Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging

Electric field induced associations in the double layer of salt-in-ionic-liquid electrolytes

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However, at large negative voltages, which are strong enough to break the alkali metal cation-anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes more aggregated while screening the electrode charge from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements.

Elucidating the Mechanism of Electro-Adsorption on Electrically Conductive Ultrafiltration Membranes via Modified Poisson-Boltzmann Equation

Electrically conductive membranes (ECMs) were prepared by coating porous ethylenediamine-modified polyacrylonitrile (PAN-EDA) UF membranes with an ultrathin layer of platinum (Pt) nanoparticles through magnetron sputtering. These ECMs were used in electrofiltration to study the removal of brilliant blue dye from an aqueous solution under positive electrical potentials (0-2.5 V). Negative electrical potentials (-1.0--2.5 V) were also investigated to regenerate the membrane by desorbing the dye from the ECM surface. At +0 V, the EC PAN-EDA membrane adsorbed the dye due to its intrinsic positive charge. Application of -2.0 V resulted in a maximum of 39% desorption of the dye. A modified Poisson-Boltzmann (MPB) model showed that -2.0 V created a repulsive force within the first 24 nm of the membrane matrix, which had a minimal effect on dye ions adsorbed deeper within the membrane, thus limiting the electro-desorption efficiency to 39%. Moreover, increasing positive potentials from +0.5 V to +2.5 V led to increased dye electro-adsorption by 9.5 times, from 132 mg/m2 to 1112 mg/m2 at pH 8 (equivalent to the membrane's isoelectric point). The MBP simulations demonstrated that increasing electro-adsorption loadings are related to increasing attractive force, indicating electro-adsorption induced by attractive force is the dominant mechanism and the role of other mechanisms (e.g., electrochemical oxidation) is excluded. At pH 5, electro-adsorption further increased to 1390 mg/m2, likely due to the additional positive charge of the membrane (zeta potential = 9.2 mV) compared to pH 8. At pH 8, complete desorption of the dye from the ECM surface was achieved with a significant repulsive force at -2.0 V. However, as pH decreased from 8 to 5, the desorption efficiency decreased by 3.9% due to the membrane's positive charge. These findings help elucidate the mechanisms of electro-adsorption and desorption on ECMs using dye as a model for organic compounds like humic acids.

Single-Particle Imaging Reveals the Electrical Double-Layer Modulated Ion Dynamics at Crowded Interface

The dynamics of ion transport at the interface is the critical factor for determining the performance of an electrochemical energy storage device. While practical applications are realized in concentrated electrolytes and nanopores, there is a limited understanding of their ion dynamic features. Herein, we studied the interfacial ion dynamics in room-temperature ionic liquids by transient single-particle imaging with microsecond-scale resolution. We observed slowed-down dynamics at lower potential while acceleration was observed at higher potential. Combined with simulation, we found that the microstructure evolution of the electric double layer (EDL) results in potential-dependent kinetics. Then, we established a correspondence between the ion dynamics and interfacial ion composition. Besides, the ordered ion orientation within EDL is also an essential factor for accelerating interfacial ion transport. These results inspire us with a new possibility to optimize electrochemical energy storage through the good control of the rational design of the interfacial ion structures.

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.

Diffusioosmotic flow reversals due to ion-ion electrostatic correlations

Existing theories of diffusioosmosis have neglected ion-ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion-ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion-ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. The mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.

Application of the symmetric Poisson-Boltzmann theory to a model colloidal mixture

A symmetric Poisson-Boltzmann theory is used to analyse the structure of a primitive model colloidal system which contains either 4 or 6 components. The approach symmetrizes the pair distribution function gij(r) between two asymmetric charged species with respect to an interchange of the indices. Good agreement is found with molecular dynamics simulation structural properties when the exclusion volume term is modelled by the Percus-Yevick uncharged hard sphere radial distribution function.

Electrohydrodynamics of diffuse porous colloids

The present article deals with the electrohydrodynamic motion of diffuse porous particles governed by an applied DC electric field. The spatial distribution of monomers as well as the charge distribution across the particle are considered to follow sigmoidal distribution involving decay length. Such a parameter measures the degree of inhomogeneity of the monomer distribution across the particle. The diffuse porous particles resemble several colloidal entities which are often seen in the environment as well as in biological and pharmaceutical industries. Considering the impact of bulk pH and ion steric effects, we modelled the electrohydrodynamics of such porous particulates based on the modified Boltzmann distribution for the spatial distribution of electrolyte ions and the Poisson equation for electric potential as well as the conservation of mass and momentum principles. We adopt regular perturbation analysis with weak field assumption and the perturbed equations are solved numerically to calculate the electrophoretic mobility and neutralization fraction of the particle charge during its motion as well as fluid collection efficiency. We further deduced the closed form relation between the drag force experienced by the charged porous particle and the fluid collection efficiency. In addition to the numerical results, we further derived the closed form analytical results for all the intrinsic parameters indicated above derived within the Debye-Hückel electrostatic framework and homogeneous distribution of monomers within the particle for which the decay length vanishes. The deduced mathematical results as indicated above will be useful to analyze several electrostatic and hydrodynamic features of a wide class of porous particulate and environmental entities.

Electrode process of mobile ions in generating space-charge polarization

Macroscopic dipole moments formed in electrolytic cells influence dielectric properties of the cells, and their magnitudes can be quantified by dielectric spectroscopy. We analyze the dielectric spectra observed for dilute electrolytic cells in low-frequency regions from two perspectives: space-charge polarization and diffuse double layers on the electrodes. The difference between the two polarization phenomena is characterized by the effective dielectric constant and the kinetic parameter introduced in the Poisson-Nernst-Planck model. The analytical results indicate that the generation of space-charge polarization is attributed to the kinetic process of mobile ions replacing solvent molecules on the electrode surface. This is an experimental confirmation of the formation process of macroscopic dipole moment due to space-charge polarization and its practical contribution to the dielectric constant of material.

Understanding the Electrode-Electrolyte Interfaces of Ionic Liquids and Deep Eutectic Solvents

Developing unconventional electrolytes such as ionic liquids (ILs) and deep eutectic solvents (DESs) has led to remarkable advances in electrochemical energy storage and conversion devices. However, the understanding of the electrode-electrolyte interfaces of these electrolytes, specifically the liquid structure and the charge/electron transfer mechanism and rates, is lacking due to the complexity of molecular interactions, the difficulty in studying the buried interfaces with nanometer-scale resolution, and the distribution of the time scales for the various interfacial events. This Feature Article outlines the standing questions in the field, summarizes some of the exciting approaches and results, and discusses our contributions to probing the electrified interfaces by electrochemical impedance spectroscopy (EIS), surface-enhanced Raman spectroscopy (SERS), and neutron reflectivity (NR). The related findings are analyzed within electrical double-layer models to provide a framework for studying ILs, DESs, and, more broadly, the concentrated hydrogen-bonded electrolytes.

Structural Evolution Governs Reversible Heat Generation in Electrical Double Layers

Electrical double layer (EDL) formation determines the reversible heat generation of supercapacitors. While classical theories suggest an exothermic nature, experiments revealed that it can be endothermic, depending on the polarization and electrolyte. Here, we perform constant-potential molecular dynamics simulations and develop a lattice gas model to explore the reversible heat of EDL formation in aqueous and ionic liquid (IL) electrolytes. Our Letter reveals that EDL formation in aqueous electrolytes exhibits endothermicity under negative polarization; it shows new complexity of endothermicity followed by exothermicity in ILs, regardless of electrode polarity. These thermal behaviors are determined by the structural evolution during EDL formation, dominated by adsorbed solvent molecules rather than ions in aqueous electrolytes but governed by "demixing" and "vacancy occupation" phenomena in ILs. This Letter provides new insights into the reversible heat of supercapacitors and presents a theoretical approach to investigating thermal behaviors involving the dynamics of EDLs.

Critical considerations in determining the surface charge of small extracellular vesicles

Small extracellular vesicles (EVs) have emerged as a focal point of EV research due to their significant role in a wide range of physiological and pathological processes within living systems. However, uncertainties about the nature of these vesicles have added considerable complexity to the already difficult task of developing EV-based diagnostics and therapeutics. Whereas small EVs have been shown to be negatively charged, their surface charge has not yet been properly quantified. This gap in knowledge has made it challenging to fully understand the nature of these particles and the way they interact with one another, and with other biological structures like cells. Most published studies have evaluated EV charge by focusing on zeta potential calculated using classical theoretical approaches. However, these approaches tend to underestimate zeta potential at the nanoscale. Moreover, zeta potential alone cannot provide a complete picture of the electrical properties of small EVs since it ignores the effect of ions that bind tightly to the surface of these particles. The absence of validated methods to accurately estimate the actual surface charge (electrical valence) and determine the zeta potential of EVs is a significant knowledge gap, as it limits the development of effective label-free methods for EV isolation and detection. In this study, for the first time, we show how the electrical charge of small EVs can be more accurately determined by accounting for the impact of tightly bound ions. This was accomplished by measuring the electrophoretic mobility of EVs, and then analytically correlating the measured values to their charge in the form of zeta potential and electrical valence. In contrast to the currently used theoretical expressions, the employed analytical method in this study enabled a more accurate estimation of EV surface charge, which will facilitate the development of EV-based diagnostic and therapeutic applications.

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.

Ultra-Scaled Si Nanowire Biosensors for Single DNA Molecule Detection

In this study, we use NEGF quantum transport simulations to study the fundamental detection limit of ultra-scaled Si nanowire FET (NWT) biosensors. A N-doped NWT is found to be more sensitive for negatively charged analytes as explained by the nature of the detection mechanism. Our results predict threshold voltage shifts due to a single-charge analyte of tens to hundreds of mV in air or low-ionic solutions. However, with typical ionic solutions and SAM conditions, the sensitivity rapidly drops to the mV/q range. Our results are then extended to the detection of a single 20-base-long DNA molecule in solution. The impact of front- and/or back-gate biasing on the sensitivity and limit of detection is studied and a signal-to-noise ratio of 10 is predicted. Opportunities and challenges to reach down to single-analyte detection in such systems are also discussed, including the ionic and oxide-solution interface-charge screening and ways to recover unscreened sensitivities.

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.

Elucidation of the pH-Dependent Electric Double Layer Structure at the Silica/Water Interface Using Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy

The silica/water interface is one of the most abundant charged interfaces in natural environments, and the elucidation of the water structure at the silica/water interface is essential. In the present study, we measured the interface-selective vibrational (χ(2)) spectra in the OH stretch region of the silica/water interface in a wide pH range of pH 2.0-12.0 while changing the salt concentration by heterodyne-detected vibrational sum-frequency generation spectroscopy. With the help of singular value decomposition analysis, it is shown that the imaginary part of the χ(2) (Imχ(2)) spectra can be decomposed into the spectra of the diffuse Gouy-Chapman layer (DL) and the compact Stern layer (SL), which enables us to quantitatively analyze the spectra of DL and SL separately. The salt-concentration dependence of the DL spectra at different pH values is analyzed using the modified Gouy-Chapman theory, and the pH-dependent surface charge density and the pKa value (4.8 ± 0.2) of the silica/water interface are evaluated. Furthermore, it is found that the pH-dependent change of the SL spectra is quantitatively explained by three spectral components that represent the three characteristic water species appearing in different pH regions in SL. The quantitative understanding obtained from the analysis of each spectral component in the Imχ(2) spectra provides a clear molecular-level picture of the electric double layer at the silica/water interface.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

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.

Galilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry

In this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e., either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume Ω, which is divided into Ω+ and Ω- by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Ω+,S,Ω-). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle, and particular care is taken in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.

Physicochemical Modeling of Electrochemical Impedance in Solid-State Supercapacitors

Solid-state supercapacitors (SSCs) consist of porous carbon electrodes and gel-polymer electrolytes and are used in novel energy storage applications. The current study aims to simulate the impedance of SSCs using a clearly defined equivalent circuit (EC) model with the ultimate goal of improving their performance. To this end, a conventional mathematical and a physicochemical model were adapted. The impedance was measured by electrochemical impedance spectroscopy (EIS). An EC consisting of electrical elements was introduced for each modeling approach. The mathematical model was purely based on a best-fit method and utilized an EC with intuitive elements. In contrast, the physicochemical model was motivated by advanced theories and allowed meaningful associations with properties at the electrode, the electrolyte, and their interface. The physicochemical model showed a higher approximation ability (relative error of 3.7%) due to the interface impedance integration in a more complex circuit design. However, this model required more modeling and optimization effort. Moreover, the fitted parameters differed from the analytically calculated ones due to uncertainties in the SSC's microscale configuration, which need further investigations. Nevertheless, the results show that the proposed physicochemical model is promising in simulating EIS data of SSCs with the additional advantage of utilizing well-reasoned property-based EC elements.

Effective Capacitance from Equivalent Electrical Circuit as a Tool for Monitoring Non-Adherent Cell Suspensions at Low Frequencies

Analyzing the electrical double layer (EDL) in electrical impedance spectroscopy (EIS) measurement at low frequencies remains a challenging task for sensing purposes. In this work, we propose two approaches to deal with the EDL in measuring impedance for particles and non-adherent cells in an electrolytic suspension. The first approach is a simple procedure to compute a normalized electrical impedance spectrum named dispersed medium index (DMi). The second is the EIS modeling through an equivalent electric circuit based on the so-called effective capacitance (Cef), which unifies the EDL phenomena. Firstly, as an experiment under controlled conditions, we examine polymer particles of 6, 15, and 48 μm in diameter suspended in a 0.9% sodium chloride solution. Subsequently, we used K-562 cells and leukocytes suspended in a culture medium (RPMI-1640 supplemented) for a biological assay. As the main result, the DMi is a function of the particle concentration. In addition, it shows a tendency with the particle size; regardless, it is limited to a volume fraction of 0.03 × 10−4 to 58 × 10−4. The DMi is not significantly different between K-562 cells and leukocytes for most concentrations. On the other hand, the Cef exhibits high applicability to retrieve a function that describes the concentration for each particle size, the K-562 cells, and leukocytes. The Cef also shows a tendency with the particle size without limitation within the range tested, and it allows distinction between the K-562 and leukocytes in the 25 cells/µL to 400 cells/µL range. We achieved a simple method for determining an Cef by unifying the parameters of an equivalent electrical circuit from data obtained with a conventional potentiostat. This simple approach is affordable for characterizing the population of non-adherent cells suspended in a cell culture medium.

Simulation Study of Electric Double-Layer Capacitance of Ordered Carbon Electrodes

Supercapacitors are electrochemical energy storage devices having high capacitance, high power density, long cycle life, low cost, easy maintenance, and negligible environmental pollution. The formation of an electric double layer at the electrode-electrolyte interface is mostly responsible for supercapacitors' energy storage. The simulation study of equilibrium electric double-layer capacitance (EDLC) in 3D arranged mesoporous carbon electrodes with a simple cubic morphology and interdigitated electrodes has been done. Continuum theory has been utilized to study the underlying processes involved in EDLC. Interfacial polarization and ion crowding depend on the electrode's critical thickness. Porosity increases the capacitance due to the increase in the electrode surface area. The diffuse-layer specific capacitance of ordered mesoporous carbon electrodes in a (C₂H₅)₄NBF₄/propylene carbonate organic electrolyte is in the range of 3.2-13.3 μF cm^-2, varying according to the electrode thickness. The Stern-layer specific capacitance is 167.6 μF cm^-2, and total equilibrium EDLC is in the range of 3.1-12.3 μF cm^-2. The effect of the electric field at the electrode-electrolyte interface on reducing electrolyte permittivity has also been discussed. The EDLC of carbonized interdigitated electrodes is analyzed in a 6 M KOH electrolyte. The diffuse-layer specific capacitance ranges from 118.7 to 352.0 μF cm^-2 depending on the width of the interdigitated electrodes. The Stern-layer specific capacitance is 91.2 μF cm^-2, and the total EDLC value is 51.6-72.4 μF cm^-2. The modeling and simulation approach can be applied to different mesoporous electrodes by varying the supercapacitor component's parameters and geometry.

Local Volume Conservation in Concentrated Electrolytes Is Governing Charge Transport in Electric Fields

While ion transport processes in concentrated electrolytes, e.g., based on ionic liquids (IL), are a subject of intense research, the role of conservation laws and reference frames is still a matter of debate. Employing electrophoretic NMR, we show that momentum conservation, a typical prerequisite in molecular dynamics (MD) simulations, is not governing ion transport. Involving density measurements to determine molar volumes of distinct ion species, we propose that conservation of local molar species volumes is the governing constraint for ion transport. The experimentally quantified net volume flux is found to be zero, implying a nonzero local momentum flux, as tested in pure ILs and IL-based electrolytes for a broad variety of concentrations and chemical compositions. This constraint is consistent with incompressibility, but not with a local application of momentum conservation. The constraint affects the calculation of transference numbers as well as comparisons of MD results to experimental findings.

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.

Gelation, Clustering and Crowding in the Electrical Double Layer of Ionic Liquids

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible Cayley tree clusters and a percolating ionic network (gel). Here we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.

Ionic-size dependent electroosmotic flow in ion-selective biomimetic nanochannels

Electrokinetic phenomena, especially electroosmosis in ion-selective environments, play a key role in many systems, from ion-selective nanopores to cellular processes. In this paper, the impact of ionic size on the electroosmotic flow through an ion-selective soft slit nanochannel is analytically studied. Meanwhile, the modified Poisson-Boltzmann and the modified Navier-Stokes equations were used for modeling the electrostatics and the electrohydrodynamics of the problem, respectively, and the derived equations were solved by linearizing method. The results reveal the importance of considering the effect of ionic size in the calculation, as the steric effects, especially at high charge densities of polyelectrolytes (PELs), dramatically alter both the ions arrangement and the electric potential; and amplify the electroosmotic flow. Considering Debye-Huckel parameters of 4 and 10 for the electrolyte layer and the PEL, respectively, we demonstrate that the dimensionless electroosmotic velocity in a soft nanochannel having a dimensionless soft layer thickness of 0.2, from 3.2 by ignoring the steric effect, can reach the value of 6 by considering the steric effect of ν=0.3.

ELECTRODE: An electrochemistry package for atomistic simulations

Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

Ionic Liquid Solutions Show Anomalous Crowding Behavior at an Electrode Surface

X-ray reflectivity was used to study the several-nanometer-thick "crowded" layers that form at the interfaces between a planar electrode and concentrated solutions of ionic liquids. The ionic liquid [P_14,6,6,6]⁺[NTf₂]^- was dissolved in either strongly polar propylene carbonate or weakly polar dimethyl carbonate. In the range of 19-100 vol % ionic liquid, between working electrode potentials +2 and +2.75 V, uniform 2-7 nm thick interfacial layers were observed. These layers are not pure anions but contain three to five times as many anions as cations and about the same percentage of solvent as the bulk solution. On the other side of the layer, the density is that of the bulk solution. These features are inconsistent with a picture of the crowded layer as a region of pure, close-packed counterions. Not only the layer thickness but also the charge density decrease with increasing dilution at any given applied voltage. This appears to indicate, counterintuitively, that a thinner layer with lower net charge density will screen an electric field as effectively as a thicker layer with higher charge density.

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.

Discrete modeling of ionic space charge zones in solids

The discrete model of space charge zones in solids reveals and remedies a variety of problems with the classic continuous Gouy-Chapman solution that occur for pronounced space charge potentials. Besides inherent problems of internal consistency, it is essentially the extremely steep profile close to the interface which makes this continuum approach questionable. Not only is quasi-1D discrete modeling a sensible approach for large space charge effects, it can also favorably be combined with the continuum description. A particularly useful application is the explicit implementation of crystallographic details and non-idealities close to the interface. This enables us to consider elastic, structural or saturation effects as well as permittivity variations in a simple but realistic way. We address details of the charge carrier profiles, but also overall properties such as space charge capacitance and space charge resistance. In the latter case the difference in the total charge (at identical concentration) is of importance, in the first case it is the inherent difference in the centroid of charge (at identical total charge) that is remarkable. The model is equally applicable for ionic charge carriers and small polarons.

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.

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.

The Role of Energy Scales for the Structure of Ionic Liquids at Electrified Interfaces: A Theory-Based Approach

Ionic liquids offer unique bulk and interfacial characteristics as battery electrolytes. Our continuum approach naturally describes the electrolyte on a macroscale. An integral formulation for the molecular repulsion, which can be quantitatively determined by both experimental and theoretical methods, models the electrolyte on the nanoscale. In this article, we perform a systematic series expansion of this integral formulation, derive a description of chemical potentials in terms of higher-order concentration gradients, and rationalize the appearance of fourth-order derivative operators in modified Poisson equations, as recently proposed in this context. In this way, we formulate a rigorous multiscale methodology from atomistic quantum chemistry calculations to phenomenological continuum models. We apply our generalized framework to ionic liquids near electrified interfaces and perform analytical asymptotic analysis. Three energy scales describing electrostatic forces between ions, molecular repulsion, and thermal motion determine the shape and width of the long-ranging charged double layer. We classify the charge screening mechanisms dependent on the system parameters as dielectricity, ion size, interaction strength, and temperature. We find that the charge density of electrochemical double layers in ionic liquids either decays exponentially, for negligible molecular repulsion, or oscillates continuously. Charge ordering across several ion diameters occurs if the repulsion between molecules is comparable with thermal energy and Coulomb interactions. Eventually, phase separation of the bulk electrolyte into ionic layers emerges once the molecular repulsion becomes dominant. Our framework predicts the exact phase boundaries among these three phases as a function of temperature, dielectricity, and ion size.

Combined electromechanically driven pulsating flow of nonlinear viscoelastic fluids in narrow confinements

Controlled microscale transport is at the core of many scientific and technological advancements, including medical diagnostics, separation of biomolecules, etc., and often involves complex fluids. One of the challenges in this regard is to actuate flows at small scales in an energy efficient manner, given the strong viscous forces opposing fluid motion. We try to address this issue here by probing a combined time-periodic pressure and electrokinetically driven flow of a viscoelastic fluid obeying the simplified linear Phan-Thien-Tanner model, using numerical as well as asymptotic tools, in view of the fact that oscillatory fields are less energy intensive. We establish that the interplay between oscillatory electrical and mechanical forces can lead to complex temporal mass flow rate variations with short-term bursts and peaks in the flow rate. We further demonstrate that an oscillatory pressure gradient or an electric field, in tandem with another steady actuating force can indeed change the net throughput significantly-a paradigm that is not realized in Newtonian or other simpler polymeric liquids. Our results reveal that the extent of augmentation in the flow rate strongly depends on the frequency of the imposed actuating forces along with their waveforms. We also evaluate the streaming potential resulting from an oscillatory pressure-driven flow and illustrate that akin to the volume throughput, the streaming potential also shows complex temporal variations, while its time average gets augmented in the presence of a time-periodic pressure gradient in a nonlinear viscoelastic medium.

Electric Potential of Citrate-Capped Gold Nanoparticles Is Affected by Poly(allylamine hydrochloride) and Salt Concentration

The structure near polyelectrolyte-coated gold nanoparticles (AuNPs) is of significant interest because of the increased use of AuNPs in technological applications and the possibility that the acquisition of polyelectrolytes can lead to novel chemistry in downstream environments. We use all-atom molecular dynamics (MD) simulations to reveal the electric potential around citrate-capped gold nanoparticles (cit-AuNPs) and poly(allylamine hydrochloride) (PAH)-wrapped cit-AuNP (PAH-AuNP). We focus on the effects of the overall ionic strength and the shape of the electric potential. The ionic number distributions for both cit-AuNP and PAH-AuNP are calculated using MD simulations at varying salt concentrations (0, 0.001, 0.005, 0.01, 0.05, 0.1, and 0.2 M NaCl). The net charge distribution (Z(r)) around the nanoparticle is determined from the ionic number distribution observed in the simulations and allows for the calculation of the electric potential (ϕ(r)). We find that the magnitude of ϕ(r) decreases with increasing salt concentration and upon wrapping by PAH. Using a hydrodynamic radius (R_H) estimated from the literature and fits to the Debye-Hü̈ckel expression, we found and report the ζ potential for both cit-AuNP and PAH-AuNP at varying salt concentrations. For example, at 0.001 M NaCl, MD simulations suggest that ζ = -25.5 mV for cit-AuNP. Upon wrapping of cit-AuNP by one PAH chain, the resulting PAH-AuNP exhibits a reduced ζ potential (ζ = -8.6 mV). We also compare our MD simulation results for ϕ(r) to the classic Poisson-Boltzmann equation (PBE) approximation and the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We find agreement with the limiting regimes─with respect to surface charge, salt concentration and particle size─in which the assumptions of the PBE and DLVO theory are known to be satisfied.

Structural Forces in Ionic Liquids: The Role of Ionic Size Asymmetry

Ionic liquids (ILs) are charged fluids composed of anions and cations of different size and shape. The ordering of charge and density in ILs confined between charged interfaces underlies numerous applications of IL electrolytes. Here, we analyze the screening behavior and the resulting structural forces of a representative IL confined between two charge-varied plates. Using both molecular dynamics simulations and a continuum theory, we contrast the screening features of a more-realistic asymmetric system and a less-realistic symmetric one. The ionic size asymmetry plays a nontrivial role in charge screening, affecting both the ionic density profiles and the disjoining pressure distance dependence. Ionic systems with size asymmetry are stronger coupled systems, and this manifests itself both in their response to the electrode polarization and spontaneous structure formation at the interface. Analytical expressions for decay lengths of the disjoining pressure are obtained in agreement with the pressure profiles computed from molecular dynamics simulations.

Effects of Frequency and Joule Heating on Height Rise between Parallel Electrodes with AC Electric Fields

High strength AC electric fields generate a body force on a dielectric medium confined between two electrodes. The body forces are due to two factors. First is the variation in permittivity across an interface such as liquid-air present between the electrodes. The second is a change in the dielectric property of the medium due to a variation in the thermodynamic properties such as temperature. The height rise of a dielectric medium between two electrodes is one of the consequences of these electrical body forces and is used here as a comparatively simple way to study these forces. In an aqueous solution with finite conductivity, the effects of the frequency of the supplied voltage source and the temperature change due to Joule heating on height rise have never been studied in this context. This study focuses on systems where the contributions of surface forces are negligible and highlights the interplay between solution conductivity, applied electric field, and the solution height/temperature behavior. Using a generic thermodynamic model for an aqueous solution under the application of an alternating current electric field, it is shown that for low conductivity solutions the resulting temperature and height rise change weakly with the applied field frequency and strongly with the applied electric field. For higher conductivity solutions, the behavior becomes more complex with respect to the electric field strength. As compared to Pellat's original model, the height rise varies from strongly suppressed to enhanced.

Localized X-Ray Photoelectron Impedance Spectroscopy (LoXPIS) for Tapping into Charge-Dynamics of Ionic-Liquid Electrolytes within Energy Storage Devices

Many electrochemical devices are based on the fundamental process of ion migration and accumulation on surfaces. Complex interplay of molecular properties of ions and device dimensions control the entire process...

Structural features and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions under low-salt conditions

Self-consistent field theory is used to systematically study the characteristics and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions for salt-free and low salt concentration systems.

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.