Double inner Helmholtz plane

Pig. 3. Representation of the electrical double layer at a metal electrode—solution interface for the case where anions occupy the inner Helmholtz plane... 

Fig. 1. The structure of the electrical double layer where Q represents the solvent CD, specifically adsorbed anions 0, anions and (D, cations. The inner Helmholtz plane (IHP) is the center of specifically adsorbed ions. The outer Helmholtz plane (OHP) is the closest point of approach for solvated cations or molecules. O, the corresponding electric potential across the double layer, is also shown.

FIGURE 1-11 Schematic representation of the electrical double layer. IHP = inner Helmholtz plane OHP = outer Helmoltz plane. 

By means of the thermodynamic theory of the double layer and the theory of the diffuse layer it is possible to determine the charge density ox corresponding to the adsorbed ions, i.e. ions in the inner Helmholtz plane, and the potential of the outer Helmholtz plane 2 in the presence of specific adsorption. 

Anions may exhibit a tendency toward specific adsorption at the O/S interface. This may be related in some way to the complexing affinity. This effect, occurring at the inner Helmholtz plane of the electrochemical double layer, may significantly change the charge transfer situation [cf. Section III(5(iii))]. 

Chemisorption of anions at the electrode interface involves dehydration of hydrated anions followed by adsorption of dehydrated anions which, then, penetrate into the compact double layer to contact the interface directly, this result is called the contact adsorption or specific adsorption. The plane of the contact adsorption of dehydrated anions is occasionally called the inner Helmholtz plane... 

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... 

Fig. 6-99. An interfacial electric double layer on semiconductor electrodes a = charge of surface states 0.1 = interfadal charge of adsorbed ions IHP = inner Helmholtz plane.

It is noted that the molecular interaction parameter described by Eq. 52 of the improved model is a function of the surfactant concentration. Surprisingly, the dependence is rather significant (Eig. 9) and has been neglected in the conventional theories that use as a fitting parameter independent of the surfactant concentration. Obviously, the resultant force acting in the inner Helmholtz plane of the double layer is attractive and strongly influences the adsorption of the surfactants and binding of the counterions. Note that surface potential f s is the contribution due to the adsorption only, while the experimentally measured surface potential also includes the surface potential of the solvent (water). The effect of the electrical potential of the solvent on adsorption is included in the adsorption constants Ki and K2. 

Not all ceramic materials behave the same at a given pH, however. As the material begins to dissolve, ions form at the snrface, water molecnles orient themselves accordingly, and an electrical double layer is established, as shown in Eigure 3.18. The first layer of charged ions and oriented water molecules is called the inner Helmholtz plane (IHP), and the second layer of oppositely charged particles is called the outer Helmholtz... 

Figure 3.18 Formation of the electrical double layer of a surface in solution, showing the inner Helmholtz plane (IHP) and outer Helmholtz plane (OHP). Reprinted, by permission, from B. D. Craig, Fundamental Aspects of Corrosion Films in Corrosion Science, p. 4. Copyright 1991 by Plenum Press.

Figure 7.4. Schematic model of the Electrical Double Layer (EDL) at the metal oxide-aqueous solution interface showing elements of the Gouy-Chapman-Stern-Grahame model, including specifically adsorbed cations and non-specifically adsorbed solvated anions. The zero-plane is defined by the location of surface sites, which may be protonated or deprotonated. The inner Helmholtz plane, or [i-planc, is defined by the centers of specifically adsorbed anions and cations. The outer Helmholtz plane, d-plane, or Stern plane corresponds to the beginning of the diffuse layer of counter-ions and co-ions. Cation size has been exaggerated. Estimates of the dielectric constant of water, e, are indicated for the first and second water layers nearest the interface and for bulk water (modified after [6]).

The Stern surface is drawn through the ions that are assumed to be adsorbed on the charged wall. (This surface is also known as the inner Helmholtz plane [IHP], and the surface running parallel to the IHP, through the surface of shear (see Chapter 12) shown in Figure 11.9, is called the outer Helmholtz plane [OHP]. Notice that the diffuse part of the ionic cloud beyond the OHP is the diffuse double layer, which is also known as the Gouy-Chapman... 

Fig. 2.2 Structure of the electric double layer under different conditions of electrode polarization (a) metal positively charged, anions present at the inner Helmholtz plane (chemically interacting with metal) and in the diffuse double layer beyond the outer Helmholtz plane (b) metal negatively charged, inner Helmholtz plane empty, cations in diffuse layer (c) metal positively charged, strong adsorption of anions in inner Helmholtz plane, balancing cations in the diffuse layer...

At the next level we also take specific adsorption of ions into account (Fig. 4.6). Specifically adsorbed ions bind tightly at a short distance. This distance characterizes the inner Helmholtz plane. In reality all models can only describe certain aspects of the electric double layer. A good model for the structure of many metallic surfaces in an aqueous medium is shown in Fig. 4.6. The metal itself is negatively charged. This can be due to an applied potential or due to the dissolution of metal cations. Often anions bind relatively strongly, and with a certain specificity, to metal surfaces. Water molecules show a distinct preferential orientation and thus a strongly reduced permittivity. They determine the inner Helmholtz plane. 

Fig. 1.10 Schematic view of the electrical double layer in agreement with the Gouy-Chapman-Stem-Grahame models. The metallic electrode has a negative net charge and the solvated cations define the inner limit of the diffuse later at the Helmholtz outer plane (OHP). There are anions adsorbed at the electrode which are located at the inner Helmholtz plane (IHP). The presence of such anions is stabilized by the corresponding images at the electrode in such a way that each adsorbed ion establishes the presence of a surface dipole at the interface...

In the discussion of the different models for the structure of double layer developed up to this point, no specific interactions have been considered. However, specific adsorption is a common phenomena in electrochemistry. Since the interactions implied have to be very short range in nature, the chemisorbed species are strongly bound to the electrode surface with the locus of their centers being the inner Helmholtz plane (IHP, see Fig. 1.10), or compact part of the double layer. 

The crucial point is that the difference of potential available to effect electrode reactions and surmount activation barriers is not simply the difference between the Galvani potential (i.e. the Fermi energy) and the potential in solution. On the side of the solid it is the Volta potential and on the side of the solution it is the potential at the inner Helmholtz plane, where species have to reach to in order for electron transfer to be possible. Corrections to rate constants for the latter are commonly carried out using the Gouy-Chapman model of the electrolyte double layer and will be described in Section 6.9. 

The various contributions to / can be envisaged from a somewhat different viewpoint by expressing the potential difference (fa - fa) across the compact layer on the basis of a simple electrostatic model in which the double-layer region enclosed between the electrode surface plane, x = 0, and the inner Helmholtz plane, x = P, is ascribed a distortional dielectric constant, Sp, while that between x = P and the... 

Conversely, according to the description of the electrical double layer based on the Stern-Gouy-Chapman (S-G-C) version of the theory [24], counter ions cannot get closer to the surface than a certain distance (plane of closest approach of counter ions). Chemically adsorbed ions are located at the inner Helmholtz plane (IHP), while non-chemically adsorbed ions are located in the outer Helmholtz plane (OHP) at a distance x from the surface. The potential difference between this plane and the bulk solution is 1 ohp- In this version of the theory, Pqhp replaces P in all equations. Two regions are discernible in the double layer the compact area between the charged surface and the OHP in which the potential decays linearly and the diffuse layer in which the potential decay is almost exponential due to screening effects. 

The adsorbed Stem layer is compensated by a compact and essentially fixed layer of hydrated counterions and water molecules which takes the form of a molecular capacitor between the inner and outer Helmholtz planes shown in Figure 9.14. The solid surface adsorbs the Stem layer ions and gives a potential of the inner Helmholtz plane, which is partially compensated by the hydrated counterions and water molecviles of the outer Helmholtz plane. The diffuse double layer of (jOuy-Chapman starts at the OHP and extends further into the liquid. 

In electrochemical environments the vibrational spectra are additionally affected by solvation effects, the electric field in the double layer, and the co-adsorption of water and/or ions in the inner Helmholtz plane. 

In fig. 3.20b specific adsorption Is also accounted for. The notion of specific adsorption has been defined In sec. 3.3. In disperse systems, its occurrence is de facto Inferred from the dependence of certain double layer properties on the natures of counter- and co-lons Generally, ions interacting specifically (non-electrostatlcally) with the surface approach it to shorter distance p < d). The plane where these specifically adsorbed ions reside is called the inner Helmholtz plane (iHp) In colloid science, the model of fig. 3.20b Is also known as the triple layer model. In this model three charges and three capacitances can be distinguished. For the two inner layer differential capacitances... 

If lattice ions or other potential-determining ions are adsorbed on a solid surface, they may be regarded as belonging to the solid and imparting an electrical charge to it. For the sake of overall electrical neutrality, an equivalent number of oppositely charged ions (counterions) exist in solution, drawn to the charged surface by electrical attraction. The counterions and the adsorbed lattice ions form an electrical double layer. The closest counterions cannot be nearer the surface than a finite distance (inner Helmholtz plane ) that depends on the ionic radius. 

The position at which o is evaluated is generally taken to be the inner limit of the electrically neutral diffusion layer, shown in Figure 5.6(b). In this way, the interface is assumed to incorporate the detailed structure of the double layer, including the diffuse region of charge and the inner Helmholtz plane associated with specifically adsorbed charged species. 

Figure 5.6 Schematic representation of an electrochemical reaction a) oxidation of ferro-cyanide to form ferricyanide and b) proposed double-layer structure revealing the components included as part of the interface where ihp refers to the inner Helmholtz plane and ohp refers to the outer Helmholtz plane.

A foreign substrate, S, is a solid with a different composition from that of Me, and is considered as electrochemically inactive in a certain potential range which is considered in this book. A 2D Me phase is considered as a specific Me adsorbate located in the inner Helmholtz plane of the electrochemical double layer existing at a substrate/electrol3de interface. A 3D Me phase can be either a bulk phase or a small atomic cluster of Me, where bulk has the meaning of infinitely large. 

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. 

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