On the dependence of the adsorption ?1-potential on the degree of coverage
Abstract Generated abstract
This paper examines whether the adsorption Psi1-potential can be represented as a simple power function of surface coverage for organic compounds adsorbed on mercury electrodes. Using a two-parallel-capacitor model of the double layer and published electrode-charge and adsorption data, the authors derive expressions for the dependence of the point of zero charge on coverage and analyze logarithmic plots for aliphatic compounds including valeric acid, diethyl ketone, and amines. The analysis indicates that the relation between adsorption potential and degree of filling is generally nonlinear and cannot be described by the previously used power-law form over a wide coverage range, with still greater complexity expected for compounds adsorbing in two orientations.
Full Text
ON THE DEPENDENCE OF THE ADSORPTION \(\Psi_1\)-POTENTIAL ON THE DEGREE OF FILLING
Yu. N. Oblivantsev, V. E. Gorodovykh
(Presented by the Scientific-Methodological Seminar of the Faculty of Chemical Technology)
The influence of the adsorption of organic surface-active substances on the rate of an electrochemical reaction, along with other factors, may also be associated with a change in the \(\Psi_1\)-potential. In the works of A. G. Stromberg [1—3], a quantitative theory of anodic-cathodic polarographic waves was developed with allowance for the value of the \(\Psi_1\)-potential at amalgam electrodes. Unfortunately, broad experimental verification of this theory is presently impossible because of the absence of experimental and computational methods for determining the adsorption \(\Psi_1\)-potential at arbitrary potentials and degrees of filling.
In work [1], devoted to the study of the influence of camphor on the anodic-cathodic waves of cadmium, from experimental values of the point of zero charge (p.z.c.) of mercury at various concentrations of camphor in solution, the following dependence was obtained between the adsorption \(\Psi_1\)-potential and the surface concentration of camphor:
\[ \Psi_1 = B\Gamma^n , \]
where \(\Gamma\) is the surface concentration,
\(B\) is a constant,
\(n = 2\).
Assuming that the form of this dependence is preserved at any potentials, the authors quantitatively explained the influence of camphor on the anodic-cathodic waves of cadmium.
It should be noted that the assumption \(\Psi_1 = \text{const}\) at \(\theta = \text{const}\), apparently, should not hold over a wide range of potentials [4].
It is of definite interest to verify the validity of relation (1) in the case of adsorption on mercury of aliphatic compounds. A nonlinear dependence of the value of the adsorption \(\Psi_1\)-potential on the degree of filling follows from the theory of the influence of the electric field on the adsorption of organic compounds [5]. Indeed, within the framework of the model of two parallel capacitors for aliphatic compounds adsorbed in one position, the relation between the electrode charge and the degree of filling has the following form [5]:
\[ \varepsilon = \varepsilon_0(1-\theta) + C_1(\varphi-\Phi_N)\theta - A\theta\frac{da}{d\varphi}(1-\Theta), \tag{2} \]
where \(\varepsilon\) is the electrode charge in the presence of organic substances;
\(\theta\) is the degree of filling;
\(\varepsilon_0\) is the electrode charge at \(\theta = 0\);
\(C_1\) is the capacitance of the double electric layer at \(\theta = 1\);
\(a\) is the attraction constant;
\(\varphi_N\) is the shift of the p.z.c. upon passing from \(\theta = 0\) to \(\theta = 1\);
\(A = RT\Gamma_\infty\) (\(\Gamma_\infty\) is the value of \(\Gamma\) at \(\theta = 1\));
\(\varphi\) is the electrode potential, measured relative to the p.z.c. of mercury at \(\theta = 0\).
If, in the first approximation, one sets \(C_0 = \text{const}\), \(C_1 = \text{const}\), \(a = \text{const}\), then from (2) it follows that the dependence of the p.z.c. \((\varphi_{\varepsilon=0})\) on the degree of filling is expressed as follows [5]:
\[ \frac{\varphi_{\varepsilon=0}}{\varphi_N} = \frac{\theta}{K - (K - 1)\theta}, \tag{3} \]
where \(K = C_0/C_1 < 1\),
\(C_0\) is the capacitance of the double electric layer at \(\theta = 0\).
Taking the logarithm of equation (3) and then differentiating with respect to \(\lg \theta\), we obtain
\[ \frac{\partial \lg(\varphi_{\varepsilon=0}/\varphi_N)}{\partial \lg \theta} = 1 - \frac{\partial \lg [K - (K - 1)\theta]}{\partial \lg \theta}. \tag{4} \]
It follows from relation (4) that the plot in the coordinates \(\lg(\varphi_{\varepsilon=0}/\varphi_N)\)—\(\lg \theta\) is not a straight line, since the right-hand side of (4) depends on \(\theta\), and, consequently, the dependence of the adsorption
Fig. 1. Dependence of the p.z.c. on the degree of filling during adsorption on mercury:
1 — n-\(\mathrm{C_4H_9COOH}\), 2 — \(\mathrm{C_2H_5OC_2H_5}\),
3 — n-\(\mathrm{C_5H_{11}NH_2}\), 4 — iso-\(\mathrm{C_5H_{11}NH_2}\) against a background of \(1\,M\,\mathrm{Na_2SO_4}\)
Fig. 2. Dependence of \(\lg \varphi_{\varepsilon=0}\)—\(\lg \Theta\) during adsorption on mercury:
1 — n-\(\mathrm{C_4H_9COOH}\),
2 — \(\mathrm{C_2H_5OC_2H_5}\), 3 — n-\(\mathrm{C_5H_{11}NH_2}\),
4 — iso-\(\mathrm{C_5H_{11}NH_2}\)
\(\varphi_1\) potential on the degree of filling in the case of adsorption of aliphatic compounds cannot be expressed by an equation of type (1).
In the general case, when the capacitance of the double electric layer and the attraction constant depend on the potential, it follows from equation (2) that
\[ \varphi_{\varepsilon=0} = \frac{\xi_0(1-\theta)-\beta A\theta^2+C_1\theta c_N^{\,n}}{C_1\theta}, \tag{5} \]
where \(\varphi_N^0\), \(\beta\) are constants.
Using this equation and literature data on the charge of the electrode [6] and adsorption parameters [7, 8], we constructed dependences of the so-called z. on the degree of filling for \(n\)-valeric acid, diethyl ketone, and aliphatic amines (Fig. 1). Fig. 2 gives the dependence \(\lg \varphi_{\varepsilon=0} - \lg \theta\). As is evident from the figures, in this case as well the relation between the adsorption \(\Psi_1\)-potential and the degree of filling cannot be expressed by equation (1) over a wide interval of \(\theta\).
An even more complex character is exhibited by the dependence of the so-called z. on the \(G_1\)-potential for organic compounds capable of being adsorbed in two different positions [9].
LITERATURE
- A. G. Stromberg, L. S. Zagaynova. Zhurn. fiz. khimii, 31, 1042, 1957.
- L. S. Zagaynova, A. G. Stromberg. DAN SSSR, 105, 747, 1955.
- A. G. Stromberg, L. S. Zagaynova. DAN SSSR, 97, 107, 1954.
- B. B. Damaskin. Zhurn. fiz. khimii, 37, 2483, 1963.
- B. B. Damaskin, O. A. Petrii, V. V. Batrakov. Adsorption of Organic Compounds on Electrodes. Moscow, “Nauka,” 1968.
- P. Delahay. Double Layer and Electrode Kinetics. Moscow, “Mir,” 1967.
- V. K. Venkatesyan, B. B. Damaskin. Zhurn. fiz. khimii, 39, 129, 1965.
- R. Lerkh, B. B. Damaskin. Zhurn. fiz. khimii, 39, 211, 1965.
- B. B. Damaskin. Elektrokhimiya, 4, 675, 1968.