V. A. IGOLINSKII, V. F. YANKAUSKAS, V. I. VERESHCHAGIN

EFFECT OF CERTAIN FACTORS ON THE DEPTH OF THE ANODIC PEAK IN AMALGAM POLAROGRAPHY WITH ACCUMULATION ON A MERCURY FILM ELECTRODE

(Presented by the scientific seminar of the Department of Physical Chemistry)

On the basis of certain theoretical considerations we have shown [1] that the depth of the anodic peak in amalgam polarography, and consequently the sensitivity as well, depends strongly on the geometric shape of the electrode.

As an electrode for determining \(10^{-13}\)—\(10^{-12}\) moles of impurities by the method of amalgam polarography with preliminary accumulation on a stationary electrode, a mercury film electrode was proposed [2]. Subsequently, the theory of amalgam polarography with accumulation on a mercury film electrode was developed and equations were derived for the current-voltage curves obtained at this electrode [3].

Theoretical and experimental studies have shown the very high sensitivity (2–3 orders of magnitude higher than the sensitivity of a stationary dropping electrode) and the high resolving power of the film electrode. These qualities of the film electrode are of great value for practical purposes in determining very small impurities (down to \(10^{-9}\%\)) in semiconductor and especially pure materials.

In order to confirm the theory and to develop a procedure for determining microimpurities using a mercury film electrode, as well as to select optimal conditions in polarography, it was necessary to study the effect of a number of factors on the depth of the anodic peak at the film electrode.

We studied the effect of the concentration of the metal in solution, the time of preliminary electrolysis, and the rate of change of the applied voltage during recording of the polarogram on the depth of the anodic peak.

In studying the effect of the concentration of the metal in solution on the depth of the anodic peak, it was shown—as was to be expected on the basis of theoretical considerations—that the peak depth is directly proportional to the concentration of metal ions in solution. An analogous dependence is also observed for the stationary mercury dropping electrode. An example of the dependence of peak depth on concentration (a calibration graph) is given for zinc against a background of \(0.1\) M \(NH_4Cl\) in Fig. 1.

From the calibration graph one can see the very high sensitivity of the electrode, since peaks suitable for practical measurements are obtained even at metal-ion concentrations on the order of \(10^{-11}\) mole/liter.

The proportionality between the peak depth and the concentration determines the possibility of analytical use of the electrode. Figure 2 shows the dependence of the zinc peak depth on the time of electrolysis.

Fig. 1. Dependence of the height of the anodic peak on the concentration of zinc in solution. Background: 0.1 M NH₄Cl; solution volume 10 ml; electrode—a silver wire with a mercury film 2 microns thick; electrode area 0.5 cm²; preliminary electrolysis time 5 min at a potential of −1.55 V; rate of potential drop 16 mV/sec; galvanometer sensitivity 0.55 mA/cm.

From the graph it is evident that for short times of preliminary electrolysis (up to 15 min) there is a direct proportionality between the peak depth and the electrolysis time, which is violated when the electrolysis time exceeds 15 min.

This violation is due to depletion of the solution during electrolysis. A similar phenomenon is also observed for the stationary dropping mercury electrode. The most interesting data were obtained by us in studying the influence of the rate of change of potential on the depth of the anodic peak.

Ševčík and Randles, studying the cathodic reduction of cations in the case of semi-infinite diffusion, obtained the equation of the current–voltage curve for a linearly changing potential. From the Ševčík–Randles equation it follows that the peak depth is proportional to the square root of the rate of change of potential. This was confirmed by them for a number of peaks. In the case of the semi-infinite character of diffusion, the Ševčík–Randles equation should also be valid for anodic processes of amalgam dissolution. Thus, in this case as well there should be a proportionality between the depth of the anodic peak and the square root of the rate of change of potential.

However, from the equations we have obtained for the volt-ampere curves, derived with allowance for the limited character of diffusion, it follows that, at low rates of change of potential, the depth of the anodic peak must be proportional to the first power of the rate of change of potential.

Fig. 2. Dependence of the height of the anodic zinc peak on the electrolysis time (conditions, see Fig. 1).

This dependence is observed up to a certain “limiting” value of the rate, and then gradually changes, approaching the dependence following from the Ševčík—Randles equation.

The depth of the anodic peak will be proportional to the square root of the rate of change of potential if, during the recording of the peak, the diffusion front does not have time to propagate to the electrode boundaries. The time of advance of the diffusion front can be written approximately as follows [4]:

\[ t \approx x^2 / D, \tag{1} \]

where \(t\) is the time for advance of the diffusion front over the distance \(x\);
\(D\) is the diffusion coefficient.

The time of recording the peak may be taken as the time of change of the potential from the equilibrium value to the peak potential

\[ t_1 = \left| \frac{\varphi_{\mathrm{p}} - \varphi_{\mathrm{r}}}{W} \right|, \tag{2} \]

where \(\varphi_{\mathrm{p}}\) is the peak potential;
\(\varphi_{\mathrm{r}}\) is the equilibrium potential;
\(W\) is the rate of change of potential.

If the inequality \(t_1 < t\) is fulfilled, that is,

\[ \left| \frac{\varphi_{\mathrm{p}} - \varphi_{\mathrm{r}}}{W} \right| < x^2 / D \quad \text{or} \quad W > \left| \frac{D(\varphi_{\mathrm{p}}-\varphi_{\mathrm{r}})}{x^2} \right|, \tag{3} \]

where \(x\) is the linear dimension of the electrode, then proportionality of the peak to \(\sqrt{W}\) will be observed. Thus, for all \(W\) greater than

\[ W' = \left| \frac{D\varphi_{\mathrm{p}}-\varphi_{\mathrm{r}}}{x^2} \right| \]

the Ševčík—Randles equation will be valid.

For \(W\) values considerably smaller than \(W^1\), proportionality of the peak of the first degree of \(W\) will be observed. To verify the latter assertion, we studied the effect of the rate of change of the potential over a wide range of variation on the depth of the anodic peaks obtained on the film electrode, using as examples the anodic waves of zinc, cadmium, and lead.

The results of the study are given in Tables 1, 2, and 3 and in Figs. 3, 4, 5.

Table 1

Effect of the rate of change of the potential on the depth of the anodic wave of Zn

Table 2

Effect of the rate of change of the potential on the depth of the anodic wave of Cd

Fig. 3. Dependence of the zinc peak height on the rate of potential change.

Fig. 4. Dependence of the cadmium peak height on the rate of potential change.

Fig. 5. Dependence of the lead peak height on the rate of potential change.

As can be seen from the figures, the dependence predicted theoretically is indeed observed.

Table 3

Effect of the rate of potential change on the depth of the anodic peak of Pd

This dependence makes it possible to resolve the question of the optimum value of the rate of potential change in polarography.

Previously, proceeding from the Ševčík—Randles equation, it was considered necessary to use as low a rate of potential change as possible, since in this case the ratio of the peak height to the interfering capacitive current increases.

Now, on the basis of a more exact equation, it may be said that the optimum value of the rate of potential change will be precisely that “limiting” value of the rate of change up to which the condition of proportionality between the peak height and the rate of potential change is fulfilled. This is an important practical conclusion.

REFERENCES

1. V. A. Igolinskii, A. G. Stromberg. On the maximum sensitivity of the amalgam polarography method with accumulation and ways of increasing it. Zav. lab. (in press).

2. V. A. Igolinskii, A. G. Stromberg. On increasing the sensitivity of the amalgam polarography method. Proceedings of the Second All-Union Conference on Polarography, Kazan, 1962.

3. V. A. Igolinskii. Theory of amalgam polarography on a mercury film electrode. ZhVKh (in press).

4. Darken, Gurry. Physical Chemistry of Metals. Metallurgizdat, 1961.