Electrocapillary parabola

Equation V-64 is that of a parabola, and electrocapillary curves are indeed approximately parabolic in shape. Because E ax tmd 7 max very nearly the same for certain electrolytes, such as sodium sulfate and sodium carbonate, it is generally assumed that specific adsorption effects are absent, and Emax is taken as a constant (-0.480 V) characteristic of the mercury-water interface. For most other electrolytes there is a shift in the maximum voltage, and is then taken to be Emax 0.480. Some values for the quantities are given in Table V-5 [113]. Much information of this type is due to Gouy [125], although additional results are to be found in most of the other references cited in this section. 

Fig. 20.5 Electrocapillary curves for KNO3, and different potassium halides showing how the former approximates to a parabola...

The dependence of the interfacial tension on the potential is termed the electrocapillary curve. It is convex to the axis of potential and often reminiscent of a parabola (see Fig. 4.2). 

The experimental y versus V curves obtained by electrocapillary measurements demonstrate this variation of surface tension y with the potential difference V across the cell. What is informative, however, is the nature of the variation (Table 6.2). A typical electrocapillary curve is almost a parabola (Fig. 6.53). The potential at which... 

The next step is obvious. Differentiate the y versus V electrocapillary curve at various values of cell potential, and plot these values of the slope (electrode charge) as a function of potential (Fig. 636). If the electrocapillary curve were a perfect parabola, then the charge (strictly, excess chaige density) on the electrode would vary linearly with the cell potential (Fig. 6.56). 

Fig. 6.56. When the electrocapillary y vs. E curve is a perfect parabola, the electrode-charge density varies linearly with potential difference. A further differentiation gives a capacity that is potential inde-pendent. However, experimental electrocapillary curves are not perfect parabolas.

If we measure electrocapillary curves of mercury in an aqueous medium which contains KF, NaF, or CsF, then we observe that the typical parabolas become narrower with increasing concentration. Explanation With increasing salt concentration the Debye-length becomes shorter, the capacity of the double layer increases. The maximum of the electrocapillarity curve, and thus the point of zero charge (pzc), remains constant, i.e., neither the cations nor fluoride adsorb strongly to mercury. 

Some results are given in fig. 3.48. At first sight the electrocapillary curves resemble parabolas but there must be considerable deviations because otherwise C has to be constant, which It is not, see fig. 3.49. 

Relationship (19.4), known as Lippmann equation, permits the evaluation of the excess of charge at the electrode surface from the electrocapillary curve y — y 4 )- Fot interfaces relatively simple such as the mercury/lM aqueous KCl interface, Eqn (19.4) results in a parabola with a maximum at dy/d0 = 0, i.e., for null charge at the electrode surface. This condition corresponds to the potential of zero charge (Pp ) for the electrode in the electrolyte solution. 

The charge q is equal to zero at the apex of the parabola, and the corresponding potential is called the point of zero charge (p.z.c.) or the potential of electrocapillary maximum (E ). Since q>0 for E > E, there is electrostatic attraction of anions by the electrode for q > 0 and attraction of cations for q < 0. Ions that are attracted near the electrode are repelled from each other and, consequently, the work needed to expand the interface is smaller than in the absence of electrostatic interaction with the electrode (q = 0). The interfacial tension thus decreases as q increases [1]. 

The integral capacitance varies with potential. It is higher on the positive side of the point of zero charge than on the negative side. The electrocapillary curve would be a second-degree parabola if C were independent of E [1]. 

Fig. 2.2, top). At the maximum of this parabola, the surface should be free from any excess charges, since every electric charging should generate repulsicm forces between molecules, which would decrease the surface tensirm. Craisequently, the first derivative of potential value at electrocapillary maximum, (Fig. 2.2, centre). A further relatirm depicted in Hg. 2.2 is... 

Were C to be a constant for a given electrode, identical electrocapillary curves would be obtained whatever the electrolyte dissolved in solution. Alkali metal nitrates do show almost identical parabolas, but other salts of given alkali metals each give their own characteristic curves (Fig. 7.7). 

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