Anal. Chem. lQ86, 58, 2761-2765
of 20 pg/cm2 and a particle size range of 100-1000 A. No attempt was made to directly correlate the exchange currents to the amount of Pt deposited in the film because different deposition techniques (e.g., CV, DPCA, SPCA) will affect the dispersion and size of metal microparticles in the film (6,23). However, i t should be noted that if the same deposition technique (e.g., DPCA) is used on films that are cross-linked in a similar manner (e.g., heated on the electrode), the exchange current increases with increasing Pt loading levels (see first four entries in Table 111). The relatively high activity of these electrodes toward hydrogen generation is the apparent result of a high ratio of the surface area to the loading level of weight of Pt. The long-term stability of the Pt/cross-linked PVP films was examined by continuous exposure to 1 N sulfuric acid solution. There was no appreciable peeling of the film or deterioration of the activity with regard to hydrogen generation on the cross-linked films after more than 24 h in the above acidic solutions. Thus, the cross-linked polymer films appear to be the most promising for long-term stability and good catalytic activity. More extensive testing of these films under a variety of conditions is in progress. In addition, work on multimetal depositions and their catalytic properties in these and other stable polymer films including attempts to covalently link the polymer to the gc surface is currently in progress. Registry No. Pt, 7440-06-4;PVP, 25232-41-1; C, 7440-44-0; H2, 1333-74-0;H2S04,7664-93-9;4-vinylpyridine, 100-43-6;triallyl isocyanurate, 1025-15-6;triallyl trimesate, 17832-16-5. LITERATURE CITED (1) Murray, R. W. Annu. Rev. Mater. Sci. 1984, 14, 145. (2) Dominey, R. N.; Lewis, N. S.;Bruce, J. A.; Bookbinder, D. C.; Wrigh-
2761
ton, M. S.J . Am. Chem. SOC. 1982, 104, 476. Bruce, J. A.; Murahashl, T.; Wrighton, M. S. J . f h y s . Chem. 1982,
86, 1552. Staider, C. J.; Chao, S.;Wrighton, M. S.J . Am. Chem. SOC. 1984, 106, 3673. Simon, R. A.; Maiiouk, T. E.; Daube, K. A,; Wrighton. M. S. Inorg. Chem. 1985, 2 4 , 3119. Kao, W. H.; Kuwana, T. J . Am. Chem. SOC. 1984, 106, 473. Weisshaar, D. E.; Kuwana, T. J . Electroanal. Chem. 1984, 163, 395. Shimazu, K.; Bartak, D., The Ohio State University, unpublished data. Shigehara, K.; Oyama, N.; Anson, F. C. J . Am. Chem. SOC. 1981,
103,2552. Hu, I. F.; Karweik, D. H.; Kuwana, T. J . Electroanal. Chem. 1985, 188, 59. Funt, B. L.; Hoang, P. M. J . Electroanal. Chem. 1983, 154, 229. Mano, E. B.;Calafate, B. A. L. J . folym. Sci., folym. Chem. Ed.. 1981, 19, 3325. Zubov, V. P.; Kumar, M. V.; Masterova, M. N.; Kabanov, V. A. J . Macromol. Sci., Chem. 1979, A 13, l l l. Laurin, D.; Parravano, G. fo/ym. Left. 1986, 4 , 797. Subremanion, R. V.; Jakubowski, J. J. folym. Eng. Sci. 1978, 18,
590. Abruna, H. D.; Denisevich, P.; Umana, M.; Meyer, T. J.; Murray, R. W. J . Am. Chem. SOC. 1981, 103, 1. Finkiea, H. 0.; Vithanage, R. S. J . Elecfroanal. Chem. 1984, 161.
203. Shaw, B. R.; Haight, G. P.; Faulkner L. F. J . Nectroanal. Chem. 1962, 140, 147. Miller, C. W.; Karweik, D. H.; Kuwana, T. Recent Adv. Anal. Spechosc .) R o c . Int. Conf. At. Spectrosc. 1982, 223. Engstrom, R . C.; Strasser, V. A. Anal. Chem. 1984, 56, 136. Cabaniss, G. E.; Diamantis, A. A,; Murphy, W. R.; Linton, R. W.; Meyer, T. J. J . Am. Chem. SOC. 1985, 107, 1845. Bushong, W. C.;Shupack, S. I.; Blubaugh, E. A.; Durst, R. A,, frepr. -Am. Chem. Soc., Div. folym. Mater. Sci. Eng. 1985, 5 3 , 123. Kao, W. H.; Weisshaar, D. E.; Kuwana, T., The Ohio State University, unpublished data.
RECEIVED for review March 10,1986. Accepted June 12,1986. This work was supported by The National Science Foundation, Koppers Co., Inc, and the Ohio State Material Research Laboratory.
Comparison of Linear Scan and Staircase Voltammetry: Experimental Results &nata Bilewicz,' R. A. Osteryoung, and Janet Osteryoung*
Department of Chemistry, State University of New York, Buffalo, New York 14214
The Influence of characterlstlc staircase parameters on the extent of slmllarlty between staircase and linear scan voitammograms Is Investigated. Condltlons for which voltammograms are in agreement within experimental error are e& tablished. Experiments using ferric oxalate show, as predicted by previous theoretlcal work, that staircase voitammograms are analogues of linear sweep vokammograms ll the current sampling Is done at one-fourth the step length and the density of data points In the staircase curve Is not too low. When the current Is sampled toward the end of the step, shapes of staircase and linear scan voltammograms differ markedly. Peak helghts are dlstlnctly smaller and peak separations larger for staircase voltammograms than for those obtalned by the linear scan technique. Even for potential steps as small as 2 mV current should be sampled at onefourth the step length In order to obtaln cyclic staircase voltammograms that can be treated as linear scan voltammograms. Permanent address: Department of Chemistry, University of Warsaw, 02093 Warsaw, Pasteura 1, Poland.
Staircase voltammetry (SCV) has been widely explored both theoretically and experimentally by many authors (1-9). It appears that this technique will replace linear scan voltammetry (LSV) not only because it discriminates against charging current but also because modern electroanalytical equipment is based on digital electronics employing discrete potential step wave forms. As the usefulness of linear scan (cyclic) voltammetry in mechanistic studies of electrode processes cannot be overestimated, it becomes of considerable interest to determine to what extent the results of staircase voltammetric experiments may be treated as linear scan results. A theoretical description of staircase voltammetry presented by Christie and Lingane (5) shows that voltammograms identical to those predicted by linear (or cyclic) scan theory (10) should be obtained, if the potential step (hE)approaches zero and the current is sampled at the end of each step. However, fulfilling the first condition poses practical difficulties. Interesting observations have been made by Reilley and coworkers (8) and Perone and co-workers (9) regarding the importance of sampling the current at some point during the staircase period to obtain voltammograms with peak current ratios and peak separations close to those predicted by the
0003-2700/S6/0358-2761$01.50/00 1986 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1986
theory of linear scan (cyclic) voltammetry. Recent theoretical work from this laboratory (11) presented a new technique for computing the integrals of the analytical solution for linear scan voltammetry that permitted direct comparison between staircase and linear scan voltammograms for reversible systems. The general result, discussed in more detail below, is that for the same scan rate (v (V/s) in LSV T in SCV, where AE is step height and T step and A E ~ (V/s) period) the two techniques yield the same voltammogram when the current in SCV is sampled at one-fourth of the period of each step. T h e aim of the present work was to investigate this conclusion experimentally to find the range of applicability of the theoretical conclusions for a reversible electrode reaction. EXPERIMENTAL SECTION Reagents. A 1 M potassium oxalate-oxalic acid buffer was prepared by mixing appropriate amounts of Baker reagent grade potassium carbonate and oxalic acid to the final value, pH 4. A concentrated standard iron solution was made by dissolving Alfa Products iron wire in hot dilute hydrochloric acid. An iron oxalate solution was prepared fresh daily as recommended by Lingane (12). The concentration of iron(II1) oxalate was 3.40 mM. The diffusion coefficient was measured using normal pulse polarography in the same experimental solution. Drop time was 2 s and pulse width 20-50 ms. The value of D obtained was 6.13 x IO4 cm2/s. This agrees with Lingane’s (12)value of 6.1 X lo4 cm2/s and Turner and co-workers values (13) of 6.2 X lo4 cm2/s. Distilled water was repurified with a Millipore Milli-Q filtration system. Solutions were deaerated with prepurified argon passed through a copper catalyst. Triple-distilled mercury (Bethlehem Apparatus Co.) was used. Cell and Electrodes. All results were obtained by using an EG&G/PARC Model 303A static mercury drop electrode (SMDE) and a water-jacketed cell thermostated at 25 “C. The “medium” drop size was selected with a surface area of 0.016 cm2. The drop weights were reproducible over short times (1day), but differences up to 4% were noted over a period of a week. A Metrohm EA4002 standard saturated calomel electrode was used. A Pt wire was employed as the auxiliary electrode. Instrumentation. A Digital Equipment Corporation PDP8/E computer equipped with dual RK05 floppy disk drives, Tektronix 603 display, LA 50 printer, and ADM 3-A terminal was interfaced with a PARC Model 273 potentiostat; experimental parameters could be entered a t the terminal and communicated to the instrument. In linear scan experiments a PARC Model 175 programmer was used as the source of the linear scan ramp. This instrumentation was used for on-line experiments and analysis of the data and permitted analysis of the staircase and linear scan voltammograms in exactly the same way. Currents were averaged over 10 drops to suppress random noise. Blanks were run for each set of experimental conditions and were subtracted from voltammograms. Some of the linear scan experiments were done using a purely analog arrangement consisting of a PARC Model 175 programmer, a PARC Model 173 potentiostat, and a Houston Instrument Model 200 XY recorder. Limitations. Some limitations on the experimental conditions should be described. Non-faradaic currents play different roles in these two techniques. In linear scan voltammetry the ratio of charging current to faradaic current is an inherent feature of the experiment, fixed by the chemical specifications and the scan rate. In SCV the ratio of charging current to faradaic current decreases with increasing time at which the current is measured. In order to retain the advantage of SCV in discriminating against charging current, this time must be larger than some minimum value. It is usually assumed that if current is sampled a t a time longer than four cell time constants the charging current should be negligible. In practice, as was postulated by Perone and co-workers (9),sampling should be done with even larger delay periods, about 25 times longer than the cell time content, i.e., about 500 ps after each voltage step is applied. In our experiments current is sampled at the end of the step ( a = 1)or at one-fourth that value (CY = 0.25). The highest voltage scan rate was 1000 mV/s, which in staircase experiments with a 2-mV step height (the smallest used) corresponds to a step width of 2 ms. This
results in the required 500-ps delay between the application of the step and the current measurement at cy = 0.25. To minimize the resistance of the solution, high concentrations of supporting electrolyte were used. For low scan rates (large values of 7) deviations from linear diffusion may appear. Therefore, in the present work voltage scan rates are always greater than 20 mV/s and T (SCV) smaller than 200 ms. Additional limitations are placed by the number of data points and the resolution (or step height). The range (R),resolution (M), and number of data points (N) are related by N = 2RJAE. For technical reasons we select 500 as the maximum value of N . This places upper limits on R and lower limits on M. On the other hand, for large potential steps it becomes difficult to attribute to the staircase voltammogram quantities such as peak current, ip,and potential at i = ip/2, Ep 2, traditionally used to characterize linear scan voltammograms. dherefore, comparison of results for SCV and LSV becomes ambiguous. The latter point will be discussed further below.
RESULTS A N D DISCUSSION Theoretical Predictions. Choice of experiments was guided by the theoretical treatment of Seralathan e t al. (11). In that work a Walsh series approximation was used for the integrals that occur in the exact theoretical description for linear scan voltammetry. The resulting equation for the linear scan voltammogram for reversible reduction of substance 0 is
where i(t) is the current at time t , IZ the number of electrons transferred per molecule of 0, F the value of the Faraday constant, A the electrode area, and Do the diffusion coefficient of 0. The quantities el are given by ti = exp[nF(E, - ElJ2)/RT] where El is the potential, Ellz the reversible half-wave PO- ’ tential, R the gas constant, and T the absolute temperature. The quantity to is associated with the initial potential, Ei. The time, t , can be expressed alternatively as (Ei- E)/v, where u is the scan rate, and the characteristic time, T , can be expressed as S / u , where AE is the potential increment used in the Walsh series approximation for the value of the integral. By inspection, eq 1 is the exact equation for the staircase voltammogram with step height AE and period T (5). It is an approximate equation for the linear scan voltammogram with scan rate v, which can be made arbitrarily accurate by making A E sufficiently small. Computational results presented in ref 11 show that when nFAEIRT I0.01 peak heights for LSV calculated from eq 1 agree with the customary quadrature result (10)within 3% and peak positions agree within 2 mV, independent of the fraction, cy, of the period at which the current is calculated and independent of sweep rate (i.e., choice of T). However, if the current is calculated at cy = 0.25, the same quality of agreement results with nFAE/RT I0.3, or nAE -< 8 mV. The present experimental investigation employs LSV and SCV as they would routinely be used. The emphasis is on the following simple question. Within what limits can the simple diagnostic criteria commonly used in LSV be applied to data obtained using SCV? Characterization of Electrode Reversibility. The theory of linear scan cyclic voltammetry (10)provides diagnostic criteria for determining if the system studied is reversible. The characteristic values of potential include E,, - E,,/, E,,+ - E,,!,, and E,, - E,, where E,, and E,, are cathodic and anodic peak potentials and EwlP,E,+, and E3w!4 are potentials at which the cathodic current attains values corresponding to one-half, one-fourth, and three-fourths the peak current value. Table I reports data obtained from linear
ANALYTICAL CHEMISTRY, VOL. _
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_
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1986
2763
~ ~
Table I. Characteristics of Experimental Cyclic Linear Scan (LS) and Cyclic Staircase (SC) Voltammograms"
Table 11. Comparison of Peak Current Ratios for Linear Scan (LS) and Staircase (SC) Voltammograms"
sc
(ip,)0/
A E = 3.126 mV
LS
-0.268 11.45 -0.209 7.32 0.059 -0.057 -0.044 -0.239
a =
0.25
-0.269 11.40 -0.211
7.30 0.058
-0.057 -0.044 -0.240
LY
AE = 6.248 mV = 1 a = 0.25 a = 1
-0.275 9.80 -0.202 5.88 0.073 -0.057 -0.045 -0.239
-0.270 11.26 -0.210 7.20 0.060 -0.057 -0.044 -0.240
-0.280 9.40 -0.200 5.64 0.080
-0.058 -0.046 -0.240
'Scan rate = 100 mV/s; scan range = 400 mV; data are mean values of 10 experiments in one solution. * T = A E / v .
U
3
t-l
8d,o
58,
-;,
-;.e
-A
-d.4
4.5
'
E, v Figure 1. Cyclic staircase (2, 2a, 3, 3a) and linear scan voltammograms (1) for 3.40 mM Fe(II1) In 1 M oxalate buffer, pH 4: v = 50 mV/s; A€ (mv), (2, 2a) 3.126 and (3, 3a) 6.248; a,(2, 3) 0.25 and (2a, 3a) 1. scan voltammograms recorded a t a scan rate of 100 mV/s in a solution containing 3.40 mM Fe(II1) in the oxalate buffer. The values obtained agree with the theoretical predictions for a reversible, one-electron process. If a staircase voltammogram is thought of as an analogue of a linear scan voltammogram, similar cirteria should apply. The characteristic experimental parameters of a staircase wave form, step height (AE) and step width ( T ) , should be adjusted so that the effective sweep rate, AE/T,is also 100 mV/s. The results of the peak shape analyis for step heights 3.126 and 6.248 mV are presented in Table I. The agreement between the linear scan and staircase experiment depends on the sampling parameter, CY.If sampling is done a t a = 0.25 the values obtained for peak separation as well as for E - E,Iqand E3,14 agree with the linear pc scan data within experimental error. When current is measured a t the end of each step the potential differences change, reflecting changes in the shape of the cyclic staircase response. The main differences appear in the peak separation, which increases with increase in step height and, for AE equal to 6.248 mV, becomes 20 mV larger than the value obtained from the corresponding linear scan voltammogram. The same trend in the differences E,, - E, with varying AE was reported by Perone and co-workers (9). However, only staircase experimenta were performed in their work. Figure 1 presents the features described above for experiments performed a t a scan rate of 50 mV/s. If sampling is done a t CY = 0.25 the staircase and linear scan curves are superimposed. Shift of the anodic peak toward positive potentials and the cathodic peak in the
AE, mV 2 3
4 5 6 7 8
9
(Y
= 0.25
(i& a = l
0.64 f O.Old 0.65 f 0.01 0.60 f 0.01 0.64 f 0.01 0.60 f 0.02 0.65 f 0.01 0.60 f 0.01 0.65 f 0.01 0.59 f 0.01 0.64 f 0.02 0.59 f 0.02 0.65 f 0.02 0.59 f 0.02 0.66 f 0.03 0.58 f 0.03 0.63 f 0.04 0.58 f 0.04
ipa/i, (corrected), 0.25 ( Y = l
a =
0.99 f 0.01d 0.99 f 0.01 0.95 f 0.01 0.99 f 0.01 0.94 f 0.02 1.00 f 0.01 0.95 f 0.01 1.01 f 0.01 0.93 f 0.02 0.99 f 0.02 0.92 f 0.01 0.99 f 0.02 0.92 f 0.02 1.00 f 0.03 0.94 f 0.03 0.98 f 0.03 0.93 f 0.03
n u = 100 mV/s; range = 400 mV; T = AE/u. bipaand i,, measured relative to zero current. Calculated according to the procedure of Nicholson (14): ipa/ipc= (ipa)o/(ipc)o + o.485iA/(i,)0 + 0.086, where i Ais the current at the switching potential. dLSV all other entries are for SCV.
opposite direction can be seen clearly if the sampling parameter, a,is changed to 1. However, the value of Ellz, calculated as the average of cathodic and anodic peaks potentials, is constant and equal to -0.239 f 0.001V. An additional criterion for reversibility of linear scan voltammograms is that the ratio i,,/i,, equal one. Table I1 presents the ratio ipa/i, obtained in linear scan experiments. The data are mean values of five experiments performed in one solution. The linear scan data are compared with the values obtained from staircase voltammograms with AE varying from 2 to 9 mV. The value of iw/ipc given in the first column is the ratio of currents measured relative to zero current. The value in the last column is corrected by measuring the current value a t the switching potential and calculating according to the semiempirical equation given by Nicholson (14). The values of the ratio i,,/i,, obtained from staircase voltammograms agree well with the linear scan data when a = 0.25. For experiments with sampling a t the end of each step the ratio is smaller even for the lowest step height used,2 mV. The deviation appears to increase with increasing AE. This trend can be seen more clearly for the uncorrected data and is in accord with Christie and Lingane's ( 5 ) theoretical prediction that linear scan and staircase voltammetry yield identical voltammograms with a equal to 1and AE equal to 0. This condition, however, cannot be realized experimentally, since a finite number of steps have to be used to obtain results. Thus, the conclusion of the theoretical work (11)that good agreement can be obtained between staircase and linear scan voltammograms with realistic choice of step height if CY = 0.25 is especially attractive. The results presented above demonstrate the validity of this suggestion. A more detailed study of current dependencies will be presented below. A t this point the conclusion should be stressed: to use criteria of linear scan cyclic voltammetry for electrode reversibility with data from staircase voltammetry requires that the current be sampled at one-fourth the step length and not at the end, as is in fact commonly done. Comparison of Current Values. Here we investigate the similarity between linear scan and staircase voltammograms with attention focused on the cathodic and anodic peak current. In earlier experimental work on cyclic staircase voltammetry (6, 9) current ratios are given. Therefore, it seemed useful to examine the dependence of the individual currents on staircase parameters. Table I11 contains the values of currents a t different potentials obtained from cyclic voltammograms recorded by both techniques at a sweep rate of 100 mV/s (AE= 2.00 mV, T = 20 ms). Comparison of these values leads to the conclusion that a staircase voltammogram with current sampled at CY = 0.25 agrees with the linear scan
ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1986
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Table 111. Comparison of Current Values in Linear Scan and Staircase Voltammograms for Some Selected Potentialsn
'IJ =
E, V
iLs, F A
isCtb F A
isc,' !.LA
-0.150 -0.200 -0.250 -0.300 -0.350 -0.360 -0.300 -0.250 -0.200 -0.150
0.630 4.368 10.600 9.844 7.262 6.936 2.642 -3.912 -6.872 -4.506
0.612 4.002 10.627 10.054 7.399 7.123 2.700 -3.941 -6.878 -4.357
0.476 3.070 8.794 9.376 7.302 6.934 3.135 -2.520 -5.996 -4.093
100 mV/s; Ai3 = 2.00 mV;
7
a
3 H
= 20 ms. * a = 0.25. c a = 1. 1
I
-0 i
-0 2
I
- 4
-03
E,V Figure 3. Comparison of (1) linear scan and (2-4) staircase cyclic voltammograms with sampling at the end of each step ( a = 1): v = 100 mV/s; A€ (mV), (2)2, (3) 3, (4) 6, (5) 9; T = A E / v .
lot
40 1
5 1
I
-0 i
I
-02
I
,
,
I
I
04
06
08
40
I
-03
-0 4
E,V Figure 2. Comparison of linear scan and staircase cyclic voltammograms at scan rate of 100 mV/s sampling at a = 0.25: A€(mV), 2 , 3, 6, 9; T = A E / v ; 3.40 mM Fe(II1) in 1 M oxalate buffer, pH 4.
curve within experimental error. Figure 2 shows the voltammograms obtained by linear scan and staircase with step heights of 2, 3, 6, and 9 mV. For step heights smaller than 6 mV the difference between the peak currents in the staircase and linear scan voltammogram is less than 2.3%. For larger values of T the accuracy of determining the peak is obscured by the small number of data points, but a trend is clear: for AE equal to 9 mV the error is 5.6%, and for 12-mV step height it increases to 8.1%. This observation will be discussed later. On the other hand, when sampling is done a t the end of each step the resulting voltammogram only approximates the linear scan curve (Figure 3), even a t the lowest value of A73 (2 mV). The current data at various points of the curve are distinctly different, as shown in Table 111. For A73 equal to 2 mV the peak currents in the linear scan and staircase voltammograms differ by 9.6% and for A23 = 6 mV by 16.4%. These results confirm the usefulness of sampling the current at CY = 0.25. Perone and co-workers (9) noted the "intriguing observation" that for CY = 0.3, staircase voltammetry exhibits features nearly identical to those predicted by the theory of linear scan cyclic voltammetry as far as peak current ratio and peak separation are concerned. On the basis of theoretical results obtained by Seralathan et al. (11) these results now are seen to have a firm theoretical basis. The experiments here confirm that the absolute magnitudes of the currents are in satisfactory accord if CY is 0.25. Influence of Scan Rate. To determine which staircase parameters besides a are important in obtaining correspondence between the two techniques, we performed experiments a t different scan rates so that in the staircase
0 00
02
2
SqRt/Scan Rate/,V/S *+4/2
Figure 4. Dependence of cathodic peak current on square root of scan rate for (1)linear scan and (2, 2a-4a) staiicase voltammetry: A€ (mV), (2, 2a) 3.9, (3, 3a) 7.8, (4, 4a) 15.6; a , (2-4) 0.25 and (2a-4a) 1.
technique only one of the parameters, T or AE,would be changed while the other is constant. Recall that the theory predicts that the quality of agreement is controlled by AE and is independent of T . As the sweep rate in staircase voltammetry is equal to U / T , in the following experiments hE was kept constant and T decreased in order to study voltammograms for sweep rates from 20 to 1000 mV/s over a range of fixed values of hE. Each staircase voltammogram was then compared with the linear scan curve obtained at the same scan rate. Excellent agreement of these curves was observed for A E = 2 mV, a = 0.25, and u I 500 mV/s. At higher scan rates the linear scan peak currents are larger than the corresponding staircase peak currents. For example, for u = 1000 mV/s the difference is 4%. This discrepancy seems to be due to inadequate subtraction of charging currents in the case of linear scan. In staircase voltammetry, as shown previously, good discrimination against charging current is still found at T = 2 ms. The dependence of cathodic peak current on the square root of scan rate was examined for both techniques. Figure 4 shows that the plots are linear and go through the origin. For linear scan and staircase voltammetry with step heights of 3.9 and 7.8 mV, the plots are identical when a is 0.25. The equations are i, = 36.22(u1/') + 0.012 (neglecting the point
ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1986
2765
Table IV. Comparison of Peak Currents for LS and SC Voltammograms at Different Scan Ratesn
sc
LS
v, v/s 0.05 0.10
0.20
,,i
PA
8.03 h 0.11 11.45 f 0.10 16.23 h 0.12
AE, mV
i,, PA
A,b %
3.9
8.02 f O . l l c 11.36 f 0.18' 15.60 f 0.50'
0.1
7.8
15.6
0.8
3.9
,i
PA
6.950 f 0.12d 9.40 f 0.20d 11.90 f 0.52d
A,b %
13.4 17.9 26.7
'Mean values of five experiments in the same solution; T = 78 ms; u = AE/T. A = (ipcs - ip,sc)/i,,~s.c a = 0.25. d a = 1.
for lo00 mV/s) with correlation coefficient 0.9999; ,i = 36.21(u1/*) 0.003 with correlation coefficient 0.9998; and i, = 35.69(u1l2) + 0.000 6 with correlation coefficient 0.9997, respectively. (The units of slope and intercept are pA(s/V)'/* and pA, respectively.) For the largest step height, 15.52 mV, peak currents were measured only for scan rates 100-1000 mV/s, as lower sweep rates result in values of T greater than 150 ms. This limitation has been explained in the Experimental Section. The slope of the line ,i vs. u1/2in this case was equal to 34.84 pA (s/V)'/', slightly lower (2%) than the value obtained with smaller step heights. This result confirms the theoretical prediction that the agreement between LSV and SCV is acceptable for nAE I8 mV with LY = 0.25, independent of 7 (or scan rate). It is fortunate, and perhaps interesting, that results of LSV and SCV agree only up to values of nAE normally considered to give acceptable resolution. In the voltammograms of Figure 3, even with A E = 9 mV, the staircase result consisting of individual (i, E ) points can be visualized readily as a continuous curve. As the density of points decreases, this becomes increasingly difficult, and finally one would have to use an ad hoc procedure for defining a hypothetical staircase peak current for comparison with the actual linear scan peak current. Thus, the quantitative equivalence of the two techniques holds over the range of step height to which one would be restricted for reasons of resolution anyway. Figure 4 also shows plots of i, vs. u1j2 for the same values of AE but with current sampled a t the end of the step. The slopes of the plots are much smaller than those obtained by linear scan and decrease with larger step heights. A similar trend was reported by Ferrier and co-workers (7) for the case of reduction of Pb(I1) in perchloric acid solution. The above results show, as predicted ( I l ) , that changes in 7 at fixed AE do not affect the quality of agreement between LSV and SCV when CY is 0.25. Changing the scan rate by changing T seems, therefore, to be a useful procedure for investigating electrode processes. On the other hand, if the scan rate is varied by changing AE a t constant T , the staircase and linear scan results differ increasingly with increasing AE. Table IV combines peak current data obtained with sampling a t CY = 0.25 and 1 in staircase experiments with different step heights. Larger step heights were not used because they provide inadequate resolution. This selection of data demonstrates the following points. First, the accuracy of agreement between LSV and SCV depends on AE,so any staircase experiments designed to test the scan rate dependence predicted for LSV should be carried out at constant AE. Second, even at small values of AE the agreement between LSV and SCV is poor when current is sampled a t the end of the step. Finally, the accuracy of agreement is quite acceptable for CY = 0.25 over the range of step heights (18/n mV) that is employed normally to obtain adequate resolution.
+
CONCLUSIONS These results confirm the practical utility of the theoretical predictions that for a reversible system LSV and SCV give
the same results, independent of scan rate, provided that current is sampled in SCV at one-fourth the staircase period and the step height is less than about 8 / n mV. This conclusion holds for uncomplicated reversible reactions under conditions of semiinfinite linear diffusion. For that case the current in SCV at fixed sampling time is proportional to CY^)-'/^, and the current at CY = 0.25 is the average current over the period 7. It is worth reemphasizing the point that SCV discriminates against charging current and as a result can be employed over a wider effective time range than can LSV. For example, if we adopt the very conservative restriction of T 2 2 ms to ensure that charging currents are negligible, for AE I8 mV, the maximum attainable scan rate is 4 V/s. again using a very conservative condition, this time to ensure that diffusion is linear, of T 1 200 ms, the lower limit of scan rate is ca. 10 mV/s. Over this range of scan rates in LSV, the magnitude of the charging current changes by a factor of 400. By use of the simple estimation that the ratio of charging current to peak current in LSV is given by ( U ' / ~ ) / ~ Owhen C ~ ~ Coo , = 0.1 mM, this fraction increases from 2.5% to 50% over that range of sweep rate. Thus, the SCV experiment provides a wider reliable range of variation of parameters, which yields a larger meaningful array of data for comparison with the theoretical predictions of LSV. Staircase and linear scan voltammetry are also being compared theoretically and experimentally for systems with kinetic complications. This work will be reported separately. ACKNOWLEDGMENT Discussion with M. Seralathan and John O'Dea aided this work. Janet Osteryoung and Robert A. Osteryoung thank the University of Southampton for their hospitality during preparation of the manuscript. Registry No. Ferric oxalate, 2944-66-3. LITERATURE CITED (1) Barker, G. C. A&. Polarogr. Proc. Int. Congr. 2nd 1960, 7 , 144. (2) Mann, C. K. Anal. Chem. 1961, 33, 1484. (3) Mann, C. K. Anal. Chem. 1965, 37, 326. (4) Nigmatullln, R. S.; Vyaseiev. M. R . Zh. Anal. Khim. 1964, 19, 545. (5) Christie, J. H.; Lingane, P. J. J. flectroanal. Chem. W65, 70, 176. (6) Zipper, J. J.; Perone, S. P. Anal. Chem. 1973, 4 5 , 452. (7) Ferrier, D.R.; Schroeder, R. R. J. flectroanal. Chem. 1973, 45, 343. (8) Suprenant, H. L.; Ridgway, T. H.; Reilley, C. N. J. flectroanal. Chem. 1977, 75, 125. (9) Miaw, L. H. L.; Boudreau, P. A.; Pichler. M. A,: Perone. S. P. Anal. Chem. 1978, 5 0 , 1988. (IO) Nicholson, R. S.;Shain, I . Anal. Chem. 1964, 36, 706. (11) Seralathan, M.; Osteryoung, R.; Osteryoung, Janet J. flectroanal. Chem., in press. (12) Lingane, J. J. J. Am. Chem. SOC. 1946, 6 8 , 2448. (13) Turner, J. A.; Christie, J. H.; Vukovic, M.; Osteryoung, R. A. Anal. Chem. 1977, 4 9 , 1904. (14) Nicholson, R . S. Anal. Chem. 1966, 38, 1406.
RECEIVED for review February 27,1986. Accepted July 1,1986. This work was supported by the National Science Foundation under Grant CHE-8305748. Janet Osteryoung gratefully acknowledges support from the Guggenheim Foundation.
