MEASUREMENT OF THE INTERFACIAL TENSION OF LIQUID INTERFACES FROM THE SHAPE OF A PENDANT DROP

II. MERCURY IN ELECTROLYTE SOLUTIONS

V. I. MELIK-GAIKAZIAN, V. V. VORONCHIKHINA, E. L. ZAKHAROVA

(Presented by the scientific seminar of the Department of Physical and Colloid Chemistry, TPI)

In the preceding communication [1], the pendant-drop method [2, 3] was used to determine the surface tension of mercury in vacuum. The value obtained, coinciding with the most reliable results determined by other methods, testified to the sufficient accuracy of the compiled tables [3], to the rationality of the measurement procedure developed, and to the possibility of applying it to the recording of electrocapillary curves from the shape of drops of a mercury electrode while simultaneously recording the differential-capacitance curves of the double electric layer.

As is known, capacitance and electrocapillary measurements (which supplement one another) provide important information on the structure of the double electric layer. From the standpoint of the identity of experimental conditions, the most reliable data should be obtained by simultaneous study of the dependence of the surface tension and the differential capacitance of the electrode on potential. A number of investigations in this direction have been carried out [4, 5, 6, 7, 8] using slowly dripping mercury drops; the relative values of the surface tension were calculated from the dropping period or from the weight of the detached drops, i.e., under nonstationary conditions.

The method proposed in the present article for estimating surface tension from the shape of a pendant mercury drop, with simultaneous measurement of the double-layer capacitance, makes it possible to conduct investigations both on freshly formed drops and on drops hanging stationary for a time sufficient to establish adsorption equilibrium at the electrode surface. In addition, this method yields absolute values of the surface tension $\sigma$, invariant with respect to the wettability of the walls of the capillary holding the drop. The method promises to be useful in studying the adsorption of organic and inorganic substances on the polarized surface of mercury, in studying sparingly soluble films formed on the surface of mercury electrodes, in studying the structure of amalgams, etc.

Apparatus, reagents, measurement procedure

For measuring the differential capacitance of the double electric layer on mercury in electrolyte solutions and for simultaneous photographing of a stationary drop, a glass cell with optical glasses carefully ground to it was used (Fig. 1). The pendant drop, serving as the cathode, was extruded from a capillary with

Fig. 1. Measurement setup and experimental cell

with an internal diameter of 1.0–2.0 mm. A platinum mesh, arranged symmetrically around the mercury drop, served as the auxiliary electrode. All potential measurements were carried out relative to a normal calomel electrode (NCE); the temperature of the solutions during the experiments was 22°C.

The differential capacitance was measured by the impedance-bridge method. Simultaneously with the constant voltage, an alternating voltage with an amplitude of 5 mV was applied to the electrode. The frequency of the alternating current was 200 and 1000 Hz.

As electrolytes, 0.5 M Na₂SO₄ and 1 M KCl were used, both pure and containing additions of surface-active substances. Great attention was paid to the purity of the mercury, glassware, water, and reagents.

tubes. The mercury was first purified chemically by passing it successively, in the form of small droplets, through columns containing solutions of KOH, Hg₂(NO₃)₂, and H₂SO₄, and was then distilled under vacuum. Chemically pure salts were calcined for several hours at \(t=800^\circ\mathrm{C}\). Before use, the cell and the flasks for preparing solutions were kept in concentrated sulfuric acid and then thoroughly rinsed with boiling distilled water obtained in an apparatus with a heated receiver and equipped, unlike the construction described earlier [9], with a higher dephlegmator and a drop trap.

The form of the capacitance curve corresponding to a pure solution (Fig. 2) did not change over the course of 3 days, which served as an indication of the purity of the reagents and mercury used.

The shape of the surface of the drops was evaluated from negatives of their images by the method of Andreas, Hauser, and Tucker [2], developed for many fixed levels [3]. When using drops 2–2.5 mm in diameter and observing the necessary precautions associated with the accuracy of estimating the photographic magnification and allowing for possible distortion, the values of \(\sigma\) can be obtained with an accuracy of \(1\ \mathrm{dyn/cm}\), i.e., 0.2% of its absolute value for mercury in a pure solution. Measurements on negatives with an image of the drop were made using a UIM-21 microscope.

Results and Discussion

Figure 2 presents electrocapillary curves calculated from the shape of a pendant drop, and differential-capacitance curves obtained simultaneously in 1 M KCl solutions containing different amounts of n-hexyl alcohol. With the addition of hexyl alcohol, the surface tension of mercury in the region of the maximum of the electrocapillary curve decreases; the differential capacitance also decreases, and the adsorption region bounded by the desorption peaks expands. Addi—

Fig. 2. Differential-capacitance curves of the double layer and electrocapillary curves recorded simultaneously on a mercury dropping electrode in a 1 M KCl solution containing n-hexyl alcohol at the following concentrations (M/l): 0; 0.001; 0.005; 0.015 (sat.); 0.015 + kerosene emulsion.

addition to a solution of 1 M KCl + \(1.5 \cdot 10^{-2}\) M \(n\)-hexyl alcohol of a kerosene emulsion (i.e., a mixture of hydrocarbons with molecules of different structure, size, and composition) causes a sharp decrease in the surface tension of mercury and the appearance of several additional peaks on the capacitance curve, which apparently indicates the formation of multilayers of adsorbed molecules.

Obtaining electrocapillary curves for mercury in the presence of a kerosene emulsion, as well as of any reagent that changes the wettability of the capillary walls, is impossible by means of the capillary electrometer, which is at present widely used for studying adsorption on mercury. Methods based on estimating the period of mercury dripping or the weight of the drops detached from it at different polarizations are also inapplicable, owing to the incomplete static character of these methods and to the possibility that adsorption equilibrium, when working with the indicated substances, will not be attained to a sufficient degree, for example because of their viscosity, low solubility, etc.

At the same time, by the proposed method these measurements can be readily performed. This opens new prospects for using the method of determining surface tension from the shape of a pendant drop in studying the action of flotation reagents, passivating films, adsorption of polymers, etc.

Table 1 gives the values of the surface tension of mercury in 0.5 M \(Na_2SO_4\), obtained by calculation from the drop shape, and also by double integration of the differential capacitance curve of the mercury electrode (according to Lippmann’s equation), measured in the same solution. The integration was carried out numerically, by the trapezoidal formula.

Table 1

Comparison of the values of the surface tension of mercury obtained by calculation from the differential-capacitance curve and from measurements of the shape of a mercury drop

Of particular interest is the value of \(\sigma\) obtained in a pure 0.5 M sodium sulfate solution at the electrocapillary maximum (\(-0.480\), versus N.C.E.), which proved to be equal to 431.8 dyn/cm. This value exceeds by approximately 1.1% the value previously obtained by other authors [10—12] from the shape of large sessile drops. The observed discrepancy may be due to various causes, for example, distortion, whose influence increases with increasing siz-

of the dimensions of the object being photographed and with the departure of the contour of its shape from a circle, insufficient purity of the solutions used by the authors cited, and also causes whose nature has not yet been clarified, but whose effect reduces to the fact that the branches of the electrocapillary curve obtained from the shape of a small pendant drop have a somewhat steeper course than the branches of the curve calculated from measurements of the double-layer capacitance (dashed curve 5 in Fig. 2) or constructed from data obtained by means of Gouy’s electrometer. When the maxima of the experimental and calculated curves are superposed, the difference in the values of $\sigma$ at the ends of these branches reaches 3–4 dyn/cm (Table 1).

It should be noted that the values of $\sigma$ at the maximum of the electrocapillary curve, close to 427 dyn/cm, were obtained by us every time when a chromic mixture was used to clean the walls of the apparatus and the glassware used in the work. There are indications in the literature of good adsorption of bichromate ions on glass; therefore, for example, the use of chromic mixture for washing glassware in the analysis of trace elements is not recommended [13].

The value 431.8 dyn/cm is the mean of many measurements differing from it by no more than 1 dyn/cm. Within these limits this quantity, like the simultaneously measured double-layer capacitance, remained unchanged for several hours when the same drop was used. The same value was obtained when electrocapillary curves were taken from the shapes of mercury drops formed in the solution after the start of the experiment at various time intervals—from one hour to three days. This can probably testify to the purity of the materials used and, consequently, to the reliability of the data obtained.

The authors express their deep gratitude to Academician A. N. Frumkin and Doctor of Chemical Sciences B. B. Damaskin for discussing the results obtained and for valuable advice.

REFERENCES

1. V. I. Melik-Gaikazyan, V. V. Voronchikhina, E. A. Zakharova. (This collection).
2. J. M. Andreas, E. A. Hauser, W. B. Tucker, J. Phys. Chem., 42, 1001, 1938.
3. V. I. Melik-Gaikazyan. Izv. TPI, 136, 110, 133, 1965.
4. M. Breiter, P. Delahay. J. Am. Chem. Soc., 81, 2938, 1959.
5. R. J. Meakins. J. Appl. Chem., 15, No. 9, 416, 1965.
6. J. O’M. Bocris, K. Müller, H. Wroblowa, Z. Kovac. J. Electroanal. Chem., 10, No. 5–6, 416, 1965.
7. Ch. Chacbet, J. Epelboin, J. C. Zestrade, P. Ravel. C. R. Acad. Sci., C, 264, No. 18, 1524, 1967.
8. J. Clavilier, C. R. Acad. Sci., C, 263, No. 3, 191, 1966.
9. V. I. Melik-Gaikazyan. Zavod. labor., 16, 242, 1950.
10. M. G. Gouy. Ann. Phys., 6, 5, 1916.
11. C. A. Smolders, E. M. Duyvis. Rec. Trav. Chim., 80, 635, 1961.
12. J. N. Butler. J. Phys. Chem., 69, 3817, 1965.
13. Collection Analysis of Trace Elements, ed. by J. Yoe and H. Koch, IL, Moscow, p. 596, 1961.