Anal. Chem. 1996,67, 986-992
Conversion of Staircase Voltammetry to Linear Sweep Voltammetry by Analog Filtering Peixin He Department of Chemistty, University of Memphis, Memphis, Tennessee 38152
The current responses for staircase voltammetry might be very differentfrom those of true linear sweep voltammetry. This is particularly true for data from surface reactions. The existing theories for linear sweep voltammetry may not be used to interpret staircase voltammetric data. In this paper, the frequency spectra of staircase ramp and linear sweep waveforms are analyzed. ' h o techniques were explored to make staircase voltammetry equivalent to linear sweep voltammetry. The first one involves shaping the output of a digitalfunction generator by using a low-pass filter to convert the staircase ramp to linear potential sweep. The second technique involves filtering the current responses before digitizing. Both techniques are effective. When the filters are properly set, the voltammograms from staircase voltammetry match those obtained by linear sweep voltammetry. Staircase voltammetry (SCV) has received more and more attention recently due to the popularity of computerized instrumentation. Instead of linear potential sweep, modem digital instruments implement a potential ramp with a series of small potential steps. Depending on the type of electrochemical reactions and the experimental parameters,the current responses for staircase voltammetry might be very different from those of true linear sweep voltammetry (LSV). The time scale of staircase voltammetric experiments and the measured currents are affected by three experimental parameters: step height, step frequency, and sampling delay time. Only one parameter, scan rate, plays a role in linear sweep voltammetry. Several theoretical works have been published to the current responses of staircase voltammetry.lI2However, it is dacult to use these theories due to the mutual influence of multiple experimental parameters. Several sampling schemes (varying the sampling delay time) were suggested to generate equivalent staircase and linear sweep voltammograms. The existing LSV theory can then be used to elucidate the electrode process and to extract quantitative chemical information. So far, only a few simple cases have been treated. In addition, it is difiicult to make instruments with exact timing control for function generation and data acquisition in a reasonably large dynamic range. For a diffusive process, the difference between staircase and linear sweep voltammograms gets smaller as the step height, AE, of staircase voltammetry decreases. When n A E is smaller than 0.26 mV, the two techniques merge.3It has been shown that it is (1) Kalapathy, U.; Tallman, D. E. Anal. Chem. 1992,64,2693-2700. (2) Seralathan, M.; Osteryoung, R; Osteryoung, J. J. Electroanal. Chem. Inferfacial Electrochem. 1986,214,141-156. (3) Penczek, M.; Stojeck, Z.; Buffie, J. J. Electroanal. Chem. Interfacial Elecfrochem. 1989,270,1-6.
986 Analytical Chemistry, Vol. 67,No. 5, March 7, 7995
relatively easy for a computer-based instrument to generate a staircase ramp function with a 0.1 mV step height and a scan rate up to 50 000 mV/s.4s5 However, the situation is much worse for surface reactions. The measured staircase and linear sweep voltammograms are quite different even for small step heights.6 This is particularly true for a reversible surface reaction. It is impossible to make staircase voltammetry equivalent to linear sweep voltammetry by varying the sampling delay time. In this paper, the frequency spectra of staircase ramp and linear sweep waveforms are analyzed. The differences in current responses of SCV and LSV for diffusive and adsorptive cases are studied. Two techniques were explored to make staircase voltammetry equivalent to linear sweep voltammetry. The first one involves shaping the output of a digital function generatorby using a low-pass filter to convert the staircase ramp to linear potential sweep. The second technique involves filtering the current responses before digitizing. Both techniques worked well. When the filters are properly set, the staircase voltammograms match those obtained by linear sweep voltammetry. EXPERIMENTAL SECTION
Chemicals. Alizarin complexone hydrate was obtained from Aldrich Chemical Co. All the other chemicals were reagent grade purity. Millipore water was used for preparation of the solution. Instrumentation. A BAS CV-27 voltammograph or a Pine AFRDE4 potentiostat was used for linear sweep voltammetry. Staircase voltammetry was carried out with a BAS100Bm electrochemical analyzer or its pr~totype.~The system was reprogrammed to allow varying of the potential waveform and the sampling time. Inside BASlOOB, there is a programmable RC filter in conjunction with the current-bvoltage (irv) converter. A thiid-order Bessel low-pass filter with selectable cutoff frequencies (1500, 150, 15, 1.5, 0.15, and 0.015 Hz) can also be used to filter the iflconverter output. For potential filtering, an external potentiostat with a second-orderButterworth low-pass filter was used. Since the 100 pV steps generated by BASlOOB are too small to be easily observed, a staircase ramp generator with 39 mV step height was built to test the effect of potential filtering. The step frequency was controlled by a function generator which was also used to test the effect of current filtering. Low-pass filters of fu-st and second order were constructed. Both input and output of the low-pass filter were recorded with a digital storage oscilloscope. A platinum disk electrode was used in diffusive systems. For adsorption studies, a BAS controlled growth mercury electrode (4) He, P.; Avery, J. P.; Faulkner, L. R. Anal. Chem. 1982,54, 1313A-1326A. (5) He, P.; Faulkner, L. R J Electroanal. Chem. Infetfucral Electrochem 1987, 224,277-283. (6) Stojek, Z.;Osteryoung, J. Anal. Chem. 1991,63, 839-841.
0 1995 American Chemical Society 0003-2700/95/0367-0986$9.00/0
The current response of a quasireversible surface reaction to a potential step is (see Appendix)
i(t) = nFA[(k,+ kdr, - k b r * ] exp[-(k,
+ kdtl
(1)
where r*is the total surface coverage of both the oxidized and the reduced species (in mol/cm2) and To is the surface coverage of the oxidized species before the potential step is applied. kfand k b are potentialdependent forward and backward surface reaction rate constants
kb
Figure I. Staircase and linear sweep voltammograms of 5 x 10M of alizarin complexone in 0.05 M HAc-NaAc solution (pH = 4.7). BAS CGME electrode. Quiet time, 60 s. (A) Linear sweep voltammogram; scan rate, 15 mV/s. (6) Staircase voltammogram without filtering, step period, 0.0333 s; step height, 0.5 mV.
(CGME) was used as working electrode. A platinum wire was used as counter electrode. The working electrode potentials were controlled versus Ag/AgCl reference electrode in 3 M NaCl solution. Solutions were degassed with argon prior to the experiments. During experiments, a blanket of argon was maintained over the solution. All experiments were conducted at room temperature (25 & 2 "C).
RESULTS A N D DISCUSSION CurrentResponses without Filtering. Staircase voltammograms for both diffusion and adsorption systems were recorded with a BAS100B/W electrochemical analyzer without current filtering. The step height was 0.1 mV. For comparison, linear sweep voltammogramswere also recorded. For diffusive systems, a reversible reaction (ferrocene in CH3CN) and a quasireversible reaction (ferricyanide in KC1) were measured. The staircase voltammograms obtained with the BASlOOB voltammographs match the linear sweep voltammograms obtained with the Pine AFRDE4 potentiostat. However, the current responses for adsorptive systems (5 x M of alizarin complexone in 0.05 M pH 4.7 HAC-NaAc solution) obtained with staircase voltammetry are quite different from those obtained with linear sweep voltammetry, as shown in Figure 1. Alizarin complexone was chosen because it is known to have a very fast electron transfer rate at the surface of mercury electrode^.^ For a diffusive system, the current response depends on the gradient of the concentration profile at the electrode/solution boundary. This concentration profile can be modified by time and interfacial concentration. When the potential step is small enough, the interfacial concentration change is insignificant and the elapsed time plays a more important role in modifying the concentration profile. The situation is quite different for surface reaction. The current response is a function of surface concentration. Depending on the reversibility of the electrode reaction, the surface concentration can be moditied instantly, and the current response will strongly depend on the potential perturbation waveforms. (7) Chen, X.:Zhuang, J.; He, 1989,271, 257-268.
P.J. Electroanal. Chem. Inteflacial Electrochem.
k, = k, exp[-anF(E - E")/RT]
(2)
= k, eXp[ (1 - U)nF(E - E")/RT]
(3)
and k, is the standard rate constant of the surface reaction (in s-1).
The current immediately following the potential step is proportional to the sum of kfand kb and decays exponentially. As the reversibility of the system improves, the transient current increases and also decays faster. For a reversible reaction, the current passed to establish the surface concentration equilibrium is instantaneous. The measured current will be 0, even with a very short sampling delay time. This remains true no matter how small the potential steps are. In this case, it is impossible to make staircase voltammogramsidentical to linear sweep voltammograms by varying the sampling delay time. Since no difference in current responses was seen for a diffusive system between linear sweep voltammetry and staircase voltammetry with 0.1 mV step height, the effects of potential and current filtering will be studied only for surface reactions. Filtering of a Digital Function Generator. One way to make staircase voltammetry equivalent to linear sweep voltammetry is to shape the potential waveform by low-pass filtering. If the cutoff frequency of the low-pass filter is properly set, one might be able to convert a staircase to a linear ramp with a reasonably small error. Discrete Fourier transform was used as the tool for analysis of spectra in order to understand the difference between the linear sweep and staircase ramp. Using a 409Gpoint data array, a linear sweep triangular waveform can be represented as
E($ = i
0 Ii I2047
E(i) = 4096 - i
2048 5 i I4095
while a staircase ramp triangular waveform can be described as
E(i) = i - i%l6
E(9 = (4096 - i> - i%16
0 Ii 5 2047 2048 Ii I4095
where the percent symbol is the modulus operator, which divides a value and gives the remainder. Each step consists of 16 points. Since one full cycle of waveform is used, no leakage effect exists. The spectra for two waveforms are shown in Figure 2. The spectra are mirror symmetric, and the line intensities of spectra beyond the maximum value of the ordinate are not shown. In both cases, the low-frequency components are predominant. The Fourier coefficient at the zero component is very large, Analytical Chemistry, Vol. 67,No. 5, March 1, 1995
987
m Component
.w
o
m
1 0 ~ 0 1x10
IOW zm 3000
]so
P , , . , .I
1000
.lW
4so
0
1wmowa4mmw1wwow
m Component
I T Component
Figure 2. Frequency spectra of linear sweep (upper curves) and staircase ramp (lower curves) triangular waveforms.
i
2.0,
compared with others, because the average value of the waveforms (dc component) is nonzero. The difference between the two spectra is that the linear sweep waveform shows only lowfrequency components, while the staircase ramp waveform also contains high-frequency components. The peak of high-frequency components for the staircase ramp waveform occurs at multiples of 256. Since one full cycle of waveform consists of 256 steps, the frequency of the steps is therefore 256 times higher than that of the triangular waveform. The peaks at high frequencies are somewhat broad, because only 16 points are used for each step. Sharper peaks can be expected if each step consists of more points. The power of the high-frequency peaks reduces as the frequency increases. This can be seen from the change of the area under the peaks. Figure 3 shows the difference spectrum for two waveforms. At low frequencies (Fourier components
