Gouy-Chapman-Stern double layer

In Figure 9.11, the expulsion of co-ions is depicted for a Gouy-Chapman-Stern double layer. Let c+ be the concentration of co-ions at a positively charged surface. In a Gouy-Chapman-Stem double layer, the co-ion expulsion per unit surface area, that is, the negative adsorption of co-ions F+ is given by... 

The outer surface of the Stern layer is the shear surface of the micelle. The core and the Stern layer together constitute what is termed the kinetic micelle. Surrounding the Stern layer is a diffuse layer called the Gouy-Chapman electrical double layer, which contains the aN counterions required to neutralise the charge on the kinetic micelle. The thickness of the double layer is dependent on the ionic strength of the solution and is greatly compressed in the presence of electrolyte. 

Figure 21. A schematic diagram of the Stern adsorption layer (top) and the average potential profile of the Stern layer and Gouy-Chapman diffuse double layer.

Figure 2. Three models of the electrochemical interface (a) the Helmholtz fixed (rigid) double layer, 1879 (b) the Gouy-Chapman diffuse double layer 1910-1913 (c)the Stern double layer, 1924, being a combination of the Helmholtz and the Gouy-Chapman concepts.

In the electrochemical literature one finds the Gouy-Chapman (GC) and Gouy-Chapman-Stern (GCS) approaches as standard models for the electric double layer [9,10]. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

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]).

As the electrode surface will, in general, be electrically charged, there will be a surplus of ionic charge with opposite sign in the electrolyte phase in a layer of a certain thickness. The distribution of jons in the electrical double layer so formed is usually described by the Gouy— Chapman—Stern theory [20], which essentially considers the electrostatic interaction between the smeared-out charge on the surface and the positive and negative ions (non-specific adsorption). An extension to this theory is necessary when ions have a more specific interaction with the electrode, i.e. when there is specific adsorption of ions. 

CFSE Crystal Field Stabilization Energy CMC Critical micelle concentration DDAC1 N-Dodecylammonium Chloride DEDTC Diethyl Dithiocarbamate EDL Electric Double Layer GChSG Gouy/Chapman/Stern/Grahame IP Isoelectric Point... 

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).

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

In the absence of specifically adsorbable ions, the double-layer structure is adequately described in terms of the Gouy-Chapman-Stern theory. The outer Helmholtz plane potential (distinguished by Grahame) is associated with a surface charge density a through the relation... 

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. 

FIGURE 9.8 Gouy-Chapman-Stern electrical double layer with specific ion adsorption in the Stern layer 0 [Pg.145]

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, ... 

FIGURE 3.15 Dimensionless mean electrostatic potential (a) and surface-ion distribution function (b) as predicted by the Gouy-Chapman-Stern (GCS) and modified Poisson-Boltzmann (MPB) theories for a 1 1 electrolyte with a = 0.425 nm and c = 0.197 M. (Outhwaite, Bhuiyan, and Levine, 1980, Theory of the electric double layer using a modified Poisson-Boltzmann equation. Journal of the Chemical Society, Faraday Transactions 2 Molecular and Chemical Physics, 76, 1388-1408. Reproduced by permission of The Royal Society of Chemistry.)... 

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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