Gouy-Chapmen model

Fig. 20.9 Experimental capacitance-potential curve for O-OOI m KCl and calculated curve using the Gouy-Chapman model. The experimental curve and the theoretical curve agree at potentials (us R.H.E.) near the p.z.c. Note the constant capacitance of 17 x 10 F m at negative potentials (after Bockris and Drazic )...

The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler-Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (k j). The potential dependence of the ET rate constant normalized by as obtained from the optical analysis of the TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a mixed-solvent layer type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (A 0) is zero. The potential drop in the aqueous side was estimated by the Gouy-Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). 

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

According to the Gouy-Chapman model, the thickness of the diffuse countercharge atmosphere in the medium (diffuse double layer) is characterised by the Debye length k 1, which depends on the electrostatic properties of the... 

A theoretical model for the adsorption of metals on to clay particles (<0.5 pm) of sodium montmorillonite, has been proposed, and experimental data on the adsorption of nickel and zinc have been discussed in terms of fitting the model and comparison with the Gouy-Chapman theory [10]. In clays, two processes occur. The first is a pH-independent process involving cation exchange in the interlayers and electrostatic interactions. The second is a pH-dependent process involving the formation of surface complexes. The data generally fitted the clay model and were seen as an extension to the Gouy-Chapman model from the surface reactivity to the interior of the hydrated clay particle. 

We shall use the familiar Gouy-Chapman model (3 ) to describe the behaviour of the diffuse double lpyer. According to this model the application of a potential iji at a planar solid/electrolyte interface will cause an accumulation of counter-ions and a depletion of co-ions in the electrolyte near the interface. The disposition of diffuse double layer implies that if the surface potential of the planar interface at a 1 1 electrolyte is t ) then its surface charge density will be given by ( 3)... 

B , while for an n-type semiconductor the reverse is true. An analog to the SCR in the semiconductor is an extended layer of ions in the bulk of the electrolyte, which is present especially in the case of electrolytes of low concentration (typically below 0.1 rnolh1). This diffuse double layer is described by the Gouy-Chap-man model. The Stern model, a combination of the Helmholtz and the Gouy-Chapman models, was developed in order to find a realistic description of the electrolytic interface layer. 

Of course, when the volume concentration of mobile charges is sufficiently high that the Debye length is comparable with the ionic radius of the mobile ion(s), a combination of the Helmholtz and Gouy-Chapman models is required. This is achieved by assuming that the measured Cdi value is a series combination of that due to the Gouy-Chapman model (Cgc) and that due to the Helmholtz model (Ch), i.e. 

Fig. 10.7 Gouy-Chapman model of the interface between a metal and an electrolyte. The metal is shown with a negative charge on its surface.

A polyelectrolyte solution contains the salt of a polyion, a polymer comprised of repeating ionized units. In dilute solutions, a substantial fraction of sodium ions are bound to polyacrylate at concentrations where sodium acetate exhibits only dissoci-atedions. Thus counterion binding plays a central role in polyelectrolyte solutions [1], Close approach of counterions to polyions results in mutual perturbation of the hydration layers and the description of the electrical potential around polyions is different to both the Debye-Huckel treatment for soluble ions and the Gouy-Chapman model for a surface charge distribution, with Manning condensation of ions around the polyelectrolyte. 

The Gouy-Chapman model assumes (1) the exchangeable cations exist as point charges, (2) colloid surfaces are planar and infinite in extent, and (3) surface charge is distributed uniformly over the entire colloid surface. Even though this assumption... 

Fig. 5.5 Distribution of electrical charges and potentials in a double layer according to (a) Gouy-Chapman model and (b) Stern model, where /q and are surface and Stern potentials, respectively, and d is the thickness of the Stern layer...

Figure 4.6. Gouy-Chapman model id) model ib) variation of the potential with distance from the electrode (c) equivalent capacitor.

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