Electrocapillarity

We start this chapter with electrocapillarity because it provides detailed information of the electric double layer. In a classical electrocapillary experiment the change of interfacial tension at a metal-electrolyte interface is determined upon variation of an applied potential (Fig. 5.1). It was known for a long time that the shape of a mercury drop which is in contact with an electrolyte depends on the electric potential. Lippmann1 examined this electrocapillary effect in 1875 for the first time [68], He succeeded in calculating the interfacial tension as a function of applied potential and he measured it with mercury. 

The change of the interfacial tension can be calculated with the help of the Gibbs-Duhem equation even when a potential is applied. In order to use the equation, we first need to find out which molecular species are present. Evidently, only those which are free to move are of interest. In the electrolyte we have the dissolved ions. In the metal the electrons can move and have to be considered. 

Since in addition to the chemical potentials also the electrical potential 99, affects the charged species, electrochemical potentials //, must be used. We use the symbol 99 instead of -ip because this is the Galvani potential (see Section 5.5). The Gibbs-Duhem equation for changes of state functions at constant temperature is 

The first term refers to the electrolyte. Accordingly, the sum runs over all ion types present in the electrolyte. The second term contains the contribution of the electrons in the metal. T and Te are the interfacial excess concentrations of the ions in solution and of the electrons in the metal, respectively, /x is the chemical potential of the particle type i, Fa is Faradays constant, and /x is the electrochemical potential of the electrons. Substitution leads to 

What are the correct values of the potentials In the metal the potential is the same everywhere and therefore 99 has one clearly defined value. In the electrolyte, the potential close to the surface depends on the distance. Directly at the surface it is different from the potential one Debye length away from it. Only at a large distance away from the surface is the potential constant. In contrast to the electric potential, the electroc/zmz caZpotential is the same everywhere in the liquid phase assuming that the system is in equilibrium. For this reason we use the potential and chemical potential far away from the interface. 

In the present section, we will focus on somewhat different electrical effects, the practical applications of which remain perhaps limited so far, but which are directly related to capillary effects—electrocapillarity and electro-osmosis. 

The surface tension 712 of the mercury/water system changes as one applies a voltage U to mercury. 

The functional dependence of yi2 U) depends critically on the type of ions present in the solution. Suppose the solution contains sodium sulfate. In such a case, in the absence of an applied voltage, the sodium ions Na attach themselves to the mercury, and a double layer forms in the water with nothing but ions over a certain screening length, roughly 30 A 

If the surface tension depends on the applied bias, it becomes possible to set a mercury column in motion in a capillary tube by applying different voltages to either end. Hence the possibility of fabricating micropumps on a tiny dimensional scale. 

Researches carried out in electrochemistry on solid electrodes and especially on the mercury-water interface have made a significant contribution to an understanding of interfacial phenomena. Although the electrode-water interfaces are typically 

The polarized Electrode-Electrolyte and the reversible Solid-Electrolyte Interface 

A polarizable Interface is represented by a (polarizable) electrode where a potential difference across the double layer is applied externally, i.e., by applying between the electrode and a reference electrode using a potentiostat. At a reversible interface the change in electrostatic potential across the double layer results from a chemical interaction of solutes (potential determining species) with the solid. The characteristics of the two types of double layers are very similar and they differ primarily in the manner in which the potential difference across the interface is established. 

Electro Capillarity and the dropping Mercury Electrode. The term electro capillarity derives from the early application of measurements of interfacial tension at the Hg-electrolyte interface. The interfacial tension, y, can be measured readily with a dropping mercury electrode. E.g., the life time of a drop, tmax. is directly proportional to the interfacial tension y. Thus, y is measured as a function of y in presence and absence of a solute that is adsorbed at the Hg-water interface this kind of data is amenable to thermodynamic interpretation of the surface chemical properties of the electrode-water interface. 

A schematic example is given in Fig. A.4.5. The slope of the electrocapillary curve depends on the nature of the solution or the equilibrium structure of the double layer and on the specific sorbability of dissolved substances. In line with the Gibbs equation (Eq. 4.3), sorbable species depress the interfacial tension. 

It has long been known that the form of a curved surface of mercury in contact with an electrolyte solution depends on its state of electrification [108, 109], and the earliest comprehensive investigation of the electrocapillary effect was made by Lippmann in 1875 [110]. A sketch of his apparatus is shown in Fig. V-10. 

Qualitatively, it is observed that the mercury surface initially is positively charged, and on reducing this charge by means of an applied potential, it is found that the height of the mercury column and hence Ae interfacial tension 

It is necessary that the mercury or other metallic surface be polarized, that is, that there be essentially no current flow across the interface. In this way no chemical changes occur, and the electrocapillary effect is entirely associated with potential changes at the interface and corresponding changes in the adsorbed layer and diffuse layer. 

Interfacial tension measurements on liquid metal electrodes, such as mercury, have provided a great deal of information about double layer structure and 

The dependence of interfacial tension upon applied potential may be derived by application of the Gibbs adsorption isotherm to the system of 

Schematic variation of interfacial tension with applied potential (electrocapillary curve) for a mercury-aqueous electrolyte solution interface. 

We are concerned, however, with charged species. When i carries charge its chemical potential is also a function of the electrical potential, yp, of the phase in which it exists. Thus, for ions of charge Wj, we define the electrochemical potential, fii, by 

So that, for ions, the Gibbs adsorption isotherm is expressed in terms of electrochemical potential by 

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A. Thermodynamics of the Electrocapillary Effect The basic equations of electrocapillarity are the Lippmann equation [110]... 

The various experimental methods associated with electrocapillarity may be divided into those designed to determine surface tension as a function of applied... 

The equations of electrocapillarity become complicated in the case of the solid metal-electrolyte interface. The problem is that the work spent in a differential stretching of the interface is not equal to that in forming an infinitesimal amount of new surface, if the surface is under elastic strain. Couchman and co-workers [142, 143] and Mobliner and Beck [144] have, among others, discussed the thermodynamics of the situation, including some of the problems of terminology. 

Electrocapillarity is the study of the interfacial tension as a function of the electrode potential. Such a study can provide useful insight into the structure and properties of... 

All the models discussed above are based on a deterministic point of view. However, there is another type of model (i.e., a nondeterministic model) that includes the concept of nonequilibrium fluctuation. In the following section, we discuss such a model, i.e., the electrocapillarity breakdown model. 

Equations (10.34) and (10.35) are different forms of the general equation of electrocapillarity. The parameters contained in them can be determined experimentally. These equations can be used to calculate one set of parameters when experimental values for another set of parameters are available. 

Every interface is more or less electrically charged, unless special care is exercised experimentally [26]. The energy of the system containing the interface hence depends on its electrical state. The thermodynamics of interfaces that explicitly takes account of the contribution of the phase-boundary potential is called the thermodynamics of electrocapillarity [27]. Thermodynamic treatments of the electrocapillary phenomena at the electrode solution interface have been generalized to the polarized as well as nonpolarized liquid liquid interface by Kakiuchi [28] and further by Markin and Volkov [29]. We summarize the essential idea of the electrocapillary equation, so far as it will be required in the following. The electrocapillary equation for a polarized liquid-liquid interface has the form... 

The presence of electrical charge affects the interfacial tension in the interphase. If one of the phases considered is a metal and the other is an electrolyte solution, then the phenomena accompanying a change in the interfacial tension are included under the term of electrocapillarity. 

The thermodynamic theory of electrocapillarity considered above is simultaneously the thermodynamic theory of the electrical double layer and yields, in its framework, quantitative data on the double layer. However, further clarification of the properties of the double layer must be based on a consideration of its structure. 

The model of the electrode/electrolyte interface proposed in the first chapter is termed the Stern model. This is now accepted as the definitive picture of the structure of the interface, primarily as a result of electrocapillarity studies. 

Electrocapillarity is the measurement of the variation of the surface tension of mercury in (usually) aqueous electrolyte with applied potential. The surface tension, y, of an interface relates to the surface free energy, C, by the expression ... 

A typical electrocapillarity system is shown in Figure 2.1(a). The mercury reservoir provides a source of clean mercury to feed a capillary tube the height of mercury in this tube can be varied such that the mass of the Hg column exactly balances the surface tension between the mercury and the capillary walls, see Figure 2.1(b). A voltage V is applied across the mercury in the capillary and a second electrode which is non-polarisable (i.e. the interface will not sustain a change in the potential dropped across it), such as the normal hydrogen electrode, NHE. The potential distribution across the two interfaces is shown in Figure 2.1(c). As can be seen ... 

Figure 2.1 (a) A schematic representation of the apparatus employed in an electrocapillarity experiment, (b) A schematic representation of the mercury /electrolyte interface in an electro-capillarity experiment. The height of the mercury column, of mass m and density p. is h, the radius of the capillary is r, and the contact angle between the mercury and the capillary wall is 0. (c) A simplified schematic representation of the potential distribution across the metal/ electrolyte interface and across the platinum/electrolyte interface of an NHE reference electrode, (d) A plot of the surface tension of a mercury drop electrode in contact with I M HCI as a function of potential. The surface charge density, pM, on the mercury at any potential can be obtained as the slope of the curve at that potential. After Modern Electrochemistry, J O M. 

Largely through the painstaking work of Grahame in the 1940s, electrocapillarity effectively established the first experimental basis for the now accepted double layer theory. The basic picture of the electrode/electrolyte interface was thus in place. 

It would seem, at first glance, that the place of electrocapillarity ties in the history of electrochemistry rather than its future, since its application appears limited only to the mercury/electrolyte interface. However, the work of Sato and colleagues (1986, 1987, 1991) has very definitely placed the technique, or at least a development of it, very firmly at the frontiers again. 

The results obtained by the method of Sato come in the form of plots of u and (j> against potential. Since u ac (dy/dE), then integrating the plot of u vs. E around the pzc (shown by the 180" change in ), gives the electrocapillarity curve of Ay vs. E, providing the proportionality constant between a and (dy/dE) can be determined. This latter is normally straightforward since dy/dE = a, which can be determined independently. 

No investigation of a solid, such as the electrode in its interface with the electrolyte, can be considered complete without information on the physical structure of that solid, i.e. the arrangement of the atoms in the material with respect to each other. STM provides some information of this kind, with respect to the 2-dimensional array of the surface atoms, but what of the 3-dimensional structure of the electrode surface or the structure of a thick layer on an electrode, such as an under-potential deposited (upd) metal At the beginning of this chapter, electrocapillarity was employed to test and prove the theories of the double layer, a role it fulfilled admirably within its limitations as a somewhat indirect probe. The question arises, is it possible to see the double layer, to determine the location of the ions in solution with respect to the electrode, and to probe the double layer as the techniques above have probed adsorption Can the crystal structure of a upd metal layer be determined In essence, a technique is required that is able to investigate long- and short-range order in matter. 

That volume within which the ions having charge opposite to that on the electrode have a concentration higher than those in the bulk of the solution (in the absence of specific adsorption). Under the conditions typically employed in electrochemical measurements, i.e. high ionic strength, this would correspond simply to a volume bounded by the outer Helmholtz plane, a few angstroms (see section on electrocapillarity). 

As was discussed in section 2.1.1, electrocapillarity measurements at mercury electrodes, which have well-defined and measurable areas, allow the double-layer capacitance, CDL, to be obtained as Fm-2. Bowden assumed that the overpotential change at the very beginning of the anodic run in H2-saturated solution was a measure of the double-layer capacity. The slope of the E vs. Q plot in this region was taken as giving 1/CDL, and this gave 2 x 10 5 F. He then assumed that, under these same conditions, the double-layer capacity, in Fm-2, of the mercury electrode is the same. This gave the real surface area of the electrode as 3.3cm 2, as opposed to its geometric area of I cm2. 

Evidently, Eq. (39) cannot be valid whenever the tip does not possess an exact hemispherical symmetry for instance, whenever traces of crystallographic planes are visible in the field-ion microscope, the value of the radius of curvature becomes nearer to infinity than to the r of Fig. 5. It is interesting to note also that the theory admits no direct effect of the electrostatic field on the value of ys. In liquids, the effect of E on y gave rise to a whole branch of science usually known as electro-capillarity. An attempt to inaugurate an electrocapillarity of solids is mentioned in Section III.9. 

Electric Effects. The science of electrocapillarity exists for over 100 years. When a liquid surface is electrically charged, its tension changes, and these changes can be followed quantitatively with the standard methods of measuring 7. It is tempting to apply the notions of electrocapillarity to solid surfaces, and a recent book162) is a particularly rich example. 

Gilkes RY (1990) Mineralogical insights into soil productivity An anatomical perspective. Proc 14th Congress of Soil Science, Kyoto, Japan. Transaction Plenary Papers pp 63-75 Grahamme DC (1947) The electrical double layer and the theory of electrocapillarity. Chem Rev 41 441-501n... 

K. Rice, Application of the Fermi Statistics to the Distribution of Electrons under Fields in Metals and the Theory of Electrocapillarity, Phys. Rev. 31 1051 (1928). 

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