Electrical double layers and differential capacitance in molten salts from density functional theory

Integrative studies of ionic liquid interface layers: bridging experiments, theoretical models and simulations

Ionic liquids (ILs) are a class of salts existing in the liquid state below 100 °C, possessing low volatility, high thermal stability as well as many highly attractive solvent and electrochemical capabilities, etc., making them highly tunable for a great variety of applications, such as lubricants, electrolytes, and soft functional materials. In many applications, ILs are first either physi- or chemisorbed on a solid surface to successively create more functional materials. The functions of ILs at solid surfaces can differ considerably from those of bulk ILs, mainly due to distinct interfacial layers with tunable structures resulting in new ionic liquid interface layer properties and enhanced performance. Due to an almost infinite number of possible combinations among the cations and anions to form ILs, the diversity of various solid surfaces, as well as different external conditions and stimuli, a detailed molecular-level understanding of their structure-property relationship is of utmost significance for a judicious design of IL-solid interfaces with appropriate properties for task-specific applications. Many experimental techniques, such as atomic force microscopy, surface force apparatus, and so on, have been used for studying the ion structuring of the IL interface layer. Molecular Dynamics simulations have been widely used to investigate the microscopic behavior of the IL interface layer. To interpret and clarify the IL structure and dynamics as well as to predict their properties, it is always beneficial to combine both experiments and simulations as close as possible. In another theoretical model development to bridge the structure and properties of the IL interface layer with performance, thermodynamic prediction & property modeling has been demonstrated as an effective tool to add the properties and function of the studied nanomaterials. Herein, we present recent findings from applying the multiscale triangle "experiment-simulation-thermodynamic modeling" in the studies of ion structuring of ILs in the vicinity of solid surfaces, as well as how it qualitatively and quantitatively correlates to the overall ILs properties, performance, and function. We introduce the most common techniques behind "experiment-simulation-thermodynamic modeling" and how they are applied for studying the IL interface layer structuring, and we highlight the possibilities of the IL interface layer structuring in applications such as lubrication and energy storage.

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.

The differential capacitance as a probe for the electric double layer structure and the electrolyte bulk composition

In this work, we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical density functional theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly and also how small ions dominate its behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.

Influence of dielectric layers on estimates of diffusion coefficients and concentrations of ions from impedance spectroscopy

We present the analysis of the impedance spectra for a binary electrolyte confined between blocking electrodes with dielectric layers. An expression for the impedance is derived from Poisson-Nernst-Planck equations in the linear approximation taking into account the voltage drop on the dielectric layer. The analysis shows that characteristic features of the frequency dependence of the impedance are determined by the ratio of the Debye length and the effective thickness of the dielectric layer. The impact of the dielectric layer is especially strong in the case of high concentrated electrolytes, where the Debye length is small and thus comparable to the effective thickness of the dielectric layer. To verify the model, measurements of the impedance spectra and transient currents in a liquid crystal 4-n-pentyl-4^{'}-cyanobiphenyl (5CB) confined between polymer-coated electrodes in cells of different thicknesses are performed. The estimates for the diffusion coefficient and ion concentration in 5CB obtained from the analysis of the impedance spectra and the transient currents are consistent and agree with previously reported data. We demonstrate that calculations of the ion parameters from the impedance spectra without taking into account the dielectric layer contribution lead in most cases to incorrect results. Application of the model to analyze violations of the low-frequency impedance scaling and contradictions in the estimates of the ion parameters recently found in some ionic electrolytes are discussed.

Electrical double layer in molten salts with account of soft repulsions

Results of Monte Carlo simulations of the electrode-molten salt interface are reported. The system was modeled by soft ions in contact with a soft wall using the Lennard-Jones potential restricted to the repulsion part. The soft wall was formed of C (graphite), Hg, and Pb atoms. Calculations were carried out for the parameter values which would permit making comparison with the real system. The paper presents information on physicochemical properties of the interfacial region, such as the ion singlet distribution functions, the mean electrostatic potential as a function of the distance from the electrode surface, and differential capacitance results as a function of the electrode charges. The differential capacitance curves have a flat and distorted bell shape which vary depending on the kind of the electrode material. The differential capacitance results are discussed and compared with the data obtained from ionic liquid simulations, density functional theory, and mean field calculations.

Analysis of electrical double layer structure in molten salts

This paper reports the results of analysis of the electrical double layer (EDL) phenomenon in molten salts to provide information on the influence of short range interaction type on the shape of charge distribution and the effect of the charge distribution shape on capacitance values. A new method of analysis is proposed, which allows a quantitative discussion. It is assumed that EDL can be modelled as a number of capacitor plates connected in series. This paper reports the application of the proposed method in quantitative analysis of the molten salt capacitance data obtained for different short range potentials. The data to be analysed were obtained from the Monte Carlo simulations of the symmetrical molten salt electrolyte for the following short range interaction potentials: hard spheres, Lennard-Jones repulsions, and full Lennard-Jones. The new analysis method gives a more detailed understanding of EDL in molten salts and can become an inspiration for new researches in this field.

The linear relationship derived from the deposition potential of Pb–Ln alloy and atomic radius

Lanthanides possess extremely similar properties because their radius only changes slightly due to lanthanide contraction.

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.