The Gouy-Chapman-Stern model

One of the fundamental problems in electrochemistry is the distribution of the potential and of the particles at the interface. Here we will expand on the subject of Chapter 3, and consider the interface between a metal and an electrolyte solution in the absence of specific adsorption. 

This Gouy-Chapman-Stern model, as it was named after its main contributors, is a highly simplified model of the interface, too simple for quantitative purposes. It has been superseded by more realistic models, which account for the electronic structure of the metal, and the existence of an extended boundary layer in the solution. It is, however, still used even in current publications, and therefore every electrochemist should be familiar with it. 

In the remainder of this chapter we will present elements of modern double-layer theory. Two phases meet at this interface the metal and 

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Figure 17.1 The Gouy-Chapman-Stern model, the solution. We will consider each phase in turn.

Eq. (6) represents the Stern portion of the Gouy-Chapman-Stern model. Stern reactions are strong interactions, represented as binding in Eqs. (1) and (2), between ions and the PM that alter cr. These associations are different from charge screening (described next), which does not eliminate surface charge but merely reduces the negativity of the potential. 

Table 1 presents parameter values for the Gouy-Chapman-Stern model. The experimental methods for their determination will be described later. 

The diffuse double layer model of Gouy and Chapman works reasonably well for systems of relatively low surface potential (electrolyte concentration (< 10 M). At higher surface potential and ionic strength the outer part of the double layer may still obey this model, but the inner part close to the surface tends toward the molecular condenser. Therefore, these two pictures are integrated in the Gouy-Chapman-Stern model. 

The Gouy-Chapman-Stern model of the electrical double layer may be understood as two condensers in series, so that for the total capacitance C, ... 

The Stern model (1924) may be regarded as a synthesis of the Helmholz model of a layer of ions in contact with the electrode (Fig. 20.2) and the Gouy-Chapman diffuse model (Fig. 20.10), and it follows that the net charge density on the solution side of the interphase is now given by... 

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]).

Various types of SCM have been assessed namely, the diffuse-layer model (DLM) [27], the constant-capacitance model [28], the Stern model [29], and the triple-layer model (TLM) [30]. They differ in complexity from the simplest, DLM, which has four adjustable parameters, to the most complex, TLM, which includes seven adjustable parameters. The number of parameters is dependent on the hypothesis relative to the model. In various researches, the DLM is selected because of its simplicity and its applicability to various solution conditions [31]. It takes into account ionic strength effects on protolysis equilibria through the Gouy-Chapman-Stern-Grahame charge-potential relationship ... 

Fig. 10.14 Schematic diagram of the double layer according to the Gouy-Chapman-Stern-Grahame model. The metal electrode has a net negative charge and solvated monatomic cations define the inner boundary of the diffuse layer at the outer Helmholtz plane (oHp).

Fig. 4. A comparison of studies in which 1/Ap and y/cw were measured and computed. For (A), parameters for a Gouy-Chapman-Stern model were evaluated for eight studies for (B), parameters for a Donnan-plus-binding model were evaluated for five studies. Optimized values for total negative sites (Rj) were computed for each study, but a single suite of binding constants was evaluated for the pooled PM data and for the pooled CW data. The figure is redrawn from Shomer et al. (2003).

We are confident that a Gouy-Chapman-Stern model and a Doiman-plus-binding model may be used to compute values for xj/p and y/cyf that are at least proportional to the actual values. With these electrical potentials, corresponding values for ion activities may be computed that are at least proportional to actual values also. Although the electrostatic theory is quite old, values for model parameters for plant cell surfaces have become available only recently. Computer programs for the electrostatic models may be requested from us. 

K.B. Oldham, A Gouy-Chapman-Stern model of the double layer at a metal ionic liquid interface,... 

To provide a theoretical description of the diffuse layer, the potential distribution shown in Figure 2.3 is used. According to the Gouy-Chapman-Stern (GCS) model [7], the ion concentration within the diffuse layer at point X can be expressed as ... 

Regarding the differential capacitance of such an electrode matrix layer, the Gouy-Chapman-Stern (GCS) double-layer modeling for capacitance is still applicable if fhe concenfrafion of fhe elecfrolyfe used is high enough to make the diffuse layer disappear. However, if a very dilufe electrolyte solution is used, the situation will become more complicated due to the potential distribution within the electrolyte channels inside the porous layer. 

Zeta Potential Measurement, Figure 1 Schematic representation of the electric double layer using Gouy-Chapman-Stern model [3]... 

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