On the temperature dependence of the double layer capacitance of ionic liquids

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

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

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

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

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.

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.

Water in the Electrical Double Layer of Ionic Liquids on Graphene

The performance of electrochemical devices using ionic liquids (ILs) as electrolytes can be impaired by water uptake. This work investigates the influence of water on the behavior of hydrophilic and hydrophobic ILs─with ethylsulfate and tris(perfluoroalkyl)trifluorophosphate or bis(trifluoromethyl sulfonyl)imide (TFSI) anions, respectively─on electrified graphene, a promising electrode material. The results show that water uptake slightly reduces the IL electrochemical stability and significantly influences graphene's potential of zero charge, which is justified by the extent of anion depletion from the surface. Experiments confirm the dominant contribution of graphene's quantum capacitance (C_Q) to the total interfacial capacitance (C_int) near the PZC, as expected from theory. Combining theory and experiments reveals that the hydrophilic IL efficiently screens surface charge and exhibits the largest double layer capacitance (C_IL ∼ 80 μF cm^-2), so that C_Q governs the charge stored. The hydrophobic ILs are less efficient in charge screening and thus exhibit a smaller capacitance (C_IL ∼ 6-9 μF cm^-2), which governs C_int already at small potentials. An increase in the total interfacial capacitance is observed at positive voltages for humid TFSI-ILs relative to dry ones, consistent with the presence of a satellite peak. Short-range surface forces reveal the change of the interfacial layering with potential and water uptake owing to reorientation of counterions, counterion binding, co-ion repulsion, and water enrichment. These results are consistent with the charge being mainly stored in a ∼2 nm-thick double layer, which implies that ILs behave as highly concentrated electrolytes. This knowledge will advance the design of IL-graphene-based electrochemical devices.

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.

On the importance of the electric double layer structure in aqueous electrocatalysis

To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and a structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.

Salt-in-Ionic-Liquid Electrolytes: Ion Network Formation and Negative Effective Charges of Alkali Metal Cations

Salt-in-ionic liquid electrolytes have attracted significant attention as potential electrolytes for next generation batteries largely due to their safety enhancements over typical organic electrolytes. However, recent experimental and computational studies have shown that under certain conditions alkali cations can migrate in electric fields as if they carried a net negative effective charge. In particular, alkali cations were observed to have negative transference numbers at small mole fractions of alkali-metal salt that revert to the expected net positive transference numbers at large mole fractions. Simulations have provided some insights into these observations, where the formation of asymmetric ionic clusters, as well as a percolating ion network, could largely explain the anomalous transport of alkali cations. However, a thermodynamic theory that captures such phenomena has not been developed, as ionic associations were typically treated via the formation of ion pairs. The theory presented herein, based on the classical polymer theories, describes thermoreversible associations between alkali cations and anions, where the formation of large, asymmetric ionic clusters and a percolating ionic network are a natural result of the theory. Furthermore, we present several general methods to calculate the effective charge of alkali cations in ionic liquids. We note that the negative effective charge is a robust prediction with respect to the parameters of the theory and that the formation of a percolating ionic network leads to the restoration of net positive charges of the cations at large mole fractions of alkali metal salt. Overall, we find excellent qualitative agreement between our theory and molecular simulations in terms of ionic cluster statistics and the effective charges of the alkali cations.

Effects of Confinement and Ion Adsorption in Ionic Liquid Supercapacitors with Nanoporous Electrodes

We investigate the effects of pore size and ion adsorption on the room-temperature ionic liquid capacitor with nanoporous electrodes, with a focus on optimizing the capacitance and energy storage. Using a recently developed modified BSK model accounting for both ion correlations and nonelectrostatic interactions, we find that ion crowding proximate to the electrode surface induced by the spontaneous charge separation due to strong ion correlations is responsible for the anomalous increase in the capacitance with decreasing pore sizes observed in experiments. Reducing the strength of ion correlations increases the capacitance and suppresses the anomalous size dependence. For a given pore size, the capacitance peak diverges when the ion correlation strength α reaches a critical value, α_sc,L. The capacitance peak shifts to smaller pore size as α decreases because of rapid decrease of α_sc,L with decreasing pore size. Asymmetric preferential ion adsorption is shown to lead to significantly enhanced energy storage close to the transition point for any pore sizes. For a given correlation strength, the energy storage is optimal at a pore size where α = α_sc,L.

Structure of cholinium glycinate biocompatible ionic liquid at graphite electrode interface

We use constant potential molecular dynamics simulations to investigate the interfacial structure of the cholinium glycinate biocompatible ionic liquid (bio-IL) sandwiched between graphite electrodes with varying potential differences. Through number density profiles, we observe that the cation and anion densities oscillate up to ∼1.5 nm from the nearest electrode. The range of these oscillations does not change significantly with increasing electrode potential. However, the amplitudes of the cation (anion) density oscillations show a notable increase with increasing potential at the negative (positive) electrode. At higher potential differences, the bulkier N(CH₃)₃CH₂ group of cholinium cations ([Ch]⁺) overcomes the steric barrier and comes closer to the negative electrode as compared to oxygen atom (O_[Ch]⁺ ). We observe an increase in the interaction between O_[Ch]⁺ and the positive electrode with a decrease in the distance between them on increasing the potential difference. We also observe hydrogen bonding between the hydroxyl group of [Ch]⁺ cations and oxygens of glycinate anions through the simulated tangential radial distribution function. Orientational order parameter analysis shows that the cation (anion) prefers to align parallel to the negative (positive) electrode at higher applied potential differences. Charge density profiles show a positive charge density peak near the positive electrode at all the potential differences because of the presence of partially positive charged hydrogen atoms of cations and anions. The differential capacitance (C_d) of the bio-IL shows two constant regimes, one for each electrode. The magnitude of these C_d values clearly suggests potential application of such bio-ILs as promising battery electrolytes.

Evaluation of static differential capacitance at the [C4mim+][TFSA-]/electrode interface using molecular dynamics simulation combined with electrochemical surface plasmon resonance measurements

Molecular dynamic (MD) simulations have been performed for 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide ([C₄mim⁺][TFSA^-]), an ionic liquid (IL), on a charged graphene electrode to achieve the quantitative analysis of the static differential capacitance using the electrochemical surface plasmon resonance (ESPR). The MD simulations have provided the surface charge density on the electrode and ionic distributions in the electric double layer, both of which are indispensable for the evaluation of static differential capacitance using ESPR but are difficult to be measured by experimental techniques. This approach has allowed the quantitative analysis and explanation of the SPR angle shift in ESPR. The major contribution to the SPR angle shift is found to be the change in ionic concentrations of the first ionic layer on the electrode, owing to higher polarizabilities of ions in the first ionic layer than those in the overlayers. Moreover, the ionic orientation on the electrode and ionic multilayer structure have also been investigated in detail. The butyl group of C₄mim⁺ in the first ionic layer is found to provide extra room for C₄mim⁺ in the second ionic layer but exclude TFSA^-, which affects the interval and regularity of ionic multilayers.

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.

Correlated Ion Transport and the Gel Phase in Room Temperature Ionic Liquids

Here we present a theory of ion aggregation and gelation of room temperature ionic liquids (RTILs). Based on it, we investigate the effect of ion aggregation on correlated ion transport-ionic conductivity and transference numbers-obtaining closed-form expressions for these quantities. The theory depends on the maximum number of associations a cation and anion can form and the strength of their association. To validate the presented theory, we perform molecular dynamics simulations on several RTILs and a range of temperatures for one RTIL. The simulations indicate the formation of large clusters, even percolating through the system under certain circumstances, thus forming a gel, with the theory accurately describing the obtained cluster distributions in all cases. However, based on the strength and lifetime of associations in the simulated RTILs, we expect free ions to dominate ionic conductivity despite the presence of clusters, and we do not expect the percolating cluster to trigger structural arrest in the RTIL.

Electrochemical surface plasmon resonance measurements of camel-shaped static capacitance and slow dynamics of electric double layer structure at the ionic liquid/electrode interface

Electrochemical surface plasmon resonance (ESPR) is applied to evaluate the relative static differential capacitance at the interface between 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide ionic liquid (IL) and a gold electrode, based on the relationship between the SPR angle and surface charge density on the electrode. Potential-step and potential-scan ESPR measurements are used to probe the dynamics of the electric double layer (EDL) structure that exhibit anomalously slow and asymmetrical characteristics depending on the direction of potential perturbation. EDL dynamics respond at least 30 times more slowly to changes of potential in the positive direction than in the negative direction. ESPR experiments with the positive-going potential scan are significantly affected by the slow dynamics even at a slow scan. The surface charge density that reflects the relative static capacitance is obtained from the negative-going potential scans. The evaluated quasi-static differential capacitance exhibits a camel-shaped potential dependence, thereby agreeing with the prediction of the mean-field lattice gas model of the EDL in ILs. ESPR is shown to be an effective experimental method for determining relative values of the static differential capacitance.

Temperature dependence of differential capacitance in the electric double layer.Symmetric valency 1:1 electrolytes

The differential capacitance of an electric double layer formed by an aqueous solution of KNO₃ on a glassy carbon electrode is measured by impedance analysis at constant frequency. Results are obtained at electrolyte concentrations of 0.1 mol/dm³, 0.5 mol/dm³, and 1.0 mol/dm³, and at a series of temperatures, viz., 288 K, 298 K, 308 K, 318 K, and 328 K. The differential capacitance envelopes reveal a rich, complex pattern of maxima, minima, and local minima, whose magnitude and position change with a change in solution concentration. At the two lower concentrations, the temperature dependence of the capacitance, for example, at zero electrode potential, shows an alternating positive-negative behavior, while at the highest concentration of 1.0 mol/dm³, the slope of the differential capacitance-electrode potential curve is always positive. The experimental results are supplemented by a numerical grand canonical Monte Carlo simulation study of a restricted primitive model double layer but with an off-center cationic charge achieved by displacing the charge center from the ion sphere center toward its surface. The simulations, performed at the electrolyte concentration of 1.0 mol/dm³ and constant cation charge center displacement, and at varying electrode potentials and temperatures, show, in general, a negative temperature dependence of the differential capacitance. However, this temperature dependence can also be positive for a negative electrode charge and for a sufficiently large gradient of the cation charge center displacement with temperature. This feature is seen to be associated with an increase in the entropy of formation of the double layer.

Effects of Surface Transition and Adsorption on Ionic Liquid Capacitors

Room-temperature ionic liquids (RTILs) are synthetic electrolytes with electrochemical stability superior to that of conventional aqueous-based electrolytes, allowing a significantly enlarged electrochemical window for application as capacitors. In this study, we propose a variant of an existing RTIL model for solvent-free RTILs, accounting for both ion-ion correlations and nonelectrostatic interactions. Using this model, we explore the phenomenon of spontaneous surface charge separation in RTIL capacitors and find that this transition is a common feature for realistic choices of the model parameters in most RTILs. In addition, we investigate the effects of asymmetric preferential ion adsorption on this charge separation transition and find that proximity of the transition in this case can result in greatly enhanced energy storage. Our work suggests that differential chemical treatment of electrodes can be a simple and useful means for optimizing energy storage in RTIL capacitors.

NaRIBaS—A Scripting Framework for Computational Modeling of Nanomaterials and Room Temperature Ionic Liquids in Bulk and Slab

Computational modeling is more and more often used in studies of novel ionic liquids. The inevitable side-effect is the growing number of similar computations that require automation. This article introduces NaRIBaS (Nanomaterials and Room Temperature Ionic Liquids in Bulk and Slab)—a scripting framework that combines bash scripts with computational codes to ease modeling of nanomaterials and ionic liquids in bulk and slab. NaRIBaS helps to organize and document all input and output data, thus, improving the reproducibility of computations. Three examples are given to illustrate the NaRIBaS workflows for density functional theory (DFT) calculations of ionic pairs, molecular dynamics (MD) simulations of bulk ionic liquids (ILs), and MD simulations of ILs at an interface.

Theory of the Double Layer in Water-in-Salt Electrolytes

One challenge in developing the next generation of lithium-ion batteries is the replacement of organic electrolytes, which are flammable and most often contain toxic and thermally unstable lithium salts, with safer, environmentally friendly alternatives. Recently developed water-in-salt electrolytes (WiSEs), which are nonflammable, nontoxic, and also have enhanced electrochemical stability, are promising alternatives. In this work, we develop a simple modified Poisson-Fermi theory for WiSEs, which demonstrates the fine interplay between electrosorption, solvation, and ion correlations. The phenomenological parameters are extracted from molecular dynamics simulations, also performed here. The theory reproduces the WiSEs' electrical double-layer structure with remarkable accuracy.

Modeling the camel-to-bell shape transition of the differential capacitance using mean-field theory and Monte Carlo simulations

Mean-field electrostatics is used to calculate the differential capacitance of an electric double layer formed at a planar electrode in a symmetric 1:1 electrolyte. Assuming the electrolyte is also ion-size symmetric, we derive analytic expressions for the differential capacitance valid up to fourth order in the surface charge density or surface potential. Our mean-field model accounts exclusively for electrostatic interactions but includes an arbitrary non-ideality in the mixing entropy of the mobile ions. The ensuing criterion for the camel-to-bell shape transition of the differential capacitance is analyzed using commonly used mixing models (one based on a lattice gas and the other based on the Carnahan-Starling equation of state) and compared with Monte Carlo simulations. We observe a reasonable agreement between all our mean-field models and the simulation data for the camel-to-bell shape transition. The absolute value of the differential capacitance for an uncharged (or weakly charged) electrode is, however, not reproduced by our mean-field approaches, not even upon introducing a Stern layer with a thickness equal of the ion radius. We show that, if a Stern layer is introduced, its thickness dependence on the ion size is non-monotonic or, depending on the salt concentration, even inversely proportional.

General theory of charge regulation and surface differential capacitance

A generalization of the mean-field approach will be derived that will take into account the ion-ion as well as ion-surface non-electrostatic effects on an equal footing, being based on the bulk and surface equations of state in the absence of electrostatic interactions. This approach will be applied to the analysis of a single planar surface with dissociable sites with several models of the specific ion-surface non-electrostatic interactions, providing a general thermodynamic insight into the characteristics of the surface differential capacitance. The ion-surface interactions and ion-ion packing considerations at the surface will be shown to be more relevant than the bulk packing constraints for ions vicinal to the surface, as well as to set in prior to the conditions where the bulk packing constraints would become relevant.

A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes. II. Accounts of ionic interactions

A size-asymmetric mean-field theory with ionic interactions is developed for the electric double layer of room temperature ionic liquid (IL) electrolytes, based on the previous work on non-interacting ions (Y. Han et al., J. Phys.: Condens. Matter, 2014, 26, 284103). By solving the modified Poisson-Boltzmann equation with some simplified assumptions following a recent work (Z. A. H. Goodwin et al., Electrochim. Acta, 2017, 225, 190-197), an analytical expression of differential capacitance can be derived, with a scaled electrode potential due to the ionic interactions. Compared with non-interacting ions, the main effect of ionic interactions is the insufficient screening of the electrode potential, and this depresses the differential capacitance compared with the non-interactive case.