Electrode Surface Charge Density Research Articles

On the contact values of the density profiles in an electric double layer using density functional theory

A recently proposed local second contact value theorem [Henderson D., Boda D., J. Electroanal. Chem., 2005, 582, 16] for the charge profile of an electric double layer is used in conjunction with the existing Monte Carlo data from the literature to assess the contact behavior of the electrode-ion distributions predicted by the density functional theory. The results for the contact values of the co- and counterion distributions and their product are obtained for the symmetric valency, restricted primitive model planar double layer for a range of electrolyte concentrations and temperatures. Overall, the theoretical results satisfy the second contact value theorem reasonably well, the agreement with the simulations being semi-quantitative or better. The product of the co- and counterion contact values as a function of the electrode surface charge density is qualitative with the simulations with increasing deviations at higher concentrations.

Evidence for a second, local contact condition for a planar electric double layer containing size and valency asymmetric ions

A generalised form of a local contact condition for the charge profile in a primitive model planar double layer [Bhuiyan, Outhwaite, and Henderson, Mol. Phys. 107, 343 (2009)] at low electrode charge is examined for completely asymmetric, binary electrolytes. The cation and anion sizes are taken to be different from each other with the valencies being 2+:1− or 1+:2−, while the electrode surface charge density is varied from being negative through zero to being positive. Monte Carlo simulation data obtained for such double layer systems at varying ionic radius ratios and electrolyte concentrations suggest the generalised contact relation to be valid at low charge on the electrode.

Electrochemical investigation of Al–Li/Li x FePO4 cells in oligo(ethylene glycol) dimethyl ether/LiPF6

1 M LiPF6 dissolved in oligo(ethylene glycol) dimethyl ether with a molecular weight, 500 g mol−1 (OEGDME500, 1 M LiPF6), was investigated as an electrolyte in experimental Al–Li/LiFePO4 cells. More than 60 cycles were achieved using this electrolyte in a Li-ion cell with an Al–Li alloy as an anode sandwiched between two Li x FePO4 electrodes (cathodes). Charging efficiencies of 96–100% and energy efficiencies of 86–89% were maintained during 60 cycles at low current densities. A theoretical investigation revealed that the specific energy can be increased up to 15% if conventional LiC6 anodes are replaced by Al–Li alloy electrodes. The specific energy and the energy density were calculated as a function of the active mass per electrode surface (charge density). The results reveal that for a charge density of 4 mAh cm−2 about 160 mWh g−1 can be reached with Al–Li/LiFePO4 batteries. Power limiting diffusion processes are discussed, and the power capability of Al–Li/LiFePO4 cells was experimentally evaluated using conventional electrolytes.

Complex dynamic behaviors of nonequilibrium atmospheric dielectric-barrier discharges

In this paper, a one-dimensional fluid model is used to investigate complex dynamic behaviors of a nonequilibrium dielectric-barrier discharge (DBD) in atmospheric helium. By projecting its evolution trajectory in the three-dimensional phase space of gas voltage, discharge current density, and electrode-surface charge density, the atmospheric DBD is shown to undergo a sequence of complex bifurcation processes when the applied voltage is increased from prebreakdown to many times of the breakdown voltage. Once the gas voltage exceeds the breakdown voltage, the discharge plasma is found to acquire negative differential conductivity and as a result its stability is compromised. For atmospheric DBD, however, the resulting low plasma stability is mitigated by a rapid accumulation of surface charges on the electrodes, thus allowing the atmospheric DBD to retain their character as a glow discharge. At certain values of the applied voltage, a highly complex phenomenon of period multiplication is observed in which the period of the discharge current is three times that of the applied voltage. This suggests that nonequilibrium atmospheric DBD may support evolution patterns that are quasiperiodic or even chaotic. These complex dynamic behaviors are likely to be critical to a full understanding of plasma stability of nonequilibrium atmospheric discharges and to the development of their instability control strategies.

Negative capacitance and instability at electrified interfaces: Lessons from the study of membrane capacitors

Various models leading to predictions of negative capacitance, C,are brieflyreviewed. Their relation to the nature of electric control is discussed. Wereconfirm that the calculated double layer capacitance can be negative un-der σ-control – an artificial construct that requires uniform distribution ofthe electrode surface charge density, σ. However, only the total charge q(or the average surface charge density σ) can be experimentally fixed inisolated cell studies (q-control). For thoseσ where C becomes negativeunder σ-control, the transition toq-control (i.e. relaxing the lateral changedensity distribution, fixing its mean value to σ) leads to instability of the uni-form distribution and a transition to a non-uniform phase. As an illustration,a “membrane capacitor” model is discussed. This exactly solvable model,allowing for both uniform and inhomogeneous relaxation of the electricaldouble layer, helps to demonstrate both the onset and some important fea-tures of the instability. Possibilities for further development are discussedbriefly.Key words: electrochemical interfaces, instabilities and phase transitions,electric double layers, capacitance, membrane electroporationPACS: 68.35.Rh, 68.35.Md, 82.45.Mp, 82.45.Rr, 82.45.Uv, 68.08.-p,73.30.+y

Effects of solvent model flexibility on aqueous electrolyte behavior between electrodes

Molecular dynamics simulations have been carried out for aqueous electrolyte solutions between model electrode surfaces. The effect of solvent model flexibility on bulk and double layer properties was observed for electrode surface charge densities of 0, ±0.1, and ±0.2 C/m2 and ion concentrations of 0, 0.5, and 1 M. Two flexible models were used to isolate the effects of flexibility from the effects of a change in the condensed-phase dipole moment. Model flexibility increases the pure water self-diffusion coefficient while a larger liquid dipole moment substantially decreases it. There is an increase in ion contact adsorption and counter ion affinity with the flexible models, suggesting that the ions are less tightly solvated. This conclusion is consistent with observed enhancements of solvated ion densities near uncharged electrodes for the flexible water case. Mobile ions in high concentration quickly damp out the electric field even at high electrode charge densities, but for dilute ion concentrations the field may extend to the center of the cell or beyond. In these cases it is more appropriate to integrate Poisson’s equation from the electrode surface outward instead of the common method of assuming zero field at the center of the simulation cell. Using this methodology, we determine the voltage drop across the half-cell for both the rigid and flexible models. The half-cell voltage drop shows some dependence on ion concentration, but solvent flexibility has little effect on that behavior.

Studies of chloride adsorption on the Ag/AgCl electrode

Experimental results supporting a non-Faradaic potential origin for the Ag/AgCl electrode and Cl −-ISE resulting from chloride ion adsorption on the AgCl membrane are presented. In this paper we show that the salt bridge commonly used in potential measurements, necessary for ion transfer in cell redox reactions, can be replaced by a platinum wire or graphite fiber. Immersion of an Ag/AgCl electrode in a KCl solution at different electrode depths, results in more negative potential reading due to a larger exposed electrode surface. Indeed, the more chloride ions adsorbed on the electrode surface the more negative is the potential. In a different experiment, when the same electrode is dipped into increasing KCl concentration solutions but kept at a constant level inside these solutions, the potential increases as function of stirring speeds except for 10 −4 M KCl where the trend was opposite. One possible explanation of this behavior can be related to the counter triple layer highly dependent on the K + concentration and its capacity to replace Cl − under increasing stirring speeds influencing this way the electrode surface charge density. We also show that Ag is not a determinant component in the electrode making. Similar experiments performed on a Cl −-ISE show stable potential reading and good calibration curves under identical experimental conditions. As expected, when the KCl solution is not stirred, the Cl −-ISE potential decreases to more negative values for increasing KCl concentrations. Electrode surface charge distribution was also followed by experiments based on stirring force effect on the ISE potential. The results are discussed here in terms of adsorption isotherm and chemical capacitor behavior of the AgCl electrode membrane.

Influence of charge density and electrolyte concentration on the electrical double layer characteristics at rough cadmium electrodes

A new effective diffuse layer thickness dependent surface roughness model, based on the non-linear Poisson–Boltzmann theory, has been used for the interpretation of impedance data for rough cadmium electrodes. The so-called electrochemical roughness function values at various electrode potentials and surface charge densities have been calculated. It was found that the roughness function values, the inverse value of Parsons–Zobel plot, as well as the fitting coefficient in the Valette–Hamelin approach, obtained from the electrochemical impedance data, are effective (seeming) parameters and do not characterise the real geometrical structure of electrode surface. However, they characterise the deviation of real experimental system from ideally smooth (flat) surface. In the region of moderate rational electrode potentials 0≤| E|≤0.2 V and surface charge densities (1≤| a|≤4 μC cm −2) the roughness function rises with the decrease of the effective thickness of diffuse layer. At higher electrode potentials and surface charge densities the surface roughness function levels of to the constant value, i.e. to the so-called geometrical surface roughness value. The new effective diffuse layer thickness dependent surface roughness theory needs future corrections taking into account the role of crystallographic inhomogeneity of the geometrically rough electrode surface, i.e. the dependence of the local surface charge density on the crystallographic structure of energetically homogeneous regions exposed on the macro-polycrystalline electrode surface.

Determination of the surface charge density of a mercury electrode by extrusion: a new method for correction of the faradaic component

The accurate determination of the surface charge density at the mercury ∣ solution interface by the method of extrusion of mercury drops is impaired by the faradaic current caused by traces of electroactive species. This paper describes a new design of a hanging mercury drop electrode with accurate control of the extruded electrode area, to within 0.1%, together with a new and reliable procedure for correction of the faradaic current. The procedure is based on first obtaining the correction parameters in the presence of increasing amounts of electroactive species and then using these parameters for correction of the faradaic component so as to obtain the surface charge density of the electrode. Implementation of the method with a microcomputer controlled system provides automatic acquisition of corrected electrode charge density values as a function of the electrode potential. The results obtained with this new method are in excellent agreement with those obtained by other methods, as illustrated for aqueous sodium fluoride solution.

In Situ Monitoring of Diffuse Double Layer Structure Changes of Electrochemically Addressable Self-Assembled Monolayers with an Atomic Force Microscope

An alkyl disulfide containing two sulfonate-substituted ferrocenes, 7,8-dithiatetradecane-1,14-di-(aminocarbonyl)-bis(1'-ferrocene-1-sulfonic acid), was synthesized and used to form electroactive self-assembled monolayers on gold electrodes. Atomic force microscope (AFM) force curves were employed to measure in situ the change in surface charge as the ferrocene groups were oxidized to compensate for the negative charges on the sulfonate groups. The electrode surface charge density was calculated from the surface coverage measured by electrochemical oxidation of the ferrocene groups, while the diffuse double layer charges were obtained from theoretical fits of the force data to solutions of the complete nonlinear Poisson-Boltzmann (PB) equation with knowledge of the silica probe surface potential. A significant difference between the AFM measured (i.e., effective) surface charge and the surface charge calculated from electrochemical measurements was found. This difference is attributed to a layer of counterions near the surface that screens a large fraction of the surface charge (variously described as ion condensation or failure of the nonlinear PB theory). The experimental results also showed that the extent of this ion screening (∼97%) was relatively constant and independent of the total electrode surface charge.

Indium adsorption at the surface of liquid In+Ga alloy electrodes in contact with an aqueous 1 M NaClO4 solution

Abstract The surface charge densities of liquid In+Ga alloy electrodes with indium bulk contents ranging from 0 to 16.5 mol% were obtained as functions of the electrode potential by means of dropping microelectrode charging current and ac impedance measurements in aqueous 1 M NaClO4 solutions of varied pH at 32°C. Using surface tension literature data of liquid In+Ga in vacuum and quasi-chemical multilayer model calculations they were integrated to electrocapillary curves. From the latter, the dependences of the indium surface excess on alloy composition, electrode potential and charge density were derived. A strong indium adsorption was found in the entire accessible range of bulk compositions. It extends over several atomic surface layers and can be accounted for by the surface tension difference between pure liquid gallium and indium, combined with the positive heat of mixing of the liquid In+Ga alloy system. It is shown that the indium surface excess decreases if the electrode potential or surface charge density is made more negative. A qualitative explanation in terms of pure component work function differences is given.

Adsorption of pyridine at the Au(311)—solution interface

The energetics of pyridine adsorption onto a Au(311) single-crystal electrode surface have been investigated using chronocoulometry. Adsorption parameters such as the relative Gibbs surface excesses, the Gibbs energies of adsorption and electrosorption valencies have been determined. The data have been analysed in terms of both the electrode potential and surface charge density. Over the potential region investigated (−0.8 V to +0.6 V), pyridine has been found to adsorb in the vertical orientation with the nitrogen end of the pyridine molecule facing the Au(311) surface. The limiting surface concentration for this orientation was found to be 6.6±0.3×10 −10 mol cm −2. The Gibbs energies of adsorption were calculated using the Henry's law isotherm. At the potential of maximum adsorption, Δ G max 0 was found to be equal to −44 kJ mol −1. The absolute value for Δ G max 0 is fairly large, indicating that pyridine is weakly chemisorbed onto the Au(311) electrode surface.

Adsorption of pyridine at the Au(111)-solution interface

The energetics of pyridine adsorption onto an Au(111) single crystal electrode surface have been characterized using chronocoulometry. The adsorption parameters such as the relative Gibbs surface excesses, the Gibbs energies of adsorption, and electrosorption valencies have been determined as a function of the electrode potential and surface charge density. Over the potential region investigated (−0.8 V to +0.6 V) pyridine has been found to adsorb in two different orientations. The flat orientation is observed on the negatively charged electrode surface while the vertical orientation is present on the positively charged surface. Reorientation between the flat and the vertical orientations takes the form of a two-dimensional phase transition. The limiting surface concentrations have been found to be 1.4 × 10 −10 mol cm −2 and 6.7 × 10 −10 mol cm −2 for flat and vertical orientations of pyridine, respectively. For pyridine adsorbed in the flat orientation the Gibbs energies of adsorption, Δ G°, were determined using the Henry's Law isotherm. At the potential of maximum adsorption, Δ G 0 max is equal to −37 kJ mol −1. The absolute value for Δ G max is fairly large indicating that the pyridine molecules are weakly chemisorbed at the Au(111)-solution interface.

A dropping mercury microelectrode (DMμE) for the direct determination of surface charge densities

A dropping mercury electrode has been constructed which produces drops with a radius of about 50 μm. The characteristics of such electrodes are similar to those of conventional electrodes except for the strongly reduced natural drop time. This drop time turns out to be very stable and virtually independent of surface tension. These properties allow for interesting applications. Here the electrode is used for the determination of electrode surface charge density, which proves to be quite accurate. Because this technique has distinct advantages over the currently available ones we consider it to be a powerful tool in double-layer research.

Monte Carlo investigation of structure and dielectric properties of the electrode-water interface depending on electrode charge density

Dependence of the dielectric and structural characteristics on the surface charge density of electrode was investigated using a Monte Carlo method (MCM) version developed for studying liquids near electrode. A similar problem was solved also for the case associated with the presence of the H 3O + cation in the electrode-water interface.

Electrochemical surface science: The study of monolayers of ad-atoms and solvent molecules at charged metal interfaces

In parallel with the spectacular advances that have been made in recent years in the field of metal/vacuum surface science, there have been corresponding interesting developments of a complementary kind in electrochemical surface science. This article describes recent advances in the latter field, and their experimental and theoretical bases. However, the molecular situation at electrode interfaces is very complex compared with that at a metal/vacuum interface, owing to adsorption and orientation of solvent molecules, and the presence of solvated ions. Hence these topics must be considered as well as the surface science of the metal electrode itself. In comparison with metal/vacuum surface science, electrochemical studies on metal interfaces can utilize the electrode potential as an additional independent variable and thus control surface charge density, coverage by Faradaically deposited ad-atoms, co-adsorption of cations or anions and solvent dipole orientation. Modulations of electrode potential in time allow the kinetic relaxation characteristics of monolayers to be followed, and the potential-modulated reflectivity and spectral absorption of species in the interphase to be studied. Electrochemically controllable sub-monolayer coverages of, e.g., metal ad-atoms have interesting catalytic effects on other continuous electrochemical reactions, such as oxygen reduction or formic acid oxidation. Experiments based on electrochemical potential pulse and sweep, and current pulse methods enable chemisorption of ad-atom monolayers to be studied in fine detail. Multiple state chemisorption in monolayers is commonly observed, even on single crystal surfaces, and fine resolution of the states can be achieved by electrochemical techniques. The kinetics of monolayer deposition and desorption can also be followed, as well as the dynamics of reconstruction processes e.g. in 0 monolayers as a function of time and potential. The electrochemical methods allow direct determination of the differential isotherm for adsorption as well as the usual integral one. The former gives details of multiple state adsorption, and provides information on interaction effects in the monolayer and kinetics of its formation. Ionicity of ad-species can also be evaluated. Recent advances in combining electrochemical systems in situ with high-vacuum LEED, Auger and ESCA apparatus are described. Since electrochemical surface science has necessarily to be able to study processes at the interfaces of metals in contact with liquid solutions, an important area of the field has been the treatment and evaluation of solvent dipole adsorption and orientation as a function of electrode potential or surface charge density.

Adsorption behaviour and orientation of adenosine molecules at the mercury drop electrode: Congruence of isotherms with respect to the electrode potential and surface charge density in neutral electrolytes

The parameters of the electrocapillary maximum of mercury in the presence of adenosine, together with the results of measurements of the differential capacitance of mercury in the same solutions, were used in calculating the total surface charge density q and the interfacial tension σ. In 1 N solutions of Na 2SO 4, NaClO 4, KNO 3, KCl and KBr the isotherms exhibited simultaneous congruence with respect to the electrode potential and surface charge density, within certain limits, for all electrolytes. The coefficient a of the adsorption isotherm was shown to have a high value, confirming that two-dimensional condensation of the adenosine molecules took place at high concentrations.

Double-layer effects on simple electrode reactions I. The reduction of Eu 3+ and Cr 3+ in the absence of specific adsorption of the supporting electrolyte

The kinetics of the reduction of Eu 3+ and Cr 3+ at mercury electrodes in various sodium and lanthanum perchlorate supporting electrolytes have been studied over as large a potential range as possible by using both chronocoulometry and d.c. polarography. The objective was to determine the effect of the diffuse double layer upon the reduction rates of these members of the simplest class of electrode reactions in the absence of specific adsorption. Possible additional influences from perchlorate specific adsorption, ion-pairing, and ionic strength-dependent formal potentials, and differences between the site of reaction and the o.H.p. were also considered. The effects of specific adsorption of an uncharged molecule were assessed by noting the changes in the reduction kinetics of Eu 3+ caused by the adsorption of thiourea. The classical Gouy-Chapman-Stern model of the double layer was found to give an adequate account of the behavior in relatively dilute lanthanum perchlorate solutions, but it failed badly in more concentrated sodium perchlorate media. Better agreement resulted if the statistical theory due to Krylov and Levich was employed but some discrepancies remained. The diffuse-layer properties evaluated here represent a useful basis for comparisons with systems where specific ionic adsorption of components of the supporting electrolyte adds a second component to the electrode surface charge density which determines the diffuse-layer potential.