The compact layer

The compact layer can be structured into what is called an inner Helmholtz plane... 

The inner layer (closest to the electrode), known as the inner Helmholtz plane (IHP), contains solvent molecules and specifically adsorbed ions (which are not hilly solvated). It is defined by the locus of points for the specifically adsorbed ions. The next layer, the outer Helmholtz plane (OHP), reflects the imaginary plane passing through the center of solvated ions at then closest approach to the surface. The solvated ions are nonspecifically adsorbed and are attracted to the surface by long-range coulombic forces. Both Helmholtz layers represent the compact layer. Such a compact layer of charges is strongly held by the electrode and can survive even when the electrode is pulled out of the solution. The Helmholtz model does not take into account the thermal motion of ions, which loosens them from the compact layer. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

C, E curves have been obtained for Zn(0001) andZn(lOTO) at various crci with different additions of tu.630,634-636 The data for Zn(0001) at Cju = const have been used to obtain C"1, Ql plots. Nonlinear plots have resulted, with the value of the reciprocal slope remarkably dependent on ctu- At c-ru = 0 1 M, the reciprocal slope of the PZ plot is 1.1, increasing with decreasing c-ru Such an effect has been related to the weak specific adsorption of OH" on Zn. This explanation has been critically discussed by Vorotyntsev,74 who has assumed that the effect635,636 is connected with the variation in the compact layer composition of the Z11/H2O + TU interface as cjv varies. 

In traditional models of an eleetrified interfaee, metal electrons are artificially localized within the eleetrode. This leads to misinterpretation of the electronic influences on the compact layer, Ch in those models would always be smaller than its ideal conductor limit (with electrode eharge spread over an infinitesimally thin region at the electrode surface x = 0)... 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

On the basis of this model, the overall differential capacity C for a system without specific adsorption, i.e. if the compact layer does not contain ions, is divided into two capacities in series, one corresponding to the compact layer Cc and the other to the diffuse layer Cd ... 

The diffuse layer is formed, as mentioned above, through the interaction of the electrostatic field produced by the charge of the electrode, or, for specific adsorption, by the charge of the ions in the compact layer. In rigorous formulation of the problem, the theory of the diffuse layer should consider ... 

The charge density on the electrode a(m) is mostly found from Eq. (4.2.24) or (4.2.26) or measured directly (see Section 4.4). The differential capacity of the compact layer Cc can be calculated from Eq. (4.3.1) for known values of C and Cd. It follows from experiments that the quantity Cc for surface inactive electrolytes is a function of the potential applied to the electrode, but is not a function of the concentration of the electrolyte. Thus, if the value of Cc is known for a single concentration, it can be used to calculate the total differential capacity C at an arbitrary concentration of the surface-inactive electrolyte and the calculated values can be compared with experiment. This comparison is a test of the validity of the diffuse layer theory. Figure 4.5 provides examples of theoretical and experimental capacity curves for the non-adsorbing electrolyte NaF. Even at a concentration of 0.916 mol dm-3, the Cd value is not sufficient to permit us to set C Cc. 

The structure of the compact layer depends on whether specific adsorption occurs (ions are present in the compact layer) or not (ions are absent from the compact layer). In the absence of specific adsorption, the surface of the electrode is covered by a monomolecular solvent layer. The solvent molecules are oriented and their dipoles are distorted at higher field strengths. The permittivity of the solvent in this region is only an operational quantity, with a value of about 12 at the Epzc in water,... 

The picture of the compact double layer is further complicated by the fact that the assumption that the electrons in the metal are present in a constant concentration which discontinuously decreases to zero at the interface in the direction towards the solution is too gross a simplification. Indeed, Kornyshev, Schmickler, and Vorotyntsev have pointed out that it is necessary to assume that the electron distribution in the metal and its surroundings can be represented by what is called a jellium the positive metal ions represent a fixed layer of positive charges, while the electron plasma spills over the interface into the compact layer, giving rise to a surface dipole. This surface dipole, together with the dipoles of the solvent molecules, produces the total capacity value of the compact double layer. 

Specific adsorption occurs, i.e. ions enter the compact layer, in a considerable majority of cases. The most obvious result of specific adsorption is a decrease and shift in the maximum of the electrocapillary curve to negative values because of adsorption of anions (see Fig. 4.2) and to positive values for the adsorption of cations. A layer of ions is formed at the interface only when specific adsorption occurs. 

At potentials far removed from the potential of zero charge, the electrical properties of the compact layer are determined by both the charge of the adsorbed ions and the actual electrode charge. The simplest model for this system is one which assumes independent action of these two types of charge. The quantity (m) — 2 can then be separated into two parts, [0(m) — 02]a(m) and [(m)-02]a,> each of which is a function of the corresponding charge alone ... 

Electroneutral substances that are less polar than the solvent and also those that exhibit a tendency to interact chemically with the electrode surface, e.g. substances containing sulphur (thiourea, etc.), are adsorbed on the electrode. During adsorption, solvent molecules in the compact layer are replaced by molecules of the adsorbed substance, called surface-active substance (surfactant).t The effect of adsorption on the individual electrocapillary terms can best be expressed in terms of the difference of these quantities for the original (base) electrolyte and for the same electrolyte in the presence of surfactants. Figure 4.7 schematically depicts this dependence for the interfacial tension, surface electrode charge and differential capacity and also the dependence of the surface excess on the potential. It can be seen that, at sufficiently positive or negative potentials, the surfactant is completely desorbed from the electrode. The strong electric field leads to replacement of the less polar particles of the surface-active substance by polar solvent molecules. The desorption potentials are characterized by sharp peaks on the differential capacity curves. 

In their classic treatment of the compact-layer capacitances, MacDonald and Barlow12 affirmed that the thickness of the space charge or penetration region in the metallic electrode is so small for a good conductor that its effect may be neglected. Their theory... 

Models for the compact layer of the metal-electrolyte interface have become more and more elaborate, providing better and better representations of observed electrocapillary data for different metals, solvents, and temperatures, but almost always leaving the metal itself out of consideration, except for consideration of image interactions of the solvent dipoles. For reviews of these models, see Parsons,13 Reeves,14 Fawcett et a/.,15 and Guidelli,16 who gives detailed discussion of the mathematical as well as the physical assumptions used. 

It may be noted that the statement made above—that the surface potential in the electrolyte phase does not depend on the orientation of the crystal face—is necessarily an assumption, as is the neglect of S s1- It is another example of separation of metal and electrolyte contributions to a property of the interface, which can only be done theoretically. In fact, a recent article29 has discussed the influence of the atomic structure of the metal surface for solid metals on the water dipoles of the compact layer. Different crystal faces can allow different degrees of interpenetration of species of the electrolyte and the metal surface layer. Nonuniformities in the directions parallel to the surface may be reflected in the results of capacitance measurements, as well as optical measurements. 

The metal-solvent interactions were put into the model of Price and Halley93 in a later paper by Halley and co-workers,97 which also remedied some of the deficiencies of the original model, such as the inability to calculate the slope of a plot of (Cc) 1 versus qM and the dependence of the compact-layer capacitance on crystal face. One can show in general [see Eq. (40)] that... 

Calculations of the capacitance of the mercury/aqueous electrolyte interface near the point of zero charge were performed103 with all hard-sphere diameters taken as 3 A. The results, for various electrolyte concentrations, agreed well with measured capacitances as shown in Table 3. They are a great improvement over what one gets104 when the metal is represented as ideal, i.e., a perfectly conducting hard wall. The temperature dependence of the compact-layer capacitance was also reproduced by these calculations. 

The calculations were subsequently extended to moderate surface charges and electrolyte concentrations.8 The compact-layer capacitance, in this approach, clearly depends on the nature of the solvent, the nature of the metal electrode, and the interaction between solvent and metal. The work8,109 describing the electrodesolvent system with the use of nonlocal dielectric functions e(x, x ) is reviewed and discussed by Vorotyntsev, Kornyshev, and coworkers.6,77 With several assumptions for e(x,x ), related to the Thomas-Fermi model, an explicit expression6 for the compact-layer capacitance could be derived ... 

By contrast, the charge of the solution, qs, is distributed in a number of layers. The layer in contact with the electrode, called the internal layer, is largely composed of solvent molecules and in a small part by molecules or anions of other species, that are said to be specifically adsorbed on the electrode. As a consequence of the particular bonds that these molecules or anions form with the metal surface, they are able to resist the repulsive forces that develop between charges of the same sign. This most internal layer is also defined as the compact layer. The distance, xj, between the nucleus of the specifically adsorbed species and the metallic electrode is called the internal Helmholtz plane (IHP). The ions of opposite charge to that of the electrode, that are obviously solvated, can approach the electrode up to a distance of x2, defined as the outer Helmholtz plane (OHP). 

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