Helmholtz double layer model

Numerous models of the electrode-electrolyte interface have been developed. The simplest of these is the Helmholtz double-layer model, which posits that the charge associated with a discrete layer of ions balances the charge associated with electrons at the metal surface. The Helmholtz double-layer model predicts incorrectly that the interfacial capacitance is independent of potential. Nevertheless, cvurent models of the charge redistribution at electrode-electrolyte interfaces owe their terminology to the original Helmholtz model. 

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [120], Gouy and Chapman [121,122], and Stern [123], and in most analytic studies, 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... 

Fig. 1 Double layer model for a cathode, (a) Helmholtz model (b) Gouy-Chapman model (c) Stern model. 

It is important to stress that the activity coefficients (and the concentrations) in equation 16.18 refer to the species close to the surface of the electrode, and so can be very different from the values in the bulk solution. This is portrayed in figure 16.6, which displays the Stern model of the double layer [332], One (positive) layer is formed by the charges at the surface of the electrode the other layer, called the outer Helmholtz plane (OHP), is created by the solvated ions with negative charge. Beyond the OHP, the concentration of anions decreases until it reaches the bulk value. Although more sophisticated double-layer models have been proposed [332], it is apparent from figure 16.6 that the local environment of the species that are close to the electrode is distinct from that in the bulk solution. Therefore, the activity coefficients are also different. As these quantities are not... 

Fig. 5-8. An interfadal double layer model (triple-layer model) SS = solid surface OHP = outer Helmholtz plane inner potential tt z excess charge <2h = distance from the solid surface to the closest approach of hydrated ions (Helmluritz layer thickness) C = electric capacity.

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... 

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. 

The first double-layer model was developed by Helmholtz more than 100 years ago [4, 13, 19, 21]. This model postulates the double layer as two charged phases, the polarized metal electrode (if the non-electrolytic phase is a metal or electronic conductor) and other parallel layer with the ions of the solution separated by a distance d. 3... 

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. 

The double layer model of Helmholtz assumes fixed layer of charges on the electrode and the outer Helmholtz plane. This model has been modified by Guoy-Chapman analysis, which assumes that the ions of charge opposite of the charge on the electrode distribute themselves in a diffuse manner as shown in Figure 1.15. 

Double layer models — The oldest model for the double layer at metal/solution interfaces was proposed by - Helmholtz. He suggested that an excess charge (- double layer, excess charge density) on the metal attracts an equivalent amount of counter ions to the interface, the two opposing layers are separated by a certain distance, which determines the capacity. His model gave rise to the concepts of the inner and outer Helmholtz planes (layers) (- Double layer). 

Calculations for two water molecules with their dipole axes and one lone pair each parallel (i.e., in parallel Verwey positions for positive ions, as would be possible in a Helmholtz double layer) in which an accurate DP point charge model was compared with a simple dipole model showed die latter to be 11.6% high at 2.0 A separation, and 4.6%, 1.5%, 0% high at 2.25, 2.5, and 2.75 A, and 1.4%, 2.6%, and 3.3% low at 3.0. 3.5. and 4.0 A. 

For one-electron transfer reactions occurring via outer-sphere mechanisms, wp and ws can be estimated on the basis of electrostatic double-layer models. Thus, if the reaction site lies at the outer Helmholtz plane (o.H.p.), wp = ZFd and ws = (Z - 1 )Fcharge number of the oxidized species and (j>d is the potential across the diffuse layer. Rewriting eqn. (7) in terms of rate constants rather than free energies yields the familiar Frumkin equation [8]... 

Figure 3.21. Gouy-Stern double layer model with specific adsorption at the outer Helmholtz plane. The inner layer has a constant capacit mce C. ...

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 earliest theoretical studies of the behavior of an electrified interface were made by Helmholtz (1879). He discussed the adsorption of ions at a fixed double layer and he believed that this double layer formed the equivalent of a parallel-plate condenser. But this double layer model is an inadequate description of particles in electrolyte-containing systems. 

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