Electrocapillary Equation Research Articles

Chloride Adsorption on Au (111) Electrodes

There are still numerous open questions with regards to adsorption phenomena and partial charge transfer at electrode interfaces. The dynamic nature electrode structure and adsorbate ordering makes an analysis solely based on thermodynamic considerations limited. Here we present recently collected data with such an analysis, using different concentrations of chloride anions in both acidic and neutral electrolytes, for well-defined Au (111) electrodes. Cyclic voltammograms and charge density data is obtained. Then the electrocapillary equation: "-dγ = σMdE + ΓCl-RTdln(cKCl)" is used to get the relative interfacial tension plot and later the electrosorption valency. In the future we will improve on this by more accurately placing the PZC of charge density measurements, using laser induced temperature jump transients and combining our interpretation with state-of-the-art molecular-dynamics using ground state machine learned potentials. Figure 1

Some remarks to the derivation of the \u201cgeneralized Lippmann equation\u201d

In the present communication, an attempt is made to demonstrate (once again) some of the problems with the derivation of the “generalized Lippmann equation” considered to be valid by many researchers for solid electrodes and to address the problems in the framework of the Gibbs model of the interface by using only the basic principles of thermodynamics. By surveying the relevant literature, it has been shown that during the derivation of the equation, it was completely ignored that the Gibbs-Duhem equation (i.e., the electrocapillary equation) is a mathematical consequence which follows directly from the homogeneous degree one property of the corresponding thermodynamic potential function; consequently, the resulting expression cannot be correct. Some alternative approaches have also been considered. The adequacy of the open system and the partly closed system approach has been critically discussed, together with the possibility of introducing new thermodynamic potential functions.

Monitoring transient changes in the structure of water at a polarised liquid-liquid interface using electrocapillary curves

The interface between two immiscible electrolyte solutions (ITIES) is a close approximation of an ideally polarisable interface, being non-equilibrated upon formation. Despite this, the formalism of equilibrium thermodynamics, e.g., electrocapillary equations, are universally applied to interpret electrochemical processes at the ITIES. This communication shows that interfacial energy measurements in real time during step potential experiments are a useful tool to detect transient changes in the structure of the electrolyte solutions at the ITIES, in particular in the presence of chaotropes or kosmotropes in the aqueous electrolyte. Molecular dynamics computer simulations substantiate our findings, quantifying the perturbation of the atomic-scale structure, dynamics and energetics of the interface in the presence of a kosmotrope.

A model of the potential-dependent adsorption of charged redox-active species at the electrode surface

A model of a non-polarizable interface is developed and considered in terms of the specific adsorption of charged redox species and the nonspecific adsorption of the supporting electrolyte. The adsorption coefficients of charged redox species depend on their charges and the potential at the inner Helmholtz plane. The adsorbed amounts of the redox species and supporting electrolyte are estimated using the Frumkin isotherm and Gouy–Chapman theory, respectively. The potential dependence of the adsorbed amount of either one or both of the oxidized and reduced forms of the redox species is maximized near its standard potential. The electrocapillary equation at a non-polarizable liquid metal–solution interface under an externally controlled potential is revisited. The derived electrocapillary equation facilitates calculating the electrocapillary curve of the non-polarizable interface based on the quantity of adsorbed ions. The electrocapillary curve calculated based on the model may have a concave part, which would indicate that the interface is thermodynamically forbidden, near the standard redox potential of the redox couple.

Comment on “Simple thermodynamic derivation of the electrocapillary equations” by L. Makkonen [Surf. Sci. 635 (2015) 61–63

• “Simple thermodynamic derivation of the electrocapillary equations” contains mathematical errors.

Simple thermodynamic derivation of the electrocapillary equations

Abstract Debate on the equations for surface excess stress and charge density on a solid continues in the literature. The various points of views are supported by complex mathematical argumentations. This hampers forming a unified understanding on the issue. To alleviate the situation, a concise but rigorous thermodynamic analysis is presented here. It shows that the Shuttleworth equation is invalid and the second Gokhshtein equation is incompatible with the formalism of thermodynamics. The validity of the Lippman equation and the first Gokhshtein equation depends on the independent variable of the system.

Application of the Lippmann electrocapillary equation to adsorption potential shift at the air/solution interface – Analysis for undissociated n-decanoic acid

The equilibrium surface pressure (Πe) and electric surface potential (Δχe) vs. concentration (c) isotherms of n-decanoic acid (DA) in 5×10−3mol/dm3 HCl were concurrently measured at the air/solution interface – the Π with a platinum Wilhelmy plate, the Δχ with the vibrating plate method (named also the dynamic condenser). The Πe–Δχe dependence was used by us for calculating the surface charge’ density basing on the Lippmann first electrocapillary equation. It was applied under the assumption that: (i) the surface charge is solely formed by orientation of the adsorbate, and (ii) the changing DA bulk concentration does not deprive the Πe–Δχe dependence of consistency with the Lippmann equations. The charge (Qe) expressed per the adsorbate molecule (basing on the Γ–c dependence predicted by the best fit of Frumkin model to the experimental Πe–c results) increases with the adsorption coverage (Θ) within a fraction of electron per the adsorbate molecule – the reasonable result for a non ionic surfactant. The Qe vs. Θ course shows a great analogy to that of quotient of the effective dipole moment to the interface’s permittivity, μ⊥εsvs.Θ, derived from the Δχe–Γ dependence. The two dependencies: Qevs.Θ and μ⊥εsvs.Θ, show a plateau within the coverage range of 20<Θ<80% and a steep increase above it. Recalculation of the Qevs.Θ dependence for the equivalent dipole moment, under the assumption that the dipole length is comparable to length of a polar bond of the head group (ca. 1.2Å) implies the bond’s inclination to the interface of 12°. Such low inclination is reasonable in view of an angular deviation of molecular dipole moment from amphiphile molecule’ long axis.

Applicability of Gibbs adsorption equation and Maxwell relations to deformed solid surfaces

Revisiting derivations of Gibbs adsorption equation show its applicability to solid surfaces without limiting requirement of constant state of strain. Some attempts to use such a restriction to prove the correctness of the Shuttleworth equation have failed. Also, we have shown that the mandatory conditions for the Maxwell's relations make its inapplicable for the description of capillary and electrocapillary phenomena on solid surfaces, as they lead, if used correctly, to trivial results - known Gibbs adsorbtion equation and Lippmann electrocapillary equation. Attempts to use Maxwell's relations for the case of solid electrodes available in the literature are based on mathematical defects and, consequently, yield erroneous results.

A model of the electrochemical instability at the liquid∣liquid interface based on the potential-dependent adsorption and Gouy’s double layer theory

A new model has been formulated for the electrochemical instability at the liquid∣liquid interface, for which only a rudimentary model [T. Kakiuchi, J. Electroanal. Chem. 536 (2002) 63–69] had been available. The new model considers the diffuse double layers in the presence of the specifically adsorbed surface-active ions, whose adsorption Gibbs energy linearly varies with the phase-boundary potential. The electrocapillary equation in the presence of the common ions partitioning in both phases is employed under the assumption that the partition of the surface-active ions is described by the Nernst equation. The excess surface charge due to the specific adsorption of surface-active ions is allowed for in calculating the structure of the diffuse part of the electrical double layers on both sides of the interface. The calculated electrocapillary curves agree with the experimental results. It is confirmed that electrocapillary curves can have positive curvature in a certain potential region, which signifies the presence of an instability window.

Determination of the entropy of formation of the Pt(111)∣ perchloric acid solution interface. Estimation of the entropy of adsorbed hydrogen and OH species

The entropy of formation of the interface between a Pt(111) electrode and a 0.1-M HClO4 solution is calculated here for the first time from the temperature dependence of total charge vs potential curves following a thermodynamic analysis based on the electrocapillary equation. From this quantity, the absolute entropies of specifically adsorbed species (hydrogen and OH) can be estimated. The present method is an alternative treatment of data that overcomes some of the limitations involved in the approach that uses a generalized isotherm. However, it requires additional experimental data: the temperature coefficient of the potential of zero total charge of the working electrode and the temperature coefficient of the reference electrode. Comparison of the results obtained by both approaches shows that, for hydrogen adsorption, the agreement is reasonable, but the differences are larger for OH adsorption, thus showing the limitations inherent in the treatment based on the generalized isotherm.

Electrochemical and spectroelectrochemical characterization of lipid organization in an electric field

The characterization of the adsorption/desorption of water insoluble surfactants onto an electrified interface is reviewed. Electrochemical and spectroelectrochemical investigations of the role of potential in controlling the nature of the surfactant present at the interface is described. The adsorption of octadecanol, cis-9-octadecenol onto Au(1 1 1) and the adsorption of DOPC (from a monolayer or from a dispersion of liposomes) onto Hg are used as examples. A general mechanism was proposed to describe the potential-dependent phase changes, desorption and subsequent readsorption process that links the results from impedance, fluorescence and elastically scattered light measurements of the surfactant-modified interface. This proposed mechanism and results from fluorescence microscopy results were used to describe the creation of a hybrid adsorbed hemi-liposomal layer onto a Hg surface. The implications for thermodynamic analysis via the electrocapillary equation for this class of surfactants were discussed. The relevance of the general mechanism towards the reductive desorption of alkyl thiol SAMs was also outlined.

Thermodynamic analysis of the cation binding to a phosphatidylcholine monolayer at a polarised interface between two immiscible electrolyte solutions

Thermodynamic analysis of the polarised interface between two immiscible electrolyte solutions (ITIES) was outlined, which accounts for the adsorption of phosphatidylcholine (PC) both as a zwitterion and a cation formed by the aqueous cation association with the zwitterionic PC form, as well as for the aqueous cation transfer facilitated by PC leading to its depletion from the interface. Electrocapillary equation was derived clarifying the physical significance of the surface charge density; the differential capacity and the PC surface excess concentration. The potential dependence of the interfacial tension calculated using the Damaskin’s adsorption model of a compound adsorbed in two different forms was found to agree well with that measured for the polarised water|1,2-dichloroethane interface in the presence of dl-α-dipalmitoylphosphatidylcholine. Experimentally observed effect of the nature of the aqueous cation on the interfacial tension was ascribed to the difference in the PC association constant.

Electrocapillary equations of solid electrodes

The electrocapillary equations and their application to solid electrodes are reviewed. Evidence is presented showing that solid electrodes exhibit two kinds of electrocapillary properties. For plastic deformation or immersion processes, thermodynamic properties of the solid electrodes are consistent with the classical Lippmann equation. For elastic processes, thermodynamic properties are inter-related by the Gokhshtein equation that accounts for the influence of elastic strain on a solid electrode’s charge density. The latter equation predicts the difference between the potential of zero charge and the potential of the maximum of the electrocapillary curve. For solid metals, the presence of the electronic dipole layer is the primary reason for the difference between these two points.

Elastic Electrocapillary Properties of Polycrystalline Gold

To establish the applicability of the classical Lippmann electrocapillary equation to a polycrystalline gold electrode, the measurements of the derivative of the surface tension (stress) with respect to charge density (q-estance) have been performed. Measurements were carried out in the solutions of the surface inactive perchlorate anions. For all investigated systems, the estansograms revealed characteristic negative shift of the potential of electrocapillary maximum with respect to the potential of zero charge of the polycrystalline gold electrode found by measurements of the differential capacity. The shift suggests the modified (by A. Gokhshtein) electrocapillary equation − ∂γ/∂E = q + ∂q/∂e should be used instead of the classical one. The second term in the modified equation appears due to the variation of the charge density of the solid electrode during the elastic stretching process. This term is positive and almost constant for gold electrode near the potential of zero charge and in the potential ...

Superficial work and surface stress at solid electrodes: a thermodynamic assessment

A Gibbs adsorption equation under surface strain is derived, that holds whether or not chemical equilibrium is established. The thermodynamic derivation does not make use of the ad hoc introduction of the ‘generalized surface parameter’, nor of the fictitious separation of surface deformation into plastic and elastic contributions. Moreover, no use is made of Euler’s theorem in connection with the functional dependence of the surface excess of internal energy upon the surface area A and the mole numbers of all components adsorbed at the interphase. Conversely, in the case of solid electrodes, account is taken of the lack of proportionality between A and the number of moles of at least one interfacial component, i.e. the surface atoms of the metal substrate. At equilibrium, this approach leads to a ( γ − Y )d ε term in the Gibbs adsorption equation, where γ is the superficial work, Y is the surface stress and ε is the surface deformation. This term is shown to be negligible under all practical conditions. Hence, the Lippmann equation and the electrocapillary equation, strictly valid for liquid electrodes, can also be applied to solid electrodes, for measuring changes of γ and surface excesses of chemisorbed species. On the other hand, experimental measurements of changes of Y induced by chemisorption have no bearing on the electrocapillary equation; rather, they are related to partial charge transfer accompanying chemisorption.

A note on the surface stress and tension of solid metal electrodes

The thermodynamics of a solid metal electrode in contact with a liquid electrolyte are briefly reviewed. The contribution of the metal to the interfacial tension γ and stress g are calculated within the jellium model. When the electrostatic terms are excluded, both quantities vary smoothly with surface charge density. Over the investigated range, the variation of the surface stress is much larger than that of the interfacial tension. The contribution of an adsorbate to γ and g is considered within the lattice gas model, which is treated in the mean-field approximation. While the interfacial tension is governed by the familiar electrocapillary equation, the surface stress depends on the energy of adsorption and on adsorbate interactions. In simple cases the surface coverage and the interfacial stress show a similar dependence on the electrode potential, and the variation of the stress resembles a cyclic voltammogram.

A thermodynamic test of the diffuse layer theory and its implications on electrode kinetics

AbstractThe thermodynamic compatibility of the diffuse layer theory with the chemical potential of ionic species in the solution bulk is introduced. From the electrocapillary equation, a compatibility equation, which relates the potential drop across the diffuse layer to the chemical potential of the ionic species in the solution bulk, is deduced for a binary electrolyte. When the Gouy–Chapman (GC) theory is introduced in the compatibility equation, the latter only becomes an identity if the ionic activity is taken as the ionic concentration, as expected. A compatible theory of the diffuse layer which has GC as the limit case at dilute solutions and fulfills the compatibility equation for whatever physical description of the ionic activity coefficients is stated. The significance of the compatible theory is that the electrode reaction rates calculated by means of the electrode kinetic equation with the Frumkin correction using this theory differ from those calculated using GC. In order to test both theories, we have studied the electroreduction of peroxodisulfate at an amalgamated copper rotating disk electrode. The experimental results fit our compatible theory better than GC does.

Potentials of Thermodynamic and Free Zero Charge at the Interface between Two Immiscible Electrolytes

Electrocapillary equations are analyzed for partially polarizable interfaces between two immiscible electrolyte solutions (ITIES), and the determination of thermodynamic and free zero charge potentials at the oil/water interface is considered. The difference between potentials corresponding to the minimum of differential capacitance and maximum of electrocapillarity curves is caused by faradaic processes and nonideal polarizability of ITIES. The difference depends on the contribution of penetrating ions to the surface charge. Because the inner layer parameters are nonlinear functions of the potential difference at ITIES, the minimum capacitance potential shifts with increasing electrolyte concentrations even when there is no specific ion adsorption.

Investigations of SO 42− adsorption at the Au(111) electrode by chronocoulometry and radiochemistry

Chronocoulometry was employed to measure charge density at the Au(111) electrode surface. Thermodynamic analysis of the charge density data for ionic adsorption from a solution with an excess of a supporting electrolyte is described and used to study SO 4 2− adsorption at the Au(111) electrode from a 0.1 M HClO 4 solution. The Gibbs excesses determined from the charge density data are compared with the Gibbs excesses determined from radiochemical measurements using 35S-labelled sulphate solutions. Very good agreement between the Gibbs excesses determined by the two techniques is observed. Essin-Markov coefficients for SO 4 2− adsorption from two series of solutions were determined: (i) at constant pH and variable K 2SO 4 concentration; (ii) at constant K 2SO 4 concentration and variable pH. The Essin-Markov coefficients were used to identify the nature of the adsorbed species (HSO 4 − or SO 4 2−). Our results indicate that SO 4 2− ion is the adsorbed species even if HSO 4 − predominates in the bulk of the solution. Chronocoulometry and radiochemistry were used to study SO 4 2− adsorption at the Au(111) electrode. Very good agreement between the Gibbs excesses determined from chronocoulometric and radiochemical measurements was observed. This agreement is an important verification of the reliability of these two in-situ techniques for measuring surface coverages. Although the two techniques give the same physical quantity, which is the Gibbs excess of adsorbed ions, each of them probes different properties of the interface and therefore has different limitations. The quantity measured by chronocoulometry is the electrode charge density. The surface concentration is calculated from σ M employing one integration step and one differentiation step and assuming the validity of the electrocapillary equation. Therefore the chronocoulometric technique can be applied only within the double-layer region of the gold electrode. However, since both the Gibbs excess and the charge density are measured simultaneously, this technique provides not only the surface coverages but also an additional electrical variable needed for the interpretation of the coverage data. In contrast, radiochemistry provides information about the Gibbs excess from direct counts of the radioactivity when the electrode with adsorbed radiolabelled material is pressed against the scintillator window. Therefore this technique can be used to study adsorption on both reactive and non-reactive materials. However, the technique is restricted by the efficiency in squeezing out the solution containing radioactive species from the thin layer between the electrode surface and the scintillator window. When the count rates from solution trapped in that gap are high with respect to surface counts, the adsorption measurements are difficult and ultimately become impossible to conduct. In fact, the method cannot be employed for adsorption measurements when the bulk concentration of labelled solute is higher than 10 −2 M [1]. In addition, the radiochemical technique provides information about the Gibbs excess only.

Liquid Motion Induced by Electrocapillary Action at Solid Metal-Liquid Interfaces

It is shown that cyclic mechanical displacements are induced in a variety of aqueous solutions and organic liquids when alternating voltages are applied across the interfaces between them and solid metal electrodes. The displacements, in the picometer-nanometer range, are proportional to the applied voltage and are determined using an interferometer technique which detects the movement of a mirror floating on the free surface of the liquid above the interfaces. The displacements, particularly in the case of a stainless steel-glycerol interface, increase considerably when steady bias voltages are applied. The experiments are in agreement with the predictions of the Lippmann electrocapillary equation for interfaces and complement those where stresses or strains generated in the solid electrode rather than the liquid side of the interfaces have been measured. Since similar displacements have been measured at solid as well as liquid contacts to metal electrodes, it is concluded that the Lippmann equation predicts quasi-piezoelectric phenomena at all condensed matter interfaces.