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Probing the electrical double layer by operando X‐ray photoelectron spectroscopy through a graphene‐carbon nanotube composite window
Abstract The electrical double layer is known to spontaneously form at the electrode‐electrolyte interface, impacting many important chemical and physical processes as well as applications including electrocatalysis, electroorganic synthesis, nanomaterial preparation, energy storage, and even emulsion stabilization. However, it has been challenging to study this fundamental phenomenon at the molecular level because the electrical double layer is deeply “buried” by the bulk electrolyte solution. Here, we report a quantitative probing of the electrical double layer of ionic liquids from the solid side of a photoelectron‐transparent graphene‐carbon nanotube hybrid membrane electrode using X‐ray photoelectron spectroscopy. The membrane window is ultrathin (1‐1.5 nm), large (~1 cm 2 ), and robust, enabling a tight seal of the electrolyte and quantitative measurement with excellent photoelectron signals. By operando monitoring the population changes of cations and anions in response to the applied electrical potentials, we experimentally resolve the chemical structure and dynamics of the electrical double layer, which corroborate results from molecular dynamics simulations. image
Electrical double layers at the oil/water interface
This review presents the historical development and current status of the theory of the electrical double layer at a liquid/liquid interface. It gives rigorous thermodynamic definitions of all basic concepts related to liquid interfaces and to the electrical double layer. The difference between the surface of a solid electrode and the interface of two immiscible electrolyte solutions (ITIES) is analyzed in connection to their electrical properties. The most important classical relationships for the electrical double layer are presented and critically discussed. The generalized adsorption isotherm is derived. After a short review of the classical Gouy-Chapman and Verwey-Niessen models, more recent developments of the double layer theory are presented. These include effects of variable dielectric permittivity, nonlocal electrostatics, hydration forces, the modified Poisson-Boltzmann equation and the ion-dipole plasma. The relative merits of different theories are estimated by comparing them with computer simulation of the ITIES and electrical double layer. Special attention is given to the structure of ITIES and its variation due to adsorption of ions and amphiphilic molecules.
Molecular-scale insights into the electrical double layer at oxide-electrolyte interfaces
The electrical double layer (EDL) at metal oxide-electrolyte interfaces critically affects fundamental processes in water splitting, batteries, and corrosion. However, limitations in the microscopic-level understanding of the EDL have been a major bottleneck in controlling these interfacial processes. Herein, we use ab initio-based machine learning potential simulations incorporating long-range electrostatics to unravel the molecular-scale picture of the EDL at the prototypical anatase TiO 2 -electrolyte interface under various pH conditions. Our large-scale simulations, capable of capturing interfacial water dissociation/recombination reactions and electrolytic proton transport, provide unprecedented insights into the detailed structure of the EDL. Moreover, the larger capacitance of the EDL under basic relative to acidic conditions, originating from the higher affinity of the cations for the oxide surface, is found to give rise to distinct charging mechanisms on negative and positive surfaces. Our results are validated by the agreement between the computed EDL capacitance and experimental data.
Modeling the electrical double layer at solid-state electrochemical interfaces
Models of the electrical double layer (EDL) at electrode/liquid-electrolyte interfaces no longer hold for all-solid-state electrochemistry. Here we show a more general model for the EDL at a solid-state electrochemical interface based on the Poisson–Fermi–Dirac equation. By combining this model with density functional theory predictions, the interconnected electronic and ionic degrees of freedom in all-solid-state batteries, including the electronic band bending and defect concentration variation in the space-charge layer, are captured self-consistently. Along with a general mathematical solution, the EDL structure is presented in various materials that are thermodynamically stable in contact with a lithium metal anode: the solid electrolyte Li 7 La 3 Zr 2 O 12 (LLZO) and the solid interlayer materials LiF, Li 2 O and Li 2 CO 3 . Here, the model further allows design of the optimum interlayer thicknesses to minimize the electrostatic barrier for lithium ion transport at relevant solid-state battery interfaces.
Effect of Soluble Corrosion Products on Electrical Double Layer in LiCl-KCl Molten Salts
Corrosion in molten salts greatly hampers the application for renewable energy applications like molten salt reactors. To develop effective strategies for corrosion mitigation, understanding the interfacial structures and properties such as specific ion adsorption and electrical double layer capacitance are crucial. Using cyclic voltammetry and electrochemical impedance spectroscopy, we systematically studied the interfaces on various model electrodes including W (solid), Bi (liquid), and the stainless steel 316 in LiCl-KCl eutectic molten salts with the addition of corrosion species CrCl 2 and FeCl 2 . Both Cr 2+ and Fe 2+ ions increased electrical double layer capacitance, with Cr 2+ showing specific adsorption behavior and shifting the potential of zero charge, while Fe 2+ had minimal effect on point of zero charge. Two-working electrode measurements revealed increasing open-circuit potential and electrical double layer capacitance during the exposure of stainless steel 316, indicating its progressive corrosion and ion accumulation at the interface. X-ray photoelectron spectroscopy and Raman confirmed Cr enrichment at the interface. This work highlights the strong correlation between electrical double layer behavior and corrosion dynamics in molten salts and suggests electrical double layer capacitance as a sensitive, in situ indicator for corrosion monitoring.
Modeling salt adsorption in electrical double layer for capacitive deionization
Abstract This work presents an electrical double layer (EDL) model for capacitive deionization (CDI) by intercorrelating the salt adsorption, the electrode voltage, and the surface charge density. The counterion condensation is considered a crucial contribution to salt adsorption because of the high surface charge density in the charged micropores. The counterions condense when the surface charge density exceeds a critical value, which is predicted by the counterion condensation theory. The EDL model accurately correlates the NaCl salt adsorption and electrode voltage with various surface charge densities and well predicts the salt adsorption in a wide range of external salt concentrations. The EDL model reproduces the non‐monotonic relationship between the salt adsorption and the specific surface area observed in experiments and provides an explanation from the modeling perspective. Exhibiting superior accuracy and predictability for salt adsorption, the EDL model could serve as an enabling tool contributing to the development of CDI processes.
Dynamic and weak electric double layers in ultrathin nanopores
The unique properties of aqueous electrolytes in ultrathin nanopores have drawn a great deal of attention in a variety of applications, such as power generation, water desalination, and disease diagnosis. Inside the nanopore, at the interface, properties of ions differ from those predicted by the classical ionic layering models (e.g., Gouy–Chapman electric double layer) when the thickness of the nanopore approaches the size of a single atom (e.g., nanopores in a single-layer graphene membrane). Here, using extensive molecular dynamics simulations, the structure and dynamics of aqueous ions inside nanopores are studied for different thicknesses, diameters, and surface charge densities of carbon-based nanopores [ultrathin graphene and finite-thickness carbon nanotubes (CNTs)]. The ion concentration and diffusion coefficient in ultrathin nanopores show no indication of the formation of a Stern layer (an immobile counter-ionic layer) as the counter-ions and nanopore atoms are weakly correlated in time compared to the strong correlation observed in thick nanopores. The weak correlation observed in ultrathin nanopores is indicative of a weak adsorption of counter-ions onto the surface compared to that of thick pores. The vanishing counter-ion adsorption (ion–wall correlation) in ultrathin nanopores leads to several orders of magnitude shorter ionic residence times (picoseconds) compared to the residence times in thick CNTs (seconds). The results of this study will help better understand the structure and dynamics of aqueous ions in ultrathin nanopores.
Structure of the Electrical Double Layer at the Interface between an Ionic Liquid and Tungsten Oxide in Ion-Gated Transistors
The structure of electrical double layers at electrified interfaces is of utmost importance for electrochemical energy storage as well as printable, flexible, and bioelectronic devices, such as ion-gated transistors (IGTs). Here we report a study based on atomic force microscopy force–distance profiling on electrical double layers forming at the interface between the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and sol–gel films of mesoporous tungsten oxide. Here, we successfully followed, under in operando conditions, the evolution of the arrangement of the ions at the interface with the tungsten oxide films used as channel materials in IGTs. Our work sheds light on the mechanism of operation of IGTs, thus offering the possibility of optimizing their performance.
A Gaussian field approach to the planar electric double layer structures in electrolyte solutions
Here, in this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.
Structure of the electrical double layer at the ice–water interface
The surface of ice in contact with water contains sites that undergo deprotonation and protonation and can act as adsorption sites for aqueous ions. Therefore, an electrical double layer should form at this interface and existing models for describing the electrical double layer at metal oxide–water interfaces should be able to be modified to describe the surface charge, surface potential, and ionic occupancy at the ice–water interface. I used a surface complexation model along with literature measurements of the zeta potential of ice in brines of various strength and pH to constrain equilibrium constants. I then made predictions of ion site occupancy, surface charge density, and partitioning of counterions between the Stern and diffuse layers. The equilibrium constant for cation adsorption is more than 5 orders of magnitude larger than the other constants, indicating that this reaction dominates even at low salinity. Deprotonated OH sites are predicted to be slightly more abundant than dangling O sites, consistent with previous work. Surface charge densities are on the order of ±0.001 C/m2 and are always negative at the moderate pH values of interest to atmospheric and geophysical applications (6–9). In this pH range, over 99% of the counterions are contained in the Stern layer. This suggests that diffuse layer polarization will not occur because the ionic concentrations in the diffuse layer are nearly identical to those in the bulk electrolyte and that electrical conduction and polarization in the Stern layer will be negligible due to reduced ion mobility.
Formation of the Electric Double Layer and its Effects on Moving Bodies in a Space Plasma Environment
In this paper we solve the self-consistent Vlasov and Poisson equations by a numerical method to determine the local distribution function of the ion and the electron, within a thin layer near the moving body, respectively. Using these ion and electron distributions, the number density for the ions and electrons are determined, such that, the electric potential is obtained within this thin layer (i.e., measured by Debye length). Numerical results are presented for temporal evolution of the electron and ion density and its corresponding electric potential within the layer which shows the formation of electric double layer and its structures. From these numerical results, we are able to determine the maximum conditions of the electric potential, it may create satellite anomaly.
Insights from machine learning of carbon electrodes for electric double layer capacitors
Recent years have witnessed the broad use of carbon electrodes for electric double layer capacitors (EDLCs) because of large surface area, high porosity and low cost. Whereas experimental investigations are mostly focused on the device performance, computational studies have been rarely concerned with electrochemical properties at conditions remote from equilibrium, limiting their direct applications to materials design. Through a comprehensive analysis of extensive experimental data with various machine-learning methods, we report herein quantitative correlations between the structural features of carbon electrodes and the in-operando behavior of EDLCs including energy and power density. Machine learning allows us to identify important characteristics of activated carbons useful to optimize their efficiency in energy storage.
Interference of electrical double layers: Confinement effects on structure, dynamics, and screening of ionic liquids
Ionic liquids are widely used as electrolytes in electronic devices in which they are subject to nanoconfinement within nanopores or nanofilms. Because the intrinsic width of an electrical double layer is on the order of several nanometers, nanoconfinement is expected to fundamentally alter the double layer properties. Furthermore, in confined systems, a large portion of the ions are interfacial, e.g., at the electrode interface, leading to significant deviations of electrostatic screening and ion dynamics as compared to bulk properties. In this article, we systematically investigate the interference between electrical double layers for nanoconfined ionic liquids and the resulting influence on the structure, dynamics, and screening behavior. We perform molecular dynamics simulations for the ionic liquids [BMIm + ][BF$^-_4$] and [BMIm + ][PF$^-_6$] confined between two flat electrodes at systematic separation distances between 1.5 nm and 4.5 nm for both conducting and insulating boundary conditions. We find that while ion dynamics is expectedly slower than in the bulk (by ~2 orders of magnitude), there is an unexpected non-linear trend with the confinement length that leads to a local maximum in dynamic rates at ~3.5–4.5 nm confinement. We show that this nonlinear trend is due to the ion correlation that arises from the interference between opposite double layers. We further evaluate confinement effects on the ion structure and capacitance and investigate the influence of electronic polarization of the ionic liquid on the resulting properties. This systematic evaluation of the connection between electrostatic screening and structure and dynamics of ionic liquids in confined systems is important for the fundamental understanding of electrochemical supercapacitors.
A Comparative Study of Electrical Double Layer Effects for CO Reduction Reaction Kinetics
Solvation models describe how the interactions between the solutes and solvents affect the reactivity and selectivity in electrochemical processes. In this study, we developed a framework for evaluating the effects of applied potential and electrical double layer on CO reduction (COR), comparing fully explicit, implicit, and hybrid solvation models at the standard hydrogen electrode (SHE) scale. We analyzed all crucial intermediates leading to the production of C 1 and C 2 products and found good agreement across these models. Some notable differences were observed in the implicit description of *C and *CO adsorption at higher overpotentials and overall trends in the adsorption energies within the hybrid model. Using this unified SHE framework, we built comparable microkinetic models for COR kinetics and rates. Despite small differences in thermodynamics, solvation-model-based microkinetic simulations showed good agreement for onset potentials against the benchmark experiment. Only qualitative difference was observed for C 1+ versus hydrogen evolution at high overpotentials for the implicit model. Finally, we constructed a generalized C 2 selectivity map in descriptor space (U SHE , ΔG electrolyte CO ), which highlights the limitations of a copper-based COR catalyst and guides the search for optimal descriptor parameters to maximize C 2 selectivity. In conclusion, these findings demonstrate the importance of considering electrical double layer effects in reduction reactions and offer a useful framework for comparing solvation models and predicting optimal electrochemical conditions for specific applications.
Evaluation of Methods for Molecular Dynamics Simulation of Ionic Liquid Electric Double Layers
We investigate how systematically increasing the accuracy of various molecular dynamics modeling techniques influences the structure and capacitance of ionic liquid electric double layers (EDLs). The techniques probed concern long-range electrostatic interactions, electrode charging (constant charge versus constant potential conditions), and electrolyte polarizability. Our simulations are performed on a quasi-two-dimensional, or slab-like, model capacitor, which is composed of a polarizable ionic liquid electrolyte, [EMIM][BF4], interfaced between two graphite electrodes. To ensure an accurate representation of EDL differential capacitance, we derive new fluctuation formulas that resolve the differential capacitance as a function of electrode charge or electrode potential. The magnitude of differential capacitance shows sensitivity to different long-range electrostatic summation techniques, while the shape of differential capacitance is affected by charging technique and the polarizability of the electrolyte. For long-range summation techniques, errors in magnitude can be mitigated by employing two-dimensional or corrected three dimensional electrostatic summations, which lead to electric fields that conform to those of a classical electrostatic parallel plate capacitor. With respect to charging, the changes in shape are a result of ions in the Stern layer (i.e. ions at the electrode surface) having a higher electrostatic affinity to constant potential electrodes than to constant charge electrodes. For electrolyte polarizability, shape changes originate from induced dipoles that soften the interaction of Stern layer ions with the electrode. The softening is traced to ion correlations vertical to the electrode surface that induce dipoles that oppose double layer formation. In general, our analysis indicates an accuracy dependent differential capacitance profile that transitions from the characteristic camel shape with coarser representations to a more diffuse profile with finer representations.
Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer
Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI) 2 ], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI) 2 ], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.