Historical development of theories of the electrochemical double layer

Capacitance Measurements for Evaluating Electrochemical Double-Layer Models and Potentials of Zero Charge: A Reassessment

Differential capacitances (DCAPs) derived from electrostatic Gouy-Chapman-type models for electrochemical double layers (DLs) typically show valley-, bell-, or camel-type profiles as a function of the potential, centered around the potential of zero charge. These DCAP profiles are routinely evaluated with measured potential dependencies of capacitances. Here, the influences of hydrogen evolution, oxygen reduction, and oxide formation on the potential dependence of the capacitance of a polished gold electrode are experimentally examined. These parasitic reactions are found to cause most of the potential-dependent capacitance features that are typically attributed to intrinsic DL properties. With these insights, the historical development of the literature regarding the development of the theoretical framework in relation to capacitance measurements is critically reevaluated. As a result, drawbacks of the 100-year-old Gouy-Chapman theory for the DL are identified. Moreover, DCAPs as differences of electrostatic states are discussed as unable to portray measured capacitances that result from capacitive-resistive and dynamic charge displacements in the DL. Hence, the links between theories and experiments are critically assessed, motivating the need for more advanced atomistic models to adequately portray the DL.

Establishment of Solid-Liquid-Solid Double-Layer Model of Silicon-Aluminum Phase in Mixed-Medium and Synergistic Stabilization Experimental Study

The issue of low resource utilization rate and high treatment cost in the disposal of construction waste and solid waste was a challenging problem. In order to seek a synergistic and efficient treatment method, based on the similarity of microstructural characteristics between clay, solid waste, and lithium slag particles, a dual-layer theory and model was used to conduct adaptive analysis at the electrochemical level, studying the solid-liquid-solid dual-layer theoretical model suitable for silicon-aluminum-phase materials. At the same time, the phenomenon of particle interface contact and the influence mechanism of ion adsorption on the surface of particles in the liquid phase were discussed, analyzing the ion selection mechanism for regulating the dual-layer of silicon-aluminum-phase materials and studying the method of clay-modified stabilization based on solid waste. Further laboratory tests and microscopic analyses were conducted to determine the engineering properties of the soil stabilized by the clay-solid waste synergistic stabilization and verified the effectiveness of the method. The research results showed that the trial soil stabilized by the theoretical model guidance was significantly stronger in unconfined compressive strength (1.44 MPa at 28 days) than the undisturbed clay (0.26 MPa at 28 days), and the scanning electron microscope (SEM) microscopic analysis results showed that the microscopic morphology of the modified stabilized soil specimen was tightly woven with a high-strength network-like structure. The research provided a theoretical basis and experimental reference for the synergistic treatment and resource utilization of waste soft soil and solid waste engineering problems.

Structural Basis of Ultralow Capacitances at Metal-Nonaqueous Solution Interfaces

Metal-nonaqueous solution interfaces, a key to many electrochemical technologies, including lithium metal batteries, are much less understood than their aqueous counterparts. Herein, on several metal-nonaqueous solution interfaces, we observe capacitances that are 2 orders of magnitude lower than the usual double-layer capacitance. Combining electrochemical impedance spectroscopy, atomic force microscopy, and physical modeling, we ascribe the ultralow capacitance to an interfacial layer of 10-100 nm above the metal surface. This nanometric layer has a Young's modulus around 2 MPa, which is much softer than typical solid-electrolyte interphase films. In addition, its AC ionic conductivity is 4-to-5 orders of magnitude lower than that of the bulk electrolyte. The temperature dependencies of the AC ionic conductivity and thickness suggest that the soft layer is formed from metal-mediated, dipole-dipole interactions of the nonaqueous solvent molecules. The observed soft layer opens new avenues of modulating battery performance via rational design of ion transport, (de)solvation, and charge transfer in this interfacial region.

How to Assess and Predict Electrical Double Layer Properties. Implications for Electrocatalysis

The electrical double layer (EDL) plays a central role in electrochemical energy systems, impacting charge transfer mechanisms and reaction rates. The fundamental importance of the EDL in interfacial electrochemistry has motivated researchers to develop theoretical and experimental approaches to assess EDL properties. In this contribution, we review recent progress in evaluating EDL characteristics such as the double-layer capacitance, highlighting some discrepancies between theory and experiment and discussing strategies for their reconciliation. We further discuss the merits and challenges of various experimental techniques and theoretical approaches having important implications for aqueous electrocatalysis. A strong emphasis is placed on the substantial impact of the electrode composition and structure and the electrolyte chemistry on the double-layer properties. In addition, we review the effects of temperature and pressure and compare solid-liquid interfaces to solid-solid interfaces.

Influence of Potentiostat Hardware on Electrochemical Measurements

We describe two operating modes for the same potentiostat, where the redox processes of hydroquinone in a hydrochloric acid medium are contrasted for cyclic voltammetry (CV) as functions of a digital/staircase scan and an analogue/linear scan. Although superficially there is not much to separate the two modes of operation as an end user, differences can be seen in the voltammograms while switching between the digital and analogue modes. The effects of quantization clearly have some impact on the measurements, with the outputs between the two modes being a function of the equivalent-circuit model of the electrochemical system under investigation. Increasing scan rates when using both modes produces higher peak redox currents, with the differences between the analogue and digital modes of operation being consistent as a function of the scan rate. Differences between the CV loops between the analogue and digital modes show key differences at certain points along the scans, which can be attributed to the nature of the electrolyte affecting the charging and discharging processes and consequently changing the peak currents of the redox processes. The faradaic processes were shown to be independent of the scan rates. Simulations of the equivalent-circuit behaviour show differences in the responses to different input signals, i.e., the step and ramp responses of the system. Both the voltage and current steps and ramp responses showed the time-domain behaviour of distinct elements of the equivalent electrochemical circuit model as an approximation of the applied digital and analogue CV input signals. Ultimately, it was concluded that similar parameters between the two modes of operation available with the potentiostat would lead to different output voltammograms and, despite advances in technology, digital systems can never fully emulate a true analogue system for electrochemical applications. These observations showcase the value of having hardware capable of true analogue characteristics over digital systems.

High-Performance Aluminum Fuels Induced by Monolayer Self-Assembly of Nano-Sized Energetic Fluoride Vesicles on the Surface

Surface modification is frequently used to solve the problems of low combustion properties and agglomeration for aluminum-based fuels. However, due to the intrinsic incompatibility between the aluminum powder and the organic modifiers, the surface coating is usually uneven and disordered, which significantly deteriorates the uniformity and performances of the Al-based fuels. Herein, a new approach of monolayer nano-vesicular self-assembly is proposed to prepare high-performance Al fuels. Triblock copolymer G-F-G is produced by glycidyl azide polymer (GAP) and 2,2'-(2,2,3,3,4,5,5-Octafluorohexane-1,6-diyl) bis (oxirane) (fluoride) ring-open addition reaction. By utilizing G-F-G vesicular self-assembly in a special solvent, the nano-sized vesicles are firmly adhered to the surface of Al powder through the long-range attraction between the fluorine segments and Al. Meanwhile, the electrostatic repulsion between vesicles ensures an extremely thin coating thickness (≈15 nm), maintaining the monolayer coating structure. Nice ignition, combustion, anti-agglomeration, and water-proof properties of Al@G-F-G(DMF) are achieved, which are superior among the existing Al-based fuels. The derived Al-based fuel has excellent comprehensive properties, which can not only inspire the development of new-generation energetic materials but also provide facile but exquisite strategies for exquisite surface nanostructure construction via ordered self-assembly for many other applications.

Choice of the Right Supporting Electrolyte in Electrochemical Reductions: A Principal Component Analysis

We present an analysis of a set of molecular, electrical, and electronic properties for a large number of the cations of quaternary ammonium salts usually employed as supporting electrolytes in cathodic reduction reactions. The goal of the present study is to define a measure for the quality of a supporting electrolyte in terms of the yield of the reaction considered. We performed a principal component analysis using the normalized values of the properties in order to lower the number of relevant reaction coordinates and find that the integral variance of 13 properties can well be represented by three principal components. The yield of the electrochemical hydrodimerization of acrylonitrile employing different quaternary ammonium salts as supporting electrolytes was determined in a series of experiments. We found only a very weak correlation between the yield and the values of the properties but a strong correlation between the yield and the values of the most important principal component. Very similar results are obtained for two further existing systematic experimental studies of the impact of the supporting electrolyte on the yield of cathodic reductions. For all three example reactions, a supervised regression using the two most important principal components as variables yields excellent values for the coefficients of determination. For comparison, we also applied our methodology to sets of purely structure-based features that are usually employed in cheminformatics and obtained results of almost similar quality. We therefore conjecture that our methodology in combination with a small number of experiments can be used to predict the yield of a given cathodic reduction on the basis of the properties of the supporting electrolyte.

How microstructures, oxide layers, and charge transfer reactions influence double layer capacitances. Part 1: impedance spectroscopy and cyclic voltammetry to estimate electrochemically active surface areas (ECSAs)

Varying the electrode potential rearranges the charges in the double layer (DL) of an electrochemical interface by a resistive-capacitive current response. The capacitances of such charge relocations are frequently used in the research community to estimate electrochemical active surface areas (ECSAs), yet the reliability of this methodology is insufficiently examined. Here, the relation of capacitances and ECSAs is critically assessed with electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV) data on polished (Au, Ti, Ru, Pt, Ni, glassy carbon, graphite plate) and porous (carbon fleeces) electrodes. By investigating this variety of electrodes, the frequency-dependencies observed in the measured capacitances are shown to arise from the inherent resistive-capacitive DL response, charge transfer reactions, and resistively damped capacitive currents in microstructures (such as pores, pinholes, or cracks). These frequency-dependencies are typically overlooked when capacitances are related to ECSAs. The capacitance at the specimen-characteristic relaxation frequency of the resistive-capacitive DL response is proposed as a standardized capacitance-metric to estimate ECSAs. In 1 M perchloric acid, the polished gold electrode and the high-surface area carbon fleeces show ratios of capacitance-metric over surface-area of around 3.7 μF cm-2. Resistively damped currents in microstructures and low-conducting oxide layers are shown to complicate trustworthy capacitance-based estimations of ECSAs. In the second part of this study, advanced equivalent circuits models to describe the measured EIS and CV responses are presented.

Charges Transfer in Interfaces for Energy Generating

Under the threat of energy crisis and environmental pollution, the technology for sustainable and clean energy extraction has received considerable attention. Owing to the intensive exploration of energy conversion strategies, expanded energy sources are successfully converted into electric energy, including mechanical energy from human motion, kinetic energy of falling raindrops, and thermal energy in the ambient. Among these energy conversion processes, charge transfer at different interfaces, such as solid-solid, solid-liquid, liquid-liquid, and gas-contained interfaces, dominates the power-generating efficiency. In this review, the mechanisms and applications of interfacial energy generators (IEGs) with different interface types are systematically summarized. Challenges and prospects are also highlighted. Due to the abundant interfacial interactions in nature, the development of IEGs offers a promising avenue of inexhaustible and environmental-friendly power generation to solve the energy crisis.

Zooming into the Inner Helmholtz Plane of Pt(111)-Aqueous Solution Interfaces: Chemisorbed Water and Partially Charged Ions

The double layer on transition metals, i.e., platinum, features chemical metal-solvent interactions and partially charged chemisorbed ions. Chemically adsorbed solvent molecules and ions are situated closer to the metal surface than electrostatically adsorbed ions. This effect is described tersely by the concept of an inner Helmholtz plane (IHP) in classical double layer models. The IHP concept is extended here in three aspects. First, a refined statistical treatment of solvent (water) molecules considers a continuous spectrum of orientational polarizable states, rather than a few representative states, and non-electrostatic, chemical metal-solvent interactions. Second, chemisorbed ions are partially charged, rather than being electroneutral or having integral charges as in the solution bulk, with the coverage determined by a generalized, energetically distributed adsorption isotherm. The surface dipole moment induced by partially charged, chemisorbed ions is considered. Third, considering different locations and properties of chemisorbed ions and solvent molecules, the IHP is divided into two planes, namely, an AIP (adsorbed ion plane) and ASP (adsorbed solvent plane). The model is used to study how the partially charged AIP and polarizable ASP lead to intriguing double-layer capacitance curves that are different from what the conventional Gouy-Chapman-Stern model describes. The model provides an alternative interpretation for recent capacitance data of Pt(111)-aqueous solution interfaces calculated from cyclic voltammetry. This revisit brings forth questions regarding the existence of a pure double-layer region at realistic Pt(111). The implications, limitations, and possible experimental confirmation of the present model are discussed.

Benefits of electrochemistry studies for the majority of students who will not become electrochemists

In teaching electrochemistry, it is of primary importance to make students always aware of the relations between electrochemistry and all the non-electrochemical topics, which are taught. The vast majority of students will not specialise in electrochemistry, but they all can very much benefit from the basics and concepts of electrochemistry. This paper is aimed to give suggestions how the teaching of electrochemistry can easily be interrelated to topics of inorganic, organic, analytical, environmental chemistry, biochemistry and biotechnology.

Recent Progresses in Adsorption Mechanism, Architectures, Electrode Materials and Applications for Advanced Electrosorption System: A Review

As an advanced strategy for water treatment, electrosorb technology has attracted extensive attention in the fields of seawater desalination and water pollution treatment due to the advantages of low consumption, environmental protection, simplicity and easy regeneration. In this work, the related adsorption mechanism, primary architectures, electrode materials, and applications of different electrosorption systems were reviewed. In addition, the developments for advanced electrosorb technology were also summarized and prospected.

Water electrolysis: from textbook knowledge to the latest scientific strategies and industrial developments

Replacing fossil fuels with energy sources and carriers that are sustainable, environmentally benign, and affordable is amongst the most pressing challenges for future socio-economic development. To that goal, hydrogen is presumed to be the most promising energy carrier. Electrocatalytic water splitting, if driven by green electricity, would provide hydrogen with minimal CO2 footprint. The viability of water electrolysis still hinges on the availability of durable earth-abundant electrocatalyst materials and the overall process efficiency. This review spans from the fundamentals of electrocatalytically initiated water splitting to the very latest scientific findings from university and institutional research, also covering specifications and special features of the current industrial processes and those processes currently being tested in large-scale applications. Recently developed strategies are described for the optimisation and discovery of active and durable materials for electrodes that ever-increasingly harness first-principles calculations and machine learning. In addition, a technoeconomic analysis of water electrolysis is included that allows an assessment of the extent to which a large-scale implementation of water splitting can help to combat climate change. This review article is intended to cross-pollinate and strengthen efforts from fundamental understanding to technical implementation and to improve the 'junctions' between the field's physical chemists, materials scientists and engineers, as well as stimulate much-needed exchange among these groups on challenges encountered in the different domains.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Selection and characterisation of weakly coordinating solvents for semiconductor electrodeposition

Weakly coordinating solvents, such as dichloromethane, have been shown to be attractive for the electrodeposition of functional p-block compound and alloy semiconductors for electronic device applications. In this work the use of solvent descriptors to define weakly coordinating solvents and to identify new candidates for electrochemical applications is discussed. A set of solvent selection criteria are identified based on Kamlet and Taft's π*, α and β parameters: suitable solvents should be polar (π* ≥ 0.55), aprotic and weakly coordinating (α and β ≤ 0.2.). Five candidate solvents were identified and compared to dichloromethane: trifluorotoluene, o-dichlorobenzene, p-fluorotoluene, chlorobenzene and 1,2-dichloroethane. The solvents were compared using a suite of measurements including electrolyte voltammetric window, conductivity, and differential capacitance, and the electrochemistry of two model redox couples (decamethylferrocene and cobaltocenium hexafluorophosphate). Ion pairing is identified as a determining feature in weakly coordinating solvents and the criteria for selecting a solvent for electrochemistry is considered. o-dichlorobenzene and 1,2-dichloroethane are shown to be the most promising of the five for application to electrodeposition because of their polarity.

A critical review on the electrosorption of organic compounds in aqueous effluent - Influencing factors and engineering considerations

Despite being an old process from the end of the 19^th century, electrosorption has attracted renewed attention in recent years because of its unique properties and advantages compared to other separation technologies and due to the concomitant development of new porous electrode materials. Electrosorption offer the advantage to separate the pollutants from wastewater with the possibility of selectively adsorbing and desorbing the targeted compounds. A comprehensive review of electrosorption is provided with particular attention given to the electrosorption of organic compounds, unlike existing capacitive deionization review papers that only focus on inorganic salts. The background and principle of electrosorption are first presented, while the influence of the main parameters (e.g., electrode materials, electrode potential, physico-chemistry of the electrolyte solutions, type of compounds, co-sorption effect, reactor design, etc.) is then detailed and the modeling and engineering aspects are discussed. Finally, the main output and future prospects about recovery studies and combination between electro-sorption/desorption and degradation processes are given. This review particularly highlights that carbon-based materials have been mostly employed (85% of studies) as porous electrode in organics electrosorption, while existing studies lack of electrode stability and durability tests in real conditions. These electrodes have been implemented in a fixed-bed reactor design most of the time (43% of studies) due to enhanced mass transport. Moreover, the electrode potential is a major criterion: it should be applied in the non-faradaic domain otherwise unwanted reactions can easily occur, especially the corrosion of carbon from 0.21 V/standard hydrogen electrode or the water oxidation/reduction. Furthermore, there is lack of studies performed with actual effluents and without addition of supporting electrolyte, which is crucial for testing the real efficiency of the process. The associated predictive model will be required by considering the matrix effect along with transport phenomena and physico-chemical characteristics of targeted organic compounds.

Electrocatalysis in Alkaline Media and Alkaline Membrane-Based Energy Technologies

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

Understanding the Effects of Interfacial Lithium Ion Concentration on Lithium Metal Anode

Despite the development of multidimensional state-of-the-art electrode materials for constructing better lithium metal anodes (LMAs), the key factors influencing the electrochemical performance of LMAs are still poorly understood. Herein, it is demonstrated that the local lithium ion concentration at the interface between the electrode and electrolyte exerts significant influence on the electrochemical performance of LMAs. The local ion concentration is multiplied by introducing pseudocapacitive nanocarbons (PNCs) containing numerous heteroatoms, because PNCs can store large numbers of lithium ions in a pseudocapacitive manner, and promote the formation of an electrochemical double layer. The high interfacial lithium ion concentration induces the formation of lithium-rich inorganic solid-electrolyte-interface layers with high ionic conductivities, and facilitates sustainable and stable supplies of lithium ion charge carriers on the overall active surfaces of the PNCs. Accordingly, the PNC-induced LMA exhibits high Coulombic efficiencies, high rate capabilities, and stable cycling performance.

Grand-Canonical Model of Electrochemical Double Layers from a Hybrid Density-Potential Functional

A hybrid density-potential functional of an electrochemical interface that encompasses major effects in the contacting metal and electrolyte phases is formulated. Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer (EDL). Specifically, metal electrons are described using the Thomas-Fermi-Dirac-Wigner theory of an inhomogeneous electron gas. The electrolyte solution is treated classically at the mean-field level, taking into account electrostatic interactions, ion size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe the short-range forces between metal cationic cores, metal electrons, and electrolyte ions and solvent molecules. Therefore, the gap between the metal skeleton and the electrolyte solution, key to properties of the EDL, varies consistently as a function of the electrode potential. Partial charge transfer in the presence of ion specific adsorption is described using an Anderson-Newns type theory. This model is parametrized with density functional theory calculations, compared with experimental data, and then employed to unravel several interfacial properties of fundamental significance in electrochemistry. In particular, a closer approach of the solution phase toward the metal surface, for example, caused by a stronger ion specific adsorption, decreases the potential of zero charge and elevates the double-layer capacitance curve. In addition, the ion specific adsorption can lead to surface depolarization of ions. The present model represents a viable framework to model (reactive) EDLs under the constant potential condition, which can be used to understand multifaceted EDL effects in electrocatalysis.

Diffuse double-layer structure in mixed electrolytes considering ions as dielectric spheres

The structure of the diffuse part of the electric double layer at solid-electrolyte solution interfaces is examined using a theoretical model that takes into account the finite ion size by modeling the solution as a suspension of polarizable insulating spheres in water. This formalism is applied to mixed electrolyte solutions using the "Boublik-Mansoori-Carnahan-Starling-Leland" (BMCSL) theory for the steric interactions among ions. It is shown that the ionic size differences have a strong bearing on the diffuse part of the electric double-layer structure of these systems. Moreover, for strong potential values, the different size-related effects become important even for binary electrolyte solutions due to the presence of H⁺ and OH^- ions that are substantially smaller than hydrated ions originated from salt dissociation. The obtained results display some of the qualitative features observed in experiments on aqueous systems that are generally interpreted in terms of totally different mechanisms.

Simultaneous Printing of Two Inks by Contact Lithography

Microcontact printing (μCP) is a valuable technique used to fabricate complex patterns on surfaces for applications such as sensors, cell seeding, self-assembled monolayers of proteins and nanoparticles, and micromachining. The process is very precise but is typically confined to depositing a single type of ink per print, which limits the complexity of using multifunctionality patterns. Here we describe a process by which two inks are printed concomitantly in a single operation to create an alternating pattern of hydrophobic and hydrophilic characteristics. The hydrophobic ink, PDMS, is deposited by evaporation on the noncontact region, while the hydrophilic polyelectrolyte is transferred on contact. We demonstrate that there is no gap between the two patterns using an optical-electrochemical method. We describe some potential applications of this method, including layer-by-layer deposition of polyelectrolytes for sensors and creation of a scaffold for cell culture.

Electrochemical characteristics of ideal polarizable interfaces with limited number of charge carriers

Recent progress in material chemistry and surface engineering has led to emergence of new electrode materials with unique physical and electrochemical properties. Here, we introduce a physical model describing charging of ideal polarizable electrode-electrolyte interface where the electrode is characterized by a limited capacity to store charge. The analytical model treats the electrode and electrolyte phases as independent nonlinear capacitors that are eventually coupled through the condition of equality of the total stored electrical charge opposite in sign. Gouy-Chapman and condensed layer theories applied to a general 1:n valent electrolyte are used to predict dependencies of differential capacitance of the electrolyte phase and surface concentration of the electrical charge on the applied potential. The model of the nonlinear capacitor for the electrode phase is described by a theory of electron donors and acceptors present in conductive solids as a result of thermal fluctuations. Both the differential capacitance and the surface concentration of the electrical charge in the electrode are evaluated as functions of the applied potential and related to the capacity of the electrode phase to accumulate charge and its ability to form electron donors and acceptors. The knowledge of capacitive properties of both phases allows to predict electrochemical characteristics of ideal polarizable interfaces, e.g., current responses in linear sweep voltammetry. The coupled model also shows significant potential drops in the electrode comparable to those in the electrolyte phase for materials with low charge carrier concentrations.

Electrocapillarity and zero-frequency differential capacitance at the interface between mercury and ionic liquids measured using the pendant drop method

Zero-frequency differential capacitance measurements at the ionic liquid|mercury interface using the pendant drop method reveal predicted and unpredicted features of the potential dependence of the capacitance.