Anal. Chem. 1991, 63, 839-841
characteristic methods). Our experience suggests that the information should probably not be trusted to more than about twice the maximum detected concentration for lowvolume injections.
ACKNOWLEDGMENT We thank Sue Smith of the Unversity of Tennessee Computing Center for her constant support. We acknowledge Alltech Associates for the gift of the BSA-7 column and the University of Tennessee Computing Center’s support of the computational effort. LITERATURE CITED Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988; Chapters 2 and 3. Thompson, K. A.; Fuller, E. L.; Jr. J. Vac. Sci. Techno/. 1987, 5 , 2522-2525. SoussenJacob. J.: Tsakirls. J.; De Lara, E. C. J. Chem. fhys. 1989, 9 1 , 2649-2655. Jaulmes. A.; Vidai-Madjar, C.; Gaspar, M.; Guiochon, G. J. fhys. Chem. 1984, 8 8 , 5385-5391. VidaCMadjar. C.; Jauimes, A.; Racine, M.; SBbiiie, B. J. Chromatogr. 1988. 458, 13-25. James, D. H.; Phillips, C. S. G. J. Chem. SOC. 1954, 1066-1070. Schay, 0.: SzBkely, G. Acta Chim. 1955, 5 , 167-182. Glueckauf, E. Trans. Faraday SOC. 1955, 1540-1551. Huang. J.-X.; HorvBth, C. J. Chromatogr. 1987. 406, 285-294. Huang, J.-X.; HorvBth. C. J. Chromatogr. 1987. 406, 275-284. Huang, J.-X.; Schudel, J.; Guiochon. G. J . Chromatogr. 1990, 504, 335-349. Glueckauf, E. J. Chem. SOC.1947, 1302-1308. Stock, R . Anal. Chem. 1961, 3 3 , 966-967. Kipping, P. J.; Winter. D. G. Nature 1985, 205, 1002. Cremer, E.; Huber, H. Angew. Chem. 1961, 73, 461-465. Kiselev, A. V.; Nlkitln, Y. S.; Pertova, R. S.;Shcherbakova, K. D.; Yashin, Y. I, Anal. Chem. 1964, 3 6 , 1526-1532. Jonsson. J. A.; Lovkvist. P. J. Chromatogr. 1987, 408, 1-7. Chuduk, N. A.; Eltekov, Y. A.: Kiselev, A. V. J. Collold Interface Sci. 1981, 8 4 , 149-154. DjordjevlE. N. M.; Laub, R. J.; KopeEnl. M. M.; MoioniE, C. K. Anal. Chem. 1986, 5 8 , 1395-1404. Heifferlch. F.; Peterson, D. L. Science 1963, 142. 661. Huber, J. F. K.; Gerriste, R. G. J. Chromatogr. 1971, 5 8 , 137-158. Valentin, P.; Guiochon, G. J. Chromatogr. Sci. 1976, 14, 56-63. Valentin, P.; Guiochon, G. J. Chromatogr. Sci. 1976, 14, 132-139. Dondl, F.; Gonnord, M.-F.; Guiochon, G. J. Collold Interface Scl. 1977, 6 2 , 303-315.
839
(25) Conder. J. R. Chromatographie 1974, 7 , 387-394. (26) Laub, R. J.; Pecsok, R. L. R?ysIcmhemlcal Applhtions of Gas Chromatography; John Wiley and Sons: New York, 1978; Chapter 2. (27) Conder, J. R.; Young, C. L. fhyslcochemicel Measurements by Gas Chromatography; John Wiby and Sons: New York, 1979. (28) Dollimore, D.; Heal, G. R.; Martin, D. R. J. Chromatogr. 1970, 50, 209-218. (29) Guiochon, G.; Golshan-Shirazl, S.; Jaulmes, A. Anal. Chem. 1988, 60, 1856-1866. (30) Golshan-Shirazi, S.; Guiochon. G. J . Chromatogr. 1990, 506, 495-545. (31) Nelder, J. A.; Mead, R. Comput. J. 1964, 308-313. (32) Aberg, E. R.; Gustavsson, A. G. T. Anal. Chim. Acta 1982, 144, 39-53. (33) Dose. E. Anal. Chem. 1987, 5 9 , 2420-2423. (34) Allenmark, S.; Bomgren, B.; Boren, H. J. Chropatogr. 1983, 264, 63-68. (35) Akima, H. ASSOC.Comput. Mach. 1970, 17, 589-602. (36) Dose, E.; Guiochon, G. Anal. Chem. 1990, 62, 816-820. (37) Brunauer, S.;Emmett, P. H.; Teller, E. J. Am. Chem. SOC.1938. 6 0 , 309. (38) Coates, 1.; Glueckauf, E. J. Chem. SOC. 1947, 1308-1314. (39) Dondl, F.; Gonnord, M.-F.; Guiochon, G. J. Cdold Interface Sci. 1977, 6 2 , 316-328. (40) Katz, S.; Gray, D. G. J. Colloa Interface Sci. 1981, 8 2 , 318-351. (41) Jaulmes, A.; Vidal-Madjar, C.; Ladurelli, A.; Guiochon. G. J. Phys. Chem. 1984, 8 8 , 5379-5385. (42) Anita, F.; Horvath, Cs. J. Chromatogr. 1989, 484, 1. (43) Carla, G. Chem. Eng. Sd. 1988, 43, 2877. (44) Lee, C. K.; Yu, Q.; Kim, S. U.; Wang, N.-H. J. Chromafogr. 1989, 484, 29. (45) Subramanian, G.; Phillips, M. W.; Cramer, S. M. J . Chromatogr. 1988, 439, 341. (46) Lin, B.; Goishan-Shirazi, S.; Guiochon, G. Anal. Chem. 1989, 9 3 , 3363-3368. (47) Courant, R.; Friedrichs, K. 0.; Lewy, H. Math. Ann. 1928, 100, 32. (48) Jacobson, S.; Golshan-Shirazi, S.; Guiochon, G. J . Chromatogr. 1990, 522, 23-36. (49) Jacobson, S.; Golshan-Shirazi, S.;Guiochon, G. J. Am. Chem. SOC. 1990, 112, 6492-6498.
RECEIVED for review October 23,1990. Accepted January 17, 1991. This work is supported in part by Grant DE-FGOB86ER13487 from the U S . Department of Energy, Office of Energy Research, by grant CHE-8901382 from the U S . National Science Foundation, and by the cooperative agreement between the University of Tennessee and Oak Ridge National Laboratory.
CORRESPONDENCE Linear Scan and Staircase Voltammetry of Adsorbed Species Sic Staircase voltammetry (SCV) can be viewed as a digital implementation of linear scan voltammetry (LSV). In today’s technical environment, in fact commercial instruments based on microcomputers typically implement LSV as SCV. The current in SCV is sampled a t some time t , during the period t , while the electrode is a t the constant potential Ei- jAE, where Ei is the initial potential, AE is the step height, and j the number of the cycle. (For a cyclic experiment, E = Ei - jAE until the switching potential (E,,) is reached, after which E = E,,
+ jhE).
By analogy with LSV, if the scan rate ( u ) is considered to be the time parameter, for SCV, u = AE/t, and each choice of u can be achieved by many choices of A E and t,. A more fundamental way to view the SCV experiment is to recognize that t, is the fundamental time parameter and that in routine practice AE is fixed at a convenient value (5 mV, e.g.) and not changed. The basis of experimental evidence and extensive theoretical development, coupled with the modern implementation of 0003-2700/9 1/0363-0839$02.50/0
“LSV” as SCV, has prompted detailed treatments of SCV and comparisons between SCV and LSV (1-9). One approach to the analysis of data relies on a convolution that transforms either result to a sigmoidal response, which is then analyzed ( 3 , 4 ) . A second approach seeks a fixed sampling time, t , = at,, 0 < a < 1, such that the SCV result is the same as the LSV result at the same scan rate (2,5-9). The Osteryoungs and co-workers (5-8) have examined theoretically and experimentally a wide range of electroanalytical mechanisms and have given conditions for sampling which make SCV equivalent to LSV. Using a Walsh series method, they assign to each process t,/t, = or t,/t, = lI2, depending on whether the corresponding integral equation is of an Abelian or non-Abelian type. Thus the SCV and LSV results are identical to first-order for the proper choice of a, depending on the mechanism. Penczek et al. (9) have chosen the different approach of computing the value of t,/t, required for exact equivalence and have found values of ca. l f 3 . It is worth noting here that 0 1991 American Chemical Society
840
ANALYTICAL CHEMISTRY, VOL. 63, NO. 8,APRIL 15, 1991
the absolute difference between the currenb sampled at the end of the potential step and at the specified value of t,/t, diminishes with decreasing AE. The differences in response of the two techniques can be neglected when the applied AE is sufficiently small ( n A E I0.26 mV). However, very often the desired potential window is so wide that maintaining very small AE values leads to an unacceptable increase in the number of data points or is simply technically impossible. All the processes discussed in the literature so far involve diffusional transport of both oxidized and reduced forms. Larger differences between SCV and LSV than those described for a process involving diffusional transport might be expected for the cases of reactants or products adsorbed, crystallized, or polymerized at the electrode surface. The aim of this paper is to present an exemplary experimental investigation of the staircase and linear scan voltammetric behavior of such processes. As the examples, the electrode processes of reduction of midazolam [8-chloro-6-(o-fluorophenyl)-l-methyl-4H-imidazo[ 1,5-a][ 1,4]benzodiazepine] a t mercury and oxidation of mercury in the presence of bromide were chosen.
EXPERIMENTAL SECTION The experimental system for SCV was based on a DEC PDP8/e computer equipped with dual RK05 disk drives, a Tektronix 603 display, a ADM 3-A terminal, and a LNO3-plw laser printer. The computer controlled an EG&G PARC Model 273 potentiostat. In LSV experiments, an EG&G PARC Model 175 programmer and Model 173 potentiostat and a Houston Instruments Model 2000 XY recorder were used. Before experiments the SCV waveform and the linear ramp were compared by using a highprecision resistor. The apparent scan rates were identical for the same experiment; (AE/tp)scv = uwv. For SCV currents were sampled at t,/t, = 1/4, l/*, and 1. Background was not subtracted. The working electrode was a PARC Model 303 SMDE ( A = 0.025 cm2),and the counter electrode consisted of a Pt wire. All potentials were measured and are reported versus SCE. All chemicals used were of reagent grade purity. Distilled water was purified with a Millipore Milli-Q filtration system. The temperature was maintained at 25 "C. Experiments on midazolam were carried out in sodium acetate, pH 4.8, ionic strength of unity. Experiments on bromide were carried out in 0.5 M NaClO, acidified to pH 1 with HC104. Solutions were deaerated with highly purified argon. RESULTS AND DISCUSSION Midazolam. Midazolam undergoes irreversible charge transfer coupled with protonation, along with strong, potential-dependent adsorption a t mercury electrodes (IO). The potential of maximal adsorption is ca. -0.6 V. Experiments with midazolam were carried out with accumulation from dilute solution at -0.6 V with stirring. Under the conditions employed, the surface is saturated and the amount of current arising from material which diffuses to the electrode during the scan is negligible. Figure 1 displays cathodic stripping curves for midazolam for AE = 1 mV and AE = 8 mV together with the dependence of peak current ratios (as defined in the figure caption) on step height. For all step heights peak currents decrease in the order SC (1/4), LS, SC ( l / & , SC (l),where the fractions indicate the fraction t , / t , at which the current is measured on each step of the staircase waveform. For AE = 1 mV the difference from smallest (t,/t, = 1) to largest (t,/t, = 1/4) current is less than 10%. As shown clearly in the voltammograms for AE = 8 mV, the larger is t,/t,, the more narrow the peak. Bromide Ion. Oxidation of mercury in the presence of bromide ion offers a more complex situation. Not only is bromide strongly adsorbed onto mercury in the positive range of the electrocapillary curve, but also the electrode reaction product, HgzBr2,can be accumulated on the electrode surface
I
.-0 a
2.0-
K U
K 2
1.5-
L
(3
3;'
1.0-
0
5
10
IS
20
Step Height, mV Figure 1. Dependence of peak currents in SCV on step height: ip(fs/fp = 1/4)/ip(t3/tp= 1) (0);i p ( t s / t p= 1 / 2 ) / i p ( t s / t=p I ) (x). Insets: vottammetric curves for reduction of adsorbed midazolam. Conditions: C = 0.25 pM; accumulation potential, -0.6 V; accumulation time, 120 s (with stirring); A€ = 1 mV; v = 200 mV/s (fp = 5 ms). Key: SCV, t31fp = '1, (O), 1/2 (+), 1 (- --); LSV (-). Conditions: A€ = 8 mV (fp = 40 ms). Key: SCV, t3/tp = (0),1/2 (X), 1 (A);LSV (-).
1.0-
4
1
I
0.0
0.2
E / V
Voltammetric curves for reduction of adsorbed Hg2Br2. Conditions: C = 0.4 pM; deposition potential, 0.300 V; deposition time, 60 s; A€ = 2 mV; v = 120 mV/s (fp = 17 ms). Key: SCV, t&tP = 1/4 (0),1 (A); LSV (-). The top curve and the bottom curve are shifted by 0.1 pA up and down, respectively, to clarify the display. Figure 2.
(11). Although not all the details of this process have been examined, it is reasonable to assume, following the example of sulfide ion (IZ),that various nondiffusional processes can be involved during electrooxidation of Hg. The formation of an adsorbed layer of Hg2Br2 can be followed by its rearrangement and the growth of subsequent layers. Various steps of the process can respond in different ways to change in t,/t,. The first experiments, like those above, employ accumulation from dilute solution so that the flux of bromide a t the electrode during the scan is negligible. The surface coverage a t the beginning of the scan is approximately one monolayer of HgzBr2. In Figure 2, the curves obtained by staircase voltammetry with AE = 2 mV and t,/t, = and 1 are presented. A linear scan curve is included as well (currents are offset for clarity). The difference between the two SCV curves is striking. The main peaks (more negative) do not differ more than usual; the first (more positive) peak is several times larger for t,/t, = '/, than for t,/t, = 1. The first anodic peak decreases sharply with an increase in AE for all current sampling points. For AE = 10 mV, the more positive peak in the curve for t,/t, = 1cannot be seen at all, and in the curve for t s / t , = 1/4, this peak is so small that it forms a small bump only on the rising part of the second anodic peak. Since the phenomena observed in this experiment should be seen also during the formation of multilayers of Hg2Br2, a series of cyclic staircase experiments were carried out in a
ANALYTICAL CHEMISTRY, VOL.
CP
R2
A' 0.04
0.08
E / V
Figure 3. Cyclic vottammetric curves of the bromide ion. Conditions: = 0.1 mM; A€ =1 mV; Y = 30 m V / s (tP = 33 ms). Key: SCV, t J t P = '1, (0),1 (A):LSV (-).
C
0.1 mM solution of bromide ion. Figure 3 presents typical cyclic curves obtained by LSV and by SCV with AI3 = 1 mV. Two cathodic and two anodic peaks are indicated in Figure 3. There is also a broad adsorptive monolayer peak in the range 0.09-0.02 V, which has not been labeled. In the cathodic part of the curve this peak overlaps with peak C2. For processes with diffusional transport (6,8), such a small potential step guarantees that the differences between the curves for SCV obtained by sampling in the range I t,/t, I 1 are within the range of a few percent. In Figure 3 these differences are small only for peak A2, where bulk HgzBrzis formed. For the monolayer peak and peaks A1 and C1 (transformation at the surface) the current for t,/t, = 1 is roughly 50% of the current for t,/t, = 1/4. The difference is 20% at peak C2, where bulk Hg,Br, is reduced. When AI3 is increased, the peaks for the A l / C l couple decrease sharply in magnitude and finally disappear a t AI3 = 6 mV. It is interesting to note that the A l / C l peaks also depend on choice of initial potential a t the larger step heights. The peaks are so narrow that a choice of initial potential can place the potentials of the staircase only on the wings of the peak, and hence the response is greatly diminished. For the situations described above the conditions of equivalence between LSV and SCV curves cannot be given in a straightforward manner. Even application of small potential steps does not ensure reasonable agreement between SCV and LSV peaks. The reason for the striking difference between these examples and the more simple comparisons possible when adsorption is not involved is that in the case of adsorbates the current is a much stronger function of time. As mentioned in the introduction, LSV is often implemented as SCV in modern microprocessor-based instruments. For example, the EG&G PARC Model 270 electrochemical analysis system offers the techniques of "linear scan" and "cyclic" voltammetry. However, it is clear from the discussion in the user's manual that the techniques are actually staircase and cyclic staircase voltammetry, with choice of step increment, U ,in the range 1-20 mV (13). Similarly, the BAS-100 electrochemical analyzer employs "linear scan" and "cyclic" voltammetry in a "digital" mode, i.e. as staircase voltammetry (14). This is not discussed in the manual; however, the direct measurement of the excitation waveform revealed a staircase with a nominal value of 1 mV for the step height.
63,NO. 8,
APRIL 15, 1991
841
In typical surveys or preliminary examinations of electrochemical systems, the quantitive difference between LSV and SCV under these conditions is not important for most types of reactions. However, for the examples given here the quantitative differences are so extreme as to constitute qualitative differences. Adsorption peaks prominent in LSV could easily be absent in SCV. Although the reaction of adsorbed species constitutes a well-defined set of problems, experimental examples seem to display endless variation in mechanism. This makes implausible any simple description of the phenomena illustrated above. We are undertaking a quantitative examination of the case exemplified by midazolam. We draw from these examples three conclusions. First, the exact experiment must be identified unambiguously by the experimenter (and the instrument manufacturer) to avoid larding the literature on surface processes with misleading or contradictory results. Second, the extreme sensitivity of the staircase response to the details of the applied waveform may be useful for the investigation of mechanisms. Third, in analytical situations, the parameters of staircase voltammetry may be manipulated to render a complex response more simple and more robust for the determination of concentration.
ACKNOWLEDGMENT We are grateful for experimental assistance from Alvaro Ribes. LITERATURE CITED (1) Christie, J. H.; Lingane, P. J. J. Electroanal. Chem. 1965, 10, 176. (2) Miaw, L. H.; Boudreau, P. A.; Pichler, M. A.; Perone. S. P. Anal. Chem. 1978, 50, 1988-1996. (3) Suprenant, H. L.; Ridgway, T. H.; Rellley, C. N. J. flectroanal. Chem. Interfacial Electrochem. 1977, 75, 125. (4) Myland, J. C.; Oldham, K. B. Anal. Chem. 1988, 6 0 , 62-66. (5) Seralathan, M.; Osteryoung, R.; Osteryoung. J. J. flectroanal. Chem. Interfacial Electrochem. 1988, 214, 141. (6) Biiewicz, R.; Osteryoung, R.; Osteryoung, J. Anal. Chem. 1988, 58. 2761-2765. (7) Seralathan, M.; Osteryoung, R.; Osteryoung, J. J . Electroanal. Chem. Interfacial Electrochem. 1987, 222, 69. (8) Bilewicz, R.; Wikiel. K.; Osteryoung, R.; Osteryoung, J. Anal. Chem. 1969, 61, 965-972. (9) Penczek, M.; Stojek, 2.; Buffle. J. J. Electroanal. Chem. Interfacial Electrochem. 1989. 270, 1. IO) Ribes, A.; Osteryoung, J. J. flectroanal. Chem. Interfacial Electrochem. 1990, 287, 125-147. 11) Wrona, P. K.; Galus, 2. I n Mercury; Encyclopedia of Electrochemistry of the Elements; Bard, A. J.. Ed.; M. Dekker, New York, 1982. 12) Peter, L. M.; Red, L. D.; Scharlfker, B. R. J. Electroanal. Chem. Interfacial Electrochem. 1981. 119, 73. 13) Model 270 Electroanalytical System User's Guide; EG8G PARC: Princeton, NJ. 1985-1990. (14) Manual for the BAS- 100 Electrochemical Ana/yzer; Bioanalytlcal Systems Inc.: West Lafayette, IN, 1964.
'
Permanent address: Department of Chemistry, Warsaw University, ul. Pasteura 1, 02-093 Warsaw, Poland.
Zbigniew Stojek' Janet Osteryoung* Department of Chemistry SUNY University of Buffalo Buffalo, New York 14214 RECEIVED for review October 29,1990. Accepted January 22, 1991. This work was supported in part by the National Science Foundation under Grant CHE8521200 and by Grant 01.15.1.03 from the Polish government.
