200
ii
150
%
-;
100
E
SO
-06x1
-BW
-
950
-1100
-1250
E I m V v s . SCE)
Figure 7.
Neopolarograms for nickel(l1)reduction with various initial
potentials Ramp-rate: 102 mV s-'; other conditions: as in Figure 6
1 dm --=
-an
slope = m, d E 86.8mV at 298 K. Using this equation and the curves shown in Figure 3, an values were calculated for each ramp-rate, the results again being collected in Table IV. Apart from the datum obtained from the 509 mVls ramp-rate (where pen response may have been a complicating factor), the values agree well and give an an average value of 0.50. Table IV permits an intercomparison of an values determined for iodate reduction by all three neopolarographic methods. Though the agreement is less than might have been hoped, the scatter averages only 0.04 and confirms that theory and experiment are in broad agreement. Possible causes of the discrepancies include: imperfect correction for sphericity, interference from nonfaradaic and other background effects, and neglect of the role of the double-layer structure (1)on the kinetics of 103- reduction. Essentially similar results were obtained for Ni2+reduction. Values of an were calculated by the same method used for 103- and the data are likewise assembled into Table IV. The agreement between an values determined by the various methods is no better than in the iodate case, but it is interesting to note that the results for the two electroreducible species do not parallel each other. This suggests that divergencies arise from idiosyncrasies of the individual systems,
rather than reflecting any general inadequacy of the theory* Finally, a method of determining an was employed that does not hinge on the theory presented in this article. This method uses Equation 7 and consists of plotting log (m, m)li vs. E . Figures 5 and 6 show these plots for iodate and nickel ion reductions respectively. From the slopes of the lines shown in these diagrams, which, it should be noted, embrace several ramp-rates, the an values reported as the final items in Table IV were calculated. Agreement with the other tabulated values is good. Figure 7 shows neopolarograms for the reduction of Ni2+ for a variety of initial potentials. We have not attempted to correlate these curves quantitatively with theory, but the qualitative agreement with Figure 2 is evident.
ACKNOWLEDGMENT The computational assistance provided by Penny Dalrymple-Alford and Chummer Farina is gratefully acknowledged. LITERATURE CITED (1) J. C. lmbeaux and J. M. Saveant, J. Electroanal. Chem., 44, 169 (1973). (2) M. Goto and K. B. Oldham, Anal. Chem., 45, 2043 (1973). (3) P. E. Whitson, H. W. VandenBorn, and D. H. Evans, Anal. Chem., 45, 1298 (1973). (4) M. Grenness and K. B. Oldham, Anal. Chem.. 44, 1121 (1972). (5) J. M. Saveant and D. Tessier, J. Electroanal. Chem., 65, 57 (1975). (6) K. B. Oldham and J. Spanier. J. Electroanal. Chem., 26, 331 (1970). (7) K. B. Oldham and J. Spanier, "The Fractional Calculus", Academic Press, New York, 1974. (8) P. Delahay and J. E. Strassner, J. Am. Chem. SOC.,73, 5219 (1951). (9) K. B. Oldham, unpublished work, details available on request. (IO) R. S. Nicholson and I. Shain, Anal. Chem., 36, 706 (1964). (11) W. H. Reinmuth, Anal. Chem., 34, 1446(1962). (12) A. Sevcik, Collect. Czech. Chem. Commun., 13, 349 (1948). (13) W. H. Reinmuth, Anal. Chem., 33, 1793 (1961). (14) M. Goto and K. 8. Oldham, Anal. Chem., 46, 1522 (1974). (15) K. B. Oldham, Anal. Chem., 45, 39(1973).
RECEIVEDfor review February 11,1974. Resubmitted March 16,1976. Accepted May 10,1976. The financial support of the National Research Council of Canada is gratefully acknowledged.
Optical PathIength Considerat ions in Transmiss ion Spectroelectrochemical Measurements F. R. Shu' and G. S. Wilson" Chemistry Department, University of Arizona, Tucson, Ariz. 8572 I
A transmission spectroelectrochemical cell is described in which the optical path length can be varied to enable consideration of its effect on electrochemical characleristlcs such as cell time constant. The utility of the short pathlength cell was demonstrated in the measurement of the second order homogeneous electron transfer rate constant for the reaction of horse heart cytochrome c and hexaammineruthenium(11).
Present address, Smith Kline Instruments, Inc. 880 W. Maude Ave., Sunnyvale, Calif. 94086 1676
In the course of investigating electron transfer reactions involving fast kinetics via transmission spectroelectrochemical techniques, it is necessary to measure the absorbance changes corresponding to chemical reactions taking place at the electrode surface or in the diffusion layer of the working electrode. Under these conditions, the diffusion layer constitutes only a small fraction of the total optical path length. Thus, it is necessary to measure a small difference between two large numbers if the original reactant absorbs appreciably. Clearly, greater sensitivity can be achieved by reducing the total path length. Such an approach might lead to the use of optically transparent thin-layer electrodes (OTTLE). These have been used to considerable advantage for both chemical and biochemical applications ( 1 4 ) , especially where final spectral
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
measurements are made under null current conditions. Unfortunately, thin-layer cells often exhibit large resistive effects which lead to poor potentiostatic control of the working electrode and nonuniform current density across the electrode surface (5, 6). In some applications (7), it is also desired to measure small absorbance changes in short times ( G O ms). It is necessary in such cases to perform multiple experiments (ensemble averaging) and this, in turn, requires that the reaction layer be “refilled” after each experiment. We have shown that this can be conveniently accomplished by stirring the solution (7). In this report, a variety of electrochemical experiments have been performed to demonstrate the conditions under which reliable spectral observations can be made in a short path length cell without interfering with the electrochemistry.
Table I. Electrochemical Evaluation of Cell Characteristics Optical path length cm
Estimateda
R (ohms)
R C (ms)
0.021 80 0.22 0.065 50 0.12 0.097 44 0.10 UEstimated from Equation 1 using solution blank, AE = 0.4 V, Elect. area z 0.27 cmz.
A I
10.1
EXPERIMENTAL t
Apparatus. The spectroelectrochemical cell was similar to that of Hawkridge and Kuwana (8)except that the body was constructed of Kel-F rather than Lucite because of superior chemical resistivity. The optical path is defined on one side by an optically transparent tin oxide electrode and on the other by an approximately 1.5-cmlight pipe (Yg-in. diameter image conduit, American Optical Co.) with its optically flat ends oriented parallel to the electrode. The light pipe was permanently mounted by drilling a 0.32-cm hole in the rear of the cell block and cementing in place. The light pipe was positioned above the center of the cell cavity so that a small stirring bar could freely rotate a t the bottom of the cell. A piece of P t wire sealed into the cell block served as the counter electrode. The wire was coiled around the light pipe near the indicating electrode end so that product generated there would not interfere with observations a t the indicating electrode. The reference electrode (Ag/AgCl) was constructed as described previously ( 8 ) except that a luggin capillary constructed of polyethylene was used to orient the reference electrode probe immediately adjacent to the end of the light pipe. This modification improved the cell response significantly. The indicating electrode was constructed with a 1.5 X 2 cm square of Sb-doped tin oxide (20 ohms/square) glass. The square was then painted with silver conductive paint so as to define a masked circular window slightly larger than the end of the light pipe. A thin layer of silicone rubber (Dow-Corning Silicone Rubber Sealer) was then applied to the electrode to mask that portion of the conducting paint which would otherwise come in contact with the solution. The electrochemicalinstrumentation included a Princeton Applied Research Model 173 Potentiostat and Exact Model 126 signal generator. A double beam spectrophotometer was constructed using a 100-watt tungsten quartz iodine light source (Sylvania 6.6A/T2 1/2 Q/CL) Jarrell-Ash Model 82-410 (0.25 meter) monochromator, matched 1P28A photomultiplier tubes, Burr-Brown (Tucson, Ariz.) Model 3402A amplifiers as current-voltage transducers, and an OEI (Tucson, Ariz.) Model 2534 high speed log ratio converter. From this apparatus, an absorbance readout of 1.0 V/absorbance unit was obtained. All experiments were run under the control of a HewlettPackard 2100 minicomputer using a data acquisition system described previously (7,9). Reagents. All chemicals used in the present study were reagent grade unless otherwise specified and were used without further purification. Cytochrome c (Sigma Type VI) was prepared in 0.2 M phosphate buffer, pH 6.45, and was used to calibrate the optical path length of the cell. Methyl viologen was obtained from K and K Laboratories. Hexaammineruthenium(II1) chloride was purchased from Strem Chemicals, Inc.
RESULTS AND DISCUSSION Evaluation of Cell Spectral Characteristics (Static). Spectroelectrochemical cells with light paths of 0.021,0.065, and 0.097 cm, respectively, were constructed for evaluation. The spectrum of reduced cytochrome c was measured from 400 to 600 nm and, in each case, was found to agree with that reported previously (10). Agreement was also observed for Beer’s law as measured by the difference in molar absorptivity of the bands at 550 and 535 nm, respectively. Thus, it can be concluded that the use of a light pipe has no apparent effect on the quality of spectral measurements in the visible region.
7
+ +
5
p / 2
,
/I
1
SEC.l/2
Figure 1. Current-time curve for potentiostatic reduction of methyl viologen Uncorrected current (++);current corrected using Equation 11, Reference 11 (AA).R = 44 ohms, RC = 0.14 ms. Concn MV2+ = M. Potential step -0.45 to -0.8 V v s Ag/AgCI electrode. Results averaged from 7 experiments
The photometric broad band noise (0.001 A.U. P-P) of the system was not appreciably affected by the presence of the light pipe. Evaluation of Cell Electrochemical Characteristics. The time constant of the electrochemical cell was evaluated using the recently described method of Perone and co-workers (11)in which it is assumed that the charging current is given by
where AE is the size of the potential step; R , the total uncompensated resistance; and C, the capacitance of the electrode double layer. The cell constant was determined from a potential step of 0.4 V in a solution containing only the phosphate buffer. The current was measured over the time interval 0 < t < 0.5 ms. The values obtained are shown in Table I. It will be noted that influence of the light pipe on the resistance begins to become pronounced below a path length of 0.065 cm. If current-time data are to be utilized in the potential-step experiment, particularly at concentrations of 10-4 M or less, correction for charging current is absolutely essential. Unfortunately, the blank solution does not take into account the effects on the cell time constant resulting from the addition of the electroactive species. To deal with this difficulty, Perone and co-workers (12)have recently proposed a theoretical model which ‘permits the estimation of the charging current in the presence of a faradaic component. Figure 1shows that it is possible to obtain linear Cottrell behavior to within less than two cell time constants by subtracting the charging current using the correction procedure (11).A similar correction procedure has been developed which does not depend on the mechanism of the associated chemical reaction (13).Virtually identical results are obtained. From the Cottrell slope, a diffusion coefficient of 7.9 X 10-6 cm2/s can be calculated for methyl viologen (MV2+)in its reduction
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
1677
z: ,001 0.0
I
00
0 10
0 05
T"',
Figure 2. Absorbance-time curve for potentiostatic reduction of methyl
viologen Conditions same as Figure 1. Monitor wavelength 602 nm. Results averaged from 35 experiments
to the free radical (MV.+). This value compares favorably with a value of 7.5 f 0.5 X cm2/s obtained from the potential step chronoabsorptometry experiments to be described subsequently. As Perone has pointed out (11),the correct Cottrell slope is not obtained until rather long times (in our case greater than 0.5 ms) where the corrected data converge. Cyclic Voltammetry. The cyclic voltammetric behavior of methyl viologen is very similar to that reported by Steckhan and Kuwana (14). The cathodic peak current (i,J varied linearly with scan rate over the range 0.039-16 V/s. The peak current ratio (ipJipa) was essentially unity over the scan range studied. The peak separation ( U pwhere ) hE, = E p c- E,, increases with scan rate ( u ) as noted previously ( 1 4 ) and this is attributed to the inherent resistance of the tin oxide film. If a plot of peak separation vs. h i s extrapolated to zero scan rate, AE, values in the range of 0.045-0.053 V are obtained. It is possible that in addition to the resistive properties of the film, the behavior also is influenced to some extent by the presence of the light pipe, especially a t low scan rates. Over the range studied, the peak separation does not depend on path length. A zero peak separation would be expected for the limiting case of a true thin-layer cell (15). Potential Step Chronoabsorptometry. The absorbance-time response to a potential step is shown in Figure 2. The least-square fit follows the Cottrell equation for times greater than one time constant. It should be noted that these data are uncorrected for charging current; however its effect is apparent at short times. If the region between the y-intercept and the first data point (100 ws) is expanded, it can be shown that the absorbance-time curve (Figure 2) will pass through the origin. Thus, a lag time is produced during which current flow occurs but no product is produced. Data appear to be usable without correction after 1-2 time constants. Thus, it is still easier, in this case, to achieve linear Cottrell behavior with absorbance monitoring in this system than with current measurements. The very high molar absorptivity of MV.+ at the monitoring wavelength contributes significantly to this conclusion. After application of a potential step, the diffusion layer will move out into solution eventually reaching the end of the light pipe. At this point, the condition of semiinfinite linear diffusion no longer applies. For the 0.021-cm cell, deviation occurs at about 250 ms. This is considerably sooner than would be expected since the diffusion layer thickness should equal the optical path length after about 60 s. Undoubtedly, the diffusion layer is distorted by the irregular current flux resulting from the cell geometry. At times less than 100 ms, no difficulties are encountered. The thin layer cell has been used to measure the second1678
T , SEC
0 15
SEC"'
I
04
02
0.0
Figure 3. Absorbance-time curve for the reaction of Ru(NH&*+Cyt."'c Reaction condition: Ru(NH3)e3+= Cyt."'c = 1 X lov4 M; 0.2M acetate buffer, pH 3.48.The potential was stepped from 0.2V to -0.5 V (vs. Ag/AgCI) and back (T = 0.2s).Absorbance monitored at 550 nm. Results averaged from 7 steps. Solid line = rate constant 6 X lo4 M-' s-'
order rate constant of the reaction between iron(II1) cytochrome c and hexaammineruthenium(I1):
(2)
R u ( N H ~ ) +~ e~ -+R u ( N H & ~ +
+
+
Ru(NH~)~~ Cyt'I'C + + R u ( N H & ~ + Cyt%
(3)
The reaction was monitored at 550 nm using a cell with a light path of 0.1 cm. As was expected, at least a sevenfold reduction in background absorbance was observed. Between 30 and 50 experiments were required to obtain a S/N ratio of 6 as compared to about 100 in the absence of the light pipe. Conditions can be further improved by signal conditioning with a 2-pole Butterworth filter (fo = 100 Hz) where only 7 to 15 cycles of signal averaging were required to achieve a smooth experimental curve (SJN = 6). A representative example of the experimental results is demonstrated together with a digital simulation curve in Figure 3. This result is in good agreement with the data reported in the literature (16).
CONCLUSION The above described cell is well suited to experiments in which the diffusion layer is kept thin with respect to the optical path length. Because of the resistive properties of the tin oxide film, correct electrode potentials cannot be maintained (even in the,absence of a light pipe) and these effects are apparently accentuated by the light pipe. Use of a more highly conducting thin film would aid this difficulty. The cell, however, will function most effectively under conditions where the current-time response is less strongly dependent on potential control, i.e., a potential step to the diffusion plateau. ACKNOWLEDGMENT We thank S. P. Perone for helpful discussions concerning this work and for providing preprints of the work cited.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 12, OCTOBER 1976
LITERATURE CITED W. R. Heineman, J. N. Burnett, and R. W. Murray, Anal. Chem., 40, 1970
(1968). G. Peychal-Heiling and G. S. Wilson, Anal. Chem., 43,545 (1971). J. G.Lanese and G. S . Wilson, J. Electrochem. Soc., 118, 1039 (1972). W. R. Heineman, B. J. Norris. and J. F. Goelz, Anal. Chem., 47, 79
(1975). I. B. Goldberg, A. J. Bard, and S.W. Feldberg, J. Phys. Chem., 76,2550
(1972).
I. B. Goldberg and A. J. Bard, J. Elecfroanal Chem., 38, 313 (1972). M. D. Ryan and G. S . Wilson, Anal. Chem., 47,885(1975).
F. M. Hawkridge and T. Kuwana, Anal. Chem., 45, 1021 (1973). L. Ramaley and G. S. Wilson, Anal. Chem., 42, 606 (1970). D. Keilin and E. C. Slater, Br. Med. Bull., 9,89 (1953). K. F. Dahnke, S. S. Fratoni, Jr.. and S. P. Perone, Anal. Chem., 48, 296 f 1976). (12) S. S. Fratoni, Jr., and S. P. Perone, Anal. Chem., 48, 287 (1976). (13) S. S. Fratoni, Jr., and S. P. Perone, J. Electrochem. SOC.,in press. (14) E. Steckhan and T. Kuwana, Ber. Bunsenges. fhys. Chem., 78, 253 (1974). (8) (9) (10) (11)
(15) A. T. Hubbard and F. C. Anson in "Electroanalytical Chemlstry", Vol. 4, A. J. Bard, Ed., Marcel Dekker, New York, 1970. (16) R. X. Ewall and L. E. Bennett, J. Am. Chem. SOC.,96, 940 (1974).
RECEIVEDfor review December 3,1975. Accepted June 21, 1976. This work was supported by National Science Foundation Grant MPS-73-08683 and by the Office Of Research.
Rotating Ring-Disk Enzyme E ectrode for Surface Cata ysis Studies F. R. Shu' and G. S. Wilson* Department of Chemistry, University of Arizona, Tucson, Ariz. 8572 7
A rotatlng rlng-disk enzyme electrode (RRDEE) has been developed and evaluated. The enzyme, glucose oxldase, Is immobilized at the surface of a carbon paste electrode. The progress of the enzymatic reaction was monitored at either the ring or disk. By varylng the electrode rotatlon speed, the rates of substrate mass transport and catalytic reaction can be distinguished. The theory describing the electrode response has been developed and Is in good agreement with experiment. The kinetic parameters of the immoblllzedenzyme have been determined along with the properties of the modified electrode surface. Performance as a selective sensor is discussed.
In recent years, there has been considerable interest in applying immobilized enzymes for specific assays. Among these applications, the so-called enzyme electrode is quite unique because it combines the enzyme specificity with the sensitivity and convenience of electroanalytical techniques in a compact form to facilitate analysis. The enzyme electrode is usually prepared by attaching an immobilized enzyme layer to an electrochemical sensor so that changes occurring as a result of the enzyme reaction can be monitored either potentiometrically or amperometrically (2-3). Regardless of the electrode sensor type, enzyme electrodes to date have been operated in a stationary manner. The mass transport of substrate to the catalytic layer is therefore controlled mainly by solution stirring and the diffusion rate inside the immobilized enzyme matrix ( 4 ) .Neither of these processes is very effective in bringing the product of the enzyme reaction to the electrode surface. A recent model study of the theoretical aspects of amperometric enzyme electrodes by Me11 and Maloy has shown that the sensitivity of a stationary enzyme electrode is determined by the proper balance of the catalysis rate of the enzyme on one hand and the diffusion rate of the substrate on the other ( 4 ) .Since both processes are inherent properties of a particular system, it becomes apparent that there is very little one can do to improve the efficiency or the sensitivity, in practice, of a stationary enzyme electrode. Furthermore, as pointed out by these authors, the lack of a well defined boundary condition to describe the mass transport represents another difficulty in predicting the steady-state current of a stationary enzyme electrode. This, in turn, limits the potential of using a stationary enzyme electrode to evaluate the kinetic
Present address, Smith Kline Instruments, 880 W. Maude Ave., Sunnyvale, Calif. 94086.
parameters of reactions at immobilized biosurfaces or other catalytic surfaces. A rotating electrode provides several attractive advantages over its stationary counterpart. First, the rate of transport of a species from the bulk of the solution to an electrode can be controlled by varying the rotation speed of the electrode. The hydrodynamics of a rotating disk electrode is well defined (5). Therefore, it is possible to make mass transport competitive with the enzyme catalysis rate. As a result, the sensitivity of a particular enzyme electrode could be significantly imbroved. Second, because of the convective nature of the electrode, one would expect that a rotating enzyme electrode should give much faster response than a stationary electrode. This, of course, would shorten the analysis time. The third advantage of a rotating enzyme electrode is its potential as a tool for investigating the kinetics of surface catalytic reactions. Since the boundary conditions of a rotating disk electrode are well defined, a reliable mathematical model can be derived to predict its behavior. We have carried out a study to develop a rotating disk enzyme electrode and to investigate the theoretical aspects of its performance. The system we selected to study is the glucose-glucose oxidase reaction: Glucose
+ 02-
glucose oxidase
Gluconic acid
+ H202
(1)
The formation of H202 is coupled with a fast indicator reaction: HzOz
+ 2H+ + 2I--
molybdate
12
+ 2H20
The amperometric detection of the formation of 12 serves to measure the overall extent of the reaction (4, 6). In addition to the theoretical studies, we also present some preliminary investigations of enzyme electrode performance.
EXPERIMENTAL Instrumentation. The four-electrode potentiostat used in the present study was similar to that described by Shabrang and Bruckenstein (7). The rotating ring-disk electrode, Model DT-6, was purchased from Pine Instrument Co., Grove City, Pa. The disk part of the electrode was a 0.5-cm deep cavity with a diameter of 0.764 cm according to the manufacturer's specifications. Therefore, the calculated area of the disk electrode was 0.46 cm2 when the cavity was filled with carbon paste. The width of the platinum ring electrode was 0.024 cm. It was separated from the disk electrode by a 0.016-cmwide epoxy gap. The collection efficiency of the DT-6 electrode was 0.18 as calculated from theory (8).A heavy gauge platinum wire counter
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
1679
