Stern model

The Stern model (1924) may be regarded as a synthesis of the Helmholz model of a layer of ions in contact with the electrode (Fig. 20.2) and the Gouy-Chapman diffuse model (Fig. 20.10), and it follows that the net charge density on the solution side of the interphase is now given by... 

The Stern model predicts that the total differential capacitance C will consist of two terms representing two capacitors in series... 

The model of the electrode/electrolyte interface proposed in the first chapter is termed the Stern model. This is now accepted as the definitive picture of the structure of the interface, primarily as a result of electrocapillarity studies. 

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... 

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 It has been superseded by more realistic models, which account for the electronic structure of the metal, and the existence of an extended boundary layer in the solution.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. 

Figure 17.1 The Gouy-Chapman-Stern model, the solution. We will consider each phase in turn.

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

Alternatively, in the literature, the constant capacitance model and the Stern model were used to describe the dependence of the surface charge density on the surface potential. In the constant capacitance model, the surface charge is defined as ... 

The surface complexation approach is distinct from the Stern model in the primacy given the specific chemical interaction at the surface over electrostatic effects, and the assignment of the surface reaction to the sorption reactions themselves (Dzombak and Morel, 1990). 

The Triple Layer Model. This model developped by Yates et al. (1974) and Davis et al. (1978) uses a similar idea as the Stern model the specifically adsorbed ions are... 

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 structure of the interface according to the Stern model and several limiting-case approximations is presented in Figure 4. The electrostatic models of the interface will be introduced in terms of the most complete one, the triple layer model (Figure 4a). Then the relationship of the triple layer model to the simplified models in Figures 4b-d will be discussed. 

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. 

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. 

Limiting Cases of the Stern Model. The electrostatic energies through the interface have been formulated in terms of capacitances. For the basic Stern model, the total capacitance of... 

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. 

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. 

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. 

Dahl, J. P. On the Einstein-Stern model of rotational heat capacities. J. Chem. Phys. 109, 10688-10691 (1998). 

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...

Figure 4.9. Stern model (a) the model (b) variation of the potential with distance from the electrode (c) equivalent capacitor.

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