Double-layer in ionic liquids: paradigm change?

Applications of ionic liquids at electrified interfaces to energy-storage systems, electrowetting devices, or nanojunction gating media cannot proceed without a deep understanding of the structure and properties of the interfacial double layer. This article provides a detailed critique of the present work on this problem. It promotes the point of view that future considerations of ionic liquids should be based on the modern statistical mechanics of dense Coulomb systems, or density-functional theory, rather than classical electrochemical theories which hinge on a dilute-solution approximation. The article will, however, contain more questions than answers. To trigger the discussion, it starts with a simplified original result. A new analytical formula is derived to rationalize the potential dependence of double-layer capacitance at a planar metal-ionic liquid interface. The theory behind it has a mean-field character, based on the Poisson-Boltzmann lattice-gas model, with a modification to account for the finite volume occupied by ions. When the volume of liquid excluded by the ions is taken to be zero (that is, if ions are extremely sparsely packed in the liquid), the expression reduces to the nonlinear Gouy-Chapman law, the canonical result typically used to describe the potential dependence of capacitance in electrochemical double layers. If ionic volume exclusion takes more realistic values, the formula shows that capacitance-potential curves for an ionic liquid may differ dramatically from the Gouy-Chapman law. Capacitance has a maximum close to the potential of zero charge, rather than the familiar minimum. At large potenials, capacitance decreases with the square root of potential, rather than increases exponentially. The reported formula does not take into account the specific adsorption of ions, which, if present, can complicate the analysis of experimental data. Since electrochemists use to think about the capacitance data in terms of the classical Gouy-Chapman theory, which, as we know, should be good only for electrolytes of moderate concentration, the question of which result is "better" arises. Experimental data are sparse, but a quick look at them suggests that the new formula seems to be closer to reality. Opinions here could, however, split. Indeed, a comparison with Monte Carlo simulations has shown that incorporation of restricted-volume effects in the mean-field theory of electrolyte solutions may give results that are worse than the simple Gouy-Chapman theory. Generally, should the simple mean-field theory work for such highly concentrated ionic systems, where the so-called ion-correlation effects must be strong? It may not, as it does not incorporate a possibility of charge-density oscillations. Somehow, to answer this question definitely, one should do further work. This could be based on density-functional theory (and possibly not on what is referred to as local density approximation but rather "weighted density approximation"), field theory methods for the account of fluctuations in the calculation of partition function, heuristic integral equation theory extended to the nonlinear response, systematic force-field computer simulations, and, most importantly, experiments with independently determined potentials of zero charge, as discussed in the paper.     

Differential capacitance of ionic liquid interface with graphite: the story of two double layers

We combine electronic density functional theory for the screening properties of graphite with a mean-field theory of the double layer in ionic liquids to reveal what underpins the morphology of the voltage dependence of electrical capacitance of a flat graphite/ionic liquids interface.     

Differential capacitance of the electric double layer: mean-field modeling approaches

Electrolytes screen the charges carried by an electrode through the formation of a diffuse double layer. The corresponding differential capacitance reflects the change of the surface charge density with the applied surface potential. Mean-field modeling of the differential capacitance is an attempt to qualitatively explain experimental findings such as the camel-to-bell shape transition in terms of physical factors including the ion size and concentration, nonelectrostatic ion–ion interactions, electrostatic ion–ion correlations, and the influence of the electrode curvature. We highlight the central role of the lattice gas model as a conceptual tool to describe concentrated electrolytes and ionic liquids, and we briefly summarize how extensions and generalizations of this model give rise to concepts known as ‘overscreening’ and ‘underscreening’.     

Interface between ionic and nonionic liquids: theoretical study

We use a Flory-Huggins type approach to calculate the structure and the surface tension coefficient of the boundary between ionic and nonionic liquids. The mixture of ionic and nonionic liquids is treated as a "three-component" system including anions, cations, and neutral molecules. We show that if the affinities of the cations and the anions to the neutral molecules are different, the interface comprises an electric double layer. The presence of this layer (uncompensated electric field) stabilizes the interface: the field inhibits the ions segregation at the interface and increases the surface tension. On the other hand, the short-range volume interactions promote the segregation and decrease the surface tension. Furthermore, the surface tension coefficient can be negative, if the difference of the affinities is high enough. It implies a possibility of microphase separation of the system.     

Double layer in ionic liquids: The nature of the camel shape of capacitance

Monte Carlo simulations of a model ionic liquid show that if ions have charged heads and neutral counterparts, the latter give rise to the camel shape of the voltage dependence of the double layer capacitance. Neutral ‘tails’ of ions play the role of latent voids that can be replaced by charged groups via rotations and translations of ions. This provides extra degrees of freedom for the field-induced charge rearrangements in the double layer which results in the peculiar double-hump capacitance profile.     

Ion penetration into an ‘unfriendly medium’ and the double layer capacitance of the interface between two immiscible electrolytes

We develop a theory of the double layer at electrolyte | electrolyte interfaces with account for the finite thickness of the interfacial region. This includes the distribution of ions between the two phases and smooth variation of dielectric properties across the interface. The theory offers simple laws for the dependence of the double layer capacitance on the nature of ions, ionic concentrations and potential, which are in line with experimental observations. The theory shows which parameters reflect the nature of ions and the structure of the interface, and how these parameters can be extracted from the capacitance data.     

Electric double layer theory for room temperature ionic liquids on charged electrodes: Milestones and prospects

In this review, we shortly summarize the basic theoretical milestones achieved in the mean-field theory of room temperature ionic liquids on charged electrodes since the publication of Kornyshev's seminal article in 2007. We pay special attention to the behavior of the differential capacitance profile and the microscopic parameters of ions that can have a substantial influence on it. Among them are parameters of short-range specific interactions, ionic diameters, static polarizabilities, and permanent dipole moments. We also discuss the recent ‘nonlocal’ mean-field theories that can describe the overscreening behavior of the local ionic concentrations, as well as the crossover from overscreening to crowding.     

Ionic liquid ion sources: suppression of electrochemical reactions using voltage alternation

The problem of electrochemical decomposition due to extraction of single polarity ions from a novel ionic liquid ion source (ILIS) is solved by periodically alternating the voltage source so that the potential difference that appears across the double layer formed between the emitter conductive material and the liquid is maintained below the electrochemical window limit, thus eliminating electronic reactions. The ionic liquid EMI-BF(4) is used to externally wet a solid tungsten emitter, establishing a physical boundary with a certain liquid-metal contact area. Theoretical and experimental evidence suggests that this area is close to the effective surface involved in the double layer charging dynamics. The extent of this surface is relatively large, thus increasing the net capacitance and consequently the double layer charging time, demonstrating that low frequency voltage alternation of the order of 1 Hz is enough to obtain clean and reliable ion emission.     

pH-Regulated nanopore conductance with overlapped electric double layers

There has been a significant growth of interest in single nanopore ionic devices that could control the transport of ions and rectify ionic current. To improve the advance of relevant nanofluidic devices, a model is derived for the first time to investigate the zeta potential and ionic conductance of a cylindrical nanopore with overlapped electric double layer as functions of pH, salt concentration as well as the Stern layer capacitance. The developed model is validated by the experimental data of the nanopore conductance. Results show that in addition to the magnitudes, the relevant behaviors of zeta potential and conductance of the nanopore might be significantly influenced by the Stern layer.     

Specific ion adsorption and surface forces in colloid science

Mean-field theories that include nonelectrostatic interactions acting on ions near interfaces have been found to accommodate many experimentally observed ion specific effects. However, it is clear that this approach does not fully account for the liquid molecular structure and hydration effects. This is now improved by using parametrized ionic potentials deduced from recent nonprimitive model molecular dynamics (MD) simulations in a generalized Poisson-Boltzmann equation. We investigate how ion distributions and double layer forces depend on the choice of background salt. There is a strong ion specific double layer force set up due to unequal ion specific short-range potentials acting between ions and surfaces.     

Ferroelectric phase transitions near ionic liquid/vacuum interfaces

A simple theoretical model is developed describing ionic liquids as regular solutions. The separation of these ionic mixtures is studied on the base of the Cahn-Hilliard theory coupled with electrostatics. It is shown that the ionic liquids decompose to thin layers of oppositely charged liquids at low temperatures. At larger temperatures the separation occurs only near the ionic liquid/vacuum surface, thus explaining the oscillatory-decaying structure of the electric double layer observed via computer simulations. In contrast to noncharged liquids the ionic ones exhibit two critical temperatures, where the temperature coefficients of all characteristic lengths possess singularities. These second order ferroelectric phase transitions are possible explanations of the experimentally measured via light scattering peculiar temperature dependence of the interfacial dipole moment density on several ionic liquid/vacuum interfaces.     

On the effects of ion-wall chemical association on the electric double layer: a density functional approach for the restricted primitive model at a charged wall

We describe a density functional theory for the restricted primitive model of ionic fluid at a charged wall with active sites to which ions can bond. The theory is an extension of our recent approach [Pizio et al., J. Chem. Phys. 121, 11957 (2004)] and is focused in the effects of specific adsorption of ions on the wall, besides the electrostatic phenomena. In order to solve the problem, we use the first-order thermodynamic perturbation theory of chemical association developed by Wertheim [J. Chem. Phys. 87, 7323 (1987)]. The microscopic structure of the electric double layer and the amount of adsorbed charge are investigated. Also, the temperature dependence of capacitance is analyzed. The capacitance depends on the kind of ions that form associative bonds with the surface sites and is determined by a net charge acting on the diffuse layer. The shape of the temperature dependence of capacitance essentially depends on the association energy and the density of bonding sites.     

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.     

Probing electric fields at the ionic liquid-electrode interface using sum frequency generation spectroscopy and electrochemistry

The arrangement of ions at the platinum electrode in the room-temperature ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate has been determined using sum frequency generation vibrational spectroscopy (SFG), electrochemical impedance spectroscopy (EIS), and the vibrational Stark effect. The results indicate that CO adsorbed on the Pt electrode has a Stark shift of 30-35 cm(-1)/V in the ionic liquid. The potential of zero charge (PZC) of the ionic liquid-Pt system is approximately -500 mV (vs Ag wire), with a capacitance of 0.12 F/m2. Further, polarization-dependent SFG experiments suggest the ions reorganize at the surface depending on the electrode charge. In combination, all these results indicate that the ions of a neat ionic liquid are organized in a Helmholtz layer at the electrified metal electrode interface.     

Structural ordering transitions in ionic liquids mixtures

Differential capacitance curves for the electrical double layer (EDL) of mixtures of imidazolium-based ionic liquids (ILs) with a common cation (1-ethyl-3-methylimidazolium, [C₂MIM]⁺) and two different anions (bis(trifuoromethylsulfonyl)imide, [Tf₂N]⁻) and tris(pentafluoroethyl)trifluorophosphate [FAP]⁻) were obtained. Sharp peaks in the differential capacitance curves were observed for a small range of mixtures compositions at positive charge densities. The appearance and position on the potential scale of the peaks were found to be dependent on the mixture composition and temperature. The occurrence of these phenomena is interpreted as corresponding to an abrupt change in the EDL structure arrangement as a result of a complex interplay of electrostatic interactions and steric effects. The use of the non-structured mercury electrode allowed to decouple the eventual potential induced restructuring occurring at the double layer from the well-known surface reconstruction effects often reported for ionic liquids in contact with single crystal face electrodes.     

Modeling electrokinetics in ionic liquids

Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson–Nernst–Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson‐Nernst‐Planck equations are coupled with Navier–Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double‐layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion‐selective surface, and electroconvective flow on a curved ion‐selective surface. We also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.     

New insights into the interface between a single-crystalline metal electrode and an extremely pure ionic liquid: slow interfacial processes and the influence of temperature on interfacial dynamics

Ionic liquids are of high interest for the development of safe electrolytes in modern electrochemical cells, such as batteries, supercapacitors and dye-sensitised solar cells. However, electrochemical applications of ionic liquids are still hindered by the limited understanding of the interface between electrode materials and ionic liquids. In this article, we first review the state of the art in both experiment and theory. Then we illustrate some general trends by taking the interface between the extremely pure ionic liquid 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate and an Au(111) electrode as an example. For the study of this interface, electrochemical impedance spectroscopy was combined with in situ STM and in situ AFM techniques. In addition, we present new results for the temperature dependence of the interfacial capacitance and dynamics. Since the interfacial dynamics are characterised by different processes taking place on different time scales, the temperature dependence of the dynamics can only be reliably studied by recording and carefully analysing broadband capacitance spectra. Single-frequency experiments may lead to artefacts in the temperature dependence of the interfacial capacitance. We demonstrate that the fast capacitive process exhibits a Vogel-Fulcher-Tamman temperature dependence, since its time scale is governed by the ionic conductivity of the ionic liquid. In contrast, the slower capacitive process appears to be Arrhenius activated. This suggests that the time scale of this process is determined by a temperature-independent barrier, which may be related to structural reorganisations of the Au surface and/or to charge redistributions in the strongly bound innermost ion layer.     

Tail aggregation and domain diffusion in ionic liquids

An extended multiscale coarse-graining model for ionic liquids is used to investigate the liquid crystal-like phase in certain ionic liquids. The tail groups of the cations with a sufficient side-chain length are found to aggregate, forming spatially heterogeneous domains, due to the competition between the electrostatic interactions between the charged head groups and the anions and the collective short-range interactions between the neutral tail groups. With a sufficiently long alkyl chain at a low enough temperature, the tail domains remain relatively stable, despite the diffusion of individual ions in the liquid phase. With increasing temperature, the average tail domains begin to diffuse, while beyond a transition temperature, their average density has an almost uniform distribution, although the tail groups still form instantaneous domains.     

Structure of the electrical double layer on the aqueous solution side of the polarized interface between water and a room-temperature ionic liquid, tetrahexylammonium bis(trifluoromethylsulfonyl)imide

The structure of the electrical double layer on the aqueous solution side has been studied by measuring electrocapillary curves at the polarized interface between a room-temperature ionic liquid (RTIL), tetrahexylammonium bis(trifluoromethylsulfonyl)imide, and water (W) at different concentrations of LiCl. Thermodynamic analysis of the electrocapillary curves indicates that Li+ ions negatively adsorb at the point of zero charge. The adsorption of Li+ and Cl- ions in the polarized potential window of about 200 mV can be explained by the Gouy's double layer model, and the specific adsorption of Li+ and Cl- ions at the RTIL|W interface is negligible within the polarized potential window.     

Relation between the ion size and pore size for an electric double-layer capacitor

The research on electrochemical double layer capacitors (EDLC), also known as supercapacitors or ultracapacitors, is quickly expanding because their power delivery performance fills the gap between dielectric capacitors and traditional batteries. However, many fundamental questions, such as the relations between the pore size of carbon electrodes, ion size of the electrolyte, and the capacitance have not yet been fully answered. We show that the pore size leading to the maximum double-layer capacitance of a TiC-derived carbon electrode in a solvent-free ethyl-methylimmidazolium-bis(trifluoro-methane-sulfonyl)imide (EMI-TFSI) ionic liquid is roughly equal to the ion size (approximately 0.7 nm). The capacitance values of TiC-CDC produced at 500 degrees C are more than 160 F/g and 85 F/cm(3) at 60 degrees C, while standard activated carbons with larger pores and a broader pore size distribution present capacitance values lower than 100 F/g and 50 F/cm(3) in ionic liquids. A significant drop in capacitance has been observed in pores that were larger or smaller than the ion size by just an angstrom, suggesting that the pore size must be tuned with sub-angstrom accuracy when selecting a carbon/ion couple. This work suggests a general approach to EDLC design leading to the maximum energy density, which has been now proved for both solvated organic salts and solvent-free liquid electrolytes.