Helmholtz-Perrin model

Thus, if E and d are taken as constants, the parallel-plate model predicts a constant capacity, i.e., one that does not change with potential. So it appears that the Helmholtz-Perrin model would be quite satisfactory for electrocapillaiy curves that are perfect parabolas (Fig. 6.56). 

However, is the electrocapillaiy curve a perfect parabola Almost, but not quite. There is always a slight asymmetry (see Fig. 6.56), and that asymmetry precludes it from having constant capacities, as the Helmholtz-Perrin model predicts. 

In the previous section it was seen that the Helmholtz-Perrin model fixes the solution charges onto a sheet parallel to the metal. I Iowcver, this model was too rigid... 

Now, the cosh function gives inverted parabolas [Fig. 6.65(b)]. Hence, according to the simple diffuse-charge theory, the differential capacity of an electrified interface should not be a constant. Rather, it should show an inverted-parabola dependence on the potential across the interface. This, of course, is a welcome result because the major weakness of the Helmholtz-Perrin model is that it does not predict any variation in capacity with potential, although such a variation is found experimentally [Fig. 6.65(b)],... 

What are the implications of Eq. (6.132) The Stem synthesis of the two models implies a synthesis of the potential-distance relations characteristic of these two models [Fig. 6.66(b)] a Z/ncar variation in the region from. v = 0 to the position of the OHP according to the Helmholtz-Perrin model (see Section 6.6.2), and an exponential potential drop in the region from OHP to the bulk of solution according to the Gouy-Chapman model (see Section 6.6.4), as shown in Fig. 6.67. 

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. 

In the Helmholtz-Perrin model, we found that (Section 6.6.2)... 

Q.19.7 Describe the Helmholtz-Perrin model and discuss one of its fundamental problems. Draw the arrangement of counter ions and electrode as proposed by the Helmholtz-Perrin model. 

A. 19.7 The Helmholtz-Perrin model proposes a double layer of ions that exactly cancels the effects of the electrode. A fundamental problem with this proposal is that it does not include the randomizing effects of thermal diffusion as part of its model. See Fig. 20.3. 

A. 19.8 The Gouy-Chapman model replaces the double layer of the Helmholtz-Perrin model with the diffuse cloud of charge that was more concentrated near the electrode. One of its fundamental problems is that it ignores the effect of the dielectric constant of high-potential fields present at the interface. See Fig. 20.4... 

The Parallel-Plate Condenser Model The Helmholtz-Perrin Theory... 

Fig. 6.62. The Helmholtz-Perrin parallel-plate model, (a) A layer of ions on the OHP constitutes the entire excess charge in the solution. (b) The electrical equivalent of such a double layer is a parallel-plate condenser, (c) The corresponding variation of potential is a linear one. (Note The solvation sheaths of the ions and electrode are not shown in this diagram nor in subsequent ones.)...

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

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. 

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