Gouy-Chapman-Stern-Grahame model

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]).

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).

FIGURE 11.1 Schematic representation (based on Figure 3.13, Gouy-Chapman-Stern-Grahame model) of the approach of an ion (right) to a charged surface (left), where an electric potential gradient is present. 

The simplified Gouy—Chapman—Stern—Grahame (GCSG) model is acceptable for the purpose of the analysis of electrode kinetics covered in the present chapter. Comprehensive and detailled treatises on this subject can be found elsewhere [6, 18—20]. 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

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 ... 

The next question concerns how these excess charges are distributed on the metal and solution sides of the interphase. We discuss these topics in the next four sections. Four models of charge distribution in the solution side of the interphase are discussed the Helmholtz, Gouy-Chapman, Stern, and Grahame models. 

The first models Helmholtz, Gouy-Chapman, Stern and Grahame Helmholtz Model (1879)... 

Q.19.3 Is tire Stern or Grahame model of the interphase to be preferred over the Gouy - Chapman or Helmholtz model in biological systems ... 

There are many models that describe the interaction between solute ions and surfaces. These have been reviewed by several authors (1,2,3) and include general ion exchange (4,5,6), surface complex formation (7,8) (the Swiss model), and various electrostatic models (Gouy-Chapman-Stern (9), Grahame (10,11), and James and Healy (12)). For hydrolyzable species sorbing onto hydrous oxide surfaces, the surface complex formation model and the solvent-ion interaction model of James and Healy have been shown to be in good agreement with observations. In this chapter, data are analyzed via the James and Healy model. 

See color insert.) Electric double-layer models at interface of electrode and electrolyte solution. (a) Diffuse layer or Gouy-Chapman model, (b) Helmholtz layer or model the d represents the double-layer thickness, (c) Stern-Grahame layer or model in which the IHP represents the inner Helmholtz plane and the OHP represents the outer Helmholtz plane. 

It is evident now why the Helmholtz and Gouy-Chapman models were retained. While each one alone fails completely when compared with experiment, a series combination of the two yields reasonably good agreement. There is room for improvement and refinement of the theory, but we shall not deal with that here. The model of Stern brings theory and experiment close enough for us to believe that it does describe the real situation at the interface. Moreover, later work of Grahame shows that the diffuse-double-layer theory, used in the proper context, yields consistent results and can be considered to be correct, within the limits of the approximations used to derive it. 

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