Layer compact

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

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

Fig. 1.90 Kinetic interpertation of paralinear oxidation. Curves a and b correspond to the growth of the inner compact layer and the outer porous layer, respectively curve c represents the total weight and is the algebraic sum of curves a and b. Note that as oxidation proceeds, y tends to a limiting value y, (curve a) and the overall rate of oxidation tends to a constant...

When tin is fully exposed out of doors, corrosion is uniform, and the rate falls only slightly with time. The metal becomes dull and accumulates a compact layer of pale grey product, mainly stannous oxide. Rates observed during exposures in the USA for periods of up to 20 years were as follows... 

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 ... 

The capacitance of the double layer consists of combination of the capacitance of die compact layer in series with that of the diffuse layer. For two capacitors in series, the total capacitance is given by... 

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... 

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. 

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... 

The surface-phase layers will difier in character depending on the stractures of metal and oxide. On certain metals (zinc, cadmium, magnesium, etc.), loose, highly porous layers are formed which can attain appreciable thicknesses. On other metals (aluminum, bismuth, titanium, etc.), compact layers with low or zero porosity are formed which are no thicker than 1 pm. In a number of cases (e.g., on iron), compact films are formed wfiicfi fiave a distorted lattice, owing to the influence of substrate metal stracture and of the effect of chemical surface forces. The physicochemical and thermodynamic parameters of such films differ from tfiose of ordinary bulk oxides. Because of the internal stresses in the distorted lattice, such films are stable only when their thickness is insignificant (e.g., up to 3 to 5 nm). 

Although it was elear that separation of an interface into surface and bulk components as in Eq, (19) is artifieial and must disappear in a consistent microscopic analysis, electronic effects were initially diseussed in terms of a compact layer and its capacitance C, It was apparent early on that the eleetrons strongly influence double layer properties [28-33],... 

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)... 

The theoretical approach by Samec based on the ion-free compact layer model established that the true apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide-Fc system provided values of a smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that k i is... 

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. 

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. 

In view of the assumed linear dependence of the electrical potential in the whole compact layer, the above authors derived the following expression for 0(m) — 02 when a(m) = 0 ... 

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. 

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