Electrocapillary Equation Research Articles

Electrocapillary phenomena at polarizable and reversible interfaces between two immiscible liquids: the generalized electro-capillary equation in hansen's representation

Abstract The thermodynamic theory of electrocapillary phenomena at the interface between two immiscible electrolyte solutions is considered. A generalized electrocapillary equation for polarizable and reversible interfaces is derived based on Hansen's method. The Gibbs equation for electrolytic systems is obtained both in variables corresponding to ion concentrations and concentrations of neutral ion combinations. The relationship between the ion concentrations in the system and EMF of the circuit consisting of immiscible electrolyte solutions whose terminals are made of identical metals is discussed. The formulae for the thermodynamic charge and the free charge of the interface between two immiscible electrolyte solutions (ITIES) are analysed. The cases of both perfectly and ideally polarizable, and also reversible (non-polarizable) interfaces are considered. Relationship between thermodynamic charges in different sets of variables is obtained.

Electrocapillary phenomena at the interface between two immiscible liquids

The thermodynamic theory of capillary phenomena is considered. The comparative analysis of Gibbs, Hansen's and Guggenheim's methods is presented. The Gibbs and Hansen's reference systems are described. An alternative geometrical interpretation of Gibbs method is developed. The adsorption equation is obtained in Hansen's representation. A symmetrized form of the adsorption equation has been derived and the relationship between Gibbs and Hansen's surface excesses established. Frumkin's interpretation of surface excesses is discussed. A description is given of the specific volume and entropy of an interface formation in a multicomponent system. The difficulties encountered in the interpretation of Hansen's method are explained. Hansen's method has been generalized for the curved surface of an arbitrary shape. The Gibbs phase rule for immiscible electrolyte solutions is considered. Methods of choosing the independent system variables that are most suitable for the electrocapillarity theory are analyzed. The thermodynamic theory of electrocapillarity phenomena at the interface between two immiscible electrolyte solutions (ITIES) is presented. A generalized electrocapillary equation for polarizable and reversible interfaces is derived using Hansen's method. The Gibbs equation for electrolytic systems is obtained both in ion concentrations and in variables corresponding to concentrations of neutral ion combinations. The relationship between the ion concentrations in the system and the EMF of the circuit consisting of immiscible electrolyte solutions with terminals made of identical metals is discussed. The formulas for the thermodynamic and the free charge of the interface between two immiscible electrolyte solutions are analysed. The cases of perfectly, ideally polarizable and reversible (nonpolarizable) interfaces are considered. Relationships between thermodynamic charges in different sets of variables are obtained.

A method for evaluating the surface concentrations of two like-charged ions simultaneously adsorbed at an electrode-solution interface

Abstract : A recent preliminary report by Gonzales and co-workers highlights the experimental difficulties in determining the amounts of specific adsorption of two types of ions simultaneously present at a mercury-aqueous interface. The authors note that the elegant analysis of Lakshmanan and Rangarajan required such a large amount of data that the method has scarely ever been employed. There are additional difficulties with this analysis when employed at solid electrode surfaces. It is desirable to find a method that could readily be applied at polycrystalline solid, as well as liquid, electrodes. This reports outlines such an analysis for determining the simultaneous adsorption of like-charged ions, based on a simple extension of the well-known Hurwitz-Parsons approach. These authors demonstrated independently that the amount of specific adsorption of, for example, an anion X can be assessed from differential capacitance-potential data for a series of mixed electrolytes containing varying proportions of the salts BX and BY at a constant total ionic strength, where Y is an anion that is not specifically adsorbed. The electrocapillary equation can be written in terms of salt chemical potentials.

Thermodynamics of the Electrocapillarity of Oil–Water Interfaces

Abstract General electrocapillary equations for the interfaces between two immiscible or partially miscible electrolyte solutions have been derived. The theory includes both nonpolarized and ideal polarized interfaces. The electrocapillary equation for the latter has been derived from the equation for the former as a special case where no common ionic species are distributed between the two phases. Implications of the general electrocapillary equation for oil–water interfaces are indicated.

A possible solution to the problem of the electrode charge density in the case of reactant adsorption

Starting from the electrocapillary equation for the ideally reversible electrode a relation has been derived between the parameters q *- q M+ nFΛ 0 ( q M=electrode charge density, Λ 0=surface excess of oxidant) and the derivatives of the free energies of adsorption of the Ox and Red component with respect to potential. In this way a model is obtained for the explicit interpretation of the low frequency capacity C LF and the high frequency capacity C HF, occurring as parameters in the expression for the electrode admittance in the case of reactant and/or product adsorption. The experimental results obtained by Timmer et al. for the Pb(II) reduction in 1 M KCl appear to fit to this model if a linear isotherm with a potential-dependent adsorption coefficient is assumed. It is concluded that most probably the neutral PbCl 2 species is adsorbed.

Gas phase electrochemistry. II. Adsorption of CH2Cl2 in CF4 on dropping mercury electrode

The specific adsorption of a polar gas on a dropping mercury electrode in the presence of an inert getter is investigated as a function of the pressure in the system and the external applied voltage. The results are compared with an electrocapillary equation which was developed in a previous work. It is found that CF4 is not specifically adsorbed on the mercury surface while CH2Cl2 is, and that the surface concentration of the latter in the presence of the former is independent of the applied voltage in the range ±3 kV.

The electrical double layer between mercury and aqueous NaBF4 solutions

Potentials of the sodium amalgam electrode have been determined with respect to a saturated calomel electrode at various concentrations of NaBF4 in the range 0.01 m to 1 m. γ± values have been evaluated by assuming that (i) the liquid junction potential EL changes trivially in the whole concentration range and (ii) the single ion activity strictly derivable from the experimental arrangement coincides with the mean ionic activity. Possible deviations of γ± from the thermodynamic value due to factors (i) and (ii) have been examined in detail and reliable estimations of the limits of accuracy have been made. As a conclusion, γ± 's as derived in this work have been estimated to be some 5 to 10 % higher than the true values at the highest concentrations, the deviation approaching rapidly negligible levels as the concentration is decreased. As a result, the γ± 's given in this Paper may be used with confidence for practical purposes, e.g in the graphical differentiation of the electrocapillary equation in the study of BF4 - adsorption.

The electrocapillary equations and the double layer charge of reversible electrodes

Summary It is shown that the separation of the double layer to electrolyte and metal sides is unnecessary for a strictly thermodynamic treatment of both ideally polarised and the reversible electrodes. The presently accepted electrocapillary equations for reversible electrodes contain thermodynamically meaningless surface excesses. This can be avoided if the redox chemical reactions are used to represent one of the redox species as a linear combination of the others. The treatment presented results in simpler and more general electrocapillary equations which are identical with that of the ideally polarised electrode and include this system as a particular case. By means of an example of a high surface carbon electrode, the method is further generalised to include a double layer system which involves several equilibrium chemical reactions. If the experimental conditions are adjusted according to the formal thermodynamic definition of the system, then the various Gibbs surface excesses—including electrical charge, are directly measurable by macroscopic methods. The thermodynamically meaningless surface excesses of the separate chemically active species cannot be measured by macroscopic methods unless some non-thermodynamic assumptions are made. They can however be determined by techniques which respond to individual molecules such as spectroscopy. Some of the ideas of Frumkin and coworkers concerning double layer thermodynamics of reversible hydrogen electrodes, are revised and reformulated to emphasize their general significance. Special attention is paid to the double layer charge of reversible electrodes.

The electrocapillary equations and the double layer charge of reversible electrodes

The electrocapillary equations and the double layer charge of reversible electrodes

On the derivation and formulation of the electrocapillary equation of ideally polarizable electrodes

On the derivation and formulation of the electrocapillary equation of ideally polarizable electrodes

On the derivation and formulation of the electrocapillary equation of ideally polarizable electrodes

On the derivation and formulation of the electrocapillary equation of ideally polarizable electrodes

Mixed adsorption at mercury/solution interfaces I. A thermodynamic analysis

A thermodynamic analysis is given of the electrocapillary equation suitable for the evaluation of individual surface excesses at the inner planes of two specifically adsorbed anions from a mixture containing these two anions along with a common cation. This analysis takes into account variation of activity coefficients of the salts in the mixture. The problem of interpreting the electrocapillary data obtained in the absence of a cation-sensitive electrode is considered and appropriate expressions are given.

Mixed adsorption at mercury/solution interfaces: I. A. Thermodynamic analysis

A thermodynamic analysis is given of the electrocapillary equation suitable for the evaluation of individual surface excesses at the inner planes of two specifically adsorbed anions from a mixture containing these two anions along with a common cation. This analysis takes into account variation of activity coefficients of the salts in the mixture. The problem of interpreting the electrocapillary data obtained in the absence of a cation-sensitive electrode is considered and appropriate expressions are given.

Thermodynamic treatment of interfacial curvature in electrocapillarity

The thermodynamic theory of electrocapillarity is extended to include the explicit dependence of the interfacial tension of an ideal polarized electrode on interfacial curvature. Interfacial curvature adds one additional independent variable to the electrocapillary equation. At any constant curvature, the form of the Lippmann equation, the other first partial differential coefficients of the interfacial tension and the relationship between interfacial tension and differential capacitance depend upon curvature. However, the second cross partial differential coefficients of interfacial tension and the Esin and Markov coefficient have the same form as for a planar electrode. The effect of varying curvature is investigated on the basis of a theory of Tolman, and the results obtained are applied to the estimation of the probable curvature dependence of a mercury electrode.