Stern-Helmholtz model

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

Thus, Grahame modified Stern s model by introducing the inner plane of closest approach [inner Helmholtz plane (IHP)], which is located at a distance X from the electrode (Fig. 4.11). The IHP is the plane of centers of partially or fully dehydrated... 

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]).

The first models Helmholtz, Gouy-Chapman, Stern and Grahame Helmholtz Model (1879)... 

Q.19.3 Is tire Stern or Grahame model of the interphase to be preferred over the Gouy - Chapman or Helmholtz model in biological systems ... 

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].

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. 

It was taken into account in the models developed in Refs 75, 78 and 80 that some portion of the counter-ions is bound to surface-active ions within the Stern-Helmholtz (S-H) layer, while another (unbound) portion is located within the diffuse region of the DEL. The equivalent relations of Eqs (56)-(58) in this case contain the difference F — y"X instead of Fj, where F x is the adsorption of counterions localized within the monolayer. It follows from the model described by Eqs (56)-(58) that if all counterions are lo-... 

However, the theory neglects the finite size of the ions, and it was Stern who postulated that ions could not approach the electrode beyond a plane of closest approach, thereby introducing in a crude way the ion size (Fig. 5.1c). Although formulated in a complex manner [1], the basis of Stern s model is a combination of the Helmholtz and Gouy-Chapman approaches. It may be noted that Fig. 5.1 also shows the potential and charge distributions resulting from the models. These will be discussed later. 

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 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... 

Equation (2.33) now defines the double layer in the final model of the structure of the electrolyte near the electrode specifically adsorbed ions and solvent in the IHP, solvated ions forming a plane parallel to the electrode in the OHP and a dilfuse layer of ions having an excess of ions charged opposite to that on the electrode. The excess charge density in the latter region decays exponentially with distance away from the OHP. In addition, the Stern model allows some prediction of the relative importance of the diffuse vs. Helmholtz layers as a function of concentration. Table 2.1 shows... 

Stern used this simplification in his calculations. The simplified model with only one Helmholtz capacitance is commonly referred to as the Stern model (Figure 4b), while the "extended" Stern model (Figure 4a) is designated the triple layer model. 

It is important to stress that the activity coefficients (and the concentrations) in equation 16.18 refer to the species close to the surface of the electrode, and so can be very different from the values in the bulk solution. This is portrayed in figure 16.6, which displays the Stern model of the double layer [332], One (positive) layer is formed by the charges at the surface of the electrode the other layer, called the outer Helmholtz plane (OHP), is created by the solvated ions with negative charge. Beyond the OHP, the concentration of anions decreases until it reaches the bulk value. Although more sophisticated double-layer models have been proposed [332], it is apparent from figure 16.6 that the local environment of the species that are close to the electrode is distinct from that in the bulk solution. Therefore, the activity coefficients are also different. As these quantities are not... 

Figure 16.6 The Stern model of the double layer. The outer Helmholtz plane (OHP) and the width of the diffusion layer (8) are indicated. The shaded circles represent solvent molecules. The drawing is not to scale The width of the diffusion layer is several orders of magnitude larger than molecular sizes.

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. 

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. 

Streaming potential The interface of a mineral (rock) in contact with an aqueous phase exhibits surface charge. The currently accepted model of this interface is the EDL model of Stem. Chemical reactions take place between the minerals and the electrolytes in the aqueous phase, which results in a net charge on the mineral. Water and electrolytes bound to the rock surface constitute the Stern (or Helmholtz) layer. In this region, the ions are tightly bound to the mineral, while away from this layer (the so-called diffuse layer), the ions are free to move about. 

A refinement of the Stern model has been proposed by Grahame89, who distinguishes between an outer Helmholtz plane to indicate the closest distance of approach of hydrated ions (i.e. the same as the Stern plane) and an inner Helmholtz plane to indicate the centres of ions, particularly anions, which are dehydrated (at least in the direction of the surface) on adsorption. 

Using this model, one cannot forecast the adsorption of the background electrolyte ions because this model do not consider the reactions responsible for such a process. Zeta potential values, calculated on the basis of this model, are usually too high, nevertheless, because of its simplicity the model is applied very often. In a more complicated model of edl, the three plate model (see Fig. 3), besides the mentioned surface plate and the diffusion layer, in Stern layer there are some specifically adsorbed ions. The surface charge is formed by = SOHJ and = SO- groups, also by other groups formed by complexation or pair formation with background electrolyte ions = SOHj An- and = SO Ct+. It is assumed that both, cation (Ct+) and anion (A-), are located in the same distance from the surface of the oxide and form the inner Helmholtz plane (IHP). In this case, beside mentioned parameters for two layer model, the additional parameters should be added, i.e., surface complex formation constants (with cation pKct or anion pKAn) and compact and diffuse layer capacities. 

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