating a pair of ions as hard spheres below the distance of closest approach and as point charges otherwise, we are able to predict ionic layering without any additional parameters or boundary conditions while still being compatible with the Poisson-Boltzmann framework. Depending on the combination of ion valence, size, and concentration, our model reveals a structured EDL with spatially oscillating ion concentrations. We report the dependence of critical ion concentration, i.e., the ion concentration above which the oscillations are observed, on the counter-ion valence and the ion size. More importantly, our model displays quantitative agreement with the results of computationally intensive models of the EDL. Finally, we analyze the nonequilibrium problem of EDL charging and demonstrate that ionic layering increases the total charge storage capacity and the charging timescale.

Exploring the Function of Ion-Exchange Membrane in Membrane Capacitive Deionization via a Fully Coupled Two-Dimensional Process Model

In the arid west, the freshwater supply of many communities is limited, leading to increased interest in tapping brackish water resources. Although reverse osmosis is the most common technology to upgrade saline waters, there is also interest in developing and improving alternative technologies. Here we focus on membrane capacitive deionization (MCDI), which has attracted broad attention as a portable and energy-efficient desalination technology. In this study, a fully coupled two-dimensional MCDI process model capable of capturing transient ion transport and adsorption behaviors was developed to explore the function of the ion-exchange membrane (IEM) and detect MCDI influencing factors via sensitivity analysis. The IEM enhanced desalination by improving the counter-ions’ flux and increased adsorption in electrodes by encouraging retention of ions in electrode macropores. An optimized cycle time was proposed with maximal salt removal efficiency. The usage of the IEM, high applied voltage, and low flow rate were discovered to enhance this maximal salt removal efficiency. IEM properties including water uptake volume fraction, membrane thickness, and fixed charge density had a marginal impact on cycle time and salt removal efficiency within certain limits, while increasing cell length and electrode thickness and decreasing channel thickness and dispersivity significantly improved overall performance.

Charging Dynamics of Overlapping Double Layers in a Cylindrical Nanopore

The charging of electrical double layers inside a cylindrical pore has applications to supercapacitors, batteries, desalination and biosensors. The charging dynamics in the limit of thin double layers, i.e., when the double layer thickness is much smaller than the pore radius, is commonly described using an effective RC transmission line circuit. Here, we perform direct numerical simulations (DNS) of the Poisson-Nernst-Planck equations to study the double layer charging for the scenario of overlapping double layers, i.e., when the double layer thickness is comparable to the pore radius. We develop an analytical model that accurately predicts the results of DNS. Also, we construct a modified effective circuit for the overlapping double layer limit, and find that the modified circuit is identical to the RC transmission line but with different values and physical interpretation of the capacitive and resistive elements. In particular, the effective surface potential is reduced, the capacitor represents a volumetric current source, and the charging timescale is weakly dependent on the ratio of the pore radius and the double layer thickness.

Ions in an AC Electric Field: Strong Long-Range Repulsion between Oppositely Charged Surfaces

Two oppositely charged surfaces separated by a dielectric medium attract each other. In contrast we observe a strong repulsion between two plates of a capacitor that is filled with an aqueous electrolyte upon application of an alternating potential difference between the plates. This long-range force increases with the ratio of diffusion coefficients of the ions in the medium and reaches a steady state after a few minutes, which is much larger than the millisecond timescale of diffusion across the narrow gap. The repulsive force, an order of magnitude stronger than the electrostatic attraction observed in the same setup in air, results from the increase in osmotic pressure as a consequence of the field-induced excess of cations and anions due to lateral transport from adjacent reservoirs.