Diffuse Layer Capacitance Research Articles

Dynamic Effect of Overscreening on Electrochemical and Thermal Properties of EDLC Electrodes during Charging/Discharging Cycles

Overscreening was commonly observed during charging/discharging cycles of electric double layer capacitors(EDLCs). This study presented a two-dimensional continuum electrochemical thermal model with a distribution function for concentration considering overscreening to investigate how overscreening affected the dynamic formation of electric double layer (EDL) near electrodes in macroscale. The results indicated that ion distribution was co-affected by EDL formation and overscreening near the electrode. Correspondingly, layered space charge density distribution resulted in a thicker diffuse layer, whose thickness was determined by the sum of co-ion and counter-ion diameters. Additionally, the diffuse layer capacitance was proportional to the reciprocal of counter-ion diameter, while the total capacitance was proportional to a linear combination of counter-ion and the larger ion diameters. Moreover, the shift from endothermic to exothermic for the total heat generation rate was dominated by heat of mixing, and was caused by the local ion mixing due to overscreening, resulting in local entropy increase. The results of this study can be used to further investigate the effect of overscreening on ion transient transport dynamic and heat generation rates.

A Review: Ion Transport of Two-Dimensional Materials in Novel Technologies from Macro to Nanoscopic Perspectives

Ion transport is a significant concept that underlies a variety of technologies including membrane technology, energy storages, optical, chemical, and biological sensors and ion-mobility exploration techniques. These applications are based on the concepts of capacitance and ion transport, so a prior understanding of capacitance and ion transport phenomena is crucial. In this review, the principles of capacitance and ion transport are described from a theoretical and practical point of view. The review covers the concepts of Helmholtz capacitance, diffuse layer capacitance and space charge capacitance, which is also referred to as quantum capacitance in low-dimensional materials. These concepts are attributed to applications in the electrochemical technologies such as energy storage and excitable ion sieving in membranes. This review also focuses on the characteristic role of channel heights (from micrometer to angstrom scales) in ion transport. Ion transport technologies can also be used in newer applications including biological sensors and multifunctional microsupercapacitors. This review improves our understanding of ion transport phenomena and demonstrates various applications that is applicable of the continued development in the technologies described.

Structure of the Electrical Double Layer Revisited: Electrode Capacitance in Aqueous Solutions.

The structure of the electrical double layer at the interface of planar electrodes and aqueous solutions is investigated. Electrical impedance spectroscopy is used to measure the impedance of aqueous solutions of sodium chloride and two different surfactants over a wide range of concentrations. The electrode capacitance is directly inferred from the admittance spectra as well as by regression of the impedance spectra to an equivalent circuit. It is found that the electrode capacitance remains on the same order of magnitude over the entire range of investigated concentrations. This is contradictive to the predictions of the Gouy-Chapman-Stern theory which predicts that, at low concentrations, the electrode capacitance should be determined by the diffuse layer. It is concluded that the Stern layer capacitance always dominates the electrode capacitance, even at very low concentrations, and the establishment of a diffuse layer capacitance requires an ionic strength of around 1 mM.

The role of Stern layer in the interplay of dielectric saturation and ion steric effects for the capacitance of graphene in aqueous electrolytes

Nano-scale devices continue to challenge our theoretical understanding of microscopic systems. Of particular interest is the characterization of the interface electrochemistry of graphene-based sensors. Typically operated in a regime of high ion concentration and high surface charge density, dielectric saturation and ion crowding become non-negligible at the interface, complicating continuum treatments based upon the Poisson-Boltzmann equation. Using the Poisson-Boltzmann equation, modified with the Bikerman-Freise model to account for non-zero ion size and the Booth model to account for dielectric saturation at the interface, we characterize the diffuse layer capacitance of both metallic and graphene electrodes immersed in an aqueous electrolyte. We find that the diffuse layer capacitance exhibits two peaks when the surface charge density of the electrode is increased, in contrast with experimental results. We propose a self-consistent (and parameter-free) method to include the Stern layer which eliminates the spurious secondary peak in the capacitance and restores the correspondence of the model with experimental observations. This study sheds light on the interplay between the ion steric effects and the dielectric saturation in solvent, exposes the importance of quantum capacitance when graphene is used as an electrode, and demonstrates the importance of a self-consistent treatment of the Stern layer in continuum models of the electrode-electrolyte interface. Furthermore, the theoretical foundation provides a base upon which more detailed models of graphene-based sensors can be built.

Surface Complexation Modeling in Variable Charge Soils: Charge Characterization by Potentiometric Titration

ABSTRACT Intrinsic equilibrium constants of 17 representative Brazilian Oxisols were estimated from potentiometric titration measuring the adsorption of H+ and OH− on amphoteric surfaces in suspensions of varying ionic strength. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. The former was fitted by calculating total site concentration from curve fitting estimates and pH-extrapolation of the intrinsic equilibrium constants to the PZNPC (hand calculation), considering one and two reactive sites, and by the FITEQL software. The latter was fitted only by FITEQL, with one reactive site. Soil chemical and physical properties were correlated to the intrinsic equilibrium constants. Both surface complexation models satisfactorily fit our experimental data, but for results at low ionic strength, optimization did not converge in FITEQL. Data were incorporated in Visual MINTEQ and they provide a modeling system that can predict protonation-dissociation reactions in the soil surface under changing environmental conditions.

Surface Complexation Modeling in Variable Charge Soils: Prediction of Cadmium Adsorption

ABSTRACT Intrinsic equilibrium constants for 22 representative Brazilian Oxisols were estimated from a cadmium adsorption experiment. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. Intrinsic equilibrium constants were optimized by FITEQL and by hand calculation using Visual MINTEQ in sweep mode, and Excel spreadsheets. Data from both models were incorporated into Visual MINTEQ. Constants estimated by FITEQL and incorporated in Visual MINTEQ software failed to predict observed data accurately. However, FITEQL raw output data rendered good results when predicted values were directly compared with observed values, instead of incorporating the estimated constants into Visual MINTEQ. Intrinsic equilibrium constants optimized by hand calculation and incorporated in Visual MINTEQ reliably predicted Cd adsorption reactions on soil surfaces under changing environmental conditions.

Electrochemical properties and relaxation times of the hematite/water interface.

Electric double layer properties and protonation rates at the surface of a mechanically and chemically polished (001) surface of hematite (α-Fe2O3) contacted with aqueous solutions of NaCl were extracted by electrochemical impedance spectroscopy (EIS). Effects of pH (4-12) and ionic strength (10-1000 mM) on the EIS response of the electrode were predicted using an electrical equivalent circuit model accounting for hematite bulk and interfacial processes. These efforts generated diffuse layer as well as compact layer capacitances and resistance values pertaining to interfacial processes. Diffuse layer capacitance values lie in the 0.5-0.6 μF cm(-2) region and are about 1.5 times smaller than those obtained on a roughened hematite surface. Compact layer capacitances are strongly pH dependent as they pertain to the transfer of ions (charge carriers) from the diffuse layer onto surface (hydr)oxo groups. These values, alongside those of resistance adsorption, pointed a 50% decrease in proton adsorption/desorption resistance under acidic and alkaline conditions relative to that of the point of zero charge (pH 8-9). Increasing ionic strength generally induces larger diffuse layer capacitances, larger adsorption capacitances, and lower resistance values. Such a response is in line with the concept for thinner electric double layers and facilitated proton adsorption reactions by solutions of high ionic strengths. Relaxation times pertaining to the transfer of charge carriers across the compact plane induced by the EIS experiments lie in the 0.7-4.2 s range and become larger under acidic conditions. Decreases in site availability and increases in electrostatic repulsion are two possible contributing factors impeding reaction rates below the point of zero charge. Collectively, these finding are underpinning important relationships between classical views on mineral surface complexation reactions and electrochemical views of semiconductor/water interfaces.

Examination of the Gouy–Chapman theory for double layer capacitance in deionized latex suspensions

An equivalent circuit of double layer capacitance composed of the inner layer capacitance and the two components of diffuse layer capacitance by considering frequency-dependence.

Electrochemical Impedance Study of the Hematite/Water Interface

Reactions taking place on hematite (α-Fe(2)O(3)) surfaces in contact with aqueous solutions are of paramount importance to environmental and technological processes. The electrochemical properties of the hematite/water interface are central to these processes and can be probed by open circuit potentials and cyclic voltammetric measurements of semiconducting electrodes. In this study, electrochemical impedance spectroscopy (EIS) was used to extract resistive and capacitive attributes of this interface on millimeter-sized single-body hematite electrodes. This was carried out by developing equivalent circuit models for impedance data collected on a semiconducting hematite specimen equilibrated in solutions of 0.1 M NaCl and NH(4)Cl at various pH values. These efforts produced distinct sets of capacitance values for the diffuse and compact layers of the interface. Diffuse layer capacitances shift in the pH 3-11 range from 2.32 to 2.50 μF·cm(-2) in NaCl and from 1.43 to 1.99 μF·cm(-2) in NH(4)Cl. Furthermore, these values reach a minimum capacitance at pH 9, near a probable point of zero charge for an undefined hematite surface exposing a variety of (hydr)oxo functional groups. Compact layer capacitances pertain to the transfer of ions (charge carriers) from the diffuse layer to surface hydroxyls and are independent of pH in NaCl, with values of 32.57 ± 0.49 μF·cm(-2)·s(-φ). However, they decrease with pH in NH(4)Cl from 33.77 at pH 3.5 to 21.02 μF·cm(-2)·s(-φ) at pH 10.6 because of the interactions of ammonium species with surface (hydr)oxo groups. Values of φ (0.71-0.73 in NaCl and 0.56-0.67 in NH(4)Cl) denote the nonideal behavior of this capacitor, which is treated here as a constant phase element. Because electrode-based techniques are generally not applicable to the commonly insulating metal (oxyhydr)oxides found in the environment, this study presents opportunities for exploring mineral/water interface chemistry by EIS studies of single-body hematite specimens.

Simulation study of capacitance of the electrical double layer of an electrolyte near a highly charged electrode

The conventional view of the structure and capacitance of the electrical double layer that is formed in an electrolyte near a charged electrode is that when the system is at high concentrations and/or high electrode charge, the interfacial (or diffuse) layer of ions near the electrode is exceedingly narrow because of the strong electrostatic forces and the resultant capacitance of the electrolyte in the interfacial region, called the diffuse layer capacitance, becomes very large so that the series-sum total capacitance equals the capacitance of the region that is devoid of ion charge (called the inner layer). Earlier work has shown that this is not the case at high concentrations. Here, we examine the case of high electrode charge and find that hard core exclusion, ionic correlations and electrostatic repulsion prevent the formation of a narrow diffuse layer; thus, the diffuse layer is thick and appears to become thicker as the electrode charge density increases. As a result, at large electrode charge density, the total capacitance is smaller than what the conventional view suggests and appears to become smaller as the electrode charge density is increased.

How well does simple RC circuit analysis describe diffuse double layer capacitance at smooth micro- and nanoelectrodes?

The capacitive charging of a diffuse double layer is discussed. Results from simple RC circuit analysis (an ideal resistor and capacitor in series) are compared with results from a more complete model in which the Nernst–Planck–Poisson equations are solved in a hemispherical space, both analytically and by simulation. This complementary approach allows an assessment of certain conditions which are required in order for RC circuit analysis to be suitable to describe the diffuse double layer. In particular, deviations are noted for nanoscale electrodes. Additionally, RC circuit behaviour breaks down for applied overpotentials greater than 25 mV ( RT/ F), such that values for solution resistance and double layer capacitance inferred from impedance spectroscopy may not apply to other experimental techniques. These conclusions apply to a smooth electrode and so are not associated with “constant phase angle” effects.

The electrochemical potential and ionic activity coefficients. A possible correction for Debye–Hückel and Maxwell–Boltzmann equations for dilute electrolyte equilibria

When the electrical contribution in the electrochemical potential of ionic species is reduced with a factor two from its traditional value, the ionic activity coefficients are closer to unity and need to account only for the short-range interactions at high concentrations. Such a change is needed to remove inconsistencies in the models and to comply with basic electrostatic principles. This will have serious implications, in many applications. For example, it will cause changes in many of the fundamental models that are used to explain measured data in the dilute range for the various disciplines that embrace classical electrochemistry. Examples are Debye–Hückel and Gouy–Chapman theories; Maxwell–Boltzmann distribution; Nernst theory; Donnan equilibrium, etc. These theories impact a wide range of observable phenomena such as activity coefficients of electrolytes, diffuse double layer capacitance, electrode potentials, membrane potentials, streaming potentials, electro-osmosis, flotation, sedimentation, corrosion, charged micellar behaviour, space-charge semiconductor behaviour, and electrical phenomena in biological tissue, e.g. membranes; cells; and nerves, etcetera.

A New Method to Evaluate the Surface Dipole Potential of Thiol and Disulfide Self-Assembled Monolayers and Its Application to a Disulfidated Tetraoxyethylene Glycol

A procedure to evaluate the surface dipole potential chi of thiol and disulfide self-assembled monolayers (SAMs) is described. The procedure consists of self-assembling the monolayers on a hanging mercury drop electrode and of measuring the charge involved in a progressive expansion of the mercury drop. This measurement is then combined with an estimate of the charge density q experienced by diffuse layer ions, obtained by measuring the diffuse layer capacitance of the SAM at different electrolyte concentrations by electrochemical impedance spectroscopy. These chi measurements, combined with chronocoulometric measurements of the total charge density sigma(M) against potential, indicate that SAMs of tetraoxyethylene glycol-D,L-alpha-lipoic acid ester (TEGL), 2,3-di-O-phytanyl-sn-glycerol-1-tetraoxyethylene glycol-D,L-alpha-lipoic ester (DPTL), and trioxyethyleneoxythiol (EO3) on mercury may undergo a reversal in the surface dipole potential of their polyoxyethylene chain with a change in the interfacial electric field. Moreover, TEGL and EO3 form stable SAMs without electron transfer to the metal, while no such conclusion can be drawn for DPTL.

Induced dipoles and dielectrophoresis of nanocolloids in electrolytes

Electric induced dipoles of nanocolloids the size of the Debye length are shown to be one order stronger than predicted by the classical Maxwell-Wagner theory and its extensions. The difference is attributed to normal ion migration within the diffuse layer, and adsorption onto the Stern layer at the poles. The characteristic relaxation frequency (the crossover frequency for dielectrophoresis) is shown to be inversely proportional to the RC time of the diffuse layer capacitance and resistance, and has an anomalous -1 scaling with respect to the product of the Debye length and the particle size.

Parsons–Zobel plots: An independent way to determine surface complexation parameters?

Parsons–Zobel plots can in principle be used to estimate inner Helmholtz-layer capacitance values and electrochemical surface areas for mineral particles. Their application to aqueous suspensions of various minerals has been documented in the literature. For the experimental data used so far, the expected linear relationship between the overall and the diffuse-layer capacitances has been reported. The extracted values either have not been used at all subsequently in a surface complexation model to describe the mineral surface charge versus pH curves, or were found not to be suitable entirely for such purposes. In the latter case, the reported failure was not explained. In one part of the present paper, the Parsons–Zobel plot concept is tested with data generated from a surface complexation model, for which the interfacial structure closely corresponds to that assumed in the application of the Parsons–Zobel plot. From the analysis of the results it turns out that electrolyte binding and non-Nernstian surface potential–pH curves more or less strongly affect the outcome of Parsons–Zobel plots. Despite the fact that the analysis in this paper is restricted to iron(III) minerals only, it is concluded, in general, that the use of Parsons–Zobel plots with aqueous mineral suspensions to determine inner Helmholtz-layer capacitances for subsequent application to surface complexation models cannot be recommended, since the reasons for failure can be traced very nicely with applications to model-generated data. Such application requires the determination of further parameters, and it was found that low electrolyte binding and Nernstian slopes should be imposed. Of these two issues, the more important is electrolyte binding. For the surface complexation models, an inner Helmholtz-layer capacitance and weak electrolyte binding were required for a good fit to experimental data. The values of the electrolyte binding constants required to achieve this end are in conflict with the assumptions of the Parsons–Zobel plot (absence of specific adsorption). However, these parameters would not necessarily cause specific adsorption in terms of a classical colloid chemistry definition (i.e., would not shift isoelectric points). The electrochemical surface areas were found to be in good agreement with the value used to generate the data. Based on this, there is a potential for using the approach to determine surface areas in situ from titration curves. Consequently, in a second part of the paper, Parsons–Zobel plots are applied to experimental data with the objective of determining electrochemical surface areas in situ. Application to various sets of published experimental titration data for hydrous ferric oxide yielded consistently very large electrochemical surface areas for fresh samples. This can be explained by very small particles and/or inclusion of substantial amounts of water in the suspended particles. As would be expected, the electrochemical surface area for aged ferrihydrite was found to be substantially lower.

Differential capacitance of the solvent primitive model diffuse layer using the inhomogeneous Poisson–Boltzmann theory with an exclusion volume term

The solvent primitive model diffuse double layer capacitance is analysed using a Poisson–Boltzmann theory which incorporates the exclusion volume term in the Boltzmann distribution. Unequal ion and solvent sizes are considered and the differential capacitance calculated for 1:1 electrolytes at different electrolyte and solvent concentrations. The unequal ion sizes cause an asymmetry in the capacity curves while the solvent can radically influence its overall shape. At low electrolyte concentrations and small surface charge, the capacitance has a minimum which changes to a maximum as the electrolyte concentration increases. At the higher surface charge densities the capacity curve approaches limiting values, these values depending on the relative counterion size.

Temperature-dependent quantized double layer charging of monolayer-protected gold clusters.

This paper describes low-temperature voltammetry of purified hexanethiolate-coated monolayer-protected Au140 clusters (C6 MPCs). Lowered temperatures enhance the resolution of quantized double layer (QDL) charging peaks in differential pulse voltammetry (DPV) observations. As many as 13 resolved peaks are seen in illustrative voltammetry at 263 K in CH2Cl2 solvent, and the concept of voltammetric peak capacity is introduced. For the one-electron MPC charge steps surrounding the E(PZC) of the MPC (small numbers of electrons added or removed from the core), the capacitance C(CLU) of the MPCs (measured from the voltage spacing between charging peaks) increases by approximately 15% as the solvent temperature is lowered from 273 to 210 K. The experimental C(CLU) temperature dependency (d[ln(C(CLU))]/dT approximately -0.0025, in 0.1 M electrolyte) is discussed in light of temperature dependencies of the compact and diffuse double layer capacitances. It is concluded that the observed temperature dependence is probably a mixed diffuse, compact dependence. The regular voltage spacing of MPC charging peaks near the potential of zero charge is generally consistent with electrical double layer properties, but the irregular pattern of charging of the nanoparticles seen at higher charge states suggests intervention of the incipient molecular behavior of Au140 cores in the spacing of energies at which further electrons are added or removed.

The capacitance of the electric double layer of electrodes in molten salts

High exchange current electrodes are reversible electrodes with an exchange current density greater than 0.1 A cm −2. Both in the time and frequency domains, their behaviour is predominantly inductive. Using the inductive model of high exchange current electrodes developed earlier, the double layer capacitance of a liquid Mg electrode in a melt composed of 20 mol% of MgCl 2 and 80 mol% of NaCl or KCl, is evaluated. As in aqueous electrolytes, the double layer capacitance is a sum of the compact and the diffuse layer capacitances. A model of the electric double layer of electrodes with high exchange current density is proposed, which allows for the calculation of the compact layer capacitance. It has been assumed in this calculation that the compact layer of the electric double layer is composed of a primary ionic shell, formed by specifically adsorbed chloride anions. The capacitance of such a layer is calculated as the Helmholtz capacitance, with the dielectric permittivity equal to 1. This capacitance is then corrected for the exchange current density. The corresponding amount of counterions to the specifically adsorbed anions in the primary ionic shell, is transferred to the neighbouring holes, creating the diffuse layer. The capacitance of the diffuse layer is thus calculated from the experimentally evaluated double layer capacitance and calculated by the present model compact layer capacitance.

Magnetite surface charge studies to 290°C from in situ pH titrations

The proton-induced surface charge of magnetite was investigated in 0.03 and 0.30 molal sodium trifluoromethanesulfonate solutions from 25°C to 290°C by potentiometric titrations using a stirred hydrogen electrode concentration cell. Pure magnetite with excellent crystallinity was produced by reaction with the Ni/NiO/H 2O hydrogen fugacity buffer at 500°C. Inflection points in the 0.03 molal proton sorption isotherms (pH infl) at 6.50, 6.24, 5.65, 5.47, 5.31 and 5.55 at temperatures of 50°C, 100°C, 150°C, 200°C, 250°C and 290°C, respectively, were used as estimates of the pristine point of zero charge (pH ppzc) for modeling purposes. These pH infl values parallel 1/2 p K w and agree within the assigned uncertainty (±0.3 pH units) at all temperatures with independent estimates of the pH ppzc calculated from an extension of 88the revised MUSIC model. The surface charging can be adequately described by a one-p K model with a surface protonation constant fitted to the pH infl values, and giving the standard state thermodynamic properties log K H,298=7.00, Δ H 298°=−32.4±0.8 kJ/mol and constant Δ C p=128±16 J K −1 mol −1, with Δ S 298° assumed to be equal to that of rutile protonation (25.5±3.4 J K −1 mol −1. The 0.03 and 0.30 molal proton sorption isotherms also exhibit pHs of common intersection (pH cip) at 6.33, 5.78, 5.37, 4.82, 4.62 and 4.90 at 50°C, 100°C, 150°C, 200°C, 250°C and 290°C, respectively. The difference between the pH cip and pH ppzc≅pH infl values can be related to specific binding of Na + on the negatively charged surface, which increases with increasing temperature, although the pH cip values may also be affected by dissolution of the solid. The electrical double layer model includes a basic Stern layer capacitance, with specific cation and anion binding at the Stern layer, and a fixed diffuse layer capacitance computed from Guoy–Chapman theory. To fit the steepness and asymmetry of the charging curves above the pH ppzc, an additional cation binding constant was invoked, which allows the cation to experience the surface potential. Significant kinetically controlled dissolution of magnetite was observed below the pH ppzc, which may be a result of leaching of Fe 2+ from the surface, to produce a magnetite+hematite assemblage, despite the high hydrogen partial pressures (ca. 10 bars) used in these experiments.

Double-layer studies in solutions of low relative permittivity

The capacitance of various electrolytes in dichloroethane, anisole and cyclohexane solutions are measured at a platinum electrode. It is found that specific adsorption occurs at large overpotentials from the potential of zero charge (pzc), but a diffuse-layer minimum is observed close to the pzc. The diffuse layer capacitance is found to be dependent upon the ionic strength of the electrolyte solutions. The appearance of capacitance ‘humps’ as a function of potential is attributed to the adsorption of ions or ion aggregates. The desorption of ions is shown to be a very slow process, particularly when long chain quaternary ammonium cations are used and, hence, the double-layer capacitance appears to be time dependent. The slow desorption of ions leads to apparent artefacts when these electrolytes are used for voltammetric studies in non-polar solvents.