Blessing and Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging

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.

Differential capacitance of curved electrodes: role of hydration interactions and charge regulation

The functioning of supercapacitors relies on establishing electrostatic double-layer capacitance across a larger surface area, offering numerous advantages over conventional batteries, such as an extended lifespan and elevated safety standards. The differential capacitance is a fundamental property within the electrical double layer, playing a pivotal role in the advancement of electrical double-layer supercapacitors. In addition to electrostatic interactions, multiple theoretical and experimental studies have indicated that the differential capacitance is influenced by factors such as the physical structure of the electrode, solvent-mediated hydration interactions, and the specific type of electrolyte utilized. In this work, we incorporate hydration interactions into the Poisson-Boltzmann theory to explore curved electrodes whose surfaces can be covered by either acidic or basic groups. We examine how the electrostatic interaction, charge regulation, hydration effects, and the finite size of ions collectively modify the differential capacitance. Furthermore, we explore different scenarios of electrode curvature and how it may be used to achieve larger capacitance depending on the electrolyte type and pH.

A network model to predict ionic transport in porous materials

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

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

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

Microfluidic Printing of Vertically-Oriented Nanosheets/MOFs Hetero-Interface for Intensive Pseudocapacitive Storage

Efficient manufacture of electroactive vertically-oriented nanosheets with enhanced electrolyte mass diffusion and strong interfacial redox dynamics is critical for realizing high energy density of miniature supercapacitor (SC), but still challenging. Herein, microfluidic droplet printing is developed to controllably construct vertically-oriented graphene/ZIF-67 hetero-microsphere (VAGS/ZIF-67), where the ZIF-67 is coordinately grown on vertically-oriented graphene framework via Co─O─C bonds. The VAGS/ZIF-67 shows ordered porous channel, high electroactivity and strong interfacial interaction, providing rapid electrolyte diffusion dynamics and high faradaic capacitance in KOH solution (1674 F g-1 , 1004 C g-1 ), which are verified by computational fluid dynamics (CFD) and density functional theory (DFT). Moreover, the VAGS/ZIF-67 based SC exhibits large energy density (100 Wh kg-1 ), excellent durability (10 000 cycles and high/low temperature), and robust power-supply applications in portable electronics.

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

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

Iontronic microscopy of a tungsten microelectrode: "seeing" ionic currents under an optical microscope

Optical methods for monitoring electrochemical reactions at an interface are advantageous because of their table-top setup and ease of integration into reactors. Here we apply EDL-modulation microscopy to one of the main components of amperometric measurement devices: a microelectrode. We present experimental measurements of the EDL-modulation contrast from the tip of a tungsten microelectrode at various electrochemical potentials inside a ferrocene-dimethanol Fe(MeOH)2 solution. Using the combination of the dark-field scattering microscope and the lock-in detection technique, we measure the phase and amplitude of local ion-concentration oscillations in response to an AC potential as the electrode potential is scanned through the redox-activity window of the dissolved species. We present the amplitude and phase map of this response, as such this method can be used to study the spatial and temporal variations of the ion-flux due to an electrochemical reaction close to metallic and semiconducting objects of general geometry. We discuss the advantages and possible extensions of using this microscopy method for wide-field imaging of ionic currents.

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.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

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.

Partial osmotic pressures of ions in electrolyte solutions and the Gibbs-Guggenheim uncertainty principle

The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be attributed to individual ions. Here I demonstrate that although the total wall force balances the bulk osmotic pressure as required by mechanical equilibrium, the individual partial osmotic pressures are extrathermodynamic quantities dependent on the electrical structure at the wall, and as such they resemble attempts to define individual ion activity coefficients. The limiting case where the wall is a barrier to only one species of ion is also considered, and with ions on both sides the classic Gibbs-Donnan membrane equilibrium is recovered, thus providing a unifying treatment. The analysis can be extended to illustrate how the electrical state of the bulk is affected by the nature of the walls and the container handling history, thus supporting the "Gibbs-Guggenheim uncertainty principle," namely the notion that the electrical state is unmeasurable and usually accidentally determined. Since this uncertainty is conferred also onto individual ion activities, it has implications for the current (2002) IUPAC definition of pH.

Three-electrode cell calorimeter for electrical double layer capacitors

A calorimeter was built to measure the heat from a porous capacitive working electrode connected in a three-electrode configuration. This makes it possible to detect differences between cathodic and anodic heat production. The electrochemical cell contains a large electrolyte solution reservoir, ensuring a constant concentration of the salt solution probed by the reference electrode via a Luggin tube. A heat flux sensor is used to detect the heat, and its calibration as a gauge of the total amount of heat produced by the electrode is done based on the net electrical work performed on the working electrode during a full charging-discharging cycle. In principle, from the measured heat and the electrical work, the change in the internal energy of the working electrode can be determined as a function of the applied potential. Such measurements inform about the potential energy and average electric potential of ions inside the pores, giving insight into the electrical double layer inside electrode micropores. Example measurements of the heat are shown for porous carbon electrodes in an aqueous salt solution.

Microscopic Model for Cyclic Voltammetry of Porous Electrodes

Cyclic voltammetry (CV) is a widespread experimental technique for characterizing electrochemical devices such as supercapacitors. Despite its wide use, a quantitative relation between CV and microscopic properties of supercapacitors is still lacking. In this Letter, we use both the microscopic "stack-electrode" model and its equivalent circuit for predicting the cyclic voltammetry of electric double-layer formation in porous electrodes. We find that the dimensionless combination ωτ_{n}, with ω the scan frequency of the time-dependent potential and τ_{n} the relaxation timescale of the stack-electrode model, governs the CV curves and capacitance: the capacitance is scan-rate independent for ωτ_{n}≪1 and scan-rate dependent for ωτ_{n}≫1. With a single fit parameter and all other model parameters dictated by experiments, our model reproduces experimental CV curves over a wide range of ω. Meanwhile, the influence of the pore size distribution on the charging dynamics is investigated to explain the experimental data.

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

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

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

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

A Theoretical Model for the Charging Dynamics of Associating Ionic Liquids

Association between cations and anions plays an important role in the interfacial structure of room-temperature ionic liquids (ILs) and their electrochemical performance. Whereas great efforts have been devoted to investigating the association effect on the equilibrium properties of ILs, a molecular-level understanding of the charging dynamics is yet to be established. Here, we propose a theoretical procedure combining reaction kinetics and the modified Poisson-Nernst-Planck (MPNP) equations to study the influences of ionic association on the dynamics of electrical double layer (EDL) in response to an applied voltage. The ionic association introduces a new decay length λS and relaxation time scale τRC=λSL/D, where L is the system size and D is ion diffusivity, that are distinctively different those corresponding to non-associative systems. Analytical expressions have been obtained to reveal the quantitative relations between the dynamic timescales and the association strength.

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.

Rheological Characteristics of Ionic Liquids under Nanoconfinement

While the dynamic properties of ionic liquids (ILs) in nanoconfinement play a crucial role in the performance of IL-based electrochemical and mechanical devices, experimental work mostly falls short at reporting "solid-like" versus "liquid-like" behavior of confined ILs. The present work is the first to conduct frequency-sweep oscillatory-shear rheology on IL nanofilms, reconciling the solid-versus-liquid debate and revealing the importance of shear rate in the behavior. We disentangle and analyze the viscoelasticity of nanoconfined ILs and shed light on their relaxation mechanisms. Furthermore, a master curve describes the scaling of the dynamic behavior of four (non-hydrogen-bonding) ILs under nanoconfinement and reveals the role of the compressibility of the flow units.

Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

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

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

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

Flow effects on the surface properties of surfactant foam films

The surface electrostatic properties of liquid foam, involving the electrokinetic (EK) phenomena in the liquid-gas interface, have significant effects on the stability of the foam. Here, we established a theoretical model for ion transport in liquid films by combining the liquid flow and surface reaction. We found that the surface electrostatic properties of liquid foams were influenced unexpectedly by the pressure-induced flow. The liquid flow will induce the potential and concentration differences in the flow direction. When the pressure drop increases to a certain high value, the induced potential and salt concentration difference increases, leading to the change of the surface electrostatic properties such as zeta potential and the surface charge density. This change shows that the surface electrostatic properties of foam films depend on the coupling of various factors including ion distribution and pressure drop, which deepens our understanding of the electrostatic properties of the foam films.

Electrification of water interface

The surface charge of a water interface determines many fundamental processes in physical chemistry and interface science, and it has been intensively studied for over a hundred years. We summarize experimental methods to characterize the surface charge densities developed so far: electrokinetics, double-layer force measurements, potentiometric titration, surface-sensitive nonlinear spectroscopy, and surface-sensitive mass spectrometry. Then, we elucidate physical ion adsorption and chemical electrification as examples of electrification mechanisms. In the end, novel effects on surface electrification are discussed in detail. We believe that this clear overview of state of the art in a charged water interface will surely help the fundamental progress of physics and chemistry at interfaces in the future.

Experimental and Numerical Studies of Gas Permeability through Orthogonal Networks for Isotropic Porous Material

With regard to the problem of gas flow through isotropic porous deposits, the issues were considered in the category of description of gas movement mechanisms for structural models of the skeleton. As part of experimental tests of gas permeability through porous material in the form of polyamide, the numerical simulation method was used, using the k–ε turbulence model. The analysis of hydrodynamic phenomena occurring in the porous material made it possible to confront experimental research with numerical calculations. The analysis shows that, for a porous polyamide bed, there is a certain limit range of gas velocity (10⁻⁴–1) ms⁻¹ at which flow resistance is the lowest. On the other hand, the highest value of the flow resistance is gradually achieved in the range of gas velocity (1–10) ms⁻¹. This is due to the different structure of the isotropic polyamide material. The validation of the numerical model with experimental data indicates the validity of the adopted research methodology. It was found that the permeability characteristics of the tested porous material practically did not depend on the direction of gas flow. For porous polyamide, the permeability characteristic is non-linear, which, from the point of view of the measurements carried out, indicates the advantage of turbulent gas flow over its laminar movement. The novelty of the article is a proprietary method of measuring gas permeability for a cube-shaped sample made of a material constituting a sinter of spherical particles of equal dimensions. The method enables the determination of gas flow (in each flow direction) in microchannels forming an orthogonal network, characteristic of isotropic materials.

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

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

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.

Charging Dynamics of Overlapping Double Layers in a Cylindrical Nanopore

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