Anal. Chem. 1986, 58,2889-2891
2889
Current Multiplier for Use with Ultramicroelectrodes H s u a n - J u n g Huang,' Peixin He,2and L a r r y R. Faulkner*
Department of Chemistry, University of Illinois, 1209 West California Street, Urbana, Illinois 61801 Since the first report by Ponchon et al. describing the use of carbon fibers as voltammetric electrodes (I), a rapidly increasing number of papers has concerned the investigation and development of ultramicroelectrodes (2-29). The interest has been driven by a set of most attractive features inherent in such electrodes. Due to the tiny characteristic dimension, steady-state diffusional mass transport exists at moderate or long electrolysis times. In linear sweep voltammetry, for example, a sigmoidal curve is obtained, instead of the conventional peak-shaped response (5). Because of the small surface areas of some ultramicroelectrodes, the double layer capacitance and the current magnitude can be reduced tremendously when compared with those of a conventional electrode. These reductions in scale yield small cell time constants and bring about an improved instrumental ability to meet the power requirements of an electrochemical system on short time scales. Thus, ultrafast voltammetry has become possible (10,18,19). The small current magnitudes can also dramatically reduce experimental distortions caused by iR drop and thus permit studies of electrochemistry in nonpolar or other very resistive solutions (10, 11). The very small electrolysis current obtained from an ultramicroelectrode, usually nano- to picoamperes, is not easy to measure with a satisfactory signal-to-noise ratio with most commercial electrochemical instruments. Most workers have forgone the convenient waveform generation and signal processing features of commerical equipment and have instead constructed apparatus involving expensive current measurement devices, such as picoammeters (13). Special potentiostats containing low-noise operational amplifiers in a two-stage current follower mode have also been designed to circumvent this problem (6, 10). We point out here that one can construct a simple current transducer to enable studies at ultramicroelectrodes with any commercial potentiostat known to us. The device is essentially a current amplifier, which boosts the current a t the ultramicroelectrode into a range that can be measured readily by the current follower in the potentiostat. The same experimental strategy is embodied in the custom-built equipment of Howell and Wightman (lo),and it seems to have been employed with commercial equipment in work soon to be reported by Fitch and Evans (19). However, we are aware of no report that brings the general possibilities of this approach and the details of its implementation to the attention of the community interested in ultramicroelectrodes. This note is offered as a convenience to that community. EXPERIMENTAL SECTION Preparation of Electrodes. The ultramicroelectrodes were prepared mainly by following Baranski's procedure (18) with Thornell P-55s grade 2K carbon fibers (Union Carbide Corp.) having a diameter of 10.24 i 0.91 pm. First, a fiber 3-4 cm long was attached with silver epoxy (Epo-Tek H20E, Epoxy Technology, Billerica, MA) to a thin copper wire. This wire was then pulled through a small piece of multiple layered polyethylene tubing made by inserting 1.8 mm 0.d. tubing into 2.2 mm 0.d. tubing. To facilitate subsequent operations, part of the carbon Permanent address: Department of Chemistry, National Sun Yat-sen University, Kaohsiung, Taiwan (SOO), Republic of China. *Permanent address: Department of Chemistry, Fudan University, Shanghai, People's Republic of China. 0003-2700/86/0358-2889$01.50/0
fiber (about 1 cm long) was allowed to protrude from the end of the polyethylene tubing. The entire assembly was then carefully inserted into a longer piece of Teflon tubing and was placed in a vacuum oven. After being heated at 160 "C for approximately 1h, the melted polyethylene inside the Teflon tubing was allowed to cool slowly. Upon subsequent removal of the Teflon sheath, a smooth, cylindrical, polyethylene-sealed electrode was obtained. The success of the preparation was ascertained by measuring the resistance between the fiber and copper wire before and after heating. A resistance of about 2-3 kQ indicated satisfactory conduction of the electrode and ensured proper operation. During heating of the polyethylene assembly, movement of the melted, viscous liquid can break the very fragile carbon fiber or loosen the contact between the copper wire and carbon fiber. Thus, it is important that no free movement of the carbon fiber be allowed during heating. Movement was prevented by taping both ends of the assembly, Le., the copper wire and the protruding fiber, onto a glass plate prior to baking and cooling. Before an experiment was run, the prepared polyethylene cylinder was cut perpendicularly to its longitudinal axis to expose a new carbon surface. The freshly cut electrode was then polished with a piece of 600-grit silicon carbide grinding paper (Buehler, Ltd., Evanston, IL) and then with successively finer grades (12.5, 1.0, and 0.05 p M ) of alumina micropolish (Buehler, Ltd). Chemicals. Ferrocene and acetonitrile (spectrophotometric grade, Gold Label, Aldrich Chemical Co., Milwaukee, WI), were used as received. Tetraethylammonium fluoroborate (TEABF4, electrometric grade Southwestern Analytical Chemicals, Austin, TX) was recrystallized three times from a mixture of ethyl acetate-pentane (5:l) and then dried for 48 h at 95 "C under vacuum (20). All other chemicals were at least of analytical grade. Current Transducer. The low-noise current transducer was assembled on a Vector board. Figure 1 shows the circuitry. A low-drift FET input operational amplifier (OPA 104 AM, BurrBrown) was used in the current follower mode as an input stage. The low bias current (less than 300 fA), the high temperature stability (drift rate less than i 2 5 fiV/OC), and the moderately fast slew rate (1.6 V/@) of the amplifier are well suited to low-level current amplification in apparatus designed for millisecond time scales or longer. The feedback loop of the current transducer was connected to one of three different precision resistors (1 MQ, 10 MQ, or 100 MQ). Phase inversion of the transduced current was made with an ordinary operational amplifier (OP 27) in a unit gain configuration, and the voltage output of this stage was used to drive a current through a 1-kQ output resistor into the normal working electrode lead of the potentiostat. In most commercial and custom-built equipment this lead feeds a virtual-ground summing junction of a current follower. Thus the net effect of the device is to amplify the cell current for the potentiostat. The amplification factor is R,/R,, where Rf is the feedback resistance in the first stage and R, is the output resistance. The net gain of this current transducer was designed to be lo2, lo3,or lo4,when the feedback resistor is 1 MQ, 10 MQ, or 100 MR, respectively. To minimize noise coupling through the power system, an inductor-capacitor decoupling network was connected to each power terminal on the operational amplifiers (21). The whole assembly was shielded in an aluminum box. Power was brought into the box from an external, dedicated h15 V modular supply. Slight noise reductions might be brought about by powering the transducer from batteries in the box. In any case, it is important to supply power independently of the instrument into which the transducer feeds. The time constants of the various RC networks in the current multiplier were set at 100 p s , a value that should provide undistorted responses for experiments on time scales of 1ms or longer. For cyclic voltammetry, the corresponding upper limit of scan rate would be about 50 V/s. Accurate responses on faster time scales could be obtained. within the bandwidth of the 0 1986 American Chemical Society
2890
ANALYTICAL CHEMISTRY, VOL. 58, NO, 13, NOVEMBER 1986 iooot
160 p"
1
REF
$
uf
1 100pH:
lp t i
I +15V
d
h
t i 5 Y -15v
-15V
Figure 1. Circuit diagram of the current transducer.
p -
I I .-.t0.m
-0.200
t0.400
,'/
to.0
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EIUOLT)
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1 E I UOLLT I
Figure 2. Cyclic voltammogram of 1.0 X M ferrocene in acetonitrile at 100 mV/s. The scan begins at -200 mV.
amplifiers employed, by reducing the capacitances placed in parallel with the feedback resistors. For the studies of performance described below, the output of the current transducer was connected to the working electrode terminal of a BAS-100 cybernetic potentiostat (Bioanalytical Systems, West Lafayette, IN), and the input was connected directly to the ultramicroelectrode in the electrolytic cell with a short coaxial shielded cable. In order to avoid ac noise, the electrolytic cell and the current amplifier were placed in a Faraday cage.
RESULTS AND DISCUSSION The performance of the current transducer was tested via voltammetric studies of ferrocene in acetonitrile. Figure 2 shows a cyclic voltammogram of 1.0 mM ferrocene in acetonitrile containing 0.10 M TEABF4 as the supporting electrolyte. The potential was measured against the Ag/Ag+ (0.01 M AgN03 in acetonitrile) electrode. The ideal sigmoidal shape of the curve indicates that steady-state behavior exists. The limiting diffusion current coincided with the theoretical value calculated according to Howell and Wightman (10). Smooth, well-defined sigmoidal curves were obtained up to a scan rate of 1000 mV/s. At about 3000 mV/s, a small hump began to appear on the reverse scan of the voltammogram, and when the scan rate was increased to approximately 5000 mV/s, a typical, conventional peak-shaped voltammogram was obtained. Figure 3 shows two Osteryoung square-wave voltammograms. The amplitude and frequency of the square wave were 25 mV and 15 Hz, and the concentrations of ferrocene were 1.0 x lom4 M and 1.0 X M in parts a and b, respectively, of Figures 3. A beautiful, almost symmetric peak was obtained for the 1.0 X M solution. The peak was distorted by background contributions but was still well defined, for the 1.0 X M solution. When the concentration was lowered down to 1.0 X 104 M, the peak was seriously distorted by the rising background current, but it was still recognizable. The signal-to-noise ratio in Figure 3b is still excellent, even though the peak has a height of only about 40 PA. As clearly demonstrated by these results, the incorporation of this current transducer into a measurement system can enhance the capability of a conventional potentiostat, therehy
t o . 400
t0.0
-0.200
EIUOLT)
Figure 3. Osteryoung square wave voltammograms for ferrocene in acetonitrile with 0.1 M TEABF,. Concentrations of ferrocene were (a) 1.0 X M and (b) 1.0 X M. Initial potential = -200 mV, final potential = 400 mV, ac amplitude = 25 mV, frequency = 15 Hz, step height = 4 mV.
making feasible ultramicroelectrode studies. Expensive or specialized systems for low current measurements may often be avoided. Registry No. Ferrocene, 102-54-5.
LITERATURE CITED (1) Ponchon, J.-L.; Gespuglio, R.; Gonon, F.;Jouvet, M.; Pujoi, J.-F. Anal. Chem. 1979, 5 1 , 1483. (2) Dayton, M. A.: Brown, J. C.: Stutts. K. J.; Wightman, R. M. Anal. Chem. 1980, 5 2 , 946. (3) Dayton, M. A,; Brown, J. C. Stutts, K. J.; Wightman, R. M. Anal. Chem. 1980, 5 2 , 2392. (4) Robinson, R. S.;McCreery, R. L. Anal. Chem. 1981, 5 3 , 997. 15) Wiohtman. R. M. Anal. Chem. 1981. 5 3 . 1125A. i 6 j EwTng, A. G.; Dayton, M. A.; Wightman, R. E. Anal. Chem. 1981, 5 3 , 1842. (7) Cushman, M. R.; Bennett, B. G.; Anderson, C. W. Anal. Chlm. Acta 1981, 130, 323. ( 8 ) Aoki, K.; Osteryoung, J. J . Electroanal. Chem. 1981, 122, 19 (9) Shoup, A.; Szabo, A. J . Electroanal. Chem. 1982, 140, 237. (10) Howell, J. 0.; Wightman, R. M. Anal. Chem. 1984, 5 4 , 524. ( 1 1) Bond, A. M.; Fieischmann, M.; Robinson, J. J . Electroanal. Chem. 1984. 180, 257. (12) Sleszynski, N.: Osteryoung, J.; Carter, M. Anal. Chem. 1984, 5 6 , 130. (13)Bond, A. M.; Fleischmann, M.; Robinson, J. J . Electroanal. Chem. 1984, 168, 299.
Anal. Chem. 1986, 58,2891-2893 (14) MacFarlane, D. R.; Wong, D. K. Y. J. €lectroanal. Chem. 1985, 785, 197. (15) Schuene, S. A.; McCreery, R. L. J. Nectroanal. Chem. 1985, 797, 329. (18) Flelschmann, M.; Ghoroghchian, J.; Pons, S. J. Phys. Chem. 1985, 8 9 , 5530. (17) Fleischmann, M.; Bandyopadhyay, S.; Pons, S. J. fhys. Chem. 1985, 89, 5537. (18) Baranskl, A. S. J. Electrochem. SOC. 1988. 733, 93. (19) Flch, A.; Evans, D. H., submitted, personal communication to L. R. Faulkner from A. Fitch, January 1988. (20) Glass, R. S.; Faulkner, L. R. J. fhys. Chem. 1981, 8 5 , 1180.
2891
(21) On, H. W. Nolse Reduction Techniques In €lectronic Systems; Wiley: New York, 1976; p 103.
RECEIVED for review March 25,1986.
Accepted June 13,1986. We are grateful to the National Science Foundation for supporting this work under Grant CHE-81-06026. We also wish to acknowledge support of H.-J.H, by a research fellowship from the National Science Council of the Republic of China.
Objective Function Aiding in the Selection of Time Windows for the Integration of Signal Peaks near the Detection Limit by the Base Line Offset Correction Method Raimund Rohl' Bayerische Landesanstalt fur Wasserforschung, Kaulbachstrasse 37, 8000 Munchen 22, Federal Republic of Germany There are many analytical methods that yield signals in the form of transient peaks superimposed on a more or less flat base line. Among these are chromatographic techniques, flow injection analysis (FIA), and certain types of atomic spectroscopy, such as graphite furnace atomic absorption spectrometry (GF-AAS) and electrothermal vaporization inductively coupled plasma atomic emission spectrometry (ETVICP-AES). Although in some cases peak height can be used as a measure of signal strength (and thereby the amount or concentration of analyte), the more generally applicable method is to determine net peak areas, i.e., to integrate the peaks above the base line. This study was prompted by efforts to optimize the signal quantification conditions for a method in which organic carbon in water is determined by combustion and ICP-AES (1) and by a recent publication on signal evaluation in Zeeman-GFAAS (2). The peaks produced by the organic carbon combustion ICP-AES method are similar in shape to those observed in FIA, GF-AAS, or ETV-ICP-AES; i.e., the signal rises sharply to a maximum and then decreases roughly exponentially and returns to the base line. In the present method, carbon emission peaks are located on the time scale by a peak-fiiding routine prior to integration. However, since there is only one peak for each sample injection and since the arrival time of the analyte at the detector is relatively well-known, it was considered possible to apply simpler signal integration methods. One technique that was investigated for this purpose is also employed in GF-AAS and has been termed the base line offset correction (BOC) method (2). With this method, two time windows are selected, one during which detector readings are recorded to estimate the base line level and one that includes with certainty the main portion (e.g., >98%) of the peak (Figure 1). The average of all base line readings is subtracted from the readings taken during the peak integration period and the sum of those corrected readings is taken as the net peak area. It has been noted (2) that the precision achievable with the BOC procedure, and thereby the detection limits of analytical methods using this technique, are dependent on the lengths of the time windows t B and ts. While Barnett et al. (2)studied the effect of choosing different values for t B and ts experimentally, it was considered desirable to develop an objective function that can aid in selecting suitable time windows without resorting to extensive series of measurements. The presentation of such a function is the purpose of this contribution. 'Current address: California Public Health Foundation, 2151 Berkeley Way, Berkeley, CA 94704. 0003-2700/86/0358-2891$01.50/0
THEORY Three assumptions are made in developing the desired mathematical model: (1) the signal measured at the detector is the sum of a flat base line, the analytical peak, and Gaussian noise, (2) the signal is recorded as a series of digital readings from the detector, and (3) the absolute standard deviation of individual readings, ui, in the peak region is the same as in the base line region. Assumption 3 is generally justified when signals near the detection limit are considered. If the number of time slices (or independent detector readings) within t B and ts are denoted with nB and ns, the net peak area xp is given by (1) xp = x s - x B n S / n B where x s and X B are the sums of intensity readings xi taken during t s and t g , respectively. With a fiied detector sensitivity and noise level, the main factor determining the detection limit obtainable by this type of signal evaluation is the uncertainty inherent in determining x p . According to the rules of error propagation, the absolute standard deviation of x p , up, is given by up = [us2 (uBn~s/nB)~]~'~ (2) where us and uB are measures of the uncertainties in the values of x s and X B given by
+
as =
ns1l2q
(3)
uB = nB1/'Ui (4) Substituting these two equations into eq 2 yields eq 5, which represents the desired function up = f(ns,nB). up = (ns ns2/nB)1/2ai (5)
+
It should be noted that in deriving this equation only high-frequency noise (e.g., detector noise) was considered as an error source. Uncertainty contributions from other sources, such as drift, were neglected in order to isolate the effects of the data handling method.
RESULTS AND DISCUSSION Inspection of eq 5 shows that for a given combination of integration time per time slice and noise (q)level, up increases with the number of time slices in the peak integration window, ns, and decreases with the number of base line readings nB. For comparative purposes it is convenient to express nB as a fraction or percentage of ns, f B = 100nB/ns. By further dividing both sides of eq 5 by ns1/2and by ui, one obtains the normalized equation
up/ns1/2ui= ( 1 0 1986 American Chemical Society
+ 1oo/fB)1/2
(6)
