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(2) Corklll, J. A.; Kuttab, S. H.; Giese, R. W. I n “Glass Capillary Chromatography. Clinical, Drug and Pharmaceutical Analysls”; Jaeger, H., Ed.; Marcel Dekker, In press. (3) Fenimore, D. C . ;Davis, C. M.; Whltfard, J. H.;Harrington, C. A. Anal. Chem. 1976, 48, 2289-2290. (4) Peterson, B. A.; Hanson, R. N.; Glese, R. W.; Karger, 8. L. J. Chromatogr. 1978, 126, 503-516. (5) Grob, K. HRC CC, J. High Resolut. Chromatogr. Chromatogr. Commun. 1980, 3 , 585-586. (6) Pelllzzari, E. D. J. Chromatogr. 1974, 98, 323-361. (7) Miller, D. A.; Grimsrud, E. P. J. Chromatogr. 1980, 190, 133-135. (8) Corkill, J. A.; Kuttab, S. H.; Giese, R. W., unpubllshed results, (9) Yang, F. J.; Brown, A. C., HI;Cram, 8 . P. J. Chromatogr. 1978, 158, 91-109. (IO) Maclouf, J.; De La Baume. H,; Caen, J.; Rabinovitch, H.; Rigaud, M. Anal. Biochem. 1980, 109, 147-155.
(11) Llpsky, S. R.; McMurray, W. J.; Hernandez, M.; Purcell, J. E.; Billeb, K. A. J. Chromatogr. Sci. 1980, 78, 1-9. (12) Shatkay, A.; Flavlan, S. Anal. Chem. 1977, 49, 2222-2228. (13) Shatkay, A. Anal. Chem. 1978, 50, 1423-1429. (14) Ravey, M. Anal. Chem. 1978, 50, 1006. (15) Royston, G. C. Anal. Chem. 1978, 50, 1005. (18) Schomburg, G. HRC CC, J. High Resolut. Chromatogr. Chromtogr. Commun. 1979, 2 , 461-474.
RECEIVED for review March 19,1981. Accepted June 15,1981. We wish to acknowledge NIH for support of this work under Grant AM21797. Contribution No. 82 from the Institute of Chemical Analysis.
Classification of Voltammetric Data by Computerized Pattern Recognition S. D. Schachterle and S.
P. Perone”
Department of Chemistry, Purdue University, West La fayette, Indiana 4 7907
Computerized pattern recognltion was used for discriminating between complicated and uncomplicated electrode processes and for ldentlfylng the mechanism of the electrode process uslng the shape lnformatlon contained In the data from a single voltammetric experlment. Features based on the Fourier transform, whlch were selected to give the best classlflcatiorl accuracy with theoretical cycllc linear sweep voltammetry (CLSV) data, could be used to classify experlmental CLSV or cyclic staircase voltammetry (CSCV) data. The theoretical data were classlfled with an accuracy of 97%. The experlmental data were correctly classlfled 93 % of the tlme when the shape of the voltammogram was determined by a single mechanism whlch was Included in the theoretical trainlng set.
Linear sweep voltammetry (LSV) is an electrochemical technique which is frequently used to gain fundamental information about redox couples and electrode processes. Its widespread use can be attributed to the large number of electrode mechanisms which have been treated theoretically. These theoretical descriptions aid in the understanding of real systems by allowing the direct comparison of experimental results with theory. The classic paper by Nicholson and Shain ( l ) ,which treats LSV theory for several cases involving coupled chemical reactions, is important for at least two reasons: First, it tied together all previous theoretical descriptions of LSV. Second, it presented methods for solving the boundary value problems in LSV which were later applied to other cases, such as adsorption (2) and amalgam formation (3). The most important variation of LSV is to employ a cyclic voltage sweep (cyclic voltammetry, CV or CLSV). The reverse scan is very useful for examining products of the forward scan and for detecting processes which might be occurring to remove these products from the solution. Four parameters are easily measured from this cyclic waveform: the two peak currents and two peak potentials. While their values may be individually compared with results presented in the original literature ( I ) , they are usually compared as the ratio of the anodic (reverse sweep) peak current to the cathodic peak
(forward sweep) current (ip/iw) and the anodic peak potential minus the cathodic peak potential (Epa- Epoor AEp). For a system with a reversible untomplicated electron transfer, these values will be ipa/ip 1.0 and AE, = 58.3 mV. Graphs of the variation of these parameters vs. scan rate are available in the literature, as well as in compilations of many of the processes which have been treated theoretically (4). Theoretical graphs of ipa/ipcand Upvs. scan rate are shown in Figures 1and 2 for all the cases considered here. To determine if an unknown experimental system is complicated by a coupled chemical reaction, the experimental ratios can be compared with the theoretical ratios for each case. An experienced operator usually contributes his intuition and experience to this classification process as he can consider the overall shape of the wave rather than looking for only four parameters for each voltammogram. This process of running several experiments and interpreting the data can. be quite time-consuming. Also, the degree which a kinetic complication affects the shape of the voltammogram may become so slight a t a particular scan rate that the effect is masked by noise. In addition, several of these complications exhibit similar trends as the scan rate is varied, so that complementary, nonvoltammetric experiments may need to be run in order to make an umambiguous decision. The effects of some elctrode processes on the shape of voltammograms are shown in Figures 3 and 4. The similarity of the shapes of these curves precludes a visual identification of the electrode process by looking a t only one voltammogram. For all of the above reasons, this seems to be an area in which the use of computers to assist the data interpretation would be cost effective. The theory for staircase voltammetry (SCV) has been published for reversible (56) and quasi-reversible (6) electrode reactions. Lam (7) developed SCV theory for preceding and following coupled chemical reactions. Miaw et al. (8) developed the theory for reversible cyclic SCV and Ryan (9) generated theoretical cyclic staircase voltammograms for various mechanisms involving coupled chemical reactions using digital simulation. A complete theoretical description of CSCV for a variety of electrode processes bas yet to be published. However, Miaw (8)and Zipper (5)found that for a value of the current sampling parameter, a’, of 0.7, cyclic f
QQQ3-2780/81/Q353-1672$01.25/0 0 1981 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 53, NO. 11, SEPTEMBER 1981 K
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SCAN RATE Figure 2. Variation of peak potential difference, EP - E c, with scan rate in cyclic linear sweep voltammetry. (Taken in part &om ref 22.)
VOLTAGE Figure 3. Examples of cyclic hear sweep voltammograms for various electrode processes with i,l i, < 1.
staircase voltammograms display characteristics similar to cyclic linear sweep voltammograms. For example, a t this sampling parameter the peak current for the forward scan is proportional to the square root of the step height. This is analogous to the dependence of the peak current in CLSV on the square root of the scan rate. Also, the peak current ratio for CSCV a t CY’ = 0.7 is unity regardless of ~ t e height p as it is in CLSV for all scan rates. The peak culrrent separation approaches the value of 58.2/n mV as the step height approaches zero in CSCV. This value corresponds to that obtained in CLSV. In addition, Goto and Ishii (IO)found that semidifferential and semiintegral staircase voltammograms taken at a’ = 0.7 could be dlirectly compared with data taken using a linear potential sweep. These observations, plus those of Ryan (9) and Lam (7) that, the peak currents and potentials in SCV for various electrode reaction mechanisms exhibit the same trends as they do in LSV, suggest that for a current sampling parameter of a’ = 0.7, the shape of a staircase voltammogram would be veiry similar to that of a linear sweep voltammogram for the same electrode process. Pattern recognition techniques have been successfully applied to electrochemical data in this laboratory in several ways. They have been used to detect severely overlapped LSV data (11-15) and to characterize heterogeneous kinetic parameters from LSV data (16). The initial work of Syhrandt (11) and Pichler (15) considered only totally reversible data sets. Thomas and DePalma (12, 13) added irreversible and qua-
si-reversible cases also. In each study, the training set used for feature selection and pattern classification was derived from LSV theory. By use of first the linear learning machine (LLM) (17)and later the k-nearest neighbor (kNN) algorithm (18), excellent results (>go% classifiction accuracy) were obtained for both theoretical and experimental data. Features used in the classifications were based on either the fast Fourier transform (PFT) or LSV theory. The best results in all of these studies seem to be obtained with a FFT-kNN approach. In each of the studies performed it was assumed that uncomplicated electron transfer was the sole process occurring. A few experimental examples were classified incorrectly (13, 16) suggesting that the theoretical training set did not include voltammograms which adequately represented some of the real systems. Upon closer examination it was determined that other processes besides the electron transfer were affecting the shapes of some of the voltammograms, and it appeared that sufficient information was present in the shapes of these voltammograms to allow pattern recognition to discriminate between different mechanisms. This work reports the development of a method for discriminating between complicated and uncomplicated electrode processes and for identifying the mechanism of the electrode process using the shape information contained in the data from a single CLSV experiment. Experimental voltammograms are classified by using computerized pattern recognition with a training set composed of theoretical curves. The use of theoretical data in the training set allows broad coverage of both the types of electrode processes and values of fundamental parameters such as rate constants, n values, etc. The parameters can be easily varied and the curves can be generated noise- and distortion-free. This well-defined training set also provides a basis for determining whether or not this type of classification is feasible. Features selected to give the best classification with theoretical CLSV data could then be used for the classification of CLSV and CSCV data.
EXPERIMENTAL SECTION Chemicals and Solutions. All chemicals used were reagent grade and were used without further purification. Solutions were made with distilled, deionized water, with background electrolyte concentrations between 0.1 and 1.0 M. The concentration of electroactive substances was between lo4 and M. Each solution was deoxygenated by bubbling purified, solvent-saturated nitrogen through it for 15 min. Cell and Electrodes. The cell was a Pyrex screw top bottle with a threaded Teflon cap used to hold the electrodes in place. The working electrode was a Metrohm micrometer-typehanging mercury drop electrode No, E-410. The reference electrode was a Coleman 3-710 saturated calomel electrode. The auxilliary electrode was a platinum spiral sealed in glass.
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 11, SEPTEMBER 1981
Potentiostat. The potentiostat was constructed in our laboratories (19) and modified to include a computer-selectable low pass filter on the current output for slower scan rates. The current measurement circuit had a computer-selectable bandpass of 800 Hz or 80 kHz and a manually selectable gain that allowed the measurement of currents through the cell from 1to 100 pA (full scale). The noise level was typically 50-100 nA. The effective cell time constant with positive feedback IR compensation was 10 ps. Computer Interface. A computer-controlled ramp generator was constructed (similar to Thomas (20))capable of producing a linear ramp up to A38 V/s. The slope of the ramp is set by the digital-to-analog converter (DAC) voltage, and the ramp is started or stopped by a digital control bit from the computer. The staircase waveform was software generated through another opt,ically isolated DAC. Timing for data acquisition came from a 20-MHz crystal clock, which was hardware scaled to 10 kHz and software scaled to give the proper resolution for the slope of the linear ramp. The choice of a CLSV or CSCV experiment was entirely under software control. Scan rates available for CLSV are from 0.001 to 20 V/s. Allowable scan rates require the interval between data points to be a multiple of the 100 p s clock time. Staircase rates range from 0.5 Hz to 1 kHz in steps of 1, 2, or 5. The timing for the current sampling parameter, a’, was derived from software scaling of the 10-kHz clock. The upper limit for the staircaserate is set by the combination of the cell time constant and the restriction that a’ = 0.7. At a 1-kHz staircase rate and this value for a’, the cell current is sampled 300 ps after the potential step. This corresponds to 30 cell time constants, the minimum required to achieve negligible values for induced charging current contributions (21). Computer Systems. The computer network used in this work consisted of a Hewlett-Packard 2100s satellite computer with 32K words RAM linked to an H P 1000 time-shared system with 64K words RAM. The satellite operated in a dedicated mode during data collection to enable data to be taken up to 10 kHz while performing real time calculations. Peripherals on the satellite computer included high-speed paper tape punch and reader, Teletype, Tektronix type 601 digital storage monitor, two optically isolated digital-to-analog converters, a link to the time-shared system, and a general purpose interface with programmable clock, digital clock, digital 1/0and timing logic, and an Analog Devices ADC-12QM analog-to-digital converter (ADC). Programming was in HP BASIC with H P Assembly Language subroutines used to control the experiment, take the data, and communicate with the time-shared computer. The time-shared computer system has the capability to operate with six on-line terminals simultaneously. Its peripherals include a floating point processor, 5-Mbyte disk, paper tape punch and reader, floppy disk paper tape emulator, Tektronix 4012 graphics terminal, Centronics 703 printer, Calcomp 565 digital plotter, Teletype, and two Radio Shack TRS-80’s operating as intelligent terminals. Programs were run under Hewlett-Packard’s RTE-IV operating system. All data processing, pattern recognition, and LSV theory calculation programs were written in FORTRAN IV. The time-shared computer was used for generating all of the theoretical LSV curves except for the adsorption cases, which were run on a Control Data Corp. 6500 under the Purdue Dual Mace operating system. Use of this system was necessary to avoid roundoff errors in these calculations. These adsorption curves were transferred to the H P lo00 system via intermediate storage onto flexible diskettes. Treatment of Experimental Data. Operator inputs to the BASIC program include: the technique (CSCV or CLSV), the scan rate, the resolution (mV/point), the number of scans to be averaged, the threshold above which to look for the peak, and the starting potential for the scan in millivolts, between 300 and 800 mV before the peak, The BASIC program then calculates appropriate DAC and clock codes before calling the proper Assembly Language subroutine to perform the desired experiment. For the LSV experiment, the Assembly Language subroutine sets the slope of the ramp, starts the ramp, and begins taking data at the correct frequency to produce the desired resolution. Once the incoming data are greater than the threshold value, the peak is detected by looking for consecutive points decreasing in value. After the peak has been located by retaining the maximum value
Table I. Electrode Processes for Theoretical Training Set abbrev process ref Electrode Phenomena uncomp O t ne
uncomplicated reversible
f
R
+-
kb
quasi-reversible
o+
QR
amalgam formation
amalg
+
0
ne = R
reversible following
47
kb
ne
2 R(Hg) -+
weak adsorption preceding
Ads Oadst n e t R Coupled Chemical Reactions K CE z;-,o O+ne;-)~ EC,,, o + ne ;z‘ R K
irreversible following ECi,
1, 48, 49
R
