Electrocapillary Phenomena

A. Frumkin. Electrocapillary phenomena and electrode potentials. Proceedings of Novorossiysk University. Odessa. 1919 (author’s abstract).

Let us denote by $\gamma$ the surface tension at the boundary mercury | solution, by $\varphi$ the potential difference between the solution and the mercury, and by $\varepsilon$ the quantity of electricity that must pass through the mercury and the solution when the surface of the mercury is increased by unity in order that the potential should remain constant. Then, as Lippmann has already shown,

\[ \frac{d\gamma}{d\varphi}=-\varepsilon . \tag{1} \]

Eq. (1) is usually considered applicable to the so-called anomalous electrocapillary curves (i.e., to curves with a maximum shifted from the position which it occupies in the case of a solution of sulfuric acid or another inactive electrolyte). However, the derivation of Eq. 1, which is a special case of Gibbs’s general equation for the surface layer, contains no restrictive assumptions. What is decisive is the experimental verification of Eq. 1, which can be carried out by the following methods:

1) Measurement of the quantities $\dfrac{d\gamma}{d\varphi}$ and $\varepsilon$. The quantity $\dfrac{d\gamma}{d\varphi}$ can be determined with the aid of a sensitive capillary electrometer, and the quantity $\varepsilon$ by measuring the current strength $i$ that flows on short-circuiting the following circuit:

Mercury flowing in drops from a tube | solution | quiescent mercury.

If the surface area of the drops formed per unit time is denoted by $s$, then $\varepsilon=i/s$. Such measurements were carried out by the author for a number of solutions; the results are given in the following table (in coul./cm²):

2) Measurement of the quantity $-\dfrac{d\varepsilon}{d\varphi}=-\dfrac{d^2\gamma}{d\varphi^2}$ (polarization capacitance). Similar measurements were made chiefly by Krüger, who found a noticeable discrepancy between the observed and calculated values of the polarization capacitance. A recalculation of the data underlying the computation of this quantity shows, however, that the discrepancy is much smaller than Krüger assumed and lies within the limits of experimental error.

3) Zero solutions. In zero solutions (i.e., those in which the quantity \(\xi = 0\); Nernst—Palmer) the quantity \(\dfrac{\partial \gamma}{\partial \varphi}\) must also be equal to zero. The measurements of Smith and Moss show that this is indeed the case, both for inactive and for active inorganic electrolytes.

4) Dropping electrodes. With an increase in the surface of the isolated mass of mercury, the content of mercury ions in the solution approaches the value corresponding to the zero solution. Consequently, if eq. (1) is correct, the potential of the dropping electrode must always coincide with the potential corresponding to the maximum of the electrocapillary curve. This conclusion is confirmed by the measurements of a number of investigators in the case of inactive and active inorganic electrolytes. The author carried out a series of measurements with solutions containing surface-active organic substances. The results are given in the table below. All potentials are referred to the normal calomel electrode.

Analogous results have also been obtained in the case of nonaqueous solutions. Thus, experimental verification gives, in all cases, data that confirm the correctness of eq. 1. Indeed, a detailed analysis of the theories that stand in opposition to Nernst’s point of view (the theory of Kossel, etc.) reveals in the latter a number of internal contradictions.

Finally, \(\xi\) in eq. 1 is evidently equal to \(\varepsilon + \Gamma'_{Hg}F\), where \(\varepsilon\) is the charge of a unit surface of mercury, and \(\Gamma'_{Hg}\) is the amount of mercury salt, in gram-equivalents per cm.\(^2\), adsorbed on the surface of the mercury, so that

\[ \frac{\partial \gamma}{\partial \varphi}=\varepsilon+\Gamma'_{Hg}F . \]

Krüger assigns a large value to the term \(\Gamma'_{Hg}F\), using it to explain the anomalies of electrocapillary curves; a simple calculation shows, however, that for the experimentally accessible part of the curves the quantity \(\Gamma'_{Hg}F\) is immeasurably small in comparison with \(\varepsilon\), so that eq. (1) is practically always reduced to the equation

\[ \frac{\partial \gamma}{\partial \varphi}=\varepsilon . \tag{2} \]

It is also significant that, with the aid of eq. (2), as Gouy showed, one can, without invoking the notion of the adsorption of ions and neutral molecules, explain all the observed anomalies of electrocapillary curves.

Interesting results are obtained in the case of a solution containing only one electrolyte; combining eq. (2) with the Gibbs adsorption equation for this electrolyte, one can arrive at the following conclusions: when the concentration of the dissolved electrolyte is decreased, the descending branch of the curve shifts to the right (i.e., toward increasing \(\varphi\)), and the ascending branch to the left (toward decreasing \(\varphi\)); when the concentration is decreased by a factor of 10 (assuming complete dissociation of the electrolyte), the magnitude of the displacement is

\[ \frac{0.059}{n}\ \text{v.}, \]

where \(n\) is the valence of the cation in the case of the descending branch and of the anion—in

in the case of an ascending one; the sign \(=\) must be taken in the case when the ions are inactive, and in the opposite case the sign \(>\). Experiment fully confirms these conclusions. The general Gibbs equation for the surface layer, of which eq. 1 is a particular case, makes it possible to give a complete theory of electrocapillary phenomena also in those more complicated cases when, instead of pure mercury, we are dealing with amalgams.

The author determined electrocapillary curves for a number of nonaqueous solutions, namely: n. and 0.1 n. \(NH_4NO_3\), n. \(NaBr\) and n. \(NaJ\) in \(CH_3OH\); 0.2 n. \(NH_4NO_3\), n. \(LiCl\) and n. \(NaJ\) in \(C_2H_5OH\); 0.9 n. \(LiNO_3\), 0.5 n. \(LiCl\), n. \(NH_4CNS\) and \(CH_3COCH_3\); n. \(NH_4CNS\) and 1.6 n. \(NaJ\) in \(C_5H_5N\). It proved that in nonaqueous solutions, as in aqueous ones, inorganic cations are surface-inactive; anions, however, are, generally speaking, active, and the order of activity is in general the same as in aqueous solutions. The activity of the anion does not affect the position of the descending branch; when the electrolyte concentration is changed, the branches of the curve are displaced, as in the case of aqueous solutions. The capacity of the double layer in the solutions investigated proved to be considerably smaller than the capacity in aqueous solutions of the same concentration. When water is added to alcoholic solutions, a strong lowering of the surface tension at the end of the descending branch of the curve occurs, while in the region of the maximum a weak increase of the surface tension is observed.

According to eq. 2 and to the above-cited data on capillary electrometers in zero solutions, at the maximum of the electrocapillary curve the charge of the mercury surface is equal to zero, so that, when a fresh surface of mercury is formed, no exchange of ions between the metal and the solution takes place. The potential difference solution | metal cannot, however, in this case, generally speaking, be equal to zero, since the position of the maximum varies strongly in different solutions. Consequently, besides the process of exchange of ions, there exist other processes which can lead to the appearance of a potential difference between the solution and the metal. Such processes are the adsorption of ions and neutral molecules, as Gouy first pointed out. From this point of view, the concentration of mercury ions in the solution determines only the total value of the potential difference between the solution and the mercury, but by no means the mode of its origin.

Finally, the question whether the potential difference solution | mercury can be considered equal to zero, at least in the case of the “ideal” maximum (i.e. one in which the mercury surface is free from any adsorbed ions and molecules, and the solvent molecules themselves are not sources of potential difference), can be answered only by comparing the position of such an “ideal” maximum in different solvents. Extrapolating the results of his measurements over nonaqueous solutions, the author arrives at the following values determining the position of the “ideal” maximum of electrocapillary curves in different solvents with respect to the normal aqueous calomel electrode: \(H_2O\)—0.56, \(CH_3OH\)—0.36, \(C_2H_5OH\)—0.30, \(CH_3COCH_3\)—0.17, \(C_5H_5N\)—0.04 (?). Thus, if the ionic layer at the boundary solvent | mercury is the source of a certain potential difference, which could be called “contact,” then, for example, mercury in “contact” with acetone is charged by \(0.56 - 0.17 = 0.33\) v more positively than in “contact” with water.

The data of the investigation of electrocapillary phenomena compel us to change the generally accepted view of the solution pressure of metals and to distinguish strictly between two entirely different concepts which are included in this term. By the solution pressure of metals one understands:

1) The osmotic pressure of mercury ions, corresponding to that concentration of them at which the potential difference solution | mercury is equal to zero. This constant (for dilute solutions), as yet immeasurable experimentally, we shall call the thermodynamic solution pressure.

2) The osmotic pressure of mercury ions, corresponding to that concentration of them at which the quantity \(\xi\) is equal to zero. This quantity, accessible to measurement, we shall call the osmotic or electrocapillary solution pressure.

The osmotic elasticity of a solution varies within the widest limits; depending on the presence in the solution of one or another adsorbed substance, it generally differs completely from the thermodynamic elasticity of the solution. Thus, the latter quantity for mercury in water is greater than in alcohol, whereas for osmotic elasticity the opposite relation holds.

A. Frumkin.