Electrochemical Kinetics of the Ferri-Ferrocyanide Couple on Platinum P. H. Daum and C. G . Enke Chemistry Department, Michigan State University, East Lansing, Mich. 48823 The current impulse technique was used to study the electrochemical kineticsof theferri-ferrocyanidecouple. The exchange rate of the reaction was strongly dependent on the oxidation state of the electrode surface. The transfer coefficient and the activation energy do not appear to be affected by surface oxidation. All experimental evidence points to a simple first order electron transfer reaction. The results of the investigation were in substantial concordancewith those measured by other techniques when surface oxidation effects are taken into account.
THECURRENT IMPULSE technique ( I ) is a perturbation method which is espectially suitable for the study of rapid electrochemical reactions. The system is perturbed from its equilibrium potential with an extremely short pulse of constant current that charges the electrical double layer capacitance to a new potential several millivolts anodic or cathodic of the equilibrium potential. The relaxation of the double layer charge through the faradaic process is observed by measuring the potential 7 as a function of time. With the absence of mass transport complications, a simple exponential decay law 7 = q I = exp( -t/RfCd) is followed where R j is the faradaic resistance ( R , = RT/nFI') and c d is the differential double layer capacitance. The exchange current of the reaction can be calculated directly from the slope of the log (+time curve if the double layer capacitance of the system is known under the exact conditions of the experiment. This technique offers two methods of determining the double layer capacitance. The log (v)-time curve can be extrapolated to zero time (defined as the time of the termination of the impulse), and the capacitance can then be calculated from the relationship Cd = ir/qC= where i is the magnitude of the applied current pulse and T is the pulse duration. It can also be determined directly by measuring the slope of the overpotential time curve while charging the double layer with a constant current from the relationship i = Cd(&/dt). Studies with the current impulse technique have been limited to the kinetics of the electrochemical reduction of the Hg(I)/Hg system ( 2 ) which appears to have mechanistic complications, and the resulting data are somewhat anomolous. It seemed desirable to show that the technique is capable of obtaining unambiguous data from a mechanistically simple reaction, and to extend its usefulness to the study of very fast electrochemical reactions at solid electrodes. A system that fulfills these requirements is the ferri-ferrocyanide couple on platinum. It has been the subject of much investigation and is regarded by many as the model of a highly reversible electrochemical reaction without complicating mechanistic effects. The study of this system with the current impulse technique has presented several intriguing aspects, and has given some new data previously unavailable with other methods. First, the current impulse technique gives an unambiguous estimate of the differential double layer capacitance under the actual conditions of the experiment, a measurement which is not readily available from other techniques with a reaction of this (1) W. D. Weir and C . G. Enke, J. Phys. Chem., 71, 275 (1967). (2) W. D. Weir and C . G. Enke, ibid., p 280.
speed. This ability is particularly important in this system because the ferricyanide and ferrocyanide anions are highly charged', and one might expect that the double layer capacitance of platinum would be a strong function of their concentration and the potential. However, this study has revealed no drastic changes in the double layer structure as a function of these variables. Second, these two anions are most certainly associated to a differing degree with the potassium ion of the supporting electrolyte (3),and the oxidation of the ferrocyanide ion or reduction of the ferricyanide ion probably involves a change in the number of potassium ions associated with the particular anion. The analyses of the overpotential cs. time curves gave no definite information regarding this proposed mechanism. Third, the exchange rates and capacitance values obtained with this system were very much dependent upon the preconditioning of the electrode. The pretreatment of the electrode with hot perchloric acid oxidized the platinum surface, which slowed the apparent exchange rate to a marked degree. When the oxidized electrode was reduced by evolution of hydrogen, the electrode became more active. These two electrode surfaces were reproducible so it was convenient to define two states, an oxidized state and a reduced state. Most of the effort of the present investigation has been directed to the establishment of the kinetic parameters for the reduced electrode system; oxidized electrodes have been measured only to demonstrate that surface oxidation affects the kinetic parameters. EXPERIMENTAL
Instrumentation. An Intercontinental Instruments PG-33 pulse generator was used as the perturbation source. It has a current output mode capable of a maximum output of 200 mA pulses with rise times of less than 7 nsec, and with durations as short as 30 nsec. In its quiescent state the impedance to ground is a minimum of 10 kohms; this is quite large with respect to the faradaic resistance of the ferri-ferrocyanide couple; thus the cell is essentially at open circuit after termination of the pulse, and relaxation takes place only through the faradaic reaction. A Tektronix 556 Dual Beam Oscilloscope with a 1A5 differential preamplifier was used to measure the potentials. The combination of the main frame and preamplifier has a rise time of less than 11 nsec, a 1 Mohm input resistance, and a maximum sensitivity of 1 mV/cm. The preamplifier has a calibrated voltage which can be subtracted from the input signal, thus allowing the measurement of charging curves at high sensitivities by offsetting the IR drop of the cell. Currents were measured by inserting a calibrated 10-ohm composition resistor in series with the pulse generator and measuring the IR drop of a 1 psec pulse with the oscilloscope; current values were estimated to be correct to within 2 %. Experiments were initiated by an external trigger pulse which started the oscilloscope sweep ; the delayed trigger output of the oscilloscope was then used to trigger the pulse generator. The experimental data were recorded photographically on Kodak Tri-X film using a Tektronix 350/C 35mm camera system. Temperature control for the activation energy studies was maintained with a Tamson TVZ-45 con(3) W. A. Eaton, P. George, and G . I. H. Hanania, ibid., p 2016. VOL. 41, NO. 4, A P R I L 1969
653
TEST ELECTRODE P t B A L L
REFER E NCE
-
A C H A R G E CAPACITANCE
ELECTRODE P t WIRE
N,
INLET 8 OUTLEl
E
0 DISCHARGE CAPACITANCE
40
T
C R = 10"M
2 cm
L
COUNTER ELECTRODE Pt GAUZE
I
U
k--+ 1.5 cm
1
I
-3.0
-4.0
I
-2.0
- 1.0
LOG(Co) M o l e s / L i t e r
EXPERIMENTAL CELL Figure 1 stant temperature bath fitted with a push-pull external circuculator. Temperature control was estimated to be within 0.1 "C of the set point. Reagents and Solutions. Solutions were prepared directly by weight from ACS reagent grade chemicals without further purification. Water was prepared by the redistillation of an alkaline permanganate solution of laboratory distilled water. Nitrogen used to purge solutions of oxygen was dried over calcium chloride, passed through an oven containing copper turnings at 350 "C to remove traces of oxygen, passed through traps containing activated charcoal at liquid nitrogen temperatures, presaturated in a 1M KCl solution, and fed to the cell via a glass and Teflon train. Cell and Electrodes. A cell of small dimensions similar to one used by Piersma, Schuldiner, and Warner (4), shown in Figure 1, was constructed and fitted to a small shielded box which was attached to male and female BNC connectors. The cell assembly was plugged directly onto the output of the pulse generator, and a short length of BNC cable was connected from it to the input of the oscilloscope. Nitrogen was led from the purification train to the cell assembly cia a small diameter Teflon tube which was immersed directly into the test solution. A second cell of slightly larger dimensions to accommodate immersion in a constant temperature bath was developed for use in the activation energy studies. It was unshielded and noisier than the first; however both cells demonstrated excellent high frequency response with minimal distortions due to stray inductances and capacitances. System settling times, defined as the time from the start of the impulse to the time at which it is possible to accurately measure the potential, were on the order of 50 nsec. Transient ringing after termination of the impulse was no more than 200 nsec. A three electrode configuration was used in both cases, because it minimized the IR drop and gave slightly less noise than a two electrode system. The test electrode was made by melting a small diameter platinum wire with a gas-oxygen torch into a small sphere of approximately 0.05 cm2 area. The geometric area of the electrode was determined by measurement with a Bausch and Lomb microscope fitted with a micrometer eyepiece, and a calibrated micrometer slide. The area was estimated to be correct to within 2%. The reference electrode was a large diameter platinum wire of approximately 0.5 cmz area arranged so that it was less than 0.5 mm from the test electrode. The area of the reference was large enough so that an insignificant amount of polarization occurred at it
(4)B. J. Piersma, S. Schuldiner, and T. B. Warner, J. Electrochem.
SOC., 113, 1319 (1966). 654
ANALYTICAL CHEMISTRY
Figure 2. Plot of differential capacitance from charge and discharge data of current impulse technique, of platinum in 1M KCl at 25 "C as a function of logFe(CN)$-]
I
I
C H A R G E CAPACITANCE
"E
20 i
!
0
DISCHARGE CAPACITANCE
40 L ~
Co:10
-2
M
I
-4.0
-3.0
-2
.o
- I .o
L O G K R ) M o l e s / Liter
Figure 3. Plot of differential capacitance from charge and discharge data of current impulse technique, of platinum in 1M KCI at 25 "C, as a function of l o g F e ( C N ) ~ ~ - ] under the conditions of the experiments. The counterelectrode was a cylinder of platinum gauze of approximately 3 cmz area, arranged concentrically about the reference and test electrodes. Prior to each experiment, the cell and electrodes were allowed to stand in hot perchloric acid for ten minutes. This served both to oxidize the surface of the electrodes and to oxidize any absorbed impurities in the cell electrode system. For the reduced electrode experiments, the cell was rinsed several times with triple distilled water, filled with 1M KCl, and the electrodes were reduced for several minutes at hydrogen evolution potentials, For the oxidized electrode experiments, the system was used after the usual rinsing with no further treatment.
RESULTS AND CONCLUSIONS Reduced Electrodes. The kinetics of the ferri-ferrocyanide couple were measured by holding the concentration of either the ferricyanide or ferrocyanide ion constant at O.OlM, and varying the concentration of the complex of the other oxidation state in seven increments from 5 x 10-4M to 7 X 10-zM. Exchange rates were measured in 1M KC1 at a total of thirteen different concentrations, and the data presented below are the
N
'iL.5
i
t
:II
%
LL
I
2a-
' 0
0
0
Table I. Values of Apparent Exchange Current Density for Solutions of Varying Concentrations of K&(CN) 6 and K4Fe(CN)6in 1.00M KCl at 25 "C Concn. Fe(CN),3mole 1.-l 0
0
0
0
0
t
1
1
0.16
0.20
0 24
0.28
0 32
E v s S.C.E. Figure 4. Plot of differential capacitance from discharge data of current impulse technique, of platinum in 1M KCl at 25 "C, as a function of measured potential vs. SCE
averages of at least three separate experiments at each concentration. Estimates of the differential capacitance were obtained in two ways; the log(?)-time curves were extrapolated to zero time, to give what is known as the discharge capacitance, and in a separate experiment, a pulse of approximately 0.8 psec duration was applied to the cell and the capacitance value (denoted hereafter as the charge capacitance) was calculated directly from the slope of the charging curve. The capacitance data are presented in Figures 2 and 3 as functions of log (C,) and log (C,). There is marked agreement between the two estimates of the capacitance at all but the highest concentration, where the measured charge capacitance is significantly higher than the discharge capacitance. This apparent anomoly can be explained by considering a simple electrical model which describes the system. The calculation of the charge capacitance assumes that the charging process is linear with respect to time; this implies that on the time scale of the measurement (approximately one half micro-second) an insignificant amount of the charge is used by the faradaic process which is in parallel with the double layer capacitance. At low concentrations this is a good approximation, and the charging curves are linear; however, as the concentration increases, the exchange current increases and a significant amount of the applied current goes to the faradaic process rather than to the charging process. This causes a progressive decrease in the slope of the charging curve and leads to a high estimate of the double layer capacitance. If the slope of the charging curve could be observed at zero time, then the two estimates would presumably be the same at all concentrations; however, with the present experimental system, the minimum time for an accurate slope measurement was about 500 nsec. In view of these considerations, it was decided that the discharge capacitance values were a better representation of the true capacitance values at the higher concentrations, since the charging time of 100 nsec for this experiment was considerably less than the 500-800 nsec required for the charging capacitance measurement. Figure 4 shows the discharge capacitance as a function of potential. This figure indicates that the differential capacitance of platinum under these conditions is essentially independent of the potential, and of the concentration of these two ions, or at least that these effects cancel. The capacitance of a series of solutions with a ratio of ferricyanide to ferrocyanide ion concentrations of 1: 1 was measured as a function of the total concentration of the two ions, from a concentration of 5 X 10-2M to 3 x 1 0 - 3 ~ of each. The differential capacitance remained constant over
7.00 x 3.00 x 1.00 x 7.00 x 3.00 x 1.00 x 5.00 x 1.00 x 1.00 x 1.00 x 1.00 x 1.00 x 1.00 x
10-2 10-2 10-3 10-3 10-3 10-4 10-2 10-2 10-2 10-2 10-2 10-2
Concn. Fe(CN),4mole 1.1.00 x 1.00 x 1.00 x 1.00 x 1.00 x 1.00 x 1.00 x 7.00 x 3.00 x 7.00 x 3.00 x 1.00 x 5.00 x
10-2 10-2 10-2 10-2 10-2 10-2 10-2 10-2 10-2 10-3 10-3 10-3 10-4
la0
amp cm-2 0.493 0.321 0.229 0.185 0.109 0.075 0.050 0.620 0.380 0.197 0.116 0.079 0.052
that concentration range within experimental error. This indicates that the differential capacitance is essentially independent of the total concentration of the two anions, at least at the potential of an equimolar solution. Exchange currents, shown in Table I, were calculated by assuming that the observed overpotential time curves followed the simple exponential decay law dictated by pure charge transfer kinetics, 17 = q t = (-t/R,C,). The use of this equation presupposes that the contributions of mass transport processes to the observed decay are minimal. There are several criteria which can be applied to test this assumption (9,one of which is:
where C,, CR,Do, D E , n, F, R , T , Cd,and I,' have their usual significance. At the above concentrations, assuming that Do = DR = 10-5 cm2/sec, this inequality is satisfied by a factor of 80 in the most favorable case to a factor of 1.5 in the least favorable case. While it appears that the linear form of the equation is not applicable in certain instances, it should be recognized that this inequality determines the condition for pure charge transfer control throughout the entire relaxation time. However, even at low concentrations where the inequality is only marginally satisfied, the decay is essentially charge transfer controlled at short times. If a measurement of the slope of the log ($-time curve is made at short enough times, a good estimate of the exchange current can be made. The reaction order plot shown in Figure 5 was calculated using the discharge capacitance for all of the measurements. It is linear over the entire concentration range and gives a transfer coefficient of 0.50. The heterogeneous rate constant, calculated at a concentration of 10PM for each ion, was found to be 0.24 cmjsec. The exchange current of a solution of 0.01M ferrocyanide and 0.01M ferricyanide was measured at several temperatures. Log(I,") was plotted as a function of 1/T,and an activation energy of 3.13 to h 0 . 2 kcal/mole was calculated. Oxidized Electrodes. The exchange rate at oxidized electrodes was measured at several concentrations. The apparent heterogeneous rate constant was found to be 0.028 =t0.001 cmisec, at the 95z confidence level, which is about a factor (5) P.Delahay, J. Phys. Chem., 66,2204 (1962). VOL. 41, NO. 4, APRIL 1969
655
~~~
~~~~~~~
Randles and Somerton Jordan Jahn and Vielstich Agarwal Wijnen and Smit Wijnen and Smit Daum and Enke Daum and Enke a
Faradaic impedance Hydrodynamic voltammetry Rotating disk electrode Faradaic rectification Cyclic potential step Cyclic coulombic step Current impulse reduced electrode Current impulse oxidized electrode
(6)
-
0.09
(7)
-
(8)
0.61
O.OS(C)
(9)
0.49
-
(IO)
0.55
O.O95(C)
(10)
0.50
0.13(C)
-
0.50
0.24
-
0.46
0.028
0.08
of 10 less than that obtained with reduced electrodes. A reaction order plot revealed a transfer coefficient of 0.46 j=0.02 which compares favorably with that of 0.50 obtained with reduced electrodes. The exchange rate of a 0.01M ferricyanide and ferrocyanide solution was measured as a function of temperature, and the activation energy was found to be 3.49 A 0.5 kcal/mole. Thus the rate of the ferri-ferrocyanide exchange is greatly reduced by the presence of surface oxidation on the platinum while the transfer coefficient and the activation energy appear to be essentially unchanged. It is not possible to postulate the mechanism by which the surface oxidation affects the reaction rate without further rate studies on a variety of carefully controlled surface oxidation states. Such studies are currently under way in this laboratory. Mechanistic Conclusions. Nothing in the present investigation suggests that the rate of this reaction is affected by anything other than the simple electron transfer step. The linearity of the reaction order plot over the entire concentration range, the independence of the differential capacitance with respect to either the applied current or the potential, and the marked agreement between the charge and discharge capacitance at all but the highest concentrations all support this conclusion. One could propose a mechanism based upon (6) J. E. B. Randles and K. W. Somerton, Trans. Faraday Soc., 48, 937 (1952). (7) J. Jordan, ANAL.CHEM.,27, 1708 (1955). (8) D. Jahn and W. Vielstich, J. Electrochem. Soc., 109, 849 (1962). (9) H. P. Agarwal, ibid., 110, 237 (1963). (10) M. D. Wijnen and W. M. Smit, Rev. Trav. Chem., 79, 289 (1960).
9
ANALYTICAL CHEMISTRY
5.00
-
0
Fa (CN),
3-
4.60-
0
0
-” \
Results designated (C) were not reported by the respective authors but are calculated from their data.
656
1
~
Table 11. Comparison of Present JGnetic Results with Results of Previous Investigators. Apparent Std rate transfer const. Investigator($ Technique Ref coeff cm sec-l
8
0
k,= 0.24 cm sad’
4.20 -
-1
3.80 -I
.oo
0.00 LOG ( CR/CO)
I .oo
Figure 5. Reaction-order plot for the ferri-ferrocyanidecouple on platinum in 1M KCI at 25 “C the association constants measured by Eaton, George, and Hanania (3) of: (KflFe(CN)a)”S
+ K+ + e-
(K. + 1Fe(CN)6)’+s
but if such steps take place, the current impulse technique gives no information to prove or disprove them. The association-dissociation reaction is probably extremely rapid with respect to the electron transfer reaction. Comparison of Results. A comparison of the results of the present investigation with those of previous investigators is presented in Table 11. The current impulse technique gives a rate constant for reduced electrodes which is about twice as large as that measured by any of the other techniques, while that measured for oxidized electrodes is substantially less than any of the others. The estimates of the apparent transfer coefficient agree very well except for the value obtained by Jahn and Vielstich with the rotating disk electrode. It is our conclusion that the observed differences in the rate constants are primarily due to differences in electrode conditioning. We have shown that the apparent rate constant is dependent on the amount of surface oxidation, though the measurement of the transfer coefficient is not. The conditioning procedures reported by previous investigators promote varying amounts of surface oxidation as has been verified in this laboratory; so their results are bound to be lower than the ones of the present investigation. RECEIVED for review October 30, 1968. Accepted February 3, 1969. Work supported by the National Science Foundation, Grant GP-6572. Presented in part at the 155th National Meeting, ACS, San Francisco, Calif., April 1968.
