Metal Stern model

This Gouy-Chapman-Stern model, as it was named after its main contributors, is a highly simplified model of the interface, too simple for quantitative purposes. It has been superseded by more realistic models, which account for the electronic structure of the metal, and the existence of an extended boundary layer in the solution. It is, however, still used even in current publications, and therefore every electrochemist should be familiar with it. 

The Triple T.aver Model and the Stern Model. The ions most intimately associated with the surface are assigned to the innermost plane where they contribute to the charge Oq and experience the potential tI>q These ions are generally referred to as primary potential determining ions. For oxide surfaces, the ions H+ and 0H are usually assigned to this innermost plane. In Stern s original model, the surface of a metal electrode was considered, and the charge cjq was due to electrons. 

One other caveat concerning the approach used here must be made. This discussion, and the studies to which it relates, are based on some version of the Stern model for the oxide-electrolyte interface. Oxide surfaces are rough and heterogeneous. Even for the mercury-electrolyte interface, or single crystal metal-electrolyte interfaces, the success of some form of the Stern model has been less than satisfactory. It is important to bear in mind the operational nature of these models and not to attach too much significance to the physical picture of the planar interface. 

The above attempts to apply the Stern model to five sets of charging curves of silica were rather unsuccessful. On the other hand, Sonnefeld [37] reports successful application of the Stern model to the surface charging of silica at five concentrations (0.005-0.3 mol dm ) of five alkali chlorides. Two adjustable parameters and the acidity constant) were independent of the nature of alkali metal cation and one parameter, C was dependent on the nature of the alkali metal cation. This result was explained in terms of the correlation between the Stern layer thickness and the size of the counterions. 

The aforementioned diffuse-layer and discreteness-of-charge effects have been taken into consideration in the model proposed by Grahame and Parsons [26,250-252]. First, it was assumed (unlike in the Stern model) that the specifically adsorbed ions were located at the distance from the metal surface (in the inner Helmholtz plane ) ensuring their maximum bond strength, owing to the combination of forces of electrostatic and quantum-mechanical origins. It shows the need for the partial or even complete desolvation of the adsorbed species and its deep penetration into the compact layer. The position of this adsorption plane depends on all components of the system, metal, solvent, and adsorbed ion. 

Within the framework of the hypothesis that no charge transfer takes place in the course of the ion transition into the adsorbed state, the value of A for each system would allow one to determine the ratio of the capacitance between the metal surface and the adsorption plane to the overall compact-layer capacitance, Eq. (88b), similar to the Grahame-Parsons treatment in Sect. 2.1.11.2. (the Helmholtz-Stern model of the compact layer as a uniform dielectric slab does not correspond to the modern view of the interfacial structure, see previous sections, so that it is hardly... 

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

The Stern Model is a combination of the Helmholtz and Gouy-Chapman models (Figure 3.47). The potential difference between the metal and the solution is comprised of two terms A h. due to the compact Helmholtz layer and A0gc, due to the diffuse Gouy-Chapman layer. 

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. 

The next question concerns how these excess charges are distributed on the metal and solution sides of the interphase. We discuss these topics in the next four sections. Four models of charge distribution in the solution side of the interphase are discussed the Helmholtz, Gouy-Chapman, Stern, and Grahame models. 

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]).

For anionic monolayers, the reversal of the tt-A isotherms can be explained in terms of a competition between the anionic head groups and the alkali metal cations for molecules of water. If a modified Stern-type model of the plane interface is assumed, this interface will be composed of distinct adsorption sites, with counterions (cations) of finite size that can adsorb on these sites if the standard free energies of adsorption are favorable. If the anionic head group is more polarizable than water, as with carboxylic acids or phosphates, the hydration shell of the cation is incompletely filled, and the order of cation sizes near the interface is K+ > Na+ > Li+. When the polarizability of the anionic group is less than that of water, as with the sulfates, the lithium cation becomes the most hydrated one, and the order of cation sizes becomes Li+ > Na+ > K+. 

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. 

Finally we shall argue that present-day theories of the nonprimitive models of the electric double layer have considerable difficulty in treating properly ion adsorption in the Stern inner region at metal-aqueous electrolyte interfaces and we suggest that this region is a useful concept which should not be dismissed as unphysical. Indeed Stern-like inner region models continue to be used in colloid and electrochemical science, for example in theories of electrokinetics and aqueous-non-metallic (e.g., oxide) interfaces. 

The reversal of the direction of the electro-osmotic flow by the adsorption onto the capillary wall of alky-lammonium surfactants and polymeric ion-pair agents incorporated into the electrolyte solution is widely employed in capillary zone electrophoresis (CZE) of organic acids, amino acids, and metal ions. The dependence of the electro-osmotic mobility on the concentration of these additives has been interpreted on the basis of the model proposed by Fuerstenau [6] to explain the adsorption of alkylammonium salts on quartz. According to this model, the adsorption in the Stern layer as individual ions of surfactant molecules in dilute solution results from the electrostatic attraction between the head groups of the surfactant and the ionized silanol groups at the surface of the capillary wall. As the concentration of the surfactant in the solution is increased, the concentration of the adsorbed alkylammonium ions increases too and reaches a critical concentration at which the van der Waals attraction forces between the hydrocarbon chains of adsorbed and free-surfactant molecules in solution cause their association into hemimicelles (i.e., pairs of surfactant molecules with one cationic group directed toward the capillary wall and the other directed out into the solution). 

Derivation of the Modified Stern-Volmer Model for Metal Complexation. The... 

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).

Figure 12. Diagram of inner region of the double layer showing outer Helmholtz (OHP) plane with oriented solvent dipoles interacting with electrostatically adsorbed solvated ions [schematic based on Stern-Grahame model (Ref. 95) BDM model (Ref. 60) includes an extra layer of solvent dipoles between the metal surface and OHP of cations].

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