Electrical Gouy-Chapman-Stern model

We are confident that a Gouy-Chapman-Stern model and a Doiman-plus-binding model may be used to compute values for xj/p and y/cyf that are at least proportional to the actual values. With these electrical potentials, corresponding values for ion activities may be computed that are at least proportional to actual values also. Although the electrostatic theory is quite old, values for model parameters for plant cell surfaces have become available only recently. Computer programs for the electrostatic models may be requested from us. 

Kinraide, T.B., 1994. Use of a Gouy-Chapman-Stern model for membrane-surface electrical potential to interpret some features of mineral rhizotoxicity. Plant Physiol. 106, 1583-1592. 

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, ... 

Zeta Potential Measurement, Figure 1 Schematic representation of the electric double layer using Gouy-Chapman-Stern model [3]... 

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]).

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. 

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...

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. 

FIGURE 6. The arrangement of water molecules and counterions near to a negatively charged membrane surface according to the Stern model. Within the Stern layer of polarized water molecules the electric potential falls linearly, and for distances further than this the potential profile follows that predicted by the Gouy-Chapman theory of electrical double layers. For ascites cells the potential drop between the surface potential and the zeta potential has been determined to be around... 

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. 

The electrical potential, ij/, at the interface between the micellar core and the surrounding water may be estimated by the Gouy-Chapman theory of the electrical double layer. In the classical theory, a uniform continuous interfacial surface charge is assumed, which is neutralized by a diffuse ionic layer of charges in the aqueous solution. In a detailed model of the Stern layer proposed by Stigter [35-37], this theory is refined to allow for the size and high concentration of the charge carriers at the micelle surface. 

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The substantial understanding of the structure of the electric double layer has been summarized in various reviews and books (e.g., Ref. 2, 81, 177-183). The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [3], Gouy and Chapman [5, 6], and Stern [7], and in most of the studies cited in the reviews 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 can overcome this restriction and describe the solvent in a more realistic fashion. They are thus able to paint a detailed picture of the microscopic structure near a metal electrode. 

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