The anatomy of the double layer and capacitance in ionic liquids with anisotropic ions: Electrostriction vs. lattice saturation

Generalized Helmholtz model describes capacitance profiles of ionic liquids and concentrated aqueous electrolytes

In this work, we propose and validate a generalization of the Helmholtz model that can account for both "bell-shaped" and "camel-shaped" differential capacitance profiles of concentrated electrolytes, the latter being characteristic of ionic liquids. The generalization is based on introducing voltage dependence of both the dielectric constant "ϵr(V)" and thickness "L(V)" of the inner Helmholtz layer, as validated by molecular dynamics (MD) simulations. We utilize MD simulations to study the capacitance profiles of three different electrochemical interfaces: (1) graphite/[BMIm+][BF4-] ionic liquid interface; (2) Au(100)/[BMIm+][BF4-] ionic liquid interface; (3) Au(100)/1M [Na+][Cl-] aqueous interface. We compute the voltage dependence of ϵr(V) and L(V) and demonstrate that the generalized Helmholtz model qualitatively describes both camel-shaped and bell-shaped differential capacitance profiles of ionic liquids and concentrated aqueous electrolytes (in lieu of specific ion adsorption). In particular, the camel-shaped capacitance profile that is characteristic of ionic liquid electrolytes arises simply from combination of the voltage-dependent trends of ϵr(V) and L(V). Furthermore, explicit analysis of the inner layer charge density for both concentrated aqueous and ionic liquid double layers reveal similarities, with these charge distributions typically exhibiting a dipolar region closest to the electrode followed by a monopolar peak at larger distances. It is appealing that a generalized Helmholtz model can provide a unified description of the inner layer structure and capacitance profile for seemingly disparate aqueous and ionic liquid electrolytes.

Differential Capacitance of Ionic Liquid Confined between Metallic Interfaces

We present here a detailed analysis of the electric double layer at the gold electrode/[BMIM][BF4] interface using a polarizable model for the electrode, based on our recent approach to include image charges [Geada et al. Nat. Commun. 2018, 9, 716]. A double bell (camel) shape is obtained for the differential capacitance, where the inclusion of metal polarization allows for a higher density of ions in the double layer, particularly around the maxima, thereby increasing the capacitance. The charging mechanism differs for the positive and negative electrodes, with counterion adsorption prevailing at the anode and co-ion desorption prevailing at the cathode. The charging mechanism is predominantly governed by the BF4 anions, serving as counterions and co-ions at the anode and cathode, respectively. Within the considered range of potentials, only minor changes are observed in the dynamical properties, specifically in the diffusion coefficients. Notably, it is interesting to observe that bulk properties are restored at a shorter distance from the gold surface in the case of the anode compared to the cathode.

Temperature-dependent differential capacitance of an ionic liquid-graphene-based supercapacitor

One of the critical factors affecting the performance of supercapacitors is thermal management. The design of supercapacitors that operate across a broad temperature range and at high charge/discharge rates necessitates understanding the correlation of the molecular characteristics of the device (such as interfacial structure and inter-ionic and ion-electrode interactions) with its macroscopic properties. In this study, we use molecular dynamics (MD) simulations to investigate the influence of Joule heating on the structure and dynamics of the ionic liquid (IL)/graphite-based supercapacitors. The temperature-dependent electrical double layer (EDL) and differential capacitance-potential (CD-V) curves of two different ([Bmim][BF4] and [Bmim][PF6]) IL-graphene pairs were studied under various thermal gradients. For the [Bmim][BF4] system, the differential capacitance curves transition from 'U' to bell shape under an applied thermal gradient (∇T) in the range from 3.3 K nm-1 to 16.7 K nm-1. Whereas in [Bmim][PF6], we find a positive dependence of differential capacitance with ∇T with a U-shaped CD-V curve. We examine changes in the EDL structure and screening potential (ϕ(z)) as a function of ∇T and correlate them with the trends observed in the CD-V curve. The identified correlation between the interfacial charge density and differential capacitance with thermal gradient would be helpful for the molecular design of the IL-electrode interface in supercapacitors or other chemical engineering applications.

Nanostructure of Locally Concentrated Ionic Liquids in the Bulk and at Graphite and Gold Electrodes

The physical properties of ionic liquids (ILs) have led to intense research interest, but for many applications, high viscosity is problematic. Mixing the IL with a diluent that lowers viscosity offers a solution if the favorable IL physical properties are not compromised. Here we show that mixing an IL or IL electrolyte (ILE, an IL with dissolved metal ions) with a nonsolvating fluorous diluent produces a low viscosity mixture in which the local ion arrangements, and therefore key physical properties, are retained or enhanced. The locally concentrated ionic liquids (LCILs) examined are 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (HMIM TFSI), 1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (HMIM FAP), or 1-butyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (BMIM FAP) mixed with 1,1,2,2-tetrafluoroethyl 2,2,2-trifluoroethyl ether (TFTFE) at 2:1, 1:1, and 1:2 (w/w) IL:TFTFE, as well as the locally concentrated ILEs (LCILEs) formed from 2:1 (w/w) HMIM TFSI-TFTFE with 0.25, 0.5, and 0.75 m lithium bis(trifluoromethylsulfonyl)imide (LiTFSI). Rheology and conductivity measurements reveal that the added TFTFE significantly reduces viscosity and increases ionic conductivity, and cyclic voltammetry (CV) reveals minimal reductions in electrochemical windows on gold and carbon electrodes. This is explained by the small- and wide-angle X-ray scattering (S/WAXS) and atomic force microscopy (AFM) data, which show that the local ion nanostructures are largely retained in LCILs and LCILEs in bulk and at gold and graphite electrodes for all potentials investigated.

Theoretical Insight into the Imidazolium-Based Ionic Liquid Interface Structure and Differential Capacitance on Au(111): Effects of the Cationic Substituent Group

Electric double layers (EDLs) play a key role in the electrochemical and energy storage of supercapacitors. It is important to understand the structure and properties of EDLs. In this work, quantum chemical calculations and molecular dynamics (MD) simulations are used to study the microstructure of EDLs of four different substituents of imidazolium-based bis(trifluoromethylsulfonyl)imide ionic liquids (ILs) on the Au(111) surface. It is shown that the particle interactions influence the different arrangements of the anion and cation. More alkyl substitutions and longer alkyl chains result in a higher ELUMO and thus a stronger interaction energy between cations and electrodes. Strong interactions produce linear patterns of anions/cations on the electrode and a maximum value of differential capacitance near PZC, whereas weak interactions generate worm-like patterns of anions/cations on Au(111) and a minimum value of differential capacitance near the PZC. We hold the opinion that the alkyl substitution has more effects on the EDLs. Our analysis provides a new perspective on EDLs structures at the atomic and molecular level. This study provides a good basis and guidance for further understanding the interface phenomena and characteristics of ionic liquids in electrochemical and energy device applications.

Microstructural probing of phosphonium-based ionic liquids on a gold electrode using colloid probe AFM

Atomic force microscopy (AFM) with a gold colloid probe modeled as the electrode surface is employed to directly capture the contact resonance frequency of two phosphonium-based ionic liquids (ILs) containing a common anion [BScB]^- and differently lengthened cations ([P_6,6,6,14]⁺ and [P_4,4,4,8]⁺). The comparative interfacial studies are performed by creating IL films on the surface of gold, followed by measuring the wettability, thickness of the films, adhesion forces, surface morphology and AFM-probed contact resonance frequency. In addition, the cyclic voltammetry and impedance spectroscopy measurements of the neat ILs are measured on the surface of the gold electrode. The IL with longer cation alkyl chains exhibits a well-defined thin film on the electrode surface and enhanced the capacitance than the shorter chain IL. The AFM contact resonance frequency and force curves reveal that the longer IL prefers to form stiffer ion layers at the gold electrode surface, suggesting the "…anion-anion-cation-cation…" bilayer structure, in contrast, the shorter-chain IL forms the softer cation-anion alternating structure, i.e., "…anion-cation-anion-cation…".

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.

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.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Double-Edged Sword of Ion-Size Asymmetry in Energy Storage of Supercapacitors

The advanced supercapacitor is of great significance for renewable energy storage. Achieving its high energy and high power densities remains a huge challenge. Herein, the contribution of ion-size asymmetry to the charging behavior of a supercapacitor is systematically studied using time-dependent density functional theory (TDDFT). We track the time evolution of the ionic microstructure inside the porous electrode and its reservoir and reveal a kinetic charge inversion in the asymmetrical ion-size cases. Compared with the symmetrical ion-size case, we find that the ion-size asymmetry has a double-edged sword effect on the energy storage of a supercapacitor: it accelerates the charging process yet reduces the differential capacitance. Additionally, the energy density and power density can simultaneously increase in the asymmetrical cases, which provides important insights toward the experimental design of supercapacitors with high energy and high power densities.

Interfacial water asymmetry at ideal electrochemical interfaces

Controlling electrochemical reactivity requires a detailed understanding of the charging behavior and thermodynamics of the electrochemical interface. Experiments can independently probe the overall charge response of the electrochemical double layer by capacitance measurements and the thermodynamics of the inner layer with potential of maximum entropy measurements. Relating these properties by computational modeling of the electrochemical interface has so far been challenging due to the low accuracy of classical molecular dynamics (MD) for capacitance and the limited time and length scales of ab initio MD. Here, we combine large ensembles of long-time-scale classical MD simulations with charge response from electronic density functional theory to predict the potential-dependent capacitance of a family of ideal aqueous electrochemical interfaces with different peak capacitances. We show that while the potential of maximum capacitance varies, this entire family exhibits an electrode charge of maximum capacitance (CMC) between -2.9 and -2.2 μC/cm², regardless of the details in the electronic response. Simulated heating of the same interfaces reveals that the entropy peaks at a charge of maximum entropy (CME) of -5.1 ± 0.6 μC/cm², in agreement with experimental findings for metallic electrodes. The CME and CMC both indicate asymmetric response of interfacial water that is stronger for negatively charged electrodes, while the difference between CME and CMC illustrates the richness in behavior of even the ideal electrochemical interface.

Imidazolium Triflate Ionic Liquids' Capacitance-Potential Relationships and Transport Properties Affected by Cation Chain Lengths

In this paper we report the effects of five imidazolium cations with varying alkyl chain lengths to study the effects of cation size on capacitance versus voltage behavior. The cations include ethyl-, butyl-, hexyl-, octyl-, and decyl-3-methylimidazolium, all paired with a triflate anion. We analyze the capacitance with respect to the cation alkyl chain length qualitatively and quantitatively by analyzing changes in the capacitance-potential curvature shape and magnitude across several standard scanning protocols and electrochemical techniques. Further, three transport properties (viscosity, diffusion coefficient, and electrical conductivity) are experimentally determined and integrated into the outcomes. Ultimately, we find higher viscosities, lower diffusion coefficients, and lower electrical conductivities when the alkyl chain length is increased. Also, capacitance values increase with cation size, except 1-octyl-3-methylimidazolium, which does not follow an otherwise linear trend. This capacitive increase is most pronounced when sweeping the potential in the cathodic direction. These findings challenge the conventional hypothesis that increasing the length of the alkyl chain of imidazolium cations diminishes the capacitance and ionic liquid performance in charge storage.

Phase Transitions and Electrochemical Properties of Ionic Liquids and Ionic Liquid-Solvent Mixtures

Recent advances in studies of ionic liquids (IL) and ionic liquid-solvent mixtures are reviewed. Selected experimental, simulation, and theoretical results for electrochemical, thermodynamical, and structural properties of IL and IL-solvent mixtures are described. Special attention is paid to phenomena that are not predicted by the classical theories of the electrical double layer or disagree strongly with these theories. We focus on structural properties, especially on distribution of ions near electrodes, on electrical double layer capacitance, on effects of confinement, including decay length of a dissjoining pressure between confinig plates, and on demixing phase transition. In particular, effects of the demixing phase transition on electrochemical properties of ionic liquid-solvent mixtures for different degrees of confinement are presented.

Structural Reorganization of Ionic Liquid Electrolyte by a Rapid Charge/Discharge Circle

The behavior of forming layers near the electrode surface is an important topic for the energy storage with ionic liquid (IL) electrolytes. Here, molecular dynamics (MD) simulations were used to study the behavior of surface active ionic liquid (SAIL) electrolytes near positive electrodes. With the increase of electrode surface charge density, a V-type conformation of the anion [AOT]^- for energy storage was shown. The V conformation is easier to replace the latent voids, which is like wedging ions into the layer near the electrodes. Meanwhile, after a rapid charge/discharge circle, there would be more V-type anions appearing in this optimized electrolyte. It is a significant point for the mechanism of nanoscale and microscale energy storage, which provides a theoretical basis for the optimization of efficient IL electrolytes and the design of related experimental research.

Electro-Responsive Surface Composition and Kinetics of an Ionic Liquid in a Polar Oil

The quartz crystal microbalance (QCM) has been used to study how the interfacial layer of an ionic liquid dissolved in a polar oil at low weight percentages responds to changes in applied potential. The changes in surface composition at the QCM gold surface depend on both the magnitude and sign of the applied potential. The time-resolved response indicates that the relaxation kinetics are limited by the diffusion of ions in the interfacial region and not in the bulk, since there is no concentration dependence. The measured mass changes cannot be explained only in terms of simple ion exchange; the relative molecular volumes of the ions and the density changes in response to ion exclusion must be considered. The relaxation behavior of the potential between the electrodes upon disconnecting the applied potential is more complex than that observed for pure ionic liquids, but a measure of the surface charge can be extracted from the exponential decay when the rapid initial potential drop is accounted for. The adsorbed film at the gold surface consists predominantly of ionic liquid despite the low concentration, which is unsurprising given the surtactant-like structures of (some of) the ionic liquid ions. Changes in response to potential correspond to changes in the relative numbers of cations and anions, rather than a change in the oil composition. No evidence for an electric field induced change in viscosity is observed. This work shows conclusively that electric potentials can be used to control the surface composition, even in an oil-based system, and paves the way for other ion solvent studies.

Self-assembled nanostructures in ionic liquids facilitate charge storage at electrified interfaces

Driven by the potential applications of ionic liquids (ILs) in many emerging electrochemical technologies, recent research efforts have been directed at understanding the complex ion ordering in these systems, to uncover novel energy storage mechanisms at IL-electrode interfaces. Here, we discover that surface-active ILs (SAILs), which contain amphiphilic structures inducing self-assembly, exhibit enhanced charge storage performance at electrified surfaces. Unlike conventional non-amphiphilic ILs, for which ion distribution is dominated by Coulombic interactions, SAILs exhibit significant and competing van der Waals interactions owing to the non-polar surfactant tails, leading to unusual interfacial ion distributions. We reveal that, at an intermediate degree of electrode polarization, SAILs display optimum performance, because the low-charge-density alkyl tails are effectively excluded from the electrode surfaces, whereas the formation of non-polar domains along the surface suppresses undesired overscreening effects. This work represents a crucial step towards understanding the unique interfacial behaviour and electrochemical properties of amphiphilic liquid systems showing long-range ordering, and offers insights into the design principles for high-energy-density electrolytes based on spontaneous self-assembly behaviour.

Off-center charge model revisited: Electrical double layer with multivalent cations

The off-center charge model of ions is a relatively simple model for introducing asymmetry in Coulomb interaction while retaining the simplicity and convenience of the spherical hard core geometry. A Monte Carlo simulation analysis of the planar electric double layer formed by this ionic model for 1+:1- valence systems [S. Lamperski et al., Langmuir 33, 11554-11560 (2017)] is extended to include solutions of multivalent (2+, 3+) hard spherical cations and single valence (1-) hard spherical anions near a uniformly charged, planar electrode. The solvent is modelled as a uniform dielectric continuum with a dielectric constant equal to that of the pure solvent, viz., the primitive model. Results are reported for the ion density, the cation charge profile, and the electrostatic potential profile at 1 mol/dm³ salt concentration. Additionally, the double layer potential drop, that is, the electrode potential, and the integral and the differential capacitances are computed as functions of the electrode surface charge density. The latter two quantities show an expected asymmetry as long as the cation valence is not too great and the charge of the off-center ion cannot approach too close to the electrode surface. It is unusual that the integral and differential capacitances are negative for high valence cations and a negatively charged electrode when the off-center charge is large and can be very near the surface of the electrode. The corresponding electrode potential versus surface charge density curve becomes non-monotonic and shows a change of slope, and thus the resultant integral and differential capacitances can become negative. This nonphysical result is the result of an incipient singularity when a large positive charge is too near a negatively charged electrode. Overall, the off-center charge model suggests a useful recipe to model electrical asymmetry within the broader context of the primitive model provided that the off-center charge is not too near the surface of the electrode.

Capacitive hysteresis at the 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)-trifluorophosphate-polycrystalline gold interface

We report potential-dependent capacitance curves over a 2-V potential range for the 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)-trifluorophosphate (Emim FAP)-polycrystalline gold interface, and examine the effect of potential scan direction on results. We find very small levels of capacitive hysteresis in the Emim FAP-polycrystalline Au electrochemical system, where capacitance curves show minor dependence on the potential scan direction employed. This is a considerably different response than that reported for the Emim FAP-Au(111) interface where significant hysteresis is observed based on the potential scan direction (Drüschler et al. in J Phys Chem C 115 (14):6802-6808, 2011). Hysteresis effects have previously been suggested to be a general feature of an ionic liquid (IL) at electrified interfaces due to slow interfacial processes and has been demonstrated for numerous electrochemical systems. We provide new evidence that the experimental procedure used to acquire capacitance data and data workup could also have implications on capacitance-potential relationships in ILs. This work serves to progress our understanding of the nature of capacitive hysteresis at the IL-electrode interface. Graphical abstract Subtle changes in experimental methods can lead to significantly different capacitance measurements in ionic liquids. Which is the best approach?

Direct Measurement of the Differential Capacitance of Solvent-Free and Dilute Ionic Liquids

Differential capacitance is a key quantity in the understanding of electrical double-layer charging of electrolytes. However, experimental observations of ionic liquid systems are controversial, inconsistent, and often unable of confirming or refuting existing theories as well as highlighting discrepancies between the measurement techniques. We study the differential capacitance in both pure and dilute ionic liquids at room temperature. Using chronoamperometry to measure the differential capacitance of the liquids at a polycrystalline platinum electrode, we find good agreement between the measured capacitance curves and the extended mean-field model of Goodwin-Kornyshev [Goodwin, Z. A.; et al. Electrochim. Acta. 2017, 225, 190-197]. A crossover is found from the pure to the dilute regime, as shown by a transition from a camel-shape capacitance curve to a U-like one, together with a nonmonotonic dependence of capacitance with electrolyte concentration.

Molecular scale structure and dynamics at an ionic liquid/electrode interface

The structural arrangement and dynamics of ions near the IL/electrode interface during charging and discharging was studied by a combination of time resolved X-ray reflectivity and impedance spectroscopy.

The metal–ionic liquid interface as characterized by impedance spectroscopy and in situ scanning tunneling microscopy

Electrochemical measurements including impedance spectroscopy and in situ scanning tunneling microscopy were performed to study the interface between solid electrodes and ionic liquids. We could reveal that the double layer rearrangement processes are not instantaneous, but that the ions can form ordered clusters at the interface.

On the thickness of the double layer in ionic liquids

The Au(111)|BF₄⁻interface model in which BF₄⁻reorients and spontaneously dissociates at surface coverageθ= 1/3.

Effects and controls of capacitive hysteresis in ionic liquid electrochemical measurements

Capacitance vs. potential relationships help electrochemists better understand electrode–liquid interfacial behaviors.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Monte Carlo Study of a Planar Electric Double Layer Formed by Ions with Off-Center Charge

Grand canonical Monte Carlo simulation results are reported for an electric double layer (EDL) modeled by a planar charged hard wall, hard sphere cations with an off-center charge, and spherical anions with a charge at the center of the sphere. The ion charge numbers are Z₊ = +1 and Z_- = -1, and the diameter, d, of a hard sphere is the same for anions and cations. The ions are immersed in a solvent mimicked by a continuum dielectric medium at standard temperature. The results are obtained for three values of charge displacement, s₊₀ = d/16, d/4, 7d/16 from the center of the sphere and the following electrolyte concentrations: 0.5, 1.0, 2.0, and 3.0 M. The profiles of electrode-ion singlet distributions, cation reduced charge density, angular function, and mean electrostatic potential are reported for an electrode surface charge density σ = -0.30 C m^-2, whereas the electrode potential and the differential capacitance of EDL are shown as functions of the electrode charge density varying from -1.00 to +1.00 C m^-2. At negative electrode charges and with increasing values of the charge separation, the differential capacitance curve rises. As the electrolyte concentration increases, the shape of the differential capacitance curve changes from that of a minimum surrounded by two maxima into that of a distorted single maximum.

The influence of water content in a proton-conducting ionic liquid on the double layer properties of the Pt/PIL interface

The influence of the water content of 2-sulfoethylmethylammonium trifluoromethanesulfonate [2-Sema][TfO] on the double layer properties of the interface of platinum and the proton conducting ionic liquid (PIL) is investigated by means of impedance spectroscopy and cyclic voltammetry. By fitting the impedance spectra as complex capacitances, up to four differential double layer capacitances and corresponding time constants are obtained, depending on the potential (U = 0-1.6 V/RHE), water content (0.7-6.1 wt%) and temperature (T = 70-110 °C). Within the whole potential range investigated, a high frequency capacitance, C₁, and a low frequency capacitance, C₂, can be calculated. In the potential region of hydrogen underpotential deposition (H_UPD), C₁ can be separated into two parts, C_1a and C_1b. Whereas the high frequency capacitive processes can mainly be attributed to ion transport processes in the double layer, the low frequency process is ascribed to changes in the interfacial layer, including ad-/desorption and Faradaic processes. Alternative interpretations regarding the reorientation of ions, reconstruction of the metal surface and partial electron transfer between anions and Pt are considered.

Dense ionic fluids confined in planar capacitors: in- and out-of-plane structure from classical density functional theory

The ongoing scientific interest in the properties and structure of electric double layers (EDLs) stems from their pivotal role in (super)capacitive energy storage, energy harvesting, and water treatment technologies. Classical density functional theory (DFT) is a promising framework for the study of the in- and out-of-plane structural properties of double layers. Supported by molecular dynamics simulations, we demonstrate the adequate performance of DFT for analyzing charge layering in the EDL perpendicular to the electrodes. We discuss charge storage and capacitance of the EDL and the impact of screening due to dielectric solvents. We further calculate, for the first time, the in-plane structure of the EDL within the framework of DFT. While our out-of-plane results already hint at structural in-plane transitions inside the EDL, which have been observed recently in simulations and experiments, our DFT approach performs poorly in predicting in-plane structure in comparison to simulations. However, our findings isolate fundamental issues in the theoretical description of the EDL within the primitive model and point towards limitations in the performance of DFT in describing the out-of-plane structure of the EDL at high concentrations and potentials.

Computational and Experimental Study of Li-Doped Ionic Liquids at Electrified Interfaces

We evaluate the influence of Li-salt doping on the dynamics, capacitance, and structure of three ionic liquid electrolytes, [pyr14][TFSI], [pyr13][FSI], and [EMIM][BF4], using molecular dynamics and polarizable force fields. In this respect, our focus is on the properties of the electric double layer (EDL) formed by the electrolytes at the electrode surface as a function of surface potential (Ψ). The rates of EDL formation are found to be on the order of hundreds of picoseconds and only slightly influenced by the addition of Li-salt. The EDLs of three electrolytes are shown to have different energy storage capacities, which we relate to the EDL formation free energy. The differential capacitance obtained from our computations exhibits asymmetry about the potential of zero charge and is consistent with the camel-like profiles noted from mean field theories and experiments on metallic electrodes. The introduction of Li-salt reduces the noted asymmetry in the differential capacitance profile. Complementary experimental capacitance measurements have been made on our three electrolytes in their neat forms and with Li-salt. The measurements, performed on glassy carbon electrodes, produce U-like profiles, and Li-salt doping is shown to strongly affect capacitance at high magnitudes of Ψ. Differences in the theoretical and experimental shapes and magnitudes of capacitance are rationalized in terms of the electrode surface and pseudocapacitive effects. In both neat and Li-doped liquids, the details of the computational capacitance profile are well described by Ψ-induced changes in the density and molecular orientation of ions in the molecular layer closest to the electrode. Our results suggest that the addition of Li+ induces disorder in the EDL, which originates from the strong binding of anions to Li+. An in-depth analysis of the distribution of Li+ in the EDL reveals that it does not readily enter the molecular layer at the electrode surface, preferring instead to be localized farther away from the surface in the second molecular layer. This behavior is validated through an analysis of the free energy of Li+ solvation as a function of distance from the electrode. Free energy wells are found to coincide with localized concentrations of Li+, the depths of which increase with Ψ and suggest a source of impedance for Li+ to reach the electrode. Finally, we make predictions of the specific energy at ideal graphite utilizing the computed capacitance and previously derived electrochemical windows of the liquids.

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes

We analyze the effect of asymmetric finite ion size in nanoconfinement in the view of osmotic pressure and electrocapillarity. When the confinement width becomes comparable with the Debye length, the overlapped electric double layer is significantly deformed by the steric effects. We derive the osmotic pressure from the modified Poisson-Boltzmann equation in a nanoslit to examine the deviation from the ideal osmotic pressure and the repulsive force on the wall considering the asymmetry of ion sizes. Then the electrocapillarity due to the steric effect is investigated under constant potential condition with the flat interface assumption. Later, the deformation by the electrocapillarity is also considered in the first order approximation.