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ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
Investigations of the Ferricyanide-Ferrocyanide System by Pulsed Rotation Voltammetry W. J. Blaedel" and R. C. Engstrom Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53 706
monotonically increasing rotation rate ( 7 ) . T h e analytical usefulness of hydrodynamic modulation has been demonstrated using a sinusoidally modulated rotation rate hith phase sensitive detection to obtain scanning voltammograms a t the 5 X 10 M concentration level (8). T h e rate constants for a quasi-reversible electron transfer reaction were obtained, also using a sinusoidal rotation rate (9). Pulsed flow work in a laminar flow regime through tubular electrodes has also been reported (20). The purpose of the following work is to demonstrate the technique of pulsed rotation voltammetry (PRV), in which the rotation rate of a rotated disk electrode is switched between a high and low value, while the potential is held constant. By measuring the difference currents a t a number of discrete applied potentials, a voltammogram may be developed and plotted pointwise. The advantages and limitations of this experiment are demonstrated using the ferricyanide-ferrocyanide redox system at a glassy carbon rotated disk electrode. The heterogeneous rate constant ( k o )and the transfer coefficient (0)of the electron transfer reaction of that sqstem are evaluated using equations based on mass transport coefficients such as those presented originally by Jordan ( 1 1 ) and later by other workers (12, 23).
The technique of pulsed rotation voltammetry (PRV) at a rotated disk electrode involves switching the rotation rate of the electrode between two values, and measuring a difference current while maintaining a constant applied potential. Extremely low background signals are achieved at glassy carbon electrodes, allowing a detection limit of 1 X lo-' M ferricyanide. Well defined current-potential curves are obtained for the ferricyanide-ferrocyanide system, and estimates of the heterogeneous rate constant ( ko)and the transfer coefficient ( a )are reported.
T h e attainment of reproducible current-voltage data for low concentrations of electroactive compounds a t solid electrodes is difficult using conventional voltage scanning techniques. Several procedures have been devised to improve t h e quality of t h e voltammograms, including t h a t of steady-state voltammetry (SSV). As described in the literature ( I ) , SSV involves the application of a constant potential to the electrodes, and waiting for the transient current to decay, until a current is reached t h a t is constant with time. T h e steady-state current is the component that is due to transport of the electroactive material in solution, uncomplicated by the transients that represent charging and electrochemical reactions of the electrode surface. With these transients eliminated, background steady-state currents are very low, permitting discernment of very low concentrations of electroactive materials. The technique has been successfully applied to the electrochemical study of nicotinamide adenine dinucleotide a t the micromolar level (2). One drawback to SSV is the time required to reach a true steady-state. As long as an hour may be required for the transient currents to decay to nanoampere levels, so that acquisition of data for an entire voltammogram may require many hours. Also, error sources like drifting backgrounds and slow decomposition of the electroactive material may become important over a long experiment that are usually unimportant for short experiments. Instead of waiting to achieve the true steady-state current, a difference current may be measured between two different rotational speeds of a rotated disk electrode. The difference current is purely convective and is not influenced significantly by transient surface reactions of the electrode. The difference current may be measured before steady-state is reached, and the time of the experiment may be greatly reduced. T h e concept of hydrodynamic modulation is not new. I t has been used in the determination of rate constants at rotated disk electrodes by measuring current as a function of linearly increasing rotation rate (3) and linearly increasing square-root of rotation rate ( 4 , 5 ) . Miller, Bruckenstein, and coworkers have done a great deal of work in developing the theory and practice of hydrodynamic modulation a t rotated disk and ring-disk electrodes. In addition to a simple square-root function of rotation rate (6),they have designed a system for programming t h e speed of rotation to give any of a number of modulations that can be superimposed on a constant or
THEORY For the electron transfer reaction, '2
f
O f n e e R k b
the faradaic current, in terms of mass transport coefficients, is given by (12-14):
i=
1 e -+ - + -
Mo
MR
1 hf
In Equation 2.
(3)
I
(E- E")
k b = k o exp
(4)
(5) i,,c = n F A M , Co
*
il,a = -nFAMR CR * In Equations 2-7: C* represents the hulk concentration (mol/cm3) of the species denoted by the subscript; M represents the mass transport coefficient (cmjs) of the species denoted by the subscript; il,c and i,,a represent the limiting cathodic and anodic currents of the voltammogram of a
'a1978 American Chemical Society
0003-2700/78/0350-0476$01.00/0
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
mixture of 0 and R; and the other terms have their usual electrochemical significance. In practice, formal rate constants (k;, k;, ko' and 0') and a formal standard potential (E"') are determined and used at a constant ionic strength, instead of the thermodynamic values designated in Equations 2-7. For the work in this paper, it will be assumed that transport coefficients of the oxidized and reduced species are equal (Mo = M R = M).This assumption is supported by an estimate of 1.11 for the ratio M o / M R for the ferricyanide-ferrocyanide system (15). Only when 8 is close to unity will this approximation cause significant error. Such error will be avoided in treating data, and currents a t potentials close to E"' will not be used in the computation of kinetic parameters. A more rigorous derivation has been worked out for the case where MO and M R are not equal (26). The equations are quite complicated algebraically, and their use does not seem justified for the treatment of the ferricyanide-ferrocyanide system, whose oxidized and reduced forms are similar in weight and size. With the approximation that Mo = MR, Equation 2 becomes
477
M,, using the verified square-root dependence of current upon rotation rate. When the rates of mass transport and electron transfer are similar, that is, for a quasi-reversible system, a simple reladoes not exist. A more accurate tionship between E" and method of estimating E"' is to find the potential a t which Ai becomes zero for a solution containing known concentrations of ferricyanide and ferrocyanide: = E"'
Co + RT - lnnF CR
A similar argument for the oxidation of the reduced form results in a quadratic expression for k b , with
EXPERIMENTAL
For purposes of calculating rate constants, it is simpler and more accurate to deal only with solutions of the oxidized form (ferricyanide) alone, or of the reduced form (ferrocyanide) alone, in which cases, Equation 8 becomes 4,c
ic =
i+e+-
(9)
M
kf
21,a
ia =
1
M
e
hb
1+-+-
T h e cathodic difference current (Ai,) between a high and a low rotation rate may be expressed as:
Ai,
-
4,c.z
=
i+e+
- M2
4,c,1
i + o + - MI
In Equation 11,the subscripts 1 and 2 designate the values of M and of il,ca t low and high rotational speeds, respectively. Equation 11 may be solved for kf in terms of the quadratic formula
kf =
-B
+ \jB2 - 4AC 2A
where
A=
( e + i12--(eA i l c Ai,
+ 1)
T h e negative square-root term results in negative rate constants, and is not used. In practice, k f may be calculated using Equations 1 2 and 13 from a voltammogram of Ai, vs. E. For the calculation, M I ,M2, and E O ' must be known. M I and M2 may be calculated from the SSV limiting currents a t low and high rotational speeds, using Equation 6. Alternatively, MI may be calculated from the SSV limiting current, and M 2 may be calculated from
Apparatus. A rotated disk electrode system was constructed similarly to one described previously ( 2 ) , but with several modifications. The motor speed controller (Model S-47, Gerald K. Heller Co., Las Vegas, Nev.) was modified by putting an additional speed control potentiometer into the circuit. A two-position rotary switch was used to select which potentiometer controlled the speed of the rotated disk electrode. Voltages were applied to the two-electrode system with a battery powered potentiometer circuit and monitored with a digital voltmeter (Model 282, B&K Precision, Chicago, Ill.) of sufficiently high input impedance so as not to load the circuit. Currents were measured with a picoammeter equipped with a current suppression option (Model 414S, Keithley Instruments, Inc., Cleveland, Ohio). The output of the picoammeter was monitored on a strip-chart recorder (Model A5113-21, Houston Instruments, Austin, Texas). The rotation counting system consisted of a combination LEDphototransistor fitted over a twelve-slotted wheel attached to the electrode chuck. Voltage pulses produced by light pzsing through the slots were counted by an events counter (Model IM-4100, Heath Co., Benton Harbor, Mich.) modified to have a 5-s count time. The display therefore read revolutions per minute directly. The counting-rotation system was found to have a standard deviation of 0.74% (95% confidence limit). Electrodes. A 0.5-cm length of 3-mm glassy carbon rod (Grade 30s. Tokai Mfg. Co., Tokyo, Japan) was epoxied int.0 the end of a 0.5-in. o.d. Lucite rod (Rohm and Haas Co., Philadelphia, Pa.) with Epotek 349 (Epoxy Technology Inc., Watertown, Mass.) and polished with successively finer polishing paper, fcdlowed by a 0.1-fim alumina slurry, until a mirrorlike finish was obtained. The reference electrode was a chloridized silver wire in 0.0100 M KC1 (2). A frit permeated with agar gave very low leakage between the reference and sample compartments of the cell. Reagents. Tap distilled water was redistilled from alkaline permanganate and this was used to prepare all solutions. The supporting electrolyte was 0.1 M phosphate buffer (pH 7.50), prepared from reagent grade potassium salts (Fisher Scientific, Fair Lawn, N.J.). K,Fe(CN), and K4Fe(CN)G.3H20(hldinckrodt Chemical Works, St. Louis, Mo.) were used without further purification for 0.01 M stock solutions of the oxidized and reduced forms. For an electrochemical experiment, aliquots of the stock solutions were injected into the supporting electrolyte to give the desired concentration. Ferrocyanide solutions were prepared with deaerated buffer just before use. Procedure. All work was performed in a thermostated cell at 25.0 f 0.2 "C. A 100-mL aliquot of buffer was pipetted into the cell and pretreatment of the electrode begun. This consisted of cycling the applied potential between +1.0 V and -1.0 V for two cycles, allowing 10 min at each voltage. The system was deaerated during pretreatment by bubbling water-saturated nitrogen through the solution. At the end of this time, the nitrogen delivery tube was raised just above the surface of the liquid for the remainder of the experiment. A background voltammogram
478
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
n
0
1 SCAN
/
I
0
I
u -0.0 -0.2 -0.4 APPLIED POTENTIAL, v o l t s
0.2
-0.6
-0.8
Figure 2. Current-potential curves for 10 pM ferricyanide in 0.1 M phosphate buffer, pH 7.5. Conditions: As in Figure 1 I
0.4
I
0.2
I
I
1
I
0.0 -0.2
-0.4 -0.6 APPLIED POTENTIAL,volts
L
-0.0
1500 rprn
Figure 1. Background current-potential curves for 0.1 M phosphate buffer, pH 7.5. Rotation rate, 500 rpm for scan and SSV, 500 and 1500 rpm for PRV. Pulsing frequency, 15 s
-
was obtained by setting the applied potential to the initial value. The current was allowed to decay until the baseline no longer changed rapidly (this usually took no more than a minute), then the rotation rate was switched from its lower value (500 rpm) to its higher value (1500 rpm). The switching was done three times at each potential, about 15 s being allowed at each rotation rate. After three pulses, the potential was reset to the next value and the pulsing repeated. For rate constant calculations, the current was allowed to reach a steady-state at the final potential, and its absolute value recorded for the calculation of mass transport coefficients. The potential was then reset to the starting point, and an appropriate amount of the analyte stock solution added with an Oxford Sampler (Oxford Laboratories, Foster City, Calif.). Five minutes of deaeration was performed before beginning the voltammogram of the analyte. Data Treatment. The strip chart recordings of the picoammeter output were read by means of a digitizer (Numonics Corp., North Wales, Pa.) interfaced to a desk-top programmable calculator (TEK 31, Tektronix Inc., Beaverton, Ore.). The calculator was programmed to compute the average difference current for each potential on the voltammogram. It also performed the calculations for the estimation of h f or k b . Plots were made of In kf or In k b vs. E - Eo', and ko' and (Y were determined from the intercept and slope, respectively. RESULTS AND DISCUSSION
Mass T r a n s p o r t . The dependence of limiting current on rotation rate was evaluated using 10 pM potassium ferricyanide over the range of 200-2000 rpm. A log-log plot of current against rotation rate was completely linear with a slope of 0.495 f 0.003 (9070 confidence limit) (17),indicating nearly ideal behavior for the rotating disk electrode. This relationship was used to calculate M 2 from the SSV measurement of MI. B a c k g r o u n d Voltammogram. Figure 1 shows a comparison of the background current-voltage curves of the phosphate buffer obtained from a conventional scanning mode, a steady-state mode, and a pulsed rotation mode. The scanned background is very large due to the current associated with double layer charging. It is also comparatively noisy, and the magnitude depends on the direction and rate of scan. The steady-state current is much smaller than the scanned current because there are no charging currents. Slow surface reactions at the electrode and electrolyte decomposition are postulated t o account for the major portion of the SSV current. The pulsed mode shows an extremely low background, indicating good correction for electrode surface currents and electrolyte
30
"oL I min
500 rprn
Figure 3. PRV current-time record for 10 pM ferricyanide, Conditions: As in Figure 1. at -0.6 V decomposition. T h e PRV curve also indicates the virtual absence of electroactive impurities in the potential range of +0.2 to -0.6 V. The nonconvective nature of solvent decomposition observed in SSV and in PRV should permit measurement to be made over a wider voltage range than for conbentional scanning voltammetry. It should be noted that the PRL' data was taken in about 20 min, compared to several hours for the SSV curve. Calculation of Electron E x c h a n g e R a t e C o n s t a n t s i n t h e Ferricyanide-Ferrocyanide System. Reduction of 10 pM Fe(CN)2-, corrected for background, by SSV and by PRV is shown in Figure 2. Very well defined waves and plateaus were obtained bq both techniques. Figure 3 is the currenttime record for a point on the plateau of the PRV curve of Figure 2. To e\ aluate the mass transfer coefficients from the limiting current and Equation 6, the electrode area must be known. This was done both electrochemically and optically. T h e electrochemical determination was done using literature values of the diffusion coefficient of ferricyanide in 0.1 M KC1 (151, and calculating the area from the limiting current in that medium, based on the Levich equation, and using the experimentally determined exponent of rotation rate. A value of 0.0847 cm2 was found. Microscopic measurement of the electrode diameter using a calibrated micrometer eyepiece yielded an area of 0.0873 i 0.0018 cm2. A 3.1% difference exists between the two measurements, and the optically determined value was used in further calculations. The formal standard potential was determined by preparing an equimolar solution of both redox species in phosphate buffer, and by PRV in the region of zero current, observing
ANALYTICAL CHEMISTRY, VOL. 50, NO. 3, MARCH 1978
Table I. Rate Constants for the Ferricyanide- Ferrocyanide System' Potential region ho'cm/s x l o 3 01 Cathodic 4.7 i 0.7 0 . 2 3 i 0.03 Anodic 5.4 0.69 ' Tabled values accomoanied bv 90% confidence limits. the potential where the current crosses the voltage axis. Triplicate determinations of Eo' gave 0.054 h 0.003 V (90% confidence limit). Triplicate voltammograms of 10 1IU ferricyanide reduction was obtained, and values of In k f , calculated from Equation 12, were plotted against the applied potential. The values of ko' and a obtained from cathodic reduction data are reported in Table I. Values are also given from the anodic oxidation of ferrocyanide. T h e values of ko' from the oxidation and reduction agree reasonably well with one another. They are similar to determinations (0.00154).0071cm/s) reported under various conditions at carbon paste rotated disk electrodes (18), and somewhat larger than values around 0.002 cm/s reported for glassy carbon tubular electrodes (13). Discrepancies among literature values of ho' for the ferricyanide-ferrocyanide system a t solid electrodes are prevalent, and may be ascribed largely to differences in history and pretreatment of the electrodes. A thorough study of modes of preparation and pretreatment of solid electrodes is called for. T h e values of the transfer coefficient, a , obtained from oxidation and reduction data, are decidedly not in agreement with one another. Associated with this is the observation that all of the plots of In kf or In k b vs. E - E"' show a deviation from linearity a t low values of overpotential. The deviation for cathodic data is in a direction t h a t approaches the slope for anodic data, and vice-versa. This phenomenon is not unique to the experimental method presented here, but has been observed in a similar chemical system a t glassy carbon turbulent tubular electrodes, where a definite change in slope occurs near zero overpotential for solutions containing both ferricyanide and ferrocyanide (13). This indicates that there is a different transfer coefficient for the oxidation than for the reduction, implying that something more than a simple electron transfer between the two species is taking place. Apparently this is not restricted to glassy carbon electrodes. At graphite rotating-disk electrodes, the formation of a dimer consisting of one molecule of ferricyanide and one molecule of ferrocyanide, which reacts more readily than either form alone, has been postulated (19). Other possible explanations for nonlinearity in Tafel plots of the ferricyanide-ferrocyanide system have been suggested: they include a potential-dependent transfer coefficient ( 2 0 , and an influence on the electron transfer by ion-pairing (21). At micromolar concentrations, this last idea can be ruled out. S e n s i t i v i t y of PRV. Two separate experiments were performed to determine the linearity between the difference current (&) and the ferricyanide concentration, for an applied potential in the current-limited region of Figure 2. The concentration range &lo pM gave a least squares slope of 19.4 f 0.2 nA/pM (90% confidence limits) and the range of 0-100 pM yielded 19.2 f 0.2 pA/fiM:
I
479
"QLm I min
IO nM K,Fe(CN),
BACKGROUND
Figure 4. PRV current-time record for 10 n M ferricyanide. Conditions: As in Figure 1, at -0.6 V
Although the blank has a definite l i signal, its noise level in this system is only nA. Based on a signal-to-noise ratio of 1,the limit of detection for ferricyanide should be around 10 nM. Current-time traces are given in Figure 4 for 10 nM potassium ferricyanide and for blank buffer solution, verifying experimentally the detectability of that concentration.
CONCLUSIONS The technique of pulsed rotation voltammetry is designed primarily t o compensate and correct for nonconvective background currents that trouble conventional voltammetric techniques at solid electrodes. It is a potentiostatic technique that is considerably more rapid than steady-state voltammetry without sacrifice of data quality. It offers both qualitative and quantitative information on the measurement of electroactive material, and on electron transfer kinetics. Instrumentation is relatively simple, and the experiment is easy to perform. PRV bas been used to obtain the rate constants for heterogeneous electron transfer in the ferricyanide-ferrocyanide system a t a glassy carbon rotated disk electrode. Electrochemical kinetic studies with PRV are in progress on systems involvipg riboflavin, nicotinamide adenine dinucleotide, and porphyrin compounds. LITERATURE CITED W. J. Blaedel and R. A. Jenkins, Anal. Chem., 46, 1952 (1974). W. J. Blaedel and R. A. Jenkins, Anal. Chem., 47, 1337 (1975). K. Prater, J . Elecfrochem. Soc., 115, 27C (1968). S. C . Creason and R. F. Nelson, J . Nectroanal. Chem , 21, 548 (1969). S. C. Creason and R. F. Nelson, J . Electroanal. Chem.. 27, 189 (1970). (8) B. Miller and S. Bruckenstein, J . Electrochem. Soc., 117, 1032 (1970). (7) B. Miller, M. I. Bellavance, and S. Bruckenstein, Anal. Chem., 44, 1983 (1972). (8) B. Miller and S. Bruckenstein. Anal. Chem.. 46, 2026 (1974). 19) B. Miller and S. Bruckenstein, J . Necfrochem. SOC., 121, 1558 (1974). (10) W. J. Blaedei and D. Iverson, Anal. Chem., 48, 2027 (1976). (11) J. Jordan, Anal. Chem., 27, 1708 (1955). (12) R. N. Adams, "Electrochemistry at Solid Electrodes", Marcel Dekker, New York, N.Y., 1969. (13) W. J. Blaedel and G. W. Schieffer, J. Electroam/. Chem., 80, 259 (1977). (14) A detailed derivation of Equation 2 is available upon request. (15) D. Sawyer and J. L. Roberts, Jr., "Experimental Electrochemistry for Chemists", John Wiley and Sons, New York, N.Y.. 19'74. p 77. (16) Younghee Hahn, unpublist@ work, University of Wisconsin-Madison, 1977. (17) W. J. Blaedel and D. Iverson, Anal. Chem., 48, 1240 (1976). (18) Z. Galus and R. N. Adams, J , Phys. Chem., 67, 866 (1963). (19) R. Sohr, L. Miller, and R. Landsberg, J. Elecfroanal. Chem., 50, 55 (1974). (20) D. N. Angel1 and T. Dickenson, J . Electroanal. Chem., 35, 55 (1972). (21) D. J. Bieman and W. R. Fawcett, J , Nectroanal. Chem.. 34, 27 (1972). (1) (2) (3) (4) (5)
RECEIVED for review September 15,1977.Accepted December 5, 1977. This work was supported in part by a grant (No. CHF-7615128) from the National Science Foundation.
