702
Anal. Chem. 1981, 53,702-706
Differential Normal Pulse Voltammetry in the Alternating Pulse Mode for Reversible Electrode Reactions Timothy R. Brumleve,’ John J. O’Dea, Robert A. Osteryoung, and Janet Osteryoung* Department of Chemistty, State University of New York at Buffalo, Buffalo. New York 14214
The technique of differential normal pulse voltammetry employlng a second pulse alternatlng In sign Is described. Theoretlcal voltammetric responses for a reversible electrode reaction are derived, and the optlmum parameters for trace analysls are discussed. The computer-controlled pulse-voltammetric Instrument Is described, and the effectiveness of the waveform is illustrated with the reverslble reductlon of Pb(I1) on mercury at micromolar concentratlons.
The technique of differential normal pulse (DNP) voltammetry is based upon the application of a double potential pulse of short duration and the differential display of sampled chronoamperometric responses. The technique is a hybridization of differential pulse (DP) (1-9) and normal pulse (NP) (10-14) waveforms and has the advantages of conventional pulse techniques: high current sensitivity due to short pulse widths and excellent discrimination against RC charging currents. Because the duration of the double pulses is short compared to the time between pulses (where no faradaic reaction occurs), the technique retains all the advantages of normal pulse and should find great utility in the study of reactions at solid electrodes and in cases of electrode passivation or filming (15). Because the method of current Sampling and display is the same as in DP voltammetry, the technique discriminates well against residual (background) currents and provides peak-shaped current-potential responses. It is a true differential technique and should not be confused with techniques involving differencing successive normal pulse currents (16). A theoretical description of DNP voltammetric responses for slow electron transfer kinetics has been presented by Aoki et al. (17). The current response to the DNP waveform is simply that of double potential step chronoamperometry. When the two step potentials lie in the limiting current region for a reaction, the current response is potential independent but time dependent. Because the current is sampled near the end of each pulse (that is, at two different times), the resulting differential current is not zero (negative for cathodic reactions) but rather contains a normal pulse component whose magnitude depends on the times of current measurement and the pulse amplitudes. This effect is illustrated in detail below. This paper is concerned with a modification of the DNP waveform in which the second pulse alternates in sign as shown in Figure 1. The current output is taken as the difference between the currents for successive double pulses. The difference current voltammogram which results is much more easily interpreted and analyzed than either the forward or reverse currents, primarily because of the elimination of the normal pulse component by subtraction. For a reversible system one thus obtains a symmetrical peak which is centered around the reversible half-wave potential and which has no diffusional “tail” in the limiting-current region. In the context Present address: Anderson Physics Laboratories, P.O.Box 2680, Station A, Champaign, IL 61820.
of classical DP polarography this amounts to subtractive elimination of the “dc effect” (2). The voltammetric response for DNP with alternating pulse direction bears a strong resemblance to that of square wave voltammetry (18-24), in which one cycle of a square wave of period T (i.e., a double pulse) is imposed upon each step of a rising base staircase. The difference of the forward and reverse currents (measured at 7/2 and T , respectively) gives rise to peak-shaped voltammograms quite similar in appearance to those of DNP with alternating pulse direction. In fact, preliminary calculations in our laboratory have shown that the voltammetric responses of the two techniques are morphologically quite similar for first-order electrochemical and chemical kinetic complications, except for that of a following chemical reaction. It must be stressed that in DNP voltammetry (in contrast with square wave voltammetry) the boundary conditions at the electrode surface are restored before each double pulse is applied: at renewable mercury electrodes by obtaining a new drop; a t a solid electrode by the long delay time (at zero current) between double pulses. This has important consequences for elucidation of electrochemical reaction mechanisms and for quantitative study of adsorption and passivation phenomena, since the mathematical treatment of the response to a single double pulse is usually tractable for first-order cases. The mode employing alternating pulse direction provides further simplification by elimination of the N P component, as noted above. In the treatment which follows the theoretical and experimental aspects of this waveform are presented and analyzed for a reversible electrode reaction. Sampling and display of the current responses are discussed, and the computer-controlled pulse voltammetric instrument is described briefly. Particular attention is given to optimization of parameters for analytical applications at trace levels. The theoretical predictions are confirmed for the reversible reduction of 9.9 pM (2.05 ppm) Pb2+ a t a static mercury drop electrode.
EXPERIMENTAL SECTION The computer-controlled pulse-voltammetric instrument used for this work is based upon a Digital Equipment Corp. PDP 8/e minicomputer and homemade interface. The computer system is similar to that described elsewhere (8, 22, 25) and will be described only briefly. The system is equipped with 32K (12-bit words) of memory, a floating-point processor, a real time programmable clock, two 12-bit digital-to-analog(D/A) converters, and four (multiplexed)12-bit analog-to-digital (A/D) converters. Also available are 12 bits of digital output. A full complement of peripheral devices including fast 1/0(19.2 kBaud) using an ADM 3-A CRT terminal, complete graphics with storage oscilloscope or hard copy, and both hard and floppy disk storage provides a very versatile laboratory computer system. The potentiostat used is homemade and uses National LF166 JFET-input operational amplifiers (see Figure 2). The gated integrator illustrated in Figure 2c uses a National LF13333 JFET switch, and an attenuator/offset circuit scales the unipolar (0-10 V) output of the D/A converter to the desired potential range of the experiment (e.g., -0.3 to -0.8 V) with full 12-bit accuracy. The output of the current-to-voltage converter (Figure 2b) or of the gated integator (Figure 2c) is fed directly to one of the bipolar 12-bit A/D converters (aperture time 40 ns).
0003-2700/81/0353-0702$01.25/0@ I981 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
703
control. The internal Ag/AgCl reference electrode provided with the SMDE was removed and a conventional SCE/salt bridge arrangement was substituted. The Pt wire provided with the SMDE was used as the auxiliary electrode. All chemicals were reagent grade except for the sodium acetate which was MC&B “suprapur” grade. Distilled water was repurified with a Millipore Milli-Q filtration system.
E
time Differential normal pulse waveform with alternating direction of the second pulse. E is scanned, and A€ is differential pulse height. At t l the potential Is stepped from El to E2 on odd drops and from E , to E l on even drops. Flgure 1.
Flgure 2. Schematic illustration and nomenclature of current sampling modes: (a) DNP waveform and conventional potentlostat circuit; (b) instantaneous sampling; the output of the I to E converter is sampled 7.5 1 s before the end of each pulse (aperture time = 40 ns), followed by 12-bit A/D conversion: (c)gated integration, the JFET switch across Cmis opened during sampling time t,. The integrator output is then sampled and converted as in (b).
All software for data acquisition and analysis is written in the FORTRAN language with the exception of one FORTRANcallable assembly language routine which controls both the D/A (potential output) and A/D (current sampling) with a timing accuracy of 7.5 ps. Since typical pulse widths are usually greater than or equal to 1 ms, timing errors are always less than 1%. Calibration of the potentiostat attenuator and of the current and integrator range settings is performed by the computer system, and a table of calibration factors is stored (obviating the need for precision components in the analog circuitry). The user selects experimental parameters directly in familiar units (e.g., volts, milliseconds) and receives the voltammetric output directly in microamperes. The data-analysis procedures which have evolved are versatile and allow operations such as background subtraction, digital filtering (e.g., Savitzky-Golay smoothing (26)), and wave-shape analysis. In the present work all experiments on the Pb2+system were conducted by using a EG&G/PARC Model 303 static mercury drop electrode (SMDE) as the working electrode. The SMDE was chosen for this work because it provided a fresh stationary mercury surface and therefore wm well suited for obtaining results which could be compared easily with the predictions of theories for stationary electrodes. This provides a substantial simplification. Ample evidence exists that the DME is sufficiently reproducible from drop to drop that currents on successive drops can be differenced to give similar results with good precision and accuracy (27). The SMDE is provided with logic inputs for computer control of the dislodgdispense function and purge-gas
RESULTS AND DISCUSSION Figure 1 shows the DNP waveform with alternating sign of the second pulse and defines the potential and time parameters. The experiment begins at potential Edelay, which is usually chosen so that no faradaic current flows. The first double pulse thus consists of a potential step to the scanned potential, El(Le., a normal pulse), followed by a small differential pulse, AE, to potential E2 The potential is then reset to Edehy at t2 The next double pulse consists of a step to the same value of El, followed by a small pulse, -AE,to E;. Each consecutive pair of double pulses is similar, except that the scanned potential Elis incremented until the desired potential range is scanned. A conventional DNP scan (17)would consist of only the odd (or even) double pulses (see Figure 1). On a DME or SMDE, a new drop is formed at t 2 so that each double pulse is applied to a fresh Hg surface with renewed boundary conditions (Le., with surface concentrations equal to bulk values). On a solid electrode restoration of the boundary conditions may be accomplished by choosing td&y >> t2 or by mechanically agitating the electrode or stirring the solution between each double pulse. The definition of the current sampling modes is schematically illustrated in Figure 2. For instantaneous sampling (Figure Zb), current il is measured exactly a t tl (at potential El), and currents i2 and iL are measured exactly a t t 2 (at potentials E2and EL). Figure 2c illustrates sampling by gated integration, which is discussed in detail below. The response of a reversible system to a double potential step is well-known (28). For the reaction
0 + ne- e R where only species 0 is present in bulk solution ifor
- l/fi)/ (1 + €0,) - (1&)0/(1 + eo1) - 1/(1+€e2))i (1)
= (nFA&Co”&)Kl/&
where, referring to Figure 2, i, = i(tn,E,),iL = i(t2, EL), ifor - i2 - il, ire, = iL - il, ern = exp(nf(E, - E o ) , E = d D 0 / D R , f = F/RT = 38.92 V-’at 25 O C , and the other symbols have their usual meaning. The current ifor,the usual DNP current, has been discussed for both reversible and charge-transferrate-controlled cases ( I 7). When El, E2, EL > t,, then eq 1 reduces to the classical equation for DP voltammetry ( I ) . For DNP with second pulses of alternating sign, the current signal is Ai = ifor- ire, = i2 - iL t 4) Performing the experiment in the alternating mode rather than, for example, obtaining Ai from subtraction of currents for two complete scans, minimizes the effect of long-term drift in the difference current, Ai. Experimentally Ai is obtained as the difference i2 - i; to avoid introduction of noise by
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 4,APRIL 1981
subtraction of successive values of il. Combining eq 1 and 2 Ai/id = i/(i ce2)- i / ( i + €e2') (5 )
+
where id = nFACobv'Do/nt,. Equation 5 can be written as
Ai/id = -sinh (nfAE)/(cosh (In Ole)
+ cosh n f A E )
(6)
Notice that Ai is independent of tl. Since cosh (In Ole) is symmetric about In Ole = 0 the voltammogram, Ai vs. E , is symmetric with peak potential, E,, given by E, = Ell,. Thus in contrast with DP voltammetry E, is independent of a.The peak current, Ai,, is given by
Aip/id = -tanh ( n f A E / 2 )
(7)
and thus approaches the maximum value, id, for large values of AE. From eq 6, the peak width at half height, Wl/,, is given by W l p = ( 2 / n f l c0sh-l ( 2 cash nfAE) (8)
-
+
For InfAEl >> 1, W,,, 21AEI. For small values of AE (InfAEl v'rDOt,. The agreement between the theoretical and experimental curves is remarkable, considering the low analyte concentration and the fact that the experimental curves have not been corrected for background. The effect of variation of time parameter tl (for constant t, = 50 ms) is illustrated for the forward and reverse DNP currents in Figure 4. As tl is increased, the constant "tail" of the DNP peaks is diminished. At the highest value of tl (500 ms) both the forward and reverse voltammograms begin to approach the classical D P voltammetric response. Both forward and reverse peak potentials (for tl = 500 ms) are shifted away from the reversible half-wave potential by about f12.5 mV as expected. Although it is not illustrated for these data, the difference currents, Ai,for all values of tl are identical (within 1 % ) to that shown in Figure 3 and are independent of tl as predicted by eq 5 . This fact has important consequences in cases where interfering electrode reactions passivate the electrode surface. By keeping the total time at the pulsed potentials ( t z )as short as possible, such effects may be minimized without affecting the wave shape or peak potential of a reversible couple. This is particularly important on solid electrodes where the electrode surface is not renewed before each double pulse. Figure 5 shows the effect of variation of the differential pulse height, AE, on the difference current and on the indi-
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
Table I. Dependence of
-
50
2 0: ,-
t, (ms)
-
0-
-25
-
-50
-
- A E , mV
and W,,, on A E
w,,,, mV
nA
Ai,,
25 -
Aip
experiment
705
theory
experiment
theory
500 200
10
41.5
47.0
48
48
IO0
25
95.0 122 128
95.0
63
62 102 200
50
100
50
122 127
102 202
/
I
4 0
100
-25
2 sf
0
500 200
50
-50 -75 - 100
-300
-400
-500
-600
vs. SCE Figure 4. Effect of variation of time parameter t I on (a) forward and (b) reverse DNP voltammograms. All conditions are as in Figure 3 except for t , as noted. For the largest t l (500 ms) both forward and reverse currents begin to approach responses obtained with conventional DP voltammetry.
-21i
E (mV)
-400
I
I
,
,
-425
-450
-475
-500
E (mV) vs SCE
Reversible peak shape analysis of difference currents of voltammograms B, C, and D of Figure 5a according to eq 10. Flgure 6.
100 h
P
w
0 50-
0-
0
-20
-40
-60
-80
-100
nAE (mV) Flgure 7. Effect of variation of nAEon normalized peak current, Alplid (0),nWl12(O),and the ratio, Aip/idnWl12 (0).The ratio plot is in arbitrary units. Solid lines are theory as glven by eq 7 and 8 for T = 25 O C . Points are experimental values from Table I corresponding to A € = -10, -25, and -50 mV. The dotted line indicates the maximum in the ratio plot.
100
- 100
, - -EO0
-300
-400
-500
-600
E (mV) vs. S C E Figure 5. Effect of variation of differential pulse height A€ on (a) difference current and (b) forward and reverse current voltammograms. Conditions are those of Figure 3 except for AEas indicated. Table I contains values of Aip and W,,2 corresponding to the voltammograms in (a).
vidual forward and reverse currents. The forward and reverse currents show a marked shift in peak potential away from as AE is increased. As predicted, the peak potential for the Ai voltammogram is independent of AE. It is interesting to note that curve E in Figure 5b (for AE = 0) is just the difference of two normal pulse voltammograms sampled at t2 and tl. The Ai voltammograms in (a) show a marked broadening as AE is increased, with the peak width approaching 21AEI a t large AE as predicted by eq 8. The peak currents (Ai,) also begin to approach a maximum value of id as predicted by eq 7 . A comparison of the experimental and theoretical values of peak height and width for the voltammograms of Figure 5a is given in Table I.
Figure 6 shows a linearized wave-shape analysis of the three Ai voltammograms of Figure 5a for pulse heights AE = -10, -25, and -50 mV. The function on the abscissa is the same as that employed in ac polarography for the evaluation of reversibility, and such a plot should give slopes of h f / 2 only for small values of AE (such that lnfAEl
