Stem model

The interaction of an electrolyte with an adsorbent may take one of several forms. Several of these are discussed, albeit briefly, in what follows. The electrolyte may be adsorbed in toto, in which case the situation is similar to that for molecular adsorption. It is more often true, however, that ions of one sign are held more strongly, with those of the opposite sign forming a diffuse or secondary layer. The surface may be polar, with a potential l/, so that primary adsorption can be treated in terms of the Stem model (Section V-3), or the adsorption of interest may involve exchange of ions in the diffuse layer. 

Fuerstenau and co-workers observed in the adsorption of a long-chain ammonium ion RNH3 on quartz that at a concentration of 10 Af there was six-tenths of a mono-layer adsorbed and the f potential was zero. At 10 M RNH3, however, the f potential was -60 mV. Calculate what fraction of a monolayer should be adsorbed in equilibrium with the 10 M solution. Assume a simple Stem model. 

Gouy-Chapman and Stem Models of the Double Layer... 

Standard potential, on the UHV scale, 13 Steady state, fluctuations in, 274 Stem model... 

Ruth, M. (2007). MacroSystem Model Overview. National Renewable Energy Laboratory, US DOE Hydrogen Program, www.hydrogen.energy.gov/ macro sy stem model. html. 

The interfacial capacitance increases with the DDTC concentration added. The relationship among potential difference t/ of diffusion layer, the electric charge density q on the surface of an electrode and the concentration c of a solution according to Gouy, Chapman and Stem model theory is as follows. 

In the Stem model, the surface charge is balanced by the charge in solution, which is distributed between the Stem layer at a distance d from the surface and a diffuse layer having an ionic Boltzman-type distribution. The total charge a is therefore due to the charge in the two layers ... 

Some Ions Stuck to the Electrode, Others Scattered in Thermal Disarray The Stem Model... 

When, however, charges are separated, potential drops result. The Stem model implies, therefore, two potential drops, i.e.,... 

Fig. 6.66. The Stem model, (a) A layer of ions stuck to the electrode and the remainder scattered in cloud fashion, (b) The potential variation according to this model, (c) The corresponding total differential capacity C is given by the Helmholtz and Gouy capacities in series.

Fig. 6.67. Helmholtz-Perrin, Gouy-Chapman, and Stem models of the double layer.

After all this analysis, can we say that the Stem model is consistent with experimental results In other words, is the Stem model able to reproduce the differential capacity curves Under certain conditions, it is. So, to some extent, the Stem model was successful. However, what are the restrictions the model imposes Recall that in the Helmholtz-Perrin model the ions lay close to the electrode on the OHP. The condition for the Stem model to succeed is that ions not be in close proximity to the electrode they are not to be adsorbed. Thus the model proved to be valid only for electrolytes such as NaF (Graliame, 1947).45 Both of these ions, Na+ and F, are known to have a hydration layer strongly attached to them in such a way that even in the proximity of the electrode they are almost not interacting with the electrode surface. The Stem model works well representing noninteracting ions. 

Nevertheless, when other ions such as Cl", Br, F, or PO are in solution, they may come in close contact with the electrode and strongly interact chemically with it. They may specifically adsorb46 on the electrode. The Stem model is not applicable in... 

The contribution of the metal to the double layer was discussed in Sections 6.6.7 to 6.6.9. However, we have said little about the ions in solution adsorbed on the electrode and how they affect the properties of the double layer. For example, when presenting the Stem model of the double layer (Section 6.6.6), we talked about ions sticking to the electrode. How does an interface look with ions stuck on the metal What is the distance of closest approach Are hydrated ions held on a hydrated electrode i.e., is an electrode covered with a sheet of water molecules Or are ions stripped of their solvent sheaths and in intimate contact with a bare electrode What are the forces that influence the sticking of ions to electrodes ... 

When we revised the different models of the interface, namely, the Helmholtz-Perrin, Gouy-Chapman, and Stem models, we left the corresponding section (Section 6.6.6) with the idea that these models were not able to reproduce the differential capacity curves [Fig. 6.65(b)]. We said that when ions specifically adsorb on the electrode, the models fail to explain the experimental facts. 

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

Later, the Gouy-Chapman-Stem model [2,19, 22-24] describes the interface in the absence of specific adsorption by assuming that the ions can approach the... 

Fig. 26 Schematic view of the growth face of an extended-chain lamellar crystal poisoned by stems of half the chain length. The row-of-stems model can be applied with the row perpendicular to the growth face, as in the previous rough growth models to describe retardation of i (rowp), or parallel to the growth face to describe retardation of v (row q). (From [29], by permission of American Chemical Society)...

Figure 3.31. Diagram of the Stem model (from Van Olphen, 1977, with permission).

The data in Figure 3.32 show the theoretical estimated concentration of Na+, Li+, and K+ or Rb+ between the Stem layer and the diffuse layer based on the Stem model. The distribution appears to be consistent, as expected, with the hydration energy of the cation. The greater the heat of hydration (see Chapter 4, Table 4.1) is, the greater the concentration of the cation in the diffuse layer in relationship to the Stern layer. The Stern model has been the basis for many variations of the model recently also known as the surface complexation model (Goldberg, 1992). 

On what basis does the Stem model distinguish the potential location of ions near a surface under the influence of an electrical potential ... 

The surface after adsorption will be chained with a potential, as in Figure 9.14, so that primary adsorption can be treated in terms of a capacitor model called the Stem model [43]. The other type of adsorption that can occur involves an exchange of ions in the diffuse layer with those of the surface. In the case of ion exchange, the primary ions are chemically bound to the structure of the solid and exchanged between ions in the diffuse double layer. 

Stem model (of the double layer), 195 Stoichiometric number, 149 Strip microelectrode, 453 Supporting electrolyte, 208, 351 Surface concentration, 131 Surface excess, 225, 229 Surface excess of anions, 256 Surface excess, relative, 236... 

Quantitatively, we have in principle 13.2.3) for the purely diffuse case, which in the zeroth-order Stem model can be modified to account for the fact that v can now maximally become. The difference between y and is dictated by the Stem capacitance C . For the specific adsorption case, 13.3.9) can be used if a is known as a function of a°. To this end, one of the Stem equations (3.6.36 or 37) can be used. 

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