Gouy-Chapman, double layer model

Dec. 6,1869, Wells, Norfolk, England - Jan. 17,1958, Oxford, England) Chapman studied in Oxford, and then he was a lecturer at Owens College (which later became part of the University of Manchester). In 1907 he returned to Oxford, and led the chemistry laboratories of the Jesus College until his retirement in 1944 [i]. Chapmans research has mostly been focused on photochemistry and chemical kinetics however, he also contributed to the theory of electrical -> double layer [ii]. His treatment of the double layer was very similar to that elaborated by -> Gouy earlier, and what has come to be called the Gouy-Chapman double-layer model [i.iii]. 

FIGURE 3.2 Gouy-Chapman double layer model. 

Electrostatic correction was made with the diffuse (Gouy-Chapman) double-layer model. The figure shows the effect of pH on the relative extent of surface complexation. 

Fig. 20.8 Gouy-Chapman diffuse layer model of the double layer...

As we have seen, the electric state of a surface depends on the spatial distribution of free (electronic or ionic) charges in its neighborhood. The distribution is usually idealized as an electric double layer, one layer is envisaged as a fixed charge or surface charge attached to the particle or solid surface while the other is distributed more or less diffusively in the liquid in contact (Gouy-Chapman diffuse layer model, Figure 9.19). A balance between electrostatic and thermal forces is attained. 

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... 

Gouy-Chapman and Stem Models of the Double Layer... 

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

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]. 

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

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

Metal binding by a hydrous oxide from a 10 7 M solution (SOH + Me2+ OMe+ + H+) for a set of equilibrium constants (see Eqs. (i) - (iii) from Example 2.3) and concentration conditions (see text). Corrected for electrostatic interactions by the diffuse double layer model (Gouy Chapman) for 1 = 01 The hydrolysis of Me2+ is neglected. 

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. 6.67. Helmholtz-Perrin, Gouy-Chapman, and Stem models of the double layer.

Fig. 1.10 Schematic view of the electrical double layer in agreement with the Gouy-Chapman-Stem-Grahame models. The metallic electrode has a negative net charge and the solvated cations define the inner limit of the diffuse later at the Helmholtz outer plane (OHP). There are anions adsorbed at the electrode which are located at the inner Helmholtz plane (IHP). The presence of such anions is stabilized by the corresponding images at the electrode in such a way that each adsorbed ion establishes the presence of a surface dipole at the interface...

Diffuse-double-layer model. The DDLM is similar to the CCM but the charge potential is formulated from the Gouy-Chapman theory ... 

The simplest, self-consistent model of the diffuse-ion swarm near a planar, charged surface like that of a smectite is modified Gouy-Chapman (MGQ theory [23,24]. The basic tenets of this and other electrical double layer models have been reviewed exhaustively by Carnie and Torrie [25] and Attard [26], who also have made detailed comparisons of model results with those of direct Monte Carlo simulations based in statistical mechanics. The postulates of MGC theory will only be summarized in the present chapter [23] ... 

The Poisson-Boltzman (P-B) equation commonly serves as the basis from which electrostatic interactions between suspended clay particles in solution are described ([23], see Sec.II. A. 2). In aqueous environments, both inner and outer-sphere complexes may form, and these complexes along with the intrinsic surface charge density are included in the net particle surface charge density (crp, 4). When clay mineral particles are suspended in water, a diffuse double layer (DDL) of ion charge is structured with an associated volumetric charge density (p ) if av 0. Given that the entire system must remain electrically neutral, ap then must equal — f p dx. In its simplest form, the DDL may be described, with the help of the P-B equation, by the traditional Gouy-Chapman [23-27] model, which describes the inner potential variation as a function of distance from the particle surface [23]. 

Double layer, diffuse double layer, or Gouy-Chapman layer — That part of the double layer which is adequately described by the Gouy-Chapman theory. Details can be found under -> double layer models. See also - Gouy, -> Chapman. 

To determine the spatial variation of a static electric field, one has to solve the Poisson equation for the appropriate charge distribution, subject to such boundary conditions as may pertain. The Poisson equation plays a central role in the Gouy-Chapman (- Gouy, - Chapman) electrical - double layer model and in the - Debye-Huckel theory of electrolyte solutions. In the first case the one-dimensional form of Eq. (2)... 

At low ionic strength, a diffuse double-layer model (Gouy-Chapman model) is used. 

Few outer-sphere electrode reactions have precursor-state concentrations that are measurable [21] so that it is usual to estimate wp and ws from double-layer models. The simplest, and by far the most commonly used, treatment is the Frumkin model embodied in eqns. (8) and (8a) whereby, as noted in Sect. 2.2, the sole contributor to wp and ws is presumed to be electrostatic work associated with transporting the reactant from the bulk solution to the o.H.p. at an average potential Gouy-Chapman (GC) theory [58],... 

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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