Helmholtz compact double-layer model

In general, the Helmholtz layer can be treated as a linear capacitor. In a theoretical model of the electric double-layer, the compact Helmholtz layer is generally treated as an ideal capacitor with a fixed thickness (d), and its capacitance is considered unchanging with the potential drop across it. Therefore, fhe capacifance of fhe Helmholtz layer can be treated as a constant if fhe femperafure, fhe dielectric constant of the electrolyte solution inside the compact layer, and its thickness are fixed. However, if the specific ion adsorpfion happened on the electrode surface, the dielectric constant of the electrolyte solution inside the compact layer may be affected, leading to non-linear behavior of the Helmholtz layer. This will be discussed more in a later section. 

The Stern model (1924) essentially combines the Helmholtz and Gouy-Chapman models as shown in Figure 5.4. Thus, the Stern model has two parts of double layer (a) compact layer ("rigid layer") of ions at the distance of closest approach (OHP) and (b) diffuse layer. The concentration of ions and the potential distribution from the electrode vary as shown in Figures 5.3 and 5.4. The potential has a sharp drop between the electrode and OHP beyond which the potential gradually falls to a value characteristic of bulk electrolyte. 

The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge... 

In the absence of specific adsorption of anions, the GCSG model regards the electrical double layer as two plate capacitors in series that correspond respectively, to two regions of the electrolyte adjacent to the electrode, (a) An inner compact layer of solvent molecules (one or two layers) and immobile ions attracted by Coulombic forces (Helmholtz inner plane in Fig. 2). Specific adsorption of anions at the electrode surface may occur in this region by electronic orbital coupling with the metal, (b) An outer diffuse region of coulombically attracted ions in thermal motion that complete the countercharge of the electrode. 

The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge on the solution side of the interphase, qs. is lined up in the same plane at a fixed distance away from the electrode, the Helmholtz plane (Fig. 4.4). This fixed distance xH is determined by the hydration sphere of the ions. It is defined as the plane of the centers of the hydrated ions. All excess charge on the metal, qM, is located at the metal surface. 

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. 

At the beginning of this century Gouy13 and Chapman13 independently developed a double layer model in which they considered that the applied potential and electrolyte concentration both influenced the value of the double layer capacity. Thus, the double layer would not be compact as in Helmholtz s description but of variable thickness, the ions being free to move (Fig. 3.6a). This is called the diffuse double layer. 

Stern15 combined the Helmholtz model for values of potential far from Ez with the Gouy-Chapman model for values close to Ez (Fig. 3.7ayb). He considered that the double layer was formed by a compact layer of ions... 

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... 

Two planes are usually associated with the double layer. The first one, the inner Helmholtz plane (IHP), passes through the centers of specifically adsorbed ions (compact layer in the Helmholtz model), or is simply located just behind the layer of adsorbed water. The second plane is called the outer Helmholtz plane (OHP) and passes through the centers of the hydrated ions that are in contact with the metal surface. The electric potentials linked to the IHP and OHP are usually written as 4 2 and 4f, respectively The diffuse layer develops outside the OHP. The concentration of cations in the diffuse layer decreases exponentially vs. the distance from the electrode surface. The hydrated ions in the solution are most often octahedral complexes however, in Fig. 1.1.2. they are shown as tetrahedral structures for simplification. 

After 20 years. Stern [23] modified these models by including both a compact and a diffuse layer. At the same time, Grahame [24] divided the Stern layer into two regions (i) an inner Helmholtz plane consisting of a layer of adsorbed ions at the surface of the electrode and (ii) an outer Helmholtz plane (referred to as Gouy plane as well), which is formed by the closest approach of diffuse ions to the electrode surface. From the Grahame model, the capacitance C of the double layer is described by Equation 8.1 as follows ... 

The second model is the Gouy-Chapman model developed in 1910 (Gouy, 1903,1906 Chapman, 1913). In this model, the double layer is not as compact as in the Helmholtz rigid layer. The ions are assumed to be able to move in solution owing to thermal forces and thus the electrostatic interactions are in competition with Brownian motion. Figure 5.3 shows the charge distribution and potential from the electrode surface. The solvated ions interact with... 

Two planes are usually associated with the double layer. The first one, the inner Helmholtz plane (IHP), passes through the centers of specifically adsorbed ions (compact layer in the Helmholtz model), or is simply located just behind the... 

Historically, the first elue for the existenee of such double layer emerged from Helmholtz s studies, in 1879. His first theory assumed the presenee of a compact layer of ions in direct contact with the eharged electrode surfaee. This first proposal was followed by the eoneepts of Gouy and Chapman (1913), who adapted the previously described model to... 

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