Diffuse double layer differential capacity

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

FIG. 8 Inverse differential capacity at the zero surface charge vs. inverse capacity Cj of the diffuse double layer for the water-nitrobenzene (O) and water-1,2-dichloroethane (, ), interface. The diffuse layer capacity was evaluated by the GC ( ) or the MPB (0,)> theory. (From Ref. 22.)... 

If qM is evaluated experimentally, e.g. from the integration of differential capacity curves, A02 can be calculated using eqn. (44) of the diffuse double layer theory. Figure 3 shows the variation of A02 with... 

It should be noticed that the Galvani potential difference, A(p2, cannot be measured directly but its value can be derived from the Gouy-Chapman theory of the diffuse double layer. If the excess charge in the metal, q , is determined experimentally, that is, from the integration of differential capacity curves, then for a 1 1 electrolyte of concentration c, then A(p2 can be calculated ... 

Since the capacity of the diffuse double layer is in series with the Helmholtz double layer, the best chance to see it in the measurements requires Cd < Ch. Equations (2.50) and (2.54) indicate that Cd increases rapidly with Q. In accordance with this conclusion, a minimum of the differential capacity was found in measurements on metals in very dilute electrolyte solutions (<10 M), which is an indication for the absence of excess charge on the electrode. 

Differential capacity Cp = dO/dE = -iPy/dE of Hg in NaF solutions of different concentrations with a peak for c < 0.01 M showing the influence of the diffuse double layer and the potential of zero charge Epzc- (From Lecoeur, J. and BeUier, J.P., Electrochim. Acta, 30,1027,1985.)... 

Fig, 6 gives the differential capacities calculated for the diffuse double layer. 

For a further interpretation of the adsorption curves of Fig 31 and for a comparison widi the results on the mercury surface it is necessary to derive the differential capacity of the double layer by differentiation of the adsorption (charge) with respect to the double layer potentiaL The capacities obtained arc given in Fig 33a and the capacities of the double layer on mercury against NaF solutions in Fig 33b The two sets of curves resemble each other very much especially for dilute solutions. As in these solutions the diffuse parts of the double layer are preponderant and there is every reason to expect that the diffuse double layers will be identical for the two cases the adsorption scale in Fig 31 and therewith the capacity scale in Fig 33 have so been adjusted that the capacities for 0 001 N solutions at the ero point of charge are identical ... 

An important quantity with respect to experimental verification is the differential capacitance of the total electric double layer. In the Stern picture it is composed of two capacitors in series the capacity of the Stem layer, Cgt, and the capacitance of the diffuse Gouy-Chapman layer. The total capacitance per unit area is given by... 

The PZC may also be seen on differential capacity curves when specific adsorption is absent and the electrolyte concentration is low (< 0.01 M). At this point the capacity of the diffuse part of the double layer is a minimum and can fall below that of the compact or inner layer. As a result the total double layer capacity may... 

Area, constant, optical absorption Activity, absorption coefficient Debye length Cyclic voltammogram Capacitance / j,F Double layer capacity / 0.F Differential double layer capacity Integral double layer capacity Concentration / M Surface concentration Bulk concentration / M Diffusion coefficient / cm s ... 

---