Electrodes compact layer

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. 

Chronocoulometry, 62 Clark electrode, 190 Coated wire electrodes, 160 Cobalt, 82, 85 Cobalt phthalocyanine, 121 Collection efficiency, 113, 135 Collection experiments, 113 Combination electrode, 148 Compact layer, 19 Composite electrodes, 47, 114, 133 Computer control, 80, 106 Concentration profile, 7, 9, 11, 29, 36, 87, 132... 

The expressions for the rates of the electrochemical reactions given in Section II. A have not taken into account the detailed structure of the interfacial region. In general, the solution adjacent to the electrode will consist of at least two regions. Immediately adjacent to the metal there will be a compact layer of ions and solvent molecules which behaves as a capacitor. A potential difference will be established between... 

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)... 

In the simple case of electrostatic attraction alone, electrolyte ions can approach to a distance given by their primary solvation sheaths, where a monomolecular solvent layer remains between the electrode and the solvated ions. The plane through the centres of the ions at maximum approach under the influence of electrostatic forces is called the outer Helmholtz plane and the solution region between the outer Helmholtz plane and the electrode surface is called the Helmholtz or compact layer. Quantities related to the outer Helmholtz plane are mostly denoted by symbols with the subscript 2. 

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. 

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,... 

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... 

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). 

Fig. 5-8. Diffuse charge layer on the solution side of metal electrode M = electrode metal S = aqueous solution HL = compact layer (Helmholtz layer) DL = diffuse charge layer x distance from the outer Helmholtz plane (OHP).

Figure 5-11 shows a simple model of the compact double layer on metal electrodes. The electrode interface adsorbs water molecules to form the first mono-molecular adsorption layer about 0.2 nm thick next, the second adsorption layer is formed consisting of water molecules and hydrated ions these two layers constitute a compact electric double layer about 0.3 to 0.5 nm thick. Since adsorbed water molecules in the compact layer are partially bound with the electrode interface, the permittivity of the compact layer becomes smaller than that of free water molecules in aqueous solution, being in the range from 5 to 6 compared with 80 of bulk water in the relative scale of dielectric constant. In general, water molecules are adsorbed as monomers on the surface of metals on which the affinity for adsorption of water is great (e.g. d-metals) whereas, water molecules are adsorbed as clusters in addition to monomers on the surface of metals on which the affinity for adsorption of water is relatively small (e.g. sp-metals). 

The potential E of metal electrodes at which the interfacial charge o is zero (hence, = 0) is the potential of zero charge (the zero charge potential), It foUows from Eqn. 5-12 that the potential, 4>pic, across the compact layer at the potential of zero charge is composed of M dip nd gs,dip as shown in Eqn. 5-13 ... 

According to observations with metal electrodes in aqueous solution [Amokrane-Badiali, 1992], the interfadal charge versus capacity curve is described for the inverse capacity, 1 /Cm, as a parabolic curve with its maximum near the zero charge the capacity, Cs, is described as a parabolic curve with its maximum near the zero charge. Both of their dependences are shown schematically in Fig. 5-22. Usually, then, the total capacity Ch of the compact layer is represented by a parabolic curve with its maximum near the zero charge (a = 0) of the interface. Figure 5-23 shows the capacity of the compact layer observed for silver and mercury electrodes in aqueous solution as a function of the interfacial charge. 

Fig. 6-23. Differential capadty Ch of a compact layer observed as a function of interfadal charge oh on a mercury electrode and on a (100) surface of silver electrode in aqueous solution. [From Schmickler, 1993.]...

As described in this section, the distance Xta, to the image plane increases with increasing electron density in the electrode metal. Correspondingly, as shown in Fig. 5-24, the capacity of fbo compact layer, Ch, of sp metal electrodes in aqueous solution increases with increasing electron density in the metal. It thus appears that the interfadal electric double layer is affected significantly by the nature (electron density) of the electrode metal. 

Fig. 6-24. Inverse differential capacity 1/Ch of a compact layer as a function of electron density n, of polycrystalline sp-metal electrodes in aqueous solution open drdes = observed solid line = calculated au s atomic unit. [From Schmidder, 1993.]...

In the course of ionic contact adsorption on the interface of metal electrode, hydrated ions are first dehydrated and then adsorbed at the inner Helmholtz plane in the compact layer as shown in Fig. 5-27 and as described in Sec. 5.6.1. In the interfacial double layer containing adsorbed ions, the combined charge of motal and adsorbed ions = z eF on the metal side is balanced with the... 

As a result of ionic contact adsorption that induces an interfacial dipole on metal electrodes, the potential, Mb, across the compact layer is altered. Figure 5-28 shows the change of the potential, ( = E — ), observed as a ftmction... 

Fig. 5-28. Potential Mu across a compact layer observed in aqueous solution and work fimction 4> observed in vacuiun as a fimction of adsorption coverage of bromine atoms on a (100) interface of single crystal silver electrode 64> = relative change of work fimction in vacuiun 64 = relative change in potential across a compact layer work fimction data corresponds to Fig. 6-25. [From Bange-Straehler-Sass-Parsons, 1987.]...

Ionic contact adsorption on metallic electrodes alters the potential profile across the compact layer at constant electrode potential. If anions are adsorbed on the metal electrode at positive potentials, the adsorption-induced dipole generates a potential across the inner Helmholtz layer (IHL) as illustrated in Fig. 5-29. The electric field in the outer part (OHL) of the compact layer, as a result, becomes dififerent fi om and frequently opposite to that in the inner part (IHL) of the compact layer. 

Fig. 6-29. Change in potential profile across a compact layer due to anionic contact adsorption at constant potential on a metal electrode solid line = without contact anion adsorption broken line = with contact anion adsorption 4m - inner potential of metal electrode, 4s = inner potential of solution 4ihp = inner potential at IHP.

Fig. 5-30. Potential profile across a compact layer estimated by calculations at various electrode potentials for a mercury electrode in a 03 M sodium chloride solution electrode potential changes fivm No. 1 (a cathodic potential) to No. 6 (an anodic potential), and contact adsorption of chloride ions takes place at anodic potentials. E = electrode potential = zero charge potential x = distance fix>m the interface. [From (3raham, 1947.]...

Further, the total potential 5 across the electrode interface is given by the sum of the three potentials across the space charge layer, the compact layer, and the diffuse layer as shown in Eqn. 5-60 ... 

The total potential A/ across the electrode interface may be expressed approximately by using the thickness of space charge layer approximated by the Debye length Ld.9c, the thickness of compact layer du, and the thickness of... 

In Eqn. 5-65 it appears that most of the change of electrode potential occurs in the space charge layer with almost no change of potential both in the compact layer and in the diffuse layer. This pattern may be regarded as characteristic of semiconductor electrodes. 

The potential i sc of the space charge layer can also be derived as a fixnction of the surface state charge Ou (the surface state density multiplied by the Fermi function). The relationship between of a. and M>sc thus derived can be compared with the relationship between and R (Eqn. 5-67) to obtain, to a first approximation, Eqn. 5-68 for the distribution of the electrode potential in the space charge layer and in the compact layer [Myamlin-Pleskov, 1967 Sato, 1993] ... 

Simple calculation gives a comparable distribution of the electrode potential in the two layers, (64< >h/64( sc) = 1 at the surface state density of about 10cm" that is about one percent of the smface atoms of semiconductors. Figure 5—40 shows the distribution of the electrode potential in the two layers as a function of the surface state density. At a surface state density greater than one percent of the surface atom density, almost all the change of electrode potential occurs in the compact layer, (6A /5d )>l, in the same way as occurs with metal electrodes. Such a state of the semiconductor electrode is called the quasi-metallic state or quasi-metallization of the interface of semiconductor electrodes, which is described in Sec. 5.9 as Fermi level pinning at the surface state of semiconductor electrodes. 

Fig. S-41. Band edge levels and Fermi level of semiconductor electrode (A) band edge level pinning, (a) flat band electrode, (b) under cathodic polarization, (c) under anodic polarization (B) Fermi level pinning, (d) initial electrode, (e) under cathodic polarization, (f) imder anodic polarization, ep = Fermi level = conduction band edge level at an interface Ev = valence band edge level at an interface e = surface state level = potential across a compact layer.

Fig. 5-42. Potential across an interlace of semiconductor electrode distributed to the space charge layer, At>sc, and to the compact layer,. as a function of total potential,...

In the state of Fermi level pinning, the Fermi level at the interface is at the surface state level both where the level density is high and where the electron level is in the state of degeneracy similar to an allowed band level for electrons in metals. The Fermi level pinning is thus regarded as quasi-metallization of the interface of semiconductor electrodes, making semiconductor electrodes behave like metal electrodes at which all the change of electrode potential occurs in the compact layer. 

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