Double layer model, Stern-Gouy-Chapman

The Gouy-Chapman theory did not prove entirely satisfactory, and in 1924 a considerable advance was made by the Germ an-American physicist Otto Stern, whose model is shown in Figure 11.18c. Stern combined the fixed double-layer model of Helmholtz with the diffuse double-layer model of Gouy and Chapman, As shown in the figure, there is a fixed layer at the surface, as well as a diffuse layer. On the whole this treatment has proved to be satisfactory, but for certain kinds of investigations it has been found necessary to develop more elaborate models. 

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 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. 

Stern-Gouy-Chapman double layer model and specific adsorption... 

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. 

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. 

To date, it has been documented that ILs can be adsorbed onto various electrode surfaces. For example, Nanjundiah et al. found that several ILs used as electrolytes can induce double-layer capacitance phenomena on the surface of an Hg electrode and obtained the respective capacitance values for various ILs. Hyk and Stojek have also studied the IL thin layer on electrode surfaces and suggested that counterions substantially influence the distribution of IL. Kornyshev further discussed IL formations on electrode surfaces, suggesting that IL studies should be based on modern statistical mechanics of dense Coulomb systems or density-functional theory rather than classical electrochemical theories that hinge on a dilute-solution approximation. There are three conventional models that describe the charge distribution of an ion near a charged surface the Helmholtz model, the Gouy-Chapman model, and the Stern model. In the case of ILs, it remains controversial which model can best explain and lit the experimental data. 

The physical meaning of the g" (ion) potential depends on the accepted model of ionic double layer. The proposed models correspond to the Gouy Chapman diffuse layer, with or without allowance for the Stern modification and/or the penetration of small counterions above the plane of the ionic heads of the adsorbed large ions [17,18]. The presence of adsorbed Langmuir monolayers may induce very high changes of the surface potential of water. For example. A/" shifts attaining ca. —0.9 (hexadecylamine hydrochloride), and ca. -bl.OV (perfluorodecanoic acid) have been observed [68]. 

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. 

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. 

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 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]).

How did the Stern model get around the limitations of the double-layer or Gouy-Chapman model ... 

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. 

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