Helmholtz model, electrical double-layer structure

D25.8 (a) There are three models of the structure of the electrical double layer. The Helmholtz model, the... 

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. 

Expression (V.25), referred to as the Helmholtz-Smoluchowski equation, relates the rate of relative phase displacement to some potential difference, Acp, within the electrical double layer. In order to understand the nature of this quantity, let us examine in detail the mutual phase displacement due to the external electric field acting parallel to the surface, taking into account the electrical double layer structure. Let us assume that the solid phase surface is stationary. Figure V-7 shows the distributions of the potential, cp(x ) (line 1), the rate of displacement of the liquid layers relative to the surface in the Helmholtz model, u(x) (line 1/), and the true distribution of the potential in the double layer (curve 2). 

Fig. 4.1 Structure of the electric double layer and electric potential distribution at (A) a metal-electrolyte solution interface, (B) a semiconductor-electrolyte solution interface and (C) an interface of two immiscible electrolyte solutions (ITIES) in the absence of specific adsorption. The region between the electrode and the outer Helmholtz plane (OHP, at the distance jc2 from the electrode) contains a layer of oriented solvent molecules while in the Verwey and Niessen model of ITIES (C) this layer is absent...

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The substantial understanding of the structure of the electric double layer has been summarized in various reviews and books (e.g., Ref. 2, 81, 177-183). The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [3], Gouy and Chapman [5, 6], and Stern [7], and in most of the studies cited in the reviews the molecular nature of the solvent has been neglected altogether, or it has been described in a very approximate way, e.g., as a simple dipolar fluid. Computer simulations can overcome this restriction and describe the solvent in a more realistic fashion. They are thus able to paint a detailed picture of the microscopic structure near a metal electrode. 

Various models have been proposed for the electric double layer at an electrode-electrolyte interface. Briefly explain the structure of the electric double layer starting from the Helmholtz model to the triple-layer model and then identify the key features of each model. 

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. 

A fourth model proposed, the Grahame model (Grahame, 1951), which is referred to as the triple-layer model, takes into consideration that ions could be dehydrated in the direction of the electrode and specifically adsorbed on the electrode. Thus, an inner layer between the electrode surface and the Helmholtz layer further modifies the structure of the double layer. The locus of electrical centers of unhydrated ions strongly attached to the electrode is called inner Helmholtz plane (IHP). Figure 5.5... 

Lastly, in 1963 John O Mara Bockris (1923-2013) together with M. Devantant and K. Muller developed a model which takes into consideration the effect of solvent (H O dipoles), of its ions and pH value of the solution on the charge of the diffusion layer. So, the modern concept was formed of the structure of double electric layer, according to which are distinguished three consecutively connected capacitors slip plane, Helmholtz plane and the interface plane (Figure 2.10). 

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