Outer Helmholtz layer

It follows from the definition cited that the size of the zeta potential depends on the structure of the diffuse part of the ionic EDL. At the outer limit of the Helmholtz layer (at X = X2) the potential is j/2, in the notation adopted in Chapter 10. Beyond this point the potential asymptotically approaches zero with increasing distance from the surface. The slip plane in all likelihood is somewhat farther away from the electrode than the outer Helmholtz layer. Hence, the valne of agrees in sign with the value of /2 but is somewhat lower in absolute value. 

Emersion has been shown to result in the retention of the double layer structure i.e, the structure including the outer Helmholtz layer. Thus, the electric double layer is characterised by the electrode potential, the surface charge on the metal and the chemical composition of the double layer itself. Surface resistivity measurements have shown that the surface charge is retained on emersion. In addition, the potential of the emersed electrode, , can be determined in the form of its work function, , since and represent the same quantity the electrochemical potential of the electrons in the metal. Figure 2.116 is from the work of Kotz et al. (1986) and shows the work function of a gold electrode emersed at various potentials from a perchloric acid solution the work function was determined from UVPES measurements. The linear plot, and the unit slope, are clear evidence that the potential drop across the double layer is retained before and after emersion. The chemical composition of the double layer can also be determined, using AES, and is consistent with the expected solvent and electrolyte. In practice, the double layer collapses unless (i) potentiostatic control is maintained up to the instant of emersion and (ii) no faradaic processes, such as 02 reduction, are allowed to occur after emersion. 

IHP). The layer between the electrode interface and the IHP is called the inner Helmholtz layer, and the layer between the IHP and the OHP is called the outer Helmholtz layer. In general, the interfacial chemisorption of dehydrated ions takes place at the IHP, and the physisorption of hydrated ions takes place at the OHP. 

In general, the contact adsorption of anions creates an electric field of intensity Sto in the inner Helmholtz layer, which may be greater than the average field intensity of. B,v = ( in +. Eout)/2, where aat is the field intensity in the outer Helmholtz layer. The rate of field increase rj may be derived from electrostatics as shown in Eqn. 5-50 [Liu, 1983] ... 

As the field intensity in the inner Helmholtz layer becomes extremely high, the field intensity E in the outer Helmholtz layer is reversed as shown in Fig. 5-29. Figure 5-30 illustrates the potential profile across the interfacial double layer of a mercury electrode in an aqueous chloride solution this result was obtained by calculations at various electrode potentials ranging fi om negative (cathodic) to positive (anodic) potentials. 

Cations and anions with a strong solvation shell retain their solvation shell and thus interact with the electrode surface only through electrostatic forces. Since the interaction is exclusively electrostatic, the amount of these ions at the interface is defined by the electrostatic bias between the sample and the counter electrodes and independent from the chemical properties of the electrode surface non-specific adsorption. Considering the size effect of their hydration shell, these ions are able to approach the electrode to a distance limited by the size of the solvation shell of the ion. The center of these ions at a distance of closest approach defined by the size of the solvation shell is called the outer Helmholtz layer. The electrode surface and the outer Helmholtz layer have charges of equal magnitude but opposite sign, resulting in the formation of an equivalent of a plate condenser on a scale of a molecular layer. Helmholtz proposed such a plate condenser on such a molecular scale for the first time in the middle of the nineteenth century. 

The term A GE represents the electrical work done in moving an ion of charge ze0 and water molecules with dipole moments fi between the outer Helmholtz layer and the inner Helmholtz layer in the electric field, X, arising from the charge of the metal (Section 6.8.2.1). Thus, it can split into AGE - AG i + AG w. If some transfer of charge (Section 6.8.2.1) occurs during the adsorption process, Eq. (6.210) can be written as... 

The second important difference is that the interface potential is present at the (outer) Helmholtz layer of the semiconductor/soiution interface. The interface potential is produced by surface dipoles of surface bonds as well as surface charges due to ionic adsorption equilibria between the semiconductor surface and the solution. If the interface potential can be regulated by a change in the chemical structure of the semiconductor surface, then the semiconductor band energies can be shifted to match the energy levels of the solution species (oxidant or reductant). This is another advantage of the semiconductor system because this enables improvement of the electron transfer rate at the semiconductor/soiution interface and the energy conversion efficiency. 

We assumed in Fig. 4.2 that no surface charge or surface dipole is present in the semiconductor. In general, however, both surface charges and surface dipoles are present in the semiconductor owing to adsorption equilibria for various ions between the electrolyte and the semiconductor surface as well as formation of polar bonds at the semiconductor surface. Such surface charges and surface dipoles change the potential difference in the (outer) Helmholtz layer and thus cause shifts in the surface band positions, as shown schematically in Fig. 4.3. The shifts can be expressed as changes in 0(0) or in the above equations, with the... 

At the electrical double layer in Fig. 4.2(a), the charges on the electrolyte side are mostly localized at the (outer) Helmholtz layer if the electrolyte concentration... 

Fig. 3. The structure of the EDL at the mineral-water-electrolyte interface. 1-Layer of charging ions 2j-inner and 2,-outer Helmholtz layer (Grahame and Stem plane, resp.) 3-diffuse layer and 4-slipping or shear plane [after Ref. 16]. V o-phase potential and -Stern s poten-tial.a - H20 dipols, b - hydrated counterions, c - negatively charged ions, d - thickness of the G-S layer o - charge density...

These terms are based on a simple geometric model of the interface. One distinguishes between an inner and an outer Helmholtz layer. The inner Helmholtz layer comprises all species that are specifically adsorbed on the electrode surface. If only one type of molecule or ion is adsorbed, and they all sit in equivalent positions, then their centers define the inner Helmholtz plane. The outer Helmholtz layer comprises the ions that are closest to the electrode surface, but are not specifically adsorbed. They have kept their -> solvation spheres intact, and are bound only by electrostatic forces. If all these ions are equivalent, their centers define the outer Helmholtz plane. 

A more sophisticated model is the triple-layer model, allowing the surface reaction of the background electrolyte (Hayes et al. 1991). The potential-determining ions (hydrogen and hydroxide) are directly on the surface (inner Helmholtz layer), the other ions are at a certain distance from the surface (outer Helmholtz layer), and there is a diffuse layer, also. 

Triplelayer Intrinsic stability constants Number of surface sites Capacity of the plane (inner and outer Helmholtz) layers -SOH - H+ <=> -SO ... 

Other ions adsorbed as outer-sphere complexes (outer Helmholtz layer)... 

Introducing the differential capacitances of the inner and outer Helmholtz layer (see [3.6.26]), assuming these to be constant, 13.6.61] can be written as... 

Apportioning the potential distributed across the oxide film, the inner Helmholtz layer and the outer Helmholtz layer, and assuming AV p to be constant with current based on dV/dq plots, b values of 120 mV were rationalized. A dK/d pH of -2.3RT/Fwasattributed topHdependenceof APo p, which results in R + = 1/2. (OHP = outer Helmholtz plane.)... 

In all situations discussed so far only one Stern layer capacitance is required. In literature it is however often assumed [7, 8, 22] that diffuse ions can approach the surface up to the Stern plane and that s.a. ions are located at a newly defined adsorption plane, the inner Helmholtz plane. The inner Helmholtz plane is located in between the surface plane and the Stern or outer Helmholtz plane. The double layer model composed of an inner and outer Helmholtz layer plus a diffuse layer is generally called the triple layer (TL) model. 

The potential drop over the inner Helmholtz layer and the outer Helmholtz layer can be described by two capacitances the inner and the outer Helmholtz layer capacitance. 

Although for ideally flat interfaces it is physically elegant to make a distinction between an inner and an outer Helmholtz plane [7, 8], this distinction is hardly relevant for ordinary solids where the presence of surface irregularities makes it impossible to obtain unique values for the capacitances of both Helmholtz layers. Therefore rather arbitrary assumptions have to be made about at least one of the capacitances, whereafter the other capacitance value is used together with other model parameters as fitting parameter. The value of 0.2 F/m often assumed for the outer Helmholtz layer capacitance is not realistic for oxide surfaces [18, 23] and may lead to obscurities with the other fitting parameters. 

As already discussed in Section 3.2 the potential across a single solid-liquid interface cannot be measured. One can only measure the potential of an electrode vs. a reference electrode. It has already been shown in Section 3.2 that a certain potential is produced at a metal or semiconductor electrode upon the addition of a redox system, because the redox system equilibriates with the electrons in the electrode, i.e. the Fermi level on both sides of the interface must be equal under equilibrium. It should be emphasized here that the potential caused upon addition of a redox couple to the solution occurs in addition to that already formed by the specific adsorption of, for instance, hydroxyl ions. A variation in the relative concentrations of the oxidized and reduced species of the redox system leads to a corresponding change of the potential across the outer Helmholtz layer, as required by Nernst s law (see Eq. 3.47), which can be detected by measuring the electrode potential vs, a reference electrode. However, there still exists a potential across the inner Helmholtz layer which remains unknown. 

As already mentioned, the charges are concentrated within the inner and outer Helmholtz layer at high ion concentrations. In this case, the double layer acts as... 

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