Capacitance Gouy-Chapman

To our knowledge this is quite a new formula for the differential capacitance. It is vahd whenever charging is equivalent to a shift in space of the position of the wall. We can verify that it is fulfilled for the Gouy-Chapman theory. One physical content of this formula is to show that for a positive charge on the wall we must have g (o-) > (o-) in order to have a positive... 

FIG. 7 Parsons-Zobel plot of 1/Q as a function of the inverse Gouy-Chapman capacitance 1 /Cqc- The plot is calculated analytically from Eqs. (54) and (85) at zero charge density. The straight line represents the case = a = For the upper... 

It is natural to consider the case when the surface affinity h to adsorb or desorb ions remains unchanged when charging the wall but other cases could be considered as well. In Fig. 13 the differential capacitance C is plotted as a function of a for several values of h. The curves display a maximum for non-positive values of h and a flat minimum for positive values of h. At the pzc the value of the Gouy-Chapman theory and that for h = 0 coincide and the same symmetry argument as in the previous section for the totally symmetric local interaction can be used to rationalize this result. 

Fig. 20.9 Experimental capacitance-potential curve for O-OOI m KCl and calculated curve using the Gouy-Chapman model. The experimental curve and the theoretical curve agree at potentials (us R.H.E.) near the p.z.c. Note the constant capacitance of 17 x 10 F m at negative potentials (after Bockris and Drazic )...

Measurements based on the Gouy-Chapman-Stem theory to determine the diffuse double-layer capacitance 10, 24,72, 74... 

FIGURE 10.2 Potential dependence of differential capacitance calculated from Gouy-Chapman theory for z+ = = 1 and various concentrations (1) 10 , (2) 10 , (3) 10 M. 

It can be shown that the differential capacitance of the diffuse layer, according to Gouy-Chapman theory, CGC, is given by ... 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

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. 

The Gouy-Chapman theory was tested experimentally on the basis of the doublelayer capacity measurements. This theory predicts a parabolic capacitance-potential relationship and a square-root dependence on concentration at constant e and T ... 

The Gouy-Chapman Model Provides a Potential Dependence of the Capacitance, but at What Cost ... 

However, even taking all these facts into account, this theory is not able to reproduce the capacitance-potential curves in the regions beyond the pzc proximity. The model seems, in fact, to be in sharp disagreement with the experimental behavior. The Gouy-Chapman theory might best be described as a brilliant failure. However, as will be seen, it represents an important contribution to a truer description of the double layer it also finds use in the understanding of the stability of colloids and, hence, of the stability of living systems (see Section 6.10.2.2). 

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