594
Anal. Chem. 1981, 53, 594-598
Determination of Reduction Potentials and Electron Transfer Stoichiometries for Biological Redox Species by Thin-Layer Pulse and Staircase Coulometry Chih-Ho Sui and William R. Heineman* Department of Chemistry, Unlversgv of Cincinnati, Cincinnati, Ohio 4522 1
Two new electrochemical technlques, thln-layer pulse coulometry and thin-layer staircase coulometry, are evaluated for determining Eo’ and n values of redox couples. Biologlcal species whlch undergo slow or negligible heterogeneous electron transfer can be studied by an indirect procedure with a mediator-tltrant. The technlques are evaluated on ferrlcyanlde, 2,6-dlchlorophenoiindophenol, and cytochrome c. Slnce the technlques do not require optical monitorlng, they complement exlstlng thin-layer spectroelectrochemlcal technlques for studylng blologlcal redox systems.
Investigating the redox characteristics of biological redox systems is important for understanding biological processes such as oxidative phosphorylation and photosynthesis (1,2). The measurement of formal reduction potentials (EO’) and electron transfer stoichiometries ( n values) is a significant aspect of these investigations. The popular electrochemical techniques of cyclic voltammetry and polarography have been useful for studying the numerous biological species that are electroactive. However, many biological species such as cytochromes (3-7) and ferredoxins (8) undergo heterogeneous electron transfer very slowly or irreversibly. Such nonideal behavior is usually attributable to severe adsorption of the biocomponent or to insulation of the redox center from the electrode by surrounding protein structure. Electrochemical techniques based on mediator-titrants have been developed and effectively used to study such systems. Kuwana and co-workers initiated the indirect coulometric titration method and applied it to the study of cytochrome c (9),cytochrome c oxidase (IO),and intact mitochondria and submitochondrial particles (11). Hawkridge and co-workers have studied soluble spinach ferredoxin by this technique (12). Heineman and co-workers developed a spectroelectrochemical method based on the optically transparent thin-layer electrode (OTTLE) and applied it to the study of cytochrome c (3,13) and myoglobin (13). Both of these techniques are based on the simultaneous acquisition of electrochemical and spectral parameters. In the case of the OTTLE spectropotentiostatic method, redox changes in the biocomponent must be optically observable. An alternative approach to the use of mediator-titrants for coupling the electrode to the biocomponent is chemical modification of the electrode. Although relatively new, this approach has already shown promising results for cytochrome c (14), myoglobin (15),and ferredoxin (8). We report here two thin-layer electrochemical techniques for the measurement of E”’and n values of biological redox components. The techniques do not require the measurement of optical changes in either the biocomponent or the mediator-titrant. They are based on the charge response to potential Present address: Department of Chemistry, University of Houston, Houston, TX 77004. 0003-270018 110353-0594$01.2510
pulse or potential staircase excitation signals. The methods are evaluated on ferricyanide and 2,6-dichlorophenolindophenol as examples of one- and two-electron reversible system and cytochrome c as a typical irreversible biocomponent.
EXPERIMENTAL SECTION Apparatus. The thin-layer cells were of a previously described O P L E design with 100 wires/in. gold minigrid (3). The property of optical transparencywas not utilized in this study. The minigrid was positioned within 4-6 mm of the cell bottom to minimize iR drop. The electrode area within the thin-layer cell was 1 X 2 cm giving a cell volume of -40 pL for a 0.02 cm thick cell. The thickness of each cell was measured spectrophotometrically at 600 nm with standard 2,6-dichlorophenolindophenolsolution (e = 2.06 X M-l cm-I). The cell was dipped in solution contained in a 0.6 X 1.0 X 3.5 cm Teflon cup. The SCE and the Pt wire auxiliary electrode were immersed in this cup. Special apparatus was used for the deoxygenation and subsequenttransfer of sample solution to the OTTLE which was blanketed with argon in a Plexiglas compartment(16). Electrochemical measurementswere made with a potentiostat of conventional operational amplifier design with an electronic integrator. Potentials were measured with a Fluke 8OOOA digital voltmeter. Cyclic voltammograms and charge-time curves were displayed on a Houston Instruments Series 2000 Omnigraphic x-y recorder with time base. All potentials were measured vs. an SCE and are reported as such unless otherwise indicated. Reagents. All solutions were prepared in pH 7.00, 0.1 M phosphate buffer (Buffer-Titrisol, EM Laboratories, Elmsford, NY), 0.1 M NaCl (Suprapur, EM Laboratories). Commercially available horse heart cytochrome c (Type VI, 95-100% pure, Sigma Chemical Co., St. Louis, MO) was used without further purification. The following chemicals were obtained in the purest available form and used without further purification: 2,6-dichlorophenolindophenol sodium salt; 1,2-naphthoquinone; toluidine blue (all Fluka, Tridom Chemical Inc., Hauppage, NY); 2-anthraquinonesulfonic acid sodium salt (Eastman Organic Chemicals, Rochester, NY); gallocyanine (ICN-K & K Laboratories, Inc., Cleveland, OH); potassium ferricyanide (Allied Chemical and Dye Corp., New York, NY); 4,4’-bipyridyl (Aldrich Chemical Co., Milwaukee, WI); sodium perchlorate (Matheson Coleman and Bell Manufacturing Chemists, Cincinnati, OH). N
RESULTS Thin-Layer Pulse Coulometry. Description of the Method. In thin-layer pulse coulometry, the electrode potential is stepped from a single initial potential, at which the redox component(s) is entirely in one oxidation state, to a series of potentials which convert an increasing fraction of the redox component(s) into another oxidation state. The excitation waveform is shown in Figure 1A. For each potential, the ratio of the concentrations of oxidized to reduced forms, [O]/[R], of the redox species in the thin solution layer adjusts by electrolysis to the value required by the Nernst equation (for a reversible system). RT 101 Eapplid= Eo’ - log ( 1) nF [RI The thin-layer electrode enables the equilibrium [O]/[R] value
+
0 1981 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981 595
A
T
B
=I
n
TIME
TIME
Flgure 1. Potential excitation signals for (A) thln-layer pulse coulometry and (B) thin-layer staircase coulometry.
corresponding to each potential step to be obtained from the charge required for electrolysis of the thin solution layer. The range of the series of potentials to which the electrode is stepped is selected to span E"' of the redox component so that charges are obtained for the extremes of complete oxidation and reduction as well as for intermediate values of [O]/[R]. A plot of the charge for each potential gives a &-E plot which resembles the traditional polarogram. E"' and n values are obtained from the intercept and slope, respectively, of a Nernst plot in the form of eq 2. Equation (2) is obtained from eq Eapplied =
E"'
400
300
200
100
0
E, mV vs SCE
Flgure 2. Thln-layer cyclic voltammogram with schernatlc reprasentation of potential excitation signals for thin-layer pulse coulometry and thin-layer staircase coulometry: 1.0 mM K3Fe(CN)8,0.2 M NaCI, pH 7.0 phosphate buffer. Scan rate = 2 mV/s.
T
QT-Q + RT - log nF Q
1by substituting the following proportionalities between the
245
uC
equilibrium concentrations of 0 and R in the thin layer and the charge, Q, required to establish this equilibrium.
Q [R] = nFV
[O] =
QT
-Q
(3) (4)
nFV where QT is the total charge required to convert all of 0 to R and V is the volume of the thin-layer cell. In order to obtain the E"' and n for a nonelectroactive biocomponent, a &-E plot is first obtained for a mediatortitrant with an E"' in close proximity to the redox potential of the biological species. The biocomponent is then added to solution and a second Q-E plot obtained. In this case, Q contains the charge required to electrolyze both the mediator-titrant (direct electron exchange with the electrode) and the biocomponent (indirect electron exchange by homogeneous reaction with the mediator-titrant) to the appropriate values of [O]/[R] as dictated by the individual Nernst equations. The 8-43plot for the biocomponent is obtained indirectly from the difference of the above two Q-E plots. E"' and n can then be calculated from a Nernst plot (eq 2) of the biocomponent's &-E plot. Evaluation with Reversible Systems. Ferricyanide and 2,6-dichlorophenolindophenol(DCIP) were chosen as reversible redox couples with well-documented E" and n values. These systems were employed for initial evaluation of the method on ideal systems. Ferricyanide undergoes a reversible, one-electronreduction at a gold electrode as evidenced by the thin-layer cyclic voltammogram in Figure 2. One set of arrows in Figure 2 shows the sequence of potential steps for the thin-layer pulse coulometry method. The electrode potential is stepped from a single initial potential of 450 mV vs. SCE, where the compound is entirely in its oxidized form, Fe(CN)63-,to a series of potentials which convert an increasing fraction of ferricyanide to ferrocyanide in the thin layer of solution. The species is completely in its reduced form when the applied potential becomes 0 mV. The charge-time curve for each potential step is shown in Figure 3. The value for Q for each step was obtained by ~
-
0
50
100
150
200
250
TIME (secl
Figure 3. Charge-time curves for thln-layer coulometry: 0.3 mM K,Fe(CN),, 0.2 M NaCI, pH 7.0 phosphate buffer. Initial potential := 400 mV vs. SCE. Final potential as indicated for each curve In the
figure.
extrapolating the linear portion of the curve to zero time, a standard procedure in thin-layer coulometry (17). Each value of Q reflects the amount of ferricyanide converted to ferrocyanide for the particular potential to which the electrode is stepped. Curve A in Figure 4 shows the Q for each potential step as a function of the potential to which the electrode was stepped. The same experiment was performed on supporting electrolyte alone, giving curve B. The faradaic component of the charge is shown by curve C, which was obtained b y subtraction of B from A. A Nernst plot (eq 2) of curve C is linear with E"' and n values of 197 mV vs. SCE and 1.00 k 0.05 ( N = 5 ) , respectively. This is in good agreement with previously reported values (3, 18). DCIP was selected as an example of a two-electron reversible process on gold. Results of Nernst plots for thin-layer pulse coulometry Q-E curves were as follows: E"' = -22 mV vs. SCE, n = 2.0 k 0.15 ( N = 3). These results are also in good agreement with previously reported values (3). Applicability to mixtures of redox components was tested with 1,2-naphthoquinone,gallocyanine,and anthraquinone2-sulfonic acid. The Q-E curve for this mixture is shown in
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
I
120+
T
-
100e n
u
3800 0
-
;600
200
-
0
-
/ /i\
DCIP
3 400 3
500
400
300
200
100
E,MV VS
0
-100
SCE
Figure 4. Charge-potential curves for thin-layer pulse coulometry: (A) 0.3 mM K3Fe(CN)B, 0.2 M NaCI, pH 7.0 phosphate buffer: (B) 0.2 M NaCi, pH 7.0 phosphate buffer; (C) faradalc component of A obtained by difference between curves A and B.
I
t
I
0.4
0.2
I
o
I
I
I
- a2
-0.4
-0.6
E , V vs. SCE
Figure 6. Thln-layercycllc voltammcgrams: (-) 0.55 mM cytochrome c , 0.8 mM DCIP, 0.2 M NaCI, pH 7.0 phosphate buffer: (---) 0.8 mM DCIP, 0.2 M NaCI, pH 7.0 phosphate buffer. ,Elnltlal = -0.6 V, lnltial scan positive.
W
I
1
0
E
a
I V
_ _ _ _ _ ----_-"
E''; - 466mV
u -
s
u
-600
-400
-200
0
200
Figure 5. Charge-potential curve for thin-layer pulse coulometry of mixture of 1.O mM anthraquinone-2-sulfonicacid, 1.O mM gallocyanhe, and 1.0 mM 1,2-naphthoquinone In 0.2 M NaCi, pH 7.0 phosphate buffer. Initial potentlai = -600 mV. Figure 5. The following half-wave potentials were obtained for the three redox components: 1,2-naphthoquinone,-20; gallocyanine, -205; and anthraquinone-2-sulfonic acid, -466 mV vs. SCE. Irreversible Biological Redox Species: Cytochrome c. The heme protein cytochrome c, a redox component of the electron transport chain, exhibits very slow exchange currents with most electrodes. No measurable current is obtained for cytochrome c by thin-layer cyclic voltammetry at a gold minigrid (19). The mediator-titrant DCIP is capable of conveying electrons between cytochrome c and an electrode (3). Figure 6 shows cyclic voltammograms obtained on a solution of DCIP and a solution containing both DCIP and cytochrome c. (The small second reduction wave of the DCIP voltammogram is reduction of residual oxygen.) The indirect electrolysis of cytochrome c is evidenced by the enhanced current flow. However, the Eo' of cytochrome c is not readily obtainable from this figure. In the thin-layer potential pulse technique, &-E plots were obtained for a solution of DCIP alone and then a solution of cytochrome c and DCIP (identical concentration to the previous solution) as shown in Figure 7 (curves A and B, respectively). The &-E plot for cytochrome c (curve C) was then calculated by subtraction of curve A from B. The Nernst plot of curve C for cytochrome c was linear. Calculated values for Eo' and n for cytochrome c are 14 mV and 1.00 f 0.05, respectively, These results are in excellent agreement with previously reported values (3, and references therein).
-0.4
-0 2
,,,,,,E,,
0
v
0.2
0.4
v s . SCE
Figure 7. Charge potential curves for thin-layer pulse coulometry: (A) 0.8 mM DCIP (B) 0.55 mM cytochrome cand 0.8 mM DCIP; (C) component of B which Is due to cytochrome c as obtained by the difference in B and A. All solutions contain 0.2 M NaCI, pH 7.0 phosphate buffer. Elnltlsl= -0.6 V. Thin-Layer Staircase Coulometry. Description of the Method. In this technique, the electrode potential is ''scanned" from an initial potential (at which the redox species is completely in one oxidation state) to a final potential (at which the redox species in the thin layer has been completely converted to another oxidation state) by means of a staircase waveform as shown in Figure 1B. Each step is sufficiently long to allow the new value of [O]/[R] to be established throughout the thin layer of solution. The current accompanying each potential change in the staircase is integrated to give the value of Q required to establish the new equilibrium value of [ O ] /[R]. The values of Q are plotted as a function of the respective potentials to which the electrode was stepped. The resulting Q-E curve is peak shaped, analogous to a differential pulse voltammogram. Eo' and n values are obtained from the peak potential and the midpoint peak width, A.El,z, respectively. Calculations show that AElp should be as follows for a reversible system: n = 1,90 mV; n = 2 , 4 5 mV; n = 3, 30 mV; etc.
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
I
E
597
I
t1
? ’
-.
TIME, s
-35
t
L 5ffi0
I
4ffi0
30E
I
200 100 0 E, MV VS SCE
100
0 E , MV VS
-100
-200
SCE
Flgure 10. Charge-potential curves for thin-layer staircase coulometry: (A) 0.25 mM DCIP; (8) 0.25 mM cytochrome c and 0.25 mM DCIP; (C) cytochrome c component of B obtained by subtracting A from B. Step height = 5 mV; scan direction, positive. All solutions contain 0.2 M NaCI, pH 7.0 phosphate buffer.
Figure 8. Charge-time curves for thin-layer staircase coulometry: 0.3 mM K,Fe(CN),, 0.2 M NaCI, pH 7.0 phosphate buffer, 5-mV steps from E,,, = 400 mV. Eth, = (A) 395, (B) 295, (C) 245, (D) 235, (E) 225, (F)215, (G) 205, (H) 195, (I) 190, (J) 185, (K) 180, (L) 170, (M) 155, 125, (P) 75 mV vs. SCE. (N) 145, (0)
35
200
-100
Flgure 9. Charge-potential curves for thin-layer staircase coulometry. 0.3 mM K,Fe(CN),, 0.2 M NaCI, pH 7.0 phosphate buffer: (top) negative potential step; (bottom) positive potential step.
A &-E curve for an “electroinactive” biocomponent is obtained by the difference of curves for solutions with mediator-titrant alone and mediator-titrant plus biocomponent. This procedure is analogous to that described above for the pulse technique. Evaluation with Reversible Systems. The potential step sequence used for ferricyanide is diagrammatically shown in Figure 2. The couple was incrementally converted from the fully oxidized (Elnitid= 400 mV) to the reduced form (EC,d = 75 mV) by potential step increments of 5 mV. Representative Q-t curves for some 5-mV steps are shown in Figure 8. The curves straighten out after about 30 s, indicating the in the cell. As attainment of the equilibrium value of [O]/[R] in the case of the pulse technique, this linear region was extrapolated to t = 0 to measure Q. The slope of the linear region is determined by edge effects (3, 20) and residual current. The slope passes from a negative value to a positive value from curve d to e as the residual current goes from anodic to cathodic. A Q-E curve for ferricyanide is shown in Figure 9 The potential was staircased first negatively to give the cathodic peak for reduction and then positively to give the anodic peak.
Both peak potentials equal 200 mV vs. SCE which is in good agreement with the Eo’obtained by the pulse technique (vida supra). AEl12 equals 87 mV for both peaks, which is close t o the expected value of 90 mV for a one-electron process. Essentially identical voltammograms were obtained regardless of whether the initial scan direction was positive or negative. The absence of iR drop effects is indicated by a 0-mV separation of anodic and cathodic peaks. The height of the cathodic peak is slightly greater than that of the anodic peak. This is attributed to the diffusion of Fe(CN)l- into the cell, Le., edge effeds (3,20). The peak height is linear as a function of ferricyanide concentration over a tested range of 0.2-1.0 mM. The peak height is also proportional to the magnitude of the potential step increment. For example, the ratio of peak heights for a 4-mV step compared to a 5-mV step was 0.80 (Ep4,v = 46 pC, Ep6mV = 57.9 pC, [Fe(CN)63-]= 0.29 mM) which is equal to the ratio of the step magnitudes themselves. AEp,,, is independent of the step increment. A Q-E m e for DCIP gave Ep= -18 mV vs. SCE and AE~,Q = 43. The E, is in good agreement with the Eo’obtained by the pulse technique (vida supra) and a l l 2 is close to the expected value of 45 for a two-electron process. Cytochrome c. Measurement of Eo’ and n for a biocomponent such as cytochrome c which is essentially electroinactive a t a gold electrode is accomplished by an indirect procedure analogous to that described above for the pulse method. A staircase voltammogram for the mediator-titrant DCIP alone is shown by curve A in Figure 10. Curve B is the voltammogram for a solution containing a concentration of DCIP identical with that for curve A plus cytochrome c. Subtraction of curve A from B gives curve C which is the Q-E plot for cytochrome c. The peak potential for this voltammogram is 18 mV vs. SCE. This agrees well with the value determined by the pulse technique. The AEllZof 86 mV is in good agreement with the expected value of 90 mV for n one-electron system. DISCUSSION Thin-layer pulse coulometry and thin-layer staircase coulometry give accurate values of Eo’and n for biocomponents which undergo heterogeneous electron transfer at a negligible rate. Values of Eo’and n for the test system cytochrome c are in excellent agreement with previously reported results. An important aspect of these two techniques is their effectiveness for biological species with no easily measurable optical properties. By comparison the spectropotentiostatic technique using an OTTLE is based on optical monitoring of the bio-
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
component (3). Thus, these coulometric techniques can be used to study biological systems with weak optical properties which are therefore not easily amenable to study by the spectropotentiostatic method. As such, the thin-layer techniques complement each other. It is also convenient that the same thin-layer cell can be used for both the spectroelectrochemical and the coulometric techniques. The thin-layer coulometry methods take advantage of the rapid electrolysis feature of a thin-layer cell. The value of [O]/[R] for both the mediator-titrant and the biological species in the thin solution layer rapidly equilibrates with the potential applied to the electrode as per the Nernst equation. This feature enables the component of charge for indirect “electrolysis” of the biological species to be easily determined by subtracting the contribution of the mediator-titrant from the total charge for a given potential step. This strategy could be invoked in a conventional bulk solution coulometry cell; however, the time required for each electrolysis would be considerably longer. The mediator-titrant is crucial for success in studying biocomponents by these thin-layer coulometry techniques. As in the spectropotentiostatic method, the mediator’s Eo’ should be sufficiently close to that of the biocomponent so that the biocomponent can be forced into the fully reduced and fully oxidized forms by the applied potential (3, 13, 21). Mixed mediator-titrants which collectively span a wider potential range should be useful in some situations (21). Appropriate chemical modification of the electrode, for example, by addition of 4,4’-bipyridyl, can obviate the need for a redox mediator-titrant (16). Although the optical transparency aspect was not used, an OTTLE was employed as a convenient cell for demonstrating the coulometry techniques. A cell of this type is open along two edges (3). This gives rise to an edge effect which is observable in a coulometry experiment (3,20) but not in an appropriately conducted spectroelectrochemical experiment (3). In the thin-layer coulometry technique, the edge effect contribution to each potential step was compensated for by extrapolating the Q-t curve for each step back to time zero, the usual procedure (17). Although the edge effect is not a significant problem in this cell due to the relatively large electrode surface area to edge ratio, other cell geometries could minimize the effect. The techniques could be used with any of the many thin-layer cell designs (22))some of which require only microliters of sample (23, 24). Another usually troublesome aspect of the OTTLE cell design is iR drop, which is easily detected as peak separation in a cyclic voltammogram, e.g., in Figure 2. The effect of iR drop is minimized in the coulometry techniques since values of Q are measured after electrolysis is complete and equilibrium achieved, i.e., i becomes very small. A small residual current flow continues to exist after equilibrium is reached in the thin layer as a result of continuing electrolysis at the
edges and residual current. This current should be sufficiently small that the true potential of the working electrode does not deviate from Eappliedby more than a few tenths of a millivolt due to iR drop. The resistances of the thin-layer cells used in this study were less than 10o0 Q. In these experimenb the residual current was less than 0.2 PA, giving an iR drop of less than 0.2 mV. Thus, the anodic and cathodic peaks in Figure 9 are separated by less than 1 mV. The two coulometric techniques gave comparable results for cytochrome e. The pulse method requires more time for each point since a reequilibration to initial conditions is necessary for each step back to the initial potential. On the other hand, more points were taken with the staircase technique in order to define the peak potential to within a few millivolts. Both techniques are ideally suited for control by microcomputer.
LITERATURE CITED Bishop, N. I. Ann. Rev. Biochem. 1971, 40, 197-226. Wilson, D. F.; Dutton, P. L.; Erecinska, M.; Lindsay, J. G.; Sato, N. Acc. Chem. Res. 1972# 5, 234-241. Heineman, W. R.; Norris, B. J.; Goeiz, J. F. Anal. Chem. 1975, 47,
79-84. Betso, S. R.; Kiapper, M. H.; Anderson, L. B. J. Am. Chem. SOC. 1972, 94,8197-8204. Scheiier, F.; Janchen, M.; Lampe, J.; Prumke, H.J.; Bianck, J.; Palecek, E. Biochim. Blophys. Acta 1975, 412, 157-167. Kono, T.; Nakamura, S.Bull, Agric. Chem. SOC. Jpn. 1958, 22,399. Yeh, P.; Kuwana, T. Chem. Left. 1977, 1145. Landrum, H. L.; Salmon, R. T.; Hawkridge, F. M. J. Am. Chem. SOC. 1977, 99,3154-3158. Hawkridge, F. M.; Kuwana, T. Anal. Chem. 1973, 45, 1021-1027. Anderson, J. L.; Kuwana, T.; Hartzeil, C. R. Biochemlstty 1978, 15,
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Szentrimay, R.; Kuwana, T. Anal. Chem. 1978, 50, 1879-1883. Rickard, L. H.; Landrum, H. L.; Hawkridge, F. M. Bioelectrochem. Bloenerg. 1978, 5, 686-696. Heineman, W. R.; Meckstroth, M. L.; Norris, 8. J.; Su, C.-H. Bioelectrochem Bioenerg 1979, 6 , 577-585. Eddowes, J. M.; Hill, H. A. 0. J. Am. Chem. SOC. 1979, 101,
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50. 930-932. Su,’ C.-H. Ph.D. Dissertation, university of Cincinnati, Cincinnati, OH,
1981. Rohrbach, D. F.; Heineman, W. R.; Deutsch, E. Inorg. Chem. 1978, 18, 2536-2542. Koithoff, I. M.; Tomsicek, W. J. J. Phys. Chem. 1935, 39, 945-954. Norris, B. J. Ph.D. Dissertation, University of Cincinnati, Clncinnati, OH,
1976. McDuffie, 8.; Anderson, L. B.; Reiiiey, C. N. Anal. Chem. 1988, 38,
803-890. Meckstroth, M. L.; Norris, B. J.; Heineman, W. R. Bloelectrochem. Bioenerg., in press. Hubbard, A. T.; Anson, F. C. I n “Electroanalytical Chemistry”; Bard, A. J., Ed.; Marcel Dekker: New York, 1970;Vol. 4,Chapter 2. Anderson, C. W.; Haisaii, H. B.; Heineman, W. R. Anal. Biochem. 1979, 93,366-372. Roston, D. A.; Brooks, E. E.; Heineman, W. R. Anal. Chem. 1979, 51,
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RECEIVED for review November 24,1980. Accepted January 16, 1981. This work was supported in part by the National Science Foundation. C.-H.S. acknowledges support provided by a University of Cincinnati Summer Research Fellowship.
