Electrolytes in conducting nanopores: Revisiting constant charge and constant potential simulations

Simulating electrolyte-electrode systems poses challenges due to the need to account for the electrode's response to ion movements in order to maintain a constant electrode potential, which slows down the simulations. To circumvent this, computationally more efficient constant charge (CC) simulations are sometimes employed. However, the accuracy of CC simulations in capturing the behavior of electrolyte-electrode systems remains unclear, especially for microporous electrodes. Herein, we consider electrolyte-filled slit nanopores and systematically analyze the in-pore ion structure and diffusivity using CC and constant potential simulations. Our results indicate that CC simulations provide comparable pore occupancies at high bulk ion densities and for highly charged pores, but they fail to accurately describe the ion structure and dynamics, particularly in quasi-2D (single-layer) pores and at low ion densities. We attribute these results to the superionic state emerging in conducting nanoconfinement and its interplay with excluded volume interactions.

Modeling of Nanomaterials for Supercapacitors: Beyond Carbon Electrodes

Capacitive storage devices allow for fast charge and discharge cycles, making them the perfect complements to batteries for high power applications. Many materials display interesting capacitive properties when they are put in contact with ionic solutions despite their very different structures and (surface) reactivity. Among them, nanocarbons are the most important for practical applications, but many nanomaterials have recently emerged, such as conductive metal-organic frameworks, 2D materials, and a wide variety of metal oxides. These heterogeneous and complex electrode materials are difficult to model with conventional approaches. However, the development of computational methods, the incorporation of machine learning techniques, and the increasing power in high performance computing now allow us to tackle these types of systems. In this Review, we summarize the current efforts in this direction. We show that depending on the nature of the materials and of the charging mechanisms, different methods, or combinations of them, can provide desirable atomic-scale insight on the interactions at play. We mainly focus on two important aspects: (i) the study of ion adsorption in complex nanoporous materials, which require the extension of constant potential molecular dynamics to multicomponent systems, and (ii) the characterization of Faradaic processes in pseudocapacitors, that involves the use of electronic structure-based methods. We also discuss how recently developed simulation methods will allow bridges to be made between double-layer capacitors and pseudocapacitors for future high power electricity storage devices.

Water, Not Salt, Causes Most of the Seebeck Effect of Nonisothermal Aqueous Electrolytes

A temperature difference between two electrolyte-immersed electrodes often yields a voltage Δψ between them. This electrolyte Seebeck effect is usually explained by cations and anions flowing differently in thermal gradients. However, using molecular simulations, we found almost the same Δψ for cells filled with pure water as with aqueous alkali halides. Water layering and orientation near polarizable electrodes cause a large temperature-dependent potential drop χ there. The difference in χ of hot and cold electrodes captures most of the thermovoltage, Δψ≈χ_{hot}-χ_{cold}.

Influence of surface nanostructure-induced innermost ion structuring on capacitance of carbon/ionic liquid double layers

Ionic liquids have drawn great interest as electrolytes for energy storage applications in which they form characteristic electrical double layers at electrode interfaces. For ionic liquids at carbon electrode interfaces, their double layers are subject to nanoscale structuring of the electrode surface, involving altered ion structure and interactions that significantly influence the double layer capacitance. In this regard, we investigate the modulation of ionic liquid double layers by electrode surface roughness and the resulting effects on the ion structure, interaction, and capacitance. We performed fixed voltage molecular dynamics simulations to compute the differential capacitance profiles for the ionic liquids [BMIm+][TFSI-] and [BMIm+][FSI-] at model carbon electrode interfaces with the surface channel width at subnanometer and nanometer scales. We find that both [BMIm+][TFSI-] and [BMIm+][FSI-] exhibit enhanced differential capacitance for the electrode surface with a subnanometer channel width relative to the flat graphene surface, but the most pronounced enhancements for these two ionic liquids unexpectedly appear at different applied potential regimes. For [BMIm+][TFSI-], the nanostructured electrode shows significant enhancement of capacitance at high positive potential. For [BMIm+][FSI-], on the other hand, this enhancement is small at positive polarization but noticeable at low negative potential. We demonstrate that differences in these capacitance trends is due to differences in ion correlation that arise from a steric constraint of nanostructured electrode surface on the voltage-mediated restructuring of ions closest to the electrode interface. For example, the TFSI- and FSI- anions tend to structure with their charged and nonpolar groups in contact with the positive electrode surface when the constraint on these close-contact anions is relaxed. This anion structuring largely retains the cation association near the nanostructured electrode, resulting in only a slight increase in capacitance at positive polarization. Our simulations highlight the sensitive dependence of the innermost ion structure on the electrode surface nanostructure and applied voltage and the resulting influence on ion correlation and capacitance of ionic liquid double layers.

CONAN─Novel Tool to Create and Analyze Liquids in Confined Space

Modeling of complex liquids at solid surfaces and in confinement is gaining attention due to an increase in computer power and advancement of simulation techniques. Therefore, tools to set up structures and for analysis are needed. In this paper, we present CONAN─a Python code designed to facilitate the study of liquids interacting with solid structures, such as walls or pores. Among other things, the program provides the option to generate a variety of different structures, including carbon walls and nanotubes and their boron nitride analogs, as well as the ability to analyze various structural properties of confined and interfacial liquids. In the case of the ionic liquid 1-butyl-3-methylimidazolium acetate in carbon nanotubes of different sizes, we demonstrate the abilities of our tool. The average density within the confinement highly depends on the carbon nanotube size, and it is generally lower than the density of the bulk liquid. The arrangement of the individual species within the tube also depends on size, with radial layers forming within the tubular confinement. The density is largely increased in the respective layers, while it is drastically reduced between the layers.

Finding Infinities in Nanoconfined Geothermal Electrolyte Static Dielectric Properties and Implications on Ion Adsorption/Pairing

Infinities should naturally occur in the dielectric responses of ionic solutions relevant to many geochemical, energy storage, and electrochemical applications at a strictly zero frequency. Using molecular dynamics simulations cross-referenced with coarse-grained Monte Carlo models, using nanoslit pore models at hydrothermal conditions, and treating confined mobile charges as polarization, we demonstrate the far reaching consequences. The dielectric permittivity profile perpendicular to the slit (ϵ⊥(z)) increases, not decreases, with ionic concentration, unlike in the more widely studied megahertz-to-gigahertz frequency range. In confined electrolytes, the divergences in ϵ⊥(z) correctly describe crossovers between bulk- and surface-dominated dielectric behavior. Nanoconfinement at low ionic concentrations changes monovalent ion energetics by 1-2 kJ/mol, but no dielectric property studied so far is universally correlated to ion adsorption or ion-ion interactions. We caution that infinities signal violation of the "electrical insulator" dielectric assumption.

Phase transitions of ionic fluids in nanoporous electrodes

In this work, we utilise grand canonical Metropolis Monte Carlo simulations, to establish pore-induced freezing of restricted primitive model fluids. A planar pore model is utilised, with walls that are initially neutral, and either non-conducting or perfectly conducting. The phase of the confined electrolyte (solid/fluid) displays an oscillatory dependence on surface separation, in narrow pores. Conditions are chosen so that the bulk is composed of a stable fluid electrolyte. The tendency for the electrolyte to freeze in narrow pores is somewhat stronger in systems with non-conducting walls. We also demonstrate that an applied potential will, above a threshold value, melt a frozen electrolyte. In these cases, the capacitance, as measured by the average surface charge density divided by the applied potential, will be almost vanishing if the applied potential is below this threshold value. We do not see any evidence for a "superionic fluid", which has been hypothesised to generate a strong capacitance in narrow pores, due to an efficient screening of like-charge repulsions by image charges.

Unprecedented energy storage in metal-organic complexes via constitutional isomerism

The essence of any electrochemical system is engraved in its electrical double layer (EDL), and we report its unprecedented reorganization by the structural isomerism of molecules, with a direct consequence on their energy storage capability. Electrochemical and spectroscopic analyses in combination with computational and modelling studies demonstrate that an attractive field-effect due to the molecule's structural-isomerism, in contrast to a repulsive field-effect, spatially screens the ion-ion coulombic repulsions in the EDL and reconfigures the local density of anions. In a laboratory-level prototype supercapacitor, those with β-structural isomerism exhibit nearly 6-times elevated energy storage compared to the state-of-the-art electrodes, by delivering ∼535 F g-1 at 1 A g-1 while maintaining high performance metrics even at a rate as high as 50 A g-1. The elucidation of the decisive role of structural isomerism in reconfiguring the electrified interface represents a major step forward in understanding the electrodics of molecular platforms.

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.

Less Is More: Can Low Quantum Capacitance Boost Capacitive Energy Storage?

We present a theoretical analysis of charge storage in electrochemical capacitors with electrodes based on carbon nanotubes. Using exact analytical solutions supported by Monte Carlo simulations, we show how the limitations of the electron density of states in such low-dimensional electrode materials may help boost the energy stored at increased voltages. While these counterintuitive predictions await experimental verification, they suggest exciting opportunities for enhancing energy storage by rational engineering of the electronic properties of low-dimensional electrodes.

Electric Potential of Ions in Electrode Micropores Deduced from Calorimetry

The internal energy of capacitive porous carbon electrodes was determined experimentally as a function of applied potential in aqueous salt solutions. Both the electrical work and produced heat were measured. The potential dependence of the internal energy is explained in terms of two contributions, namely the field energy of a dielectric layer of water molecules at the surface and the potential energy of ions in the pores. The average electric potential of the ions is deduced, and its dependence on the type of salt suggests that the hydration strength limits how closely ions can approach the surface.

Nanoionics from Biological to Artificial Systems: An Alternative Beyond Nanoelectronics

Ion transport under nanoconfined spaces is a ubiquitous phenomenon in nature and plays an important role in the energy conversion and signal transduction processes of both biological and artificial systems. Unlike the free diffusion in continuum media, anomalous behaviors of ions are often observed in nanostructured systems, which is governed by the complex interplay between various interfacial interactions. Conventionally, nanoionics mainly refers to the study of ion transport in solid-state nanosystems. In this review, to extent this concept is proposed and a new framework to understand the phenomena, mechanism, methodology, and application associated with ion transport at the nanoscale is put forward. Specifically, here nanoionics is summarized into three categories, i.e., biological, artificial, and hybrid, and discussed the characteristics of each system. Compared with nanoelectronics, nanoionics is an emerging research field with many theoretical and practical challenges. With this forward-looking perspective, it is hoped that nanoionics can attract increasing attention and find wide range of applications as nanoelectronics.

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.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.

Origin of Enhanced Performance in Nanoporous Electrical Double Layer Capacitors: Insights on Micropore Structure and Electrolyte Composition from Molecular Simulations

We explore the effect of solvation and micropore structure on the energy storage performance of electrical double layer capacitors using constant potential molecular dynamics simulations of realistically modeled nanoporous carbon electrodes and ionic liquid/organic solvent mixtures. We show that the time-dependent charging profiles of electrodes with larger pores reach the plateau regime faster, while the charging time has a nonmonotonic dependence on ion concentration, mirroring the composition dependence of bulk electrolyte conductivity. When the average pore size of the electrode is similar to or slightly larger than the size of a solvated ion, the solvation enhances ion electrosorption into nanopores by disrupting anion-cation coordination and decreasing the barrier to counterion penetration while blocking the co-ions. In these systems, areal capacitance exhibits a significant nonmonotonic dependence on ion concentration, in which capacitance increases with the introduction of solvent in the concentrated regime followed by a decrease with further dilution. This gives rise to a maximum in capacitance at intermediate dilution levels. When pores are significantly larger than solvated ions, capacitance maximum weakens and eventually disappears. These findings provide novel insights on the combined effect of electrolyte composition and electrode pore size on the charging kinetics and equilibrium behavior of realistically modeled electrical double layer capacitors. Generalization of the approach developed here can facilitate the rational optimization of material properties for electrical double layer capacitor applications.

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.

Specific Ion Effects in Lanthanide-Amphiphile Structures at the Air-Water Interface and Their Implications for Selective Separation

The use of surfactants to attract dissolved ions to water surfaces and interfaces is an essential step in both solvent-based and solvent-free separation processes. We have studied the interactions of lanthanide ions in the aqueous subphase with monolayers of dihexadecyl phosphate at air-water interfaces. With heavier lanthanides (atomic number Z ≥ 65) in the subphase, the floating layer can be compressed to an area/molecule of about half the molecular cross section, indicating bilayer formation. X-ray fluorescence and reflectivity data support this conclusion. In the presence of lighter lanthanides (Z < 65), only monolayers are observed. Subphase-concentration-dependent studies using Er³⁺ (heavier) and Nd³⁺ (lighter) lanthanides show a stepwise progression, with ions attaching to the monolayer only when the solution concentration is >3 × 10^-7 M. Above ∼10^-5 M, bilayers form but only in the presence of the heavier lanthanide. Grazing incidence X-ray diffraction shows evidence of lateral ion-ion correlations in the bilayer structure but not in monolayers. Explicit solvent all-atom molecular dynamics simulations confirm the elevated ion-ion correlation in the bilayer system. This bilayer structure isolates heavier lanthanides but not lighter lanthanides from an aqueous solution and is therefore a potential mechanism for the selective separation of heavier lanthanides.

Molecular dynamics investigation of charging process in polyelectrolyte-based supercapacitors

Supercapacitors are one of the technologically impressive types of energy storage devices that are supposed to fill the gap between chemical batteries and dielectric capacitors in terms of power and energy density. Many kinds of materials have been investigated to be used as supercapacitors' electrolytes to overcome the known limitations of them. The properties of polymer-based electrolytes show a promising way to defeat some of these limitations. In this paper, a simplified model of polymer-based electrolytes between two electrodes is numerically investigated using the Molecular Dynamics simulation. The simulations are conducted for three different Bjerrum lengths and a typical range of applied voltages. The results showed a higher differential capacitance compared to the cases using ionic-liquid electrolytes. Our investigations indicate a rich domain in molecular behaviors of polymer-based electrolytes that should be considered in future supercapacitors.

Metal-Ion Oligomerization Inside Electrified Carbon Micropores and its Effect on Capacitive Charge Storage

Ion adsorption inside electrified carbon micropores is pivotal for the operation of supercapacitors. Depending on the electrolyte, two main mechanisms have been identified so far, the desolvation of ions in solvents and the formation of superionic states in ionic liquids. Here, it is shown that upon confinement inside negatively charged micropores, transition-metal cations dissolved in water associate to form oligomer species. They are identified using in situ X-ray absorption spectroscopy. The cations associate one with each other via hydroxo bridging, forming ionic oligomers under the synergic effect of spatial confinement and Coulombic screening. The oligomers display sluggish dissociation kinetics and accumulate upon cycling, which leads to supercapacitor capacitance fading. They may be dissolved by applying a positive potential, so an intermittent reverse cycling strategy is proposed to periodically evacuate micropores and revivify the capacitance. These results reveal new insights into ion adsorption and structural evolution with their effects on the electrochemical performance, providing guidelines for designing advanced supercapacitors.

Capacitive energy storage in single-file pores: Exactly solvable models and simulations

Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion and water desalination. Exactly solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly solvable, one-dimensional off-lattice model for charging single-file pores. Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, by changing cation-anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, C ∼ u^-2. This dependence follows from hard-core interactions and is not captured by the lattice model.

Electrolyte structure near electrodes with molecular-size roughness

Understanding electrodes' surface morphology influence on ions' distribution is essential for designing supercapacitors with enhanced energy density characteristics. We develop a model for the structure of electrolytes near the rough surface of electrodes. The model describes an effective electrostatic field's increase and associated intensification of ions' spatial separation at the electrode-electrolyte interface. These adsorption-induced local electric and structure properties result in notably increased values and a sharpened form of the differential capacitance dependence on the applied potential. Such capacitance behavior is observed in many published simulations, and its description is beyond the capabilities of the established flat-electrodes theories. The proposed approach could extend the quantitatively verified models providing a new instrument of the electrode surface-parameter optimization for specific electrolytes.

Structural transitions at electrodes, immersed in simple ionic liquid models

We used a recently developed classical Density Functional Theory (DFT) method to study the structures, phase transitions, and electrochemical behaviours of two coarse-grained ionic fluid models, in the presence of a perfectly conducting model electrode. Common to both is that the charge of the cationic component is able to approach the electrode interface more closely than the anion charge. This means that the cations are specifically attracted to the electrode, due to surface polarization effects. Hence, for a positively charged electrode, there is competition at the surface between cations and anions, where the latter are attracted by the positive electrode charge. This generates demixing, for a range of positive voltages, where the two phases are structurally quite different. The surface charge density is also different between the two phases, even at the same potential. The DFT formulation contains an approximate treatment of ion correlations, and surface polarization, where the latter is modelled via screened image interactions. Using a mean-field DFT, where ion correlations are neglected, causes the phase transition to vanish for both models, but there is still a dramatic drop in the differential capacitance as proximal cations are replaced by anions, for increasing surface potentials. While these findings were obtained for relatively crude coarse-grained models, we argue that the findings can also be relevant in "real" systems, where we note that many ionic liquids are composed of a spherically symmetric anion, and a cation that is asymmetric both from a steric and a charge distribution point of view.

High-Performance and High-Voltage Supercapacitors Based on N-Doped Mesoporous Activated Carbon Derived from Dragon Fruit Peels

Designing the mesopore-dominated activated carbon electrodes has witnessed a significant breakthrough in enhancing the electrolyte breakdown voltage and energy density of supercapacitors. Herein, we designed N-doped mesoporous-dominated hierarchical activated carbon (N-dfAC) from the dragon fruit peel, an abundant biomass precursor, under the synergetic effect of KOH as the activating agent and melamine as the dopant. The electrode with the optimum N-doping content (3.4 at. %) exhibits the highest specific capacitance of 427 F g-1 at 5 mA cm-2 and cyclic stability of 123% capacitance retention until 50000 charge-discharge cycles at 500 mA cm-2 in aqueous 6 M KOH electrolytes. We designed a 4 V symmetric coin cell supercapacitor cell, which exhibits a remarkable specific energy and specific power of 112 W h kg-1 and 3214 W kg-1, respectively, in organic electrolytes. The cell also exhibits a significantly higher cycle life (109% capacitance retention) after 5000 GCD cycles at the working voltage of ≥3.5 V than commercial YP-50 AC (∼60% capacitance retention). The larger Debye length of the diffuse ion layer permitted by the mesopores can explain the higher voltage window, and the polar N-doped species in the dfAC enhance capacitance and ion transport. The results endow a new path to design high-capacity and high-working voltage EDLCs from eco-friendly and sustainable biomass materials by properly tuning their pore structures.

Superionic Liquids in Conducting Nanoslits: Insights from Theory and Simulations

Mapping the theory of charging supercapacitors with nanostructured electrodes on known lattice models of statistical physics is an interesting task, aimed at revealing generic features of capacitive energy storage in such systems. The main advantage of this approach is the possibility to obtain analytical solutions that allow new physical insights to be more easily developed. But how general the predictions of such theories could be? How sensitive are they to the choice of the lattice? Herein, we address these questions in relation to our previous description of such systems using the Bethe-lattice approach and Monte Carlo simulations. Remarkably, we find a surprisingly good agreement between the analytical theory and simulations. In addition, we reveal a striking correlation between the ability to store energy and ion ordering inside a pore, suggesting that such ordering can be beneficial for energy storage.

Surface Charge Density in Electrical Double Layer Capacitors with Nanoscale Cathode-Anode Separation

Using a dynamic density functional theory, we study the charging dynamics, the final equilibrium structure, and the energy storage in an electrical double layer capacitor with nanoscale cathode-anode separation in a slit geometry. We derive a simple expression for the surface charge density that naturally separates the effects of the charge polarization due to the ions from those due to the polarization of the dielectric medium and allows a more intuitive understanding of how the ion distribution within the cell affects the surface charge density. We find that charge neutrality in the half-cell does not hold during the dynamic charging process for any cathode-anode separation, and also does not hold at the final equilibrium state for small separations. Therefore, the charge accumulation in the half-cell in general does not equal the surface charge density. The relationships between the surface charge density and the charge accumulation within the half-cell are systematically investigated by tuning the electrolyte concentration, cathode-anode separation, and applied voltage. For high electrolyte concentrations, we observe charge inversion at which the charge accumulation exceeds the surface charge at special values of the separation. In addition, we find that the energy density has a maximum at intermediate electrolyte concentrations for a high applied voltage.

How to speed up ion transport in nanopores

Electrolyte-filled subnanometre pores exhibit exciting physics and play an increasingly important role in science and technology. In supercapacitors, for instance, ultranarrow pores provide excellent capacitive characteristics. However, ions experience difficulties in entering and leaving such pores, which slows down charging and discharging processes. In an earlier work we showed for a simple model that a slow voltage sweep charges ultranarrow pores quicker than an abrupt voltage step. A slowly applied voltage avoids ionic clogging and co-ion trapping—a problem known to occur when the applied potential is varied too quickly—causing sluggish dynamics. Herein, we verify this finding experimentally. Guided by theoretical considerations, we also develop a non-linear voltage sweep and demonstrate, with molecular dynamics simulations, that it can charge a nanopore even faster than the corresponding optimized linear sweep. For discharging we find, with simulations and in experiments, that if we reverse the applied potential and then sweep it to zero, the pores lose their charge much quicker than they do for a short-circuited discharge over their internal resistance. Our findings open up opportunities to greatly accelerate charging and discharging of subnanometre pores without compromising the capacitive characteristics, improving their importance for energy storage, capacitive deionization, and electrochemical heat harvesting.

Narrowing pores filled with an electrolyte usually slows down their charge-discharge dynamics. Here the authors demonstrate through molecular dynamics simulations and experiments with novolac-derived carbon electrodes how non-linear voltage sweeps can accelerate charging and discharging of subnanometer pores.

Selective adsorption of monovalent cations in porous electrodes

To clarify the mechanisms involved in the electrochemical adsorption of ions of aqueous electrolytes in porous electrodes, we performed molecular dynamics simulations of systems composed of porous carbon electrodes with various pore sizes and aqueous solutions containing a Li⁺, Na⁺, K⁺, or Cs⁺ cation and a Cl^- anion. The free energy barrier preventing the cation from entering the pore in the electrode and the hydration structure around the cation were calculated for each cation species and each pore size of the electrode. As the cation moved toward the porous electrode from the bulk electrolyte, rearrangement of the hydration network occurred. The energetic cost of this rearrangement of the hydration network was identified as the cause of the free energy barrier. We estimated the likelihood of cations becoming adsorbed by the porous electrode for different pore sizes and applied voltages and found that the specificity of the magnitude of the free energy barrier for different ions is determined by two factors: ion size (Li⁺ < Na⁺ < K⁺ < Cs⁺) and the strength of hydration (Li⁺ > Na⁺ > K⁺ > Cs⁺). With no or a low applied voltage, the ion size dominates the selectivity, and with a high applied voltage, the strength of hydration dominates, although there were some exceptions. The ion specificity of the free energy barrier could be utilized in the selective adsorption of ions from multi-component electrolytes by controlling the pore size of the electrode and the applied voltage.

Structural and thermodynamic properties of the electrical double layer in slit nanopores: A Monte Carlo study

Grand canonical Monte Carlo (GCMC) simulation techniques at a constant electrode-electrolyte potential drop are employed to study the differential capacitance of a planar electric double layer in slit nanopores. According to the technique, a single randomly selected ion is exchanged between a simulation box and a reservoir. The probability of this step is given by the GCMC algorithm. To preserve the electroneutrality of the system after the ion exchange, the electrode charge is adequately modified, which produces electrode charge fluctuations. The charge fluctuations are used to calculate the differential capacitance of the double layer. Results for the ion distributions, electrode surface charge density, and differential capacitance in slit nanopores are reported for a symmetric system of +1:-1 ionic valences with a common ionic diameter of 0.4 nm at electrolyte concentrations of 0.2M, 1.0M, and 2.5M, pore widths of 0.6 nm, 0.8 nm, and 1.2 nm, a potential drop of 0.05 V, a relative permittivity of 78.5, and a temperature of 298.15 K. These results are compared with the corresponding data for a +1:-2 valence asymmetric system and a size asymmetric system with ionic diameters of 0.4 nm and 0.3 nm. The results show that with increasing electrolyte concentration, the range of confinement effects decreases. For divalent anions, the width dependence of electrode charge and differential capacitance reveals a maximum. The differential capacitance curves show a camel shape to bell shape transition as the electrolyte concentration increases. Asymmetry in both ionic valences and diameters leads to asymmetric capacitance curves.

Grand canonical simulations of ions between charged conducting surfaces using exact 3D Ewald summations

We present a useful methodology to simulate ionic fluids confined by two charged and perfectly conducting surfaces. Electrostatic interactions are treated using a modified 3D Ewald sum, which accounts for all image charges across the conductors, as well as the 2D periodicity, parallel to the surfaces. The energy expression is exact, and the method is trivial to implement in existing Ewald codes. We furthermore invoke a grand canonical scheme that utilizes a bias potential, that regulates the surface charge density. The applied bias potential also enables us to calculate individual chemical potentials of the ions. Finally, we argue that our approach leads to a pedagogically appealing description of the Donnan potential, and what it measures in these systems.

Ising models of charge storage in multifile metallic nanopores

Ising type models of charging of conductive nanopores with ions have already been proposed and investigated for single file cylindrical or single layer slit nanopores. In such pores, the state of ions, the coulombic interactions of which are exponentially screened by their images in pore walls, was named superionic. In the present work we extend the analysis of the superionic state to nanopores that can accommodate multiple rows of ions. By grouping multiple charges in the same row into 'supercharges', we map the arrangement of ions in polarised electrodes on a multi-row Ising model in an external field. We investigate one-, two- and three-row cases, which we solve exactly, using a purpose-built semi-numerical transfer matrix method. For pores of different radii, which can accommodate the corresponding number of ion rows, we calculate the dependence of the electrical capacitance and stored energy density on electrode potential. As in charging the single file pores, we find that in narrower pores higher energy densities can be achieved at low applied potentials, while wider pores perform better as the voltage is increased.

Theoretical Insights into the Structures and Capacitive Performances of Confined Ionic Liquids

Room-temperature ionic liquids (RTILs) together with nano-porous electrodes are the most promising materials for supercapacitors and batteries. Many theoretical works have addressed the structures and performances of RTILs inside nanopores. However, only limited attention has been given to how the dispersion forces of RTILs influence the behavior of ions inside the slit pores. Toward this aim, we investigate the effects of various dispersion forces between ions on the macroscopic structures in nanoconfinement and the capacitance performance of supercapacitors by the classical density functional theory (CDFT). The results show that the dispersion force can significantly change the mechanism of the charging process and even the shape of differential capacitance curves. In addition, the voltage-dependent structures of RTILs with appropriate dispersion force appears in a given silt pore, which leads to extremely high capacitance and enhances the energy storage density. We hope that this work could further offer guidance for the optimizing of electrolytes for electrical double layer capacitors, like tuning the dispersion force between ions by adding/removing certain chemical groups on the cations and anions of RTILs.

Ion Structure Transition Enhances Charging Dynamics in Subnanometer Pores

Using electrodes with subnanometer pores and ionic liquid electrolytes can improve the charge storage capacity at the expense of the charging rate. The fundamental understanding of the charging dynamics of nanoporous electrodes can help to avoid compromising the power density. In this work, we performed molecular dynamics simulations to reveal the charging mechanism of subnanometer pores in ionic liquids. Different from the traditional view that a smaller pore results in slower charging, a non-monotonic relation is found between the charging rate and pore size, in which the charging process is accelerated in some subnanometer pores. Our analysis uncovers that the mechanism of the charging enhancement can be attributed to the transition of in-pore ion structure.

Ultrasonic-assisted preparation and characterization of hierarchical porous carbon derived from garlic peel for high-performance supercapacitors

Ultrasonic-assisted impregnation is used to synthesize physically modified garlic peel-based 3D hierarchical porous carbons (PCs), and the effect on PCs is investigated by changing ultrasonic time. The results show that ultrasonic waves can effectively peel off surface attachments of the carbonized product, so that activator has a better mass transfer process and create more active sites. The connectivity of 3D pore network is enhanced as well, so the structure and electrochemical properties of garlic peel-based porous carbon (GBPC) are improved. The ultrasonic disperser is used as an ultrasonic generator, specific conditions are as follows: ultrasonic frequency is 40 kHz, ultrasonic power is 500 W, and ultrasonic time is 0, 3, 6, and 9 min, respectively. With the increase of ultrasonic time, impurities again block the pore structure during dynamic movement, resulting in a decrease in electrochemical performance. Specifically, the performance of GBPC-6 is the most excellent, the specific surface area (SSA) increases from 2548 m² g^-1 to 3887 m² g^-1, the specific capacitance increases from 304 F g^-1 to 426 F g^-1 at a current density of 1 A g^-1 in a two-electrode test system. Energy density and cycle performance are also improved at the same time, which are attributed to rational structure. In addition, the effectiveness of the strategy of ultrasonic-assisted synthesis has been confirmed on another precursor material-scallion, meaning that this work proposes a new and simple modification method for improving the performance of biomass-based PCs.

Nanoporous carbon for electrochemical capacitive energy storage

This review summarizes the recent advances of nanoporous carbon materials in the application of EDLCs, including a better understanding of the charge storage mechanisms by combining the advanced techniques and simulations methods.

Influence of Hydrogen Bonding between Ions of Like Charge on the Ionic Liquid Interfacial Structure at a Mica Surface

Ionic liquids (ILs) have attracted increasing interest in science and technology because of their remarkable properties, which can be tuned via varying ion structures to control the relative strengths of Coulomb interactions, hydrogen bonding (H-bonding), and dispersion forces. Here we use atomic force microscopy to probe the interfacial nanostructures of hydroxy functionalized ILs at negatively charged mica surfaces. H-bonding between hydroxy functionalized cations (c-c) produces cation clusters and a stronger interfacial nanostructure. H-bond stabilized cation clusters form despite opposing electrostatic repulsions between charge groups, cation-anion (c-a) electrostatic attractions, and (c-a) H-bonds. Comparison of ILs with and without OH functionalized cations shows directional H-bonding enhances interfacial structure more strongly than the dispersion forces between alkyl groups. These findings reveal a new means of controlling IL interfacial nanostructure via H-bonding between like-charged ions, which impact diverse areas including electrochemical charge storage (batteries and catalysis), electrodeposition, lubrication, etc.

Carbons with Regular Pore Geometry Yield Fundamental Insights into Supercapacitor Charge Storage

We conduct molecular dynamics simulations of electrical double-layer capacitors (EDLCs) using a library of ordered, porous carbon electrode materials called zeolite templated carbons (ZTCs). The well-defined pore shapes of the ZTCs enable us to determine the influence of pore geometry on both charging dynamics and charge storage mechanisms in EDLCs, also referred to as supercapacitors. We show that charging dynamics are negatively correlated with the pore-limiting diameter of the electrode material and display signatures of both progressive charging and ion trapping. However, the equilibrium capacitance, unlike charging dynamics, is not strongly correlated to commonly used, purely geometric descriptors such as pore size. Instead, we find a strong correlation of capacitance to the charge compensation per carbon (CCpC), a descriptor we define in this work as the average charge of the electrode atoms within the coordination shell of a counterion. A high CCpC indicates efficient charge storage, as the strong partial charges of the electrode are able to screen counterion charge, enabling higher ion loading and thus more charge storage within the electrode at a fixed applied voltage. We determine that adsorption sites with a high CCpC tend to be found within pockets with a smaller radius of curvature, where the counterions are able to minimize their distance with multiple points on the electrode surface, and therefore induce stronger local partial charges.