Electric Stern model

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. 

The representation of the data for TiC in terms of the monoprotic surface group model of the oxide surface and the basic Stern model of the electric double layer is shown in Figure 5. It is seen that there is good agreement between the model and the adsorption data furthermore, the computed potential Vq (not shown in the figure) is almost Nernstian, as is observed experimentally. 

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...

From the discussion so far it can be appreciated that the Stern model of the electric double layer presents only a rough picture of what is undoubtedly a most complex situation. Nevertheless, it provides a good basis for interpretating, at least semiquantitatively, most experimental observations connected with electric double layer phenomena. In particular, it helps to account for the magnitude of... 

The inner layer is a concept within the framework of the classical Gouy-Chap-man-Stern model of the double layer [57]. Recent statistical-mechanical treatments of electrical double layers taking account of solvent dipoles has revealed a microscopic structure of inner layer" and other intriguing features, including pronounced oscillation of the mean electrostatic potential in the vicinity of the interface and its insensitivity at the interface to changes in the salt concentration [65-69]. 

Also the choice of the electrostatic model for the interpretation of primary surface charging plays a key role in the modeling of specific adsorption. It is generally believed that the specific adsorption occurs at the distance from the surface shorter than the closest approach of the ions of inert electrolyte. In this respect only the electric potential in the inner part of the interfacial region is used in the modeling of specific adsorption. The surface potential can be estimated from Nernst equation, but this approach was seldom used In studies of specific adsorption. Diffuse layer model offers one well defined electrostatic position for specific adsorption, namely the surface potential calculated in this model can be used as the potential experienced by specifically adsorbed ions. The Stern model and TLM offer two different electrostatic positions each, namely, the specific adsorption of ions can be assumed to occur at the surface or in the -plane. 

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. 

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... 

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, ... 

The Stern model provides a reasonable description of the electric behavior of the metal-electrode interface for electrochemical systems, but it does not allow us to explain all experimental observations. In particular, it does not offer a satisfactory explanation for the influence of crystal orientation on the capacity of the double layer, nor for the effect of the chemical nature of anions. Figure 3.49 [17] shows the capacity of the double layer of a monocrystalline silver electrode, with three different orientations. The resulting curves are similar, but they are displaced along the axis of the potential. 

FIGURE 14.15 Schematic representation of phosphate, FA, and HA at goethite surface in which the extended Stern model is used to describe the structure of the electric double layer. (Reprinted with permission from Weng, L. et al.. Environ. Sci. TechnoL, 42, 23, 8747-8752, 2008. Copyright 2008 American Chemical Society.)... 

Figure 4.5 The Stern model for the electric double layer showing compression from (a) low to (b) high ionic strength...

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

Figure 3.2 Models for the electric double layer around a charged colloid particle (a) diffuse double layer model, (b) Stern model...

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]. 

To complement the models for the surface reactions, a model for the electric double layer is needed. Current models for the electric double layer are based on the work of Stern (21), who viewed the interface as a series of planes or layers, into which species were adsorbed by chemical and electrical forces. A detailed discussion of the application of these models to oxide surfaces is given by Westall and Hohl (2). 

While Stern recognized that formally one should include the capacitance between the 1HP and OHP in the interface model, he concluded that the error introduced into the electrical properties predicted for the interface would usually be small if the second capacitance were neglected, and 2 were set equal to. ... 

Two models of surface hydrolysis reactions and four models of the electrical double layer have been discussed. In this section two examples will be discussed the diprotic surface group model with constant capacitance electric double layer model and the monoprotic surface group model with a Stern double layer model. More details on the derivation of equations used in this section are found elsewhere (3JL). ... 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

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]).

Stern Combination of Parallel-Plate and Diffuse-Charge Models 9m = -9S = "[9h + J t 1 1 C Qi Qi maV=waVhaV Pole r R 1 of ,ial. linear variation V, ions are under the combined influence of the ordering electrical and the disordering thermal forces. Agrees with the experiment only for ions nonspecificaHy adsorbed on the electrode (e g. NaF). 

One of the most important theoretical contributions of the 1970s was the work of Rudnick and Stern [26] which considered the microscopic sources of second harmonic production at metal surfaces and predicted sensitivity to surface effects. This work was a significant departure from previous theories which only considered quadrupole-type contributions from the rapid variation of the normal component of the electric field at the surface. Rudnick and Stern found that currents produced from the breaking of the inversion symmetry at the cubic metal surface were of equal magnitude and must be considered. Using a free electron model, they calculated the surface and bulk currents for second harmonic generation and introduced two phenomenological parameters, a and b , to describe the effects of the surface details on the perpendicular and parallel surface nonlinear currents. In related theoretical work, Bower [27] extended the early quantum mechanical calculation of Jha [23] to include interband transitions near their resonances as well as the effects of surface states. 

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