On Methods for Calculating the \(\psi'\)-Potential in the Presence of Organic Substances Adsorbed on the Electrode

A. G. Stromberg, V. E. Gorodovykh, T. V. Gomza

The reaction center of an electroactive particle entering into reaction is most often located near the outer Helmholtz plane; therefore the potential corresponding to this plane \((\psi')\) is an important factor influencing the kinetics of electrode processes. Molecules of organic surface-active substances (SAS) adsorbed on the electrode change the structure of the electrical double layer and the magnitude of the \(\psi'\)-potential, thereby exerting a substantial influence on the kinetics of electrode processes [1–3]. Correct determination of the adsorption \(\psi'\)-potential is one of the most important tasks in studying the effect of adsorption of organic compounds on the kinetics of electrode processes.

In the absence of specific adsorption, the magnitude of the \(\psi'\)-potential is determined, according to the Gouy–Chapman theory, from the following relation:

\[ \psi'=\frac{2RT}{zF}\operatorname{arcsh}\left[\frac{\varepsilon}{(8RTDC_0)^{1/2}}\right]; \tag{1} \]

where \(C_0\) is the electrolyte concentration in the bulk of the solution;
\(D\) is the dielectric permittivity of water;
\(\varepsilon\) is the charge of the electrode surface.

This method has become widely used for determining the \(\psi'\)-potential of ionic electrical double layers [5]. The relation was used to determine the \(\psi'\)-potential in the presence of specific adsorption. However, the authors themselves [3, 5] indicate that, when formula (1) is applied to an electrode with an adsorbed organic substance, only those changes in the \(\psi'\)-potential are taken into account which are consequences of a change in surface charge in the presence of adsorbed organic molecules. Changes in the \(\psi'\)-potential associated with the oriented adsorption of dipoles of the organic substance are not taken into account.

Recently, the method of measuring differential capacitance has been widely used to study the adsorption of SAS. The model concepts underlying the theory of this method make it possible to calculate the value of \(\psi'\) rather simply, if it is known that the organic molecules are adsorbed in the same position [6, 7]. If the orientation of SAS molecules remains constant or changes only very slightly with changes in potential and SAS concentration (or the range of these changes is sufficiently narrow), the calculation of the \(\psi'\)-potential is carried out by ממ

relations following from the model of two parallel capacitors:

\[ \psi'=\frac{\varphi_N \Theta}{\dfrac{C_0}{C_1}(1-\Theta)-\Theta}, \tag{2} \]

where \(\Theta\) is the degree of coverage of the electrode surface by organic molecules;

\(\varphi_N\) is the shift of the p.z.c. of the electrode in passing from \(\Theta=0\) to \(\Theta=1\);

\(C_0, C_1\) are the electrode capacitances, respectively, at \(\Theta=0\) and \(\Theta=1\).

In the case where changes in the electrode potential or in the concentration of the surfactant cause a substantial change in the orientation of the molecules, calculation of the \(\psi'\)-potential by formula (2) gives only approximate results. Its application to calculations of regularities derived for the model of three parallel capacitors requires an exact determination of the degree of filling of the surface by molecules of a definite orientation, knowledge of attraction factors, etc., and makes the calculation extremely cumbersome and practically feasible only on an electronic computer.

An approximate determination of the \(\psi'\)-potential in the presence of adsorbed surfactants is often carried out from the shift of the maximum of the electrocapillary curve [2, 8]. A. G. Stromberg and L. S. Zagainova [2], studying the effect of camphor on electrode processes, determined adsorption \(\psi'\)-potentials as the shift of the maximum of the electrocapillary curve at a given concentration of camphor in the solution in comparison with the maximum of the electrocapillary curve in the absence of camphor in the solution. It was assumed here that the \(\psi'\)-potential corresponding to any electrode potential also depends unambiguously on the amount of adsorbed substance \(\Gamma\), as at the potentials of the maximum of the ECC. It is thereby assumed that the arrangement of surfactant molecules at the mercury–solution boundary does not depend on the presence or absence, at the interface, of the ionic double layer and is determined only by the amount of adsorbed substance. From the dependence of the \(\psi'\)-potential on \(\Gamma\), constructed for the maxima of the ECC, or from an analytical expression corresponding to this dependence, the \(\psi'\)-potential can be determined for any electrode potential from the known value of \(\Gamma\).

As an example, let us consider the results of calculating the \(\psi'\)-potential for the case of adsorption of \(\beta\)-naphthol on mercury. The adsorption behavior of \(\beta\)-naphthol was studied by us earlier [9].

Figure 1 presents the \(\psi'\), \(\varphi\)-curves calculated by formula (1). The subscripts \((\varepsilon,\Theta,\Gamma)\) of the quantity \(\psi'\) correspond to the argument of the calculation equation.

Calculation by formula (2) gives a family of \(\psi'_{\Theta},\varphi\)-curves (Fig. 1), located in a more negative region than the \(\psi'_{\varepsilon},\varphi\)-curves, including the \(\psi'_{\varepsilon},\varphi\)-curve corresponding to the pure solution (Fig. 1,a, curve 1).

Figure 2,a shows the dependence of the shift of the maximum of the ECC on the amount of adsorbed substance \(\Gamma\). The \(\psi'_{\Gamma}-\varphi\) curves (Fig. 2,b) were constructed graphically using Fig. 2,a. It was assumed here that the \(\psi'\)-potential corresponding to potentials differing from the point of zero charge is a single-valued function of \(\Gamma\).

Comparison of Figs. 1,a, 1,b, and 2,b shows that the values of the \(\psi'\)-potential determined by the three methods differ substantially from one another. For a solution containing, for example, \(1.22 \cdot 10^{-3}\) M \(\beta\)-naphthol, at \(\varphi=-0.8\) V, \(\psi'_{\varepsilon}\), \(\psi'_{\Theta}\), and \(\psi'_{\Gamma}\) are equal, respectively, to \(-9\), \(-156\), and \(-188\) mV.

In the working range of potentials of the dropping mercury electrode, the concentration of β-naphthol affects the value of \(\psi'\) in the opposite way as compared with \(\psi'_0\) and \(\psi'_g\): \(|\psi'_\varepsilon|\) decreases, whereas \(|\psi'_0|\) increases. \(\psi'_g\) changes with increasing surfactant concentration in a more complicated manner than \(\psi'_0\) (Fig. 2, a), but in the region \(C_{\mathrm{surf}} < 2.4 \times 10^{-4}\ M\), \(\psi'_g\) also increases.

All these facts once again emphasize the unsuitability of the equations of the Gouy–Chapman theory for calculating the \(\psi'\)-potential in the presence of organic surfactants [10].

Let us analyze the sources of errors possible in determining \(\psi'_g\) and \(\psi'_+\).

As was already stated above, both methods are applicable only in the absence of reorientation of molecules relative to the electrode surface. However, we have shown [9] that the orientation of the β-naphthol molecule changes both with changes in the electrode potential and with increasing surfactant concentration: in the region of positive potentials the β-naphthol molecule is arranged flat on the electrode surface, and with increasing negative potential it gradually turns into a vertical position; an increase in β-naphthol concentration accelerates this process.

Fig. 1. Curves of \(\psi' - \psi_0\), calculated: a) by formula (1), b) by formula (2). β-Naphthol content in solution, mol/l \(\times 10^4\):
a) 1) 0.00; 2) 1.22; 3) 2.44; 4) 6.1; 5) 12.2;
b) 1) 1.83; 2) 2.44; 3) 4.88; 4) 7.32; 5) 9.76; 6) 12.2.

Fig. 2. Dependence of the shift of the maximum of the electrocapillary curve on the amount of adsorbed substance (a) and calculated \(\psi'\), \(\psi_0\)-curves (b) for β-naphthol concentrations, mol/l \(\times 10^4\): 1) 1.22; 2) 1.83; 3) 2.44; 4) 3.66; 5) 6.1; 6) 7.32; 7) 9.76; 8) 12.2.

When calculating \(\Theta\) for \(-0.4 < \varphi < -0.9\ \mathrm{V}\), we choose the capacitance at maximum coverage corresponding to the vertical position of the molecule, thereby completely denying the possibility of any other orientation.

Determination of \(\psi'_g\) from the shift of the potential of zero charge (p.z.c.) assumes the same orientation of the organic substance along the entire potential axis.

… molecules, as also in the region of the p.z.c. In this connection, upon transition to positive potentials, the error in determining \(\psi'_r\) for \(\beta\)-naphthol will increase owing to reorientation of its molecules into a flatter position. In the region of potentials adjacent to the p.z.c., a potential shift by \(\pm 0.1\) V will not cause a substantial change in the orientation of the molecule in comparison with its position at the p.z.c. Expanding the interval of potentials in which \(\psi_r\) is determined increases the error of the result. The change in molecular orientation caused by an increase in the concentration of the surfactant is taken into account by the dependence \(\Delta\varphi_{\max} — \Gamma\) (Fig. 2, a).

From the foregoing it is clear that calculation of the \(\psi'\)-potential using any of the methods listed gives results with a substantial error, since each method is based on certain simplifying model assumptions. For organic substances capable of changing their orientation on the electrode surface, the most acceptable, in our opinion, is the Stromberg method [2], which is based on a more flexible model.

REFERENCES

1. A. N. Frumkin, V. S. Bagotskii, Z. A. Iofa, B. N. Kabanov. Kinetics of Electrode Processes. Moscow, Moscow State University Publishing House, 1952.

2. A. G. Stromberg, L. S. Zagainova. Journal of Physical Chemistry, 31, 1042, 1957.

3. V. K. Venkatesan, B. B. Damaskin, N. V. Nikolaeva-Fedorovich. Journal of Physical Chemistry, 39, 129, 1965.

4. S. G. Mairanovskii. The Double Layer and Its Effects in Polarography. Moscow, Nauka Publishing House, 1971.

5. M. M. Andrusev, N. V. Nikolaeva-Fedorovich, B. B. Damaskin. Electrochemistry, 3, 1094, 1957.

6. B. B. Damaskin, O. A. Petrii, V. V. Batrakov. Adsorption of Organic Compounds on Electrodes. Moscow, Nauka Publishing House, 1968.

7. V. F. Voloshin, F. I. Danilov, M. A. Loshkarev. Chemical Technology, Kharkov, Kharkov State University Publishing House, issue 17, 36, 1971.

8. M. A. Loshkarev, E. I. Dubyago. Journal of Physical Chemistry, 34, 1430, 1960.

9. Yu. N. Oblivantsev, T. V. Gomza, V. E. Gorodovykh. Advances in Stripping Polarography. Tomsk, Tomsk State University Publishing House, 1973, p. 101.

10. P. Delahay. Double Layer and Electrode Kinetics. Moscow, Mir Publishing House, 1967.