KINETICS OF ADSORPTION OF ORGANIC SURFACTANTS AND THE APN METHOD

V. E. Gorodovykh, Yu. N. Oblivantsev

(Presented by the scientific seminar of the Department of PNV and EKhP)

In the experimental study of electrochemical reactions in the presence of surface-active substances (surfactants), it is necessary to take into account the kinetics of establishment of adsorption equilibrium. This circumstance is not always considered and leads either to obtaining nonreproducible results or to unreliable data, since they are obtained under nonequilibrium conditions. How important it is to take into account the kinetics of the adsorption process follows at least from the fact that, according to estimates by a number of authors, the time required to reach the equilibrium degree of coverage, especially at low surfactant concentrations in solution, may amount to tens of minutes \[1—3\].

The influence of surfactant adsorption on anodic peaks, taking into account the kinetics of establishment of adsorption equilibrium, has not previously been considered in the literature.

In a first approximation, this problem can be solved on the basis of the following model: 1) surfactant molecules adsorbed on the electrode inhibit the cathodic process by the mechanism of “pure” blocking and do not affect the stage of electro-dissolution of the amalgam; 2) the concentration of surfactant in the solution is high, so that at a certain moment of time the electrode is completely covered by a surfactant layer; 3) the process of surfactant diffusion to the electrode is described by the equation of linear semi-infinite diffusion.

It is easy to show that in this case the degree of coverage is related to time by the relation

\[ \theta(t)=\left(\frac{t}{\tau}\right)^{1/2}, \tag{1} \]

where \(\theta(t)\) is the degree of coverage at the time \(t\);

\(\tau\) is the time required to reach the equilibrium degree of coverage \(\theta=1\).

Taking (1) into account, the expression for the concentration of metal ions in solution will have the following form:

\[ C_0(t)=C_0^0 e^{-bt} e^{2/3bt^{3/2}\tau^{1/2}} \tag{2} \]

where \(C\) is the initial concentration of metal ions;

\[ b=\frac{k_1 S}{zFv_p}. \]

Relation (2) differs from the known formulas of A. G. Stromberg’s parametric theory of the APN method by the factor \(\exp [2/3bt_{\mathrm{e}}^{3/2}/\tau^{1/2}]\), which is thus a correction for the influence of surfactants. From (2) it follows that, in the presence of surfactants, the ion concentration decreases with increasing electrolysis time more slowly than in a pure solution.

Using (2), for the depth of the anodic peak one may write

\[ I(t)=\frac{\varkappa_1\varkappa_2 s^2 c_0^0}{zFv_{\mathrm{e}}} \int_0^{t_{\mathrm{e}}} e^{-bt+2/3bt^{3/2}/\tau^{1/2}} \left[1-\left(\frac{t}{\tau}\right)^{1/2}\right]\,dt, \tag{3} \]

where \(I(t)\) is the peak depth at an electrolysis time equal to \(t_{\mathrm{e}}\). The remaining notation is that generally accepted for the parametric theory of the APN method.

By numerical integration of equation (3), dependences of the relative depth and of the relative decrease in the depth of the anodic peak on electrolysis time were obtained (Tables 1 and 2).

Table 1

Dependence of the relative peak depth on electrolysis time and the parameter \(b'\)

Notation: \(b'=\dfrac{\varkappa_1 s}{tFV_p}\tau;\quad T=t_{\mathrm{e}}/\tau;\)

\(I\) — peak depth in the pure solution;
\(I_{\mathrm{surf}}\) — peak depth in the presence of surfactants.

Table 2

Dependence of the relative decrease in peak depth on electrolysis time and the parameter \(b'\)

Notation: \(b'=\dfrac{\varkappa_1 s}{zFV_p}\tau;\quad T=t_{\mathrm{e}}/\tau;\)

\[ \Delta I/I=\frac{I_{\mathrm{surf}}-I}{I} \]

— the relative decrease in peak depth.

From Tables 1 and 2 it is evident that, with increasing electrolysis time and hence with increasing degree of coverage, the relative peak depth decreases.

The differences between the peak depth in the pure solution and in the presence of surfactants decrease with increasing parameter \(b' = bt\). This is also physically understandable, since with increasing \(b'\) the degree of depletion of the solution increases, while the anodic process in the presence of surfactants is, by assumption, not inhibited.

It is interesting to note that by the moment the electrode is completely covered with a surfactant layer (\(T = 1\)), the relative decrease in peak depth has still not reached its limiting value, equal to unity. Thus, diffusional limitations on the rate of the adsorption process lead to the result that, at a surfactant concentration in solution ensuring the equilibrium value \(\Theta_{\mathrm{eq}} = 1\), the relative decrease in peak depth will be less than unity even at an electrolysis time exceeding the time of complete coverage of the electrode.

It seems to us that the results obtained will prove useful in substantiating a method for studying the influence of surfactants on electrode processes in the APN method.

REFERENCES

1. P. Delahay, I. Trachtenberg. J. Am. Chem. Soc., 79, 2355 (1957); 80, 2094 (1958).
2. W. H. Reinmuth. J. Phys. Chem., 65, 473 (1961).
3. J. Heyrovský, J. Kuta. Fundamentals of Polarography, Moscow, “Mir,” 1965.