Interfacial capacity

Therefore the lattice-gas model has proved most useful for the study of those processes in which the ionic double layer plays a major role, and there are quite a few. So it has been used to investigate the interfacial capacity, electron and ion-transfer reactions, and even such complex processes as ion pairing and assisted ion transfer. Because of its simplicity we carmot expect this model to give quantitative results for particular systems, but it is ideally suited to qualitative investigations such as the prediction of trends and orders of magnitude for various effects. 

Of course, the lattice gas is not the only simple model that has been proposed for liquid-liquid interfaces. So we will conclude this review by a survey of several other models, which have usually been devised for certain aspects such as the interfacial capacity or ion transfer. Some of these models give a similar view of the interface, while others are radically different. 

The interfacial capacity is then obtained by calculating the profiles for various potential drops A0 and subsequent differentiation. Figure 7 shows several examples of capacity-potential characteristics for several widths of the interface. Obviously, the wider the interface, the higher the capacity. In all cases investigated it was higher than that calculated from the Verwey-Niessen model, in which ... 

Huber et al. [12] investigated the same model by Monte Carlo simulations however, they focused on a different aspect the dependence of the interfacial capacity on the nature of the ions, which in this model is characterized by the interaction constant u. Samec et al. [13] have observed the following experimental trend the wider the potential window in which no reactions take place, the lower the interfacial capacity. Since the width of the window is determined by the free energy of transfer of the ions, which is 2mu in this model, the capacity should be lower, the higher u. ... 

Ion pairing increases the charge that is stored at a given potential, and hence the interfacial capacity. The capacity characteristics in Fig. 11 show the asymmetry that is quite typical for ion pairing [15]. 

FIG. 11 Interfacial capacity as a function of the total potential drop in the presence and in the absence (solid line) of ion pairing. Dotted line v = —9kT dashed line v = —lOkT. 

The Gouy-Chapman theory for metal-solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid-liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17) this is known as the modified Verwey-Niessen model. Since the interfacial capacity of liquid-liquid interfaces is... 

Recently, these authors have treated specific adsorption at corrugated liquid-liquid interfaces [39] however, because of the complicated mathematics involved this work does not fall under the heading simple models. Also, Urbakh et al. [40] have extended the results for the interfacial capacity to the nonlinear region. 

Unfortunately the development of models is hindered by a lack of reliable experimental data. For example, the rates of ion-transfer reactions measured at different times and by different groups vary widely. Also, it has been suggested that the high interfacial capacities that are measured in certain systems are an experimental artifact [13]. While this is frustrating for the researcher who wants to decide between competing models, it can also be viewed as a sign that the electrochemistry of liquid-liquid interfaces is an active field, where fundamental issues are just being explored. 

Kakiuchi et al. [75] used the capacitance measurements to study the adsorption of dilauroylphosphatidylcholine at the ideally polarized water-nitrobenzene interface, as an alternative approach to the surface tension measurements for the same system [51]. In the potential range, where the aqueous phase had a negative potential with respect to the nitrobenzene phase, the interfacial capacity was found to decrease with the increasing phospholipid concentration in the organic solvent phase (Fig. 11). The saturated mono-layer in the liquid-expanded state was formed at the phospholipid concentration exceeding 20 /amol dm, with an area of 0.73 nm occupied by a single molecule. The adsorption was described by the Frumkin isotherm. 

Kakiuehi et al. [84] studied the adsorption properties of two types of nonionic surfactants, sorbitan fatty acid esters and sucrose alkanoate, at the water-nitrobenzene interface. These surfactants lower the interfacial capacity in the range of the applied potential with no sign of desorption. On the other hand, the remarkable adsorption-desorption capacity peak analogous to the adsorption peak seen for organic molecules at the mercury-electrolyte interface can be observed in the presence of ionic surfactants, such as triazine dye ligands for proteins [85]. 

This contribution involves the positive-ion and electron density profiles of the metal, and the former is often assumed not to change with charging of the interface. In 1983 and 1984, several workers30-32,79 showed how certain features of the interfacial capacity curves should depend on the metal. 

Kornyshev et al.76 proposed several models of the interface, including both orienting solvent dipoles and polarizable metal electrons, to calculate the position of the capacitance hump. Although it had been shown32,79 101 that this was one of the features of the interfacial capacity curves that should depend on the nature of the metal, available calculations did not give the proper position of the hump. The solvent molecules in the surface layer were modeled as charged layers, associated with the protons and the oxygen atoms of molecules oriented either toward or away from the surface. These layers also carried Harrison-type pseudopoten-... 

Consider a plane metal electrode situated at z = 0, with the metal occupying the half-space z < 0, the solution the region z > 0. In a simple model the excess surface charge density a in the metal is balanced by a space charge density p(z) in the solution, which takes the form p(z) = Aexp(—kz), where k depends on the properties of the solution. Determine the constant A from the charge balance condition. Calculate the interfacial capacity assuming that k is independent of a. 

The total interfacial capacity C is a series combination of the space-charge capacities C c of the semiconductor and C oi of the solution side of the interface. However, generally Csoi Csc, and the contribution of... 

The interfacial capacity follows the Mott-Schottky equation (7.4) over a wide range of potentials. Figure 8.4 shows a few examples for electrodes with various amounts of doping [5]. The dielectric constant of Sn02 is e 10 so the donor concentration can be determined from the slopes of these plots. 

The potentials (f>j on the two sides of the interface can differ by an interfacial dipole potential. If this changes with the applied potential it gives an extra contribution to the interfacial capacity, and Eq. (12.9) must be replaced by ... 

On the whole, the Gouy-Chapman theory seems to work well for ITIES, indicating that any contribution from the dipole potential is small. In particular the interfacial capacity exhibits a minimum at the potential of zero charge for low electrolyte concentrations (see Fig. 12.3). 

This equation further indicates that the interfacial tension has an extremum at the pzc differentiating again gives the differential interfacial capacity ... 

Figure 16.4 Differential interfacial capacity for a Au(110) surface in contact with aqueous solutions containing 0.1 M KCIO4 and various amounts of pyridine. (1) no pyridine (2) 3 x 10-5 M (3) 10 2 3 4 M (4) 6 x 10 4 M pyridine. Data taken from Ref. 2.

Determine the pzc of the electrode in the absence of the adsorbate this can be done by finding the minimum of the interfacial capacity for a low concentration of the supporting electrolyte. 

As was pointed out in Chapters 2 and 3, a dipole layer exists at the surface of a metal, which gives rise to a concomitant surface dipole potential x- The magnitude of this potential changes in the presence of an external electric field. A field E directed away from the surface induces an excess charge density, o e0e E, where e is the dielectric constant of the medium outside the metal. The field E pushes the electrons into the metal, producing the required excess charge, and decreasing the dipole potential (see Fig. 3.4). This has consequences for the interfacial capacity. 

Even though this contribution is always negative, the total capacity must be positive - otherwise the capacitor would accumulate charge spontaneously. Thus Eq. (17.4) is only valid if f > rjm, so that there is no electronic overlap between the two plates. Similarly the use of a macroscopic dielectric constant in Eq. (17.5) presupposes a plate separation of macroscopic dimensions, and again the total capacity is positive. Only unphysical models or bad mathematical approximations can produce negative interfacial capacities, which enjoyed a brief spell of fame under the name of the Cooper-Harrison catastrophe [2]. 

For the interfacial capacity we require the variation of % with the charge density o on the metal so we must modify our trial functions to accommodate a charge. We consider small excess charges only, so that the following simple modification suffices [7] ... 

The new algebraic equation for a is easily derived by differentiation, and can be solved numerically (a simple analytical approximation is outlined in the problems). From Eq. (17.6) the contribution of the metal to the inverse interfacial capacity is ... 

The most important result is the existence of an extended boundary region, where the structure of solution differs significantly from the bulk, and where the potential deviates from the predictions of the Gouy-Chapman theory. In this model the interfacial capacity can be... 

The interfacial charge-related capacity, Cum, due to the internal polarization of adsorbed water molecules remains constant in the potential range where no reorganization of adsorbed water molecules occurs. On the other hand, the interfacial capacity related to water dipoles, Cs.di i, on the aqueous solution side depends on the orientation of adsorbed water molecules which changes with the interfacial charge and, hence, with the electrode potential. Further, the dipole capacity. Cm, dtp > on the metal side appears to slightly depend upon the interfacial charge and, hence, the electrode potential. Equation 5-11, then, yields Eqn. 5-12 ... 

---