Abstract
Full Text
PHYSICAL CHEMISTRY
Ya. I. Tur’yan
THE MECHANISM OF THE CHANGE IN OXYGEN OVERVOLTAGE WITH TIME ON A NICKEL ANODE AT CONSTANT CURRENT DENSITY
(Presented by Academician A. N. Frumkin, January 28, 1960)
The phenomenon of the growth of the oxygen overvoltage \(\eta\) with time \(t\) on a Ni anode at \(i = \mathrm{const}\) has so far not found a quantitative explanation. We have assumed \((^{1,2})\) that the cause of the growth of \(\eta\), due at large \(i\) to the slowness of the discharge of \(\mathrm{OH}'\) ions \((^{1-3})\), is that \(\eta\) on \(\mathrm{NiO_2}\) \(\left(\mathrm{Ni_2O_4}\right)\) \((^4)\), the concentration of which in the surface solid solution \(\mathrm{Ni_2O_3 + Ni_2O_4}\) gradually increases, is greater than \(\eta\) on \(\mathrm{Ni_2O_3}\) (the anode, already at \(t = 0\), is considered to be completely covered with \(\mathrm{Ni_2O_3}\)). The assumption that \(\eta\) on \(\mathrm{Ni_2O_4}\) is greater than \(\eta\) on \(\mathrm{Ni_2O_3}\) is to some extent confirmed by work \((^5)\), which showed that \(\eta\) on \(\mathrm{Ni_2O_3}\) is greater than \(\eta\) on \(\mathrm{NiO}\).
For the purpose of quantitatively checking these ideas, experimental data on the dependence of \(\eta\) on \(t\) at \(i = \mathrm{const}\) from \((^1)\) and \((^6)\) were used (Fig. 1, 6–7.5 \(N\) KOH). The results from \((^6)\) at small \(t\) and \(18^\circ\) showed an anomalous course of the \(\eta\)—\(t\) curve, possibly because of the nonstationarity of the anode surface area \((^1)\) or incomplete coverage by \(\mathrm{Ni_2O_3}\). These data were discarded, and \((\eta)_{t=0}\) was found by extrapolation (Fig. 1).
At large \(i\), the evolution of \(\mathrm{O_2}\) through the formation and decomposition of \(\mathrm{Ni_2O_4}\) must be insignificant in comparison with another parallel process \((^2)\), for example
\[ 2\mathrm{OH} \to \mathrm{H_2O} + \mathrm{O}. \tag{1} \]
Taking this into account, the kinetics of the accumulation of \(\mathrm{Ni_2O_4}\)
\[ \mathrm{Ni_2O_3} + 2\mathrm{OH} \to \mathrm{Ni_2O_4} + \mathrm{H_2O} \tag{2} \]
with simultaneous decomposition of \(\mathrm{Ni_2O_4}\)
\[ \mathrm{Ni_2O_4} \to \mathrm{Ni_2O_3} + \mathrm{O} \tag{3} \]
can be described by the expression
\[ \frac{dS}{dt} = K_1(1 - S) - K_2S; \tag{4} \]
\(S\) is the part of the anode surface occupied by \(\mathrm{Ni_2O_4}\) (the closeness of the molar surfaces of \(\mathrm{Ni_2O_3}\) and \(\mathrm{Ni_2O_4}\) is assumed); \(K_1 = K'_1[\mathrm{OH}]^2\); \(K'_1\) and \(K_2\) are the rate constants of processes (2) and (3), respectively.
According to the theory of slow discharge \((^7)\), taking into account the discharge of \(\mathrm{OH}'\) ions on the surface of the solid solution \(\mathrm{Ni_2O_3 + Ni_2O_4}\) \(([\mathrm{OH}'] = \mathrm{const})\), we obtain:
\[ i = K_3(1 - S)\exp\left(\frac{\eta F}{2RT}\right) + K_4S\exp\left(\frac{\eta F}{2RT}\right). \tag{5} \]
From (4) and (5) (at \(t = 0\), \(S = 0\)), assuming \(K_3 \gg K_4\), we find:
\[ \eta = \frac{2RT}{F}\ln i - \frac{2RT}{F}\ln \frac{K_1K_3}{K_1 + K_2} - \frac{2RT}{F}\ln\left[ \left(\frac{K_2}{K_1} + \frac{K_4}{K_3}\right) + e^{-(K_1+K_2)t} \right]. \tag{6} \]
Table 1
| \(T\), °C | \multicolumn{3}{c|}{Current density, A/cm²: 0.01} | \multicolumn{3}{c|}{Current density, A/cm²: 0.05} | \multicolumn{3}{c|}{Current density, A/cm²: 0.1} | \multicolumn{3}{c|}{Current density, A/cm²: 0.3} |
|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| | \(a\) | \(b\) | \(\varphi_{t=0}\), mV (N.H.E.) | \(a\) | \(b\) | \(\varphi_{t=0}\), mV (N.H.E.) | \(a\) | \(b\) | \(\varphi_{t=0}\), mV (N.H.E.) | \(a\) | \(b\) | \(\varphi_{t=0}\), mV (N.H.E.) |
| 18 | \(6.94\cdot10^{-3}\) | | 632 | \(2.3\cdot10^{-4}\) | \(7.9\cdot10^{-2}\) | 690 | \(2.7\cdot10^{-4}\) | 0.158 | 750 | | | |
| 25 | | | | | | | | | | \(1.4\cdot10^{-4}\) | 1.37 | 794 |
| 60 | | | | | | | \(5.0\cdot10^{-4}\) | \(3.6\cdot10^{-2}\) | 660 | | | |
| 80 | | | | | | | | | | \(1.0\cdot10^{-3}\) | \(7.0\cdot10^{-2}\) | 696 |
Note. \(a=\dfrac{K_2}{K_1}+\dfrac{K_4}{K_3}\), \(b\) (h\(^{-1}\)) \(=K_1+K_2\approx K_1\).
Equation (6) agrees well with the experimental results (Fig. 1) for the values of the constants indicated in Table 1, and under the condition
\[ (\eta)_{t=0}=\frac{2RT}{F}\ln i-\frac{2RT}{F}\ln\frac{K_1K_3}{K_1+K_2}. \tag{7} \]
Fig. 1. Dependence of \(\varphi\) on \(t\). Points are calculated data; curves are experimental. \(1\)—0.3 A/cm², 25° (1); \(2\)—0.1 A/cm², 18° (6); \(3\)—0.05 A/cm², 18° (6); \(4\)—0.3 A/cm², 80° (1); \(5\)—0.1 A/cm², 60° (6); \(6\)—0.01 A/cm², 18° (6).
Since
\[ \left(\frac{K_2}{K_1}+\frac{K_4}{K_3}\right)\ll 1 \]
(Table 1) and \(K_3\gg K_4\), it follows that \(K_1\gg K_2\). This is also confirmed by expression (7), which at \(t=0,\ S=0\) must be transformed into
\[ (\eta)_{t=0}=\frac{2RT}{F}\ln i-\frac{2RT}{F}\ln K_3, \tag{8} \]
which is possible for \(K_1\gg K_2\).
The dependence found by us of \((\eta)_{t=0}\) on \(\lg i\) is a straight line with slope
\[ \frac{2RT}{F}\cdot 2.3 \]
(Fig. 2), in good agreement with (8).
Thus, equation (6) takes the form
\[ \eta=(\eta)_{t=0}-\frac{2RT}{F}\ln\left[\left(\frac{K_2}{K_1}+\frac{K_4}{K_3}\right)+e^{-K_1t}\right]. \tag{9} \]
At small values of \(t\), and taking into account the magnitudes of \(K_1\) and
\[ \left(\frac{K_2}{K_1}+\frac{K_4}{K_3}\right) \]
(Table 1), equation (9) can be transformed into a linear dependence of \(\eta\)
of \(t\):
\[ \eta=(\eta)_{t=0}+\frac{2RT}{F}K_1t, \tag{10} \]
which agrees with experiment (Fig. 1).
With increasing \(t\), \(\eta\) tends to the value established in time \((\eta_{\text{st}})\):
\[ \eta_{\text{st}}=(\eta)_{t=0}-\frac{2RT}{F}\ln\left(\frac{K_2}{K_1}+\frac{K_4}{K_3}\right), \tag{11} \]
which also agrees with experiment (Fig. 1).
As is seen from Table 1, \(K_1\) depends on \(i\), which apparently is connected with a certain inhibition also at other stages of the process (change in \([\mathrm{OH}]\)), considerably less than at the stage of discharge of \(\mathrm{OH}'\) ions. A similar picture was observed \({}^{(8)}\) also in the study of \(\eta\) on a Pb anode.
Fig. 2. 1 — dependence of \(\varphi_{\text{st}}\) on \(\lg i\) (\(a\) — according to \({}^{(2)}\), \(b\) — according to \({}^{(9)}\)); 2 — dependence of \(\lg k_1\) on \(\lg i\); 3 — dependence of \(\varphi_{t=0}\) on \(\lg i\)
Since at constant temperature \(K_1\) increases with increasing \(i\) (Table 1), at large \(i\) one may expect
\[ \frac{K_4}{K_3}\gg\frac{K_2}{K_1}, \]
and at small \(i\)
\[ \frac{K_4}{K_3}\ll\frac{K_2}{K_1}. \]
Hence at large \(i\), from (11), taking (8) into account,
\[ \eta_{\text{st}}=\frac{2RT}{F}\ln i-\frac{2RT}{F}\ln K_4, \tag{12} \]
and at small \(i\)
\[ \eta_{\text{st}}=\frac{2RT}{F}\ln i-\frac{2RT}{F}\ln K_3- \]
\[ -\frac{2RT}{F}\ln\frac{K_2}{K_1}. \tag{13} \]
If it is taken into account that \(K_1=K'_1 i^{1.55}\) (Fig. 2) and (13), then
\[ \eta_{\text{st}}=2.55\frac{2RT}{F}\ln i-\frac{2RT}{F}\ln K_3-\frac{2RT}{F}\ln K_2+\frac{2RT}{F}\ln K'_1. \tag{14} \]
Equation (12) agrees with experiment already at \(i>0.1\ \mathrm{A/cm^2}\). This is the upper linear segment (Fig. 2) of the dependence of \(\eta_{\text{st}}\) on \(\lg i\), with slope \(\sim \frac{2RT}{F}\,2.3\) \({}^{(2,9,10)}\). The presence of this segment, corresponding, according to (12), to complete coverage of the anode by \(\mathrm{Ni_2O_4}\), was also confirmed \({}^{(11)}\).
Equations (13) and (14) are confirmed at smaller \(i\) (\(i<0.01\)—\(0.02\ \mathrm{A/cm^2}\), but not below \(10^{-3}\ \mathrm{A/cm^2}\), when the mechanism of \(\eta\) changes \({}^{(2)}\)) in the region of the steep segment of the dependence of \(\eta_{\text{st}}\) on \(\lg i\) \({}^{(2,10)}\)—a straight line with angular coefficient 0.320 (Fig. 2), which is close to the theoretical value 0.303 (equation (14)). From (5) and (13) it follows that in this segment the discharge process of \(\mathrm{OH}'\) ions proceeds mainly on \(\mathrm{Ni_2O_3}\). To each value of \(\eta_{\text{st}}\) there corresponds a definite value of \(S\). As the surface concentration of \(\mathrm{Ni_2O_4}\) increases (with increasing \(i\)), the process also proceeds on \(\mathrm{Ni_2O_4}\).
On the basis of (14) and the experimental dependences of \(\eta_{\text{st}}\) on \(\lg i\) \({}^{(2)}\), \(\eta_{t=0}\) on \(\lg i\), and \(K_1\) on \(i\), we calculated that \(K_2=1\cdot10^{-5}\ \mathrm{h^{-1}}\) at \(25^\circ\), i.e., as also follows
one should expect, \(K_1 \gg K_2\). Approximately the same value of \(K_2\) was obtained from the dependence of \(\eta\) on \(t\). Such a low value of \(K_2\) does not confirm assumption \((^4)\) about process (3) as the rate-controlling stage even at very low \(i\), since in this case the calculation gives an unrealistically large concentration of \(\mathrm{Ni_2O_4}\) (for example, at \(i = 10^{-5}\ \mathrm{a/cm^2}\), \([\mathrm{Ni_2O_4}] = 1.1 \cdot 10^{22}\ \mathrm{molec./cm^2}\)).
The assumption of the process
\[ 2\,\mathrm{Ni_2O_4} \to 2\,\mathrm{Ni_2O_3} + \mathrm{O_2} \tag{15} \]
is not confirmed by the dependence of \(\eta\) on \(t\).
On the basis of the dependence of \(\eta_{\text{ust}}\) on \(\lg i\) (at \(i > 0.1\ \mathrm{a/cm^2}\)) and the dependence of \(\eta_{t=0}\) on \(\lg i\), we calculated \(K_4/K_3 = 1.7 \cdot 10^{-4}\), which agrees exceptionally well with the value of \(K_4/K_3\) from the dependence of \(\eta\) on \(t\) (Table 1).
It is seen from Table 1 that, with increasing temperature, \(K_1\) decreases. This is the result of the predominant influence of temperature on lowering the surface concentration of OH radicals in comparison with the concomitant increase of \(K'_1\).
In conclusion, we note that equation (5), also under the condition \(K_3 \gg K_4\), has already been used \((^{12})\) to describe the dependence of \(\eta\) on \(t\) for a Pt anode. However, the kinetics of oxide accumulation is represented in \((^{12})\) not by the same dependence as in our work, and therefore the dependence of \(\eta\) on \(t\) in \((^{12})\) came out completely different.
Lysychansk Branch
of the State Institute of the Nitrogen Industry and
Products of Organic Synthesis
Received
28 I 1960
CITED LITERATURE
- Ya. I. Tur’yan, Dissertation, Central Asian Industrial Institute, 1948.
- V. N. Fiseiskii, Ya. I. Tur’yan, ZhFKh, 24, 567 (1950).
- S. A. Gantman, P. D. Lukovtsev, Proc. 3rd Conference on Electrochemistry, Publishing House of the Academy of Sciences of the USSR, 1953, p. 504.
- L. M. Elina, T. I. Borisova, P. I. Zalkind, ZhFKh, 28, 785 (1954).
- O. K. Davtyan, The Problem of the Direct Conversion of the Chemical Energy of Fuel into Electrical Energy, Publishing House of the Academy of Sciences of the USSR, 1947.
- G. Grube, A. Vogt, Zs. Elektrochem., 44, 353 (1938).
- A. N. Frumkin, V. S. Bagotskii, Z. A. Iofa, B. N. Kabanov, Kinetics of Electrode Processes, Moscow, 1951.
- B. N. Kabanov, Proc. 4th Conference on Electrochemistry, Publishing House of the Academy of Sciences of the USSR, 1959, p. 252.
- Ya. I. Tur’yan, I. S. Gol’dshtein, ZhFKh, 28, 379 (1956).
- Ya. I. Tur’yan, ZhFKh, 33, 948 (1959).
- T. Mine, T. Seiyama, W. Sakai, J. Chem. Soc. Japan, Industr. Chem. Soc., 58, 725 (1955).
- J. Bockris, A. Huq, Proc. Roy. Soc., A, 237, 277 (1956).