Communication—A Linear Equation Relating Interfacial Tension and Isotension Potentials to Describe Asymmetry in Electrocapillary Curves

It has been known for more than a century that the interfacial tension of mercury dipped in electrolyte solutions changes with applied potential following a near parabolic course known as the electrocapillary curve. Solution components which are adsorbable on mercury produce asymmetric curves with respect to the potential at the electrocapillary maximum. A simple mathematical description of this asymmetry has, to date, excited and eluded many scientists. Here, a simple new linear relation which describes the electrocapillary curves for the existing data has been shown for the ﬁrst time. (Hg), silver,

Mercury (Hg), also known as quick silver, derives its symbol from its name 'hydrargyrum', meaning water-silver. It has a high surface tension in both air (20 • C, 486.5 dyne.cm −1 ) and water (20 • C, 415 dyne.cm −1 ). 1 Its electrical conductivity as a liquid metal makes it an ideal renewable electrode in polarography. 2 The change in the interfacial tension (γ) of mercury in solutions at different applied voltages (E) fascinated pioneers like Lippmann 3 and Guoy, 4,5 and the parabolic γ vs E electrocapillary curves have since been of great value in the study of interfacial phenomena.

Theoretical
A large body of literature exists on the properties and study of electrocapillary curves. For a detailed introduction, see References 6 and 7. The parabolic dependence of γ on E is usually described by 2 where γ m is the interfacial tension at the electrocapillary maximum (ecm) corresponding to the potential E m and C = − d 2 γ/dE 2 is the specific capacity. In the ideal case of a parabola, C must be a constant. However, this is not the case because the ionic components of the solution interact with the charged mercury surface in different ways at different potentials. The electrocapillary curve is therefore not a symmetrical parabola; see for many examples References 2,6 and 7. This asymmetry has been resolved mathematically by many researchers. To cite a recent example, the γ = f (E) curves are described by an empirical polynomial of the sixth order. 8 Ionic components like halides, which adsorb on the positively charged mercury surface to the left of the electrocapillary maximum, lower the γ m values and shift the corresponding potential to negative values. This short article is confined to presenting a new, simple and hitherto not known linear relation between the surface tensions and the corresponding isotension potentials, using the existing data 9 for the electrocapillary curves for aqueous KBr solutions. It is hoped that further analyses of results with more solutions will bring out the significance of the slopes of these straight lines and information on the interaction of the dissolved species with mercury at electrified interfaces.

Results and Discussion
Here, the existing data 9 for aqueous solutions of KBr have been used to show a simple linear relation that describes the asymmetry of the curves. For a preliminary report of these results, see Reference 10. The data for γ at various potentials (-E, with reference to 0.1 M KCl calomel electrode, with 0.1 M KBr bridge) for aqueous solutions of KBr at 25 • C taken from Reference 9 are assembled in Table I. Figure 1 shows the graphs of γ as a function of E. It can be seen that the curves are not symmetrical parabolas and that the electrocapillary maximum (ecm) values of γ m and E m shift with the concentration as shown. In this work, the author examined the relationship between the two isotension potentials E(+) and E(−) on either side of the electrocapillary maximum for the same value of γ. The potentials E(+) and E(−) at various values of γ were obtained from graphs of γ vs E drawn on a large scale. These are given in are given in Table II along with the following shifts of isotension potentials [ 2 ] and the ratios, R(+) and R(−),    From the data in Table II, it can be seen that R(+) increases with increasing γ for any given concentration, and also that it increases with concentration for any given value of γ. On eliminating the constants by using the values γ m and R(+) m for the ecm, one gets the simple linear relation, where K s = dγ/d(R(+) = constant (dyne.cm −1 ) is the slope of the γ vs R(+) straight lines. A proper interpretation of the slopes can be made after analyzing the electrocapillary curves for other adsorbable halides.
The last rows in a-c in Table II show the ratios E(+)/ E(−) = R(+)/R(−). It can be seen that with increasing concentration, these ratios increase. Graphs of γ vs these ratios and of γ vs E are also   nearly linear, but Eq. 7 seems to be the good choice for the data used here.

Summary
A new solution for the long-unsolved problem of the asymmetry of γ vs E electrocapillary curves has been provided in terms of the isotension potentials, E(+) and E(−) (see Eq. 2). Using the existing data 9 for aqueous KBr solutions, it is shown here for the first time that γ vs the potential ratio R(+) (see Eq. 3) follows the simple linear Eq. 7, where, K s is a constant independent of γ and E, but dependent on the solute (s) and its concentration. Similar results, which confirm Eq. 7, were obtained for HCl, HClO 4 , and Na 2 SO 4 . These will be presented in a future longer paper.