Surface charge density, electrocapillary curve

Which is the preferred approach Should one obtain the surface charge density, for example, by differentiating the electrocapillary curve or by integrating the differential capacitance curve Theory does... 

In agreement with the Lippmann equation (III.21), the differentiation of the electrocapillary curve, o(cp), with respect to cp yields the surface charge density as a function of the surface potential, the second differentiation yields the value of the differential capacity, which can be compared with the results of the EDL theory. Based on such a comparison one can draw conclusions with respect to the validity of theoretical models and look for ways for further improvements. 

Fig. 3. Comparison of the surface charge densities in the aqueous phase obtained by differentiation of the electrocapillary curve (o) and by integration of the differential capacity curve ( ) for the interface between O.lmoldm- TBATPB nitrobenzene solution and 0.1 mol dm LiCl aqueous solution...

The values of surface charge density obtained by numerical differentiation of the electrocapillary curve agreed well with those obtained by numerical integration of the differential capacity curve [17,29] (Fig. 3). These results indicate that the interface between a nitrobenzene solution of TBATPB and an aqueous solution of LiCl actually behaves as an ideal-polarized interface in a certain potential range and also that the differential capacity measurements should give essentially the same information on the electrocapillarity and the double layer structure of nitrobenzene/water interfaces as the electrocapillary curve measurements, provided that their electrocapillary maximum potential which is now equal to the potential of zero charge (pzc) and interfacial tension at the pzc (y J known. 

These equations clearly show that the the slope of the electrocapillary curve of nonpolarized interface does not give the surface charge density but the relative surface excess of ionic components, as defined by Eq. (18) for case Ilb. In other words, the electrocapillary maximum potential does not correspond to the potential of zero charge . An approach to investigate the surface charge density and the double layer structure may be predicted as follows. When the values of the second terms of the right-hand sides of Eq. (18) (that is, the and Tnb values), are known or estimated on reasonable argument, Fd and F(so that by Eq. (19)) can be found from the slope... 

Using a drop time method for the determination of interfacial tension and a four-electrode potentiostat to polarize the interface, Kakiuchi and Senda measured electrocapillary curves for ideally polarized systems, in particular for the interface between an aqueous solution of lithium chloride and a solution in nitrobenzene of TBATPB. They showed that the surface charge density, Q, obtained by differentiation of the electrocapillary curve was equal to that calculated from the integration of the corresponding differential capacity versus potential curves. This demonstrated the validity of the Lippmann equation for the polarized ITIES ... 

Kakiuchi and Senda [36] measured the electrocapillary curves of the ideally polarized water nitrobenzene interface by the drop time method using the electrolyte dropping electrode [37] at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. An example of the electrocapillary curve for this system is shown in Fig. 2. The surface excess charge density Q, and the relative surface excess concentrations T " and rppg of the Li cation and the tetraphenylborate anion respectively, were evaluated from the surface tension data by using Eq. (21). The relative surface excess concentrations and of the d anion and the... 

Fig. 3.3 Schematic plots of the double layer region, (a) Electrocapillary curve (surface tension, y, vs. potential) (b) Charge density on the electrode, aM, vs. potential (c) Differential capacity, Cd, vs. potential. Curve (b) is obtained by differentiating curve (a), and (c) by differentiation of (b), Ez is the point of zero...

Let us briefly review which of the listed values and in what manner can be determined. It is possible to calculate the distribution of complex species in the solution, that is, bulk concentrations or activities, by means of the methods discussed in Chapter 1. Besides, the composition of solutions can be changed so that Eqs. (7.8)-(7.10) would become simpler. For example, one can use a series of solutions with constant concentration of free ligand for which i In l = 0- In the series of isopotential solutions (see Section 2.1), the condition dlna = 0 holds. By differentiation of the electrocapillary curve with respect to E for a solution of constant composition, one can obtain the value of the charge density e and use Eq. (7.6) for the calculation of total adsorptions Fj x nd Flx. Thus, electrocapillary measurements, as well as a number of other methods (radioactive indicator, surface stress, piezoelectric, extensometer methods), give information only about the total amounts of adsorbed metal and ligand. Consequently, for further solution of the problem posed, some model images are necessary. 

---