Anal. Chem. 1090, 62, 2643-2646
ion appearance energies. Subtle differences of this type are usually accentuated in a mass spectrum when the parent ion internal energy is low (12). In the 118-nm photoionization spectra, low parent ion internal energies are indicated by high parent ion relative abundances and metastable broadening of the fragment ions. Enhanced isomer distinction has also been observed for other types of laser-produced ions (13,14).
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(12) Codts, R. G.; Beynon, J. H.; Caprloli, R. M.; Lester, G. R. Metastable Ions; Elsevier: Amsterdam, 1973. (13) Kinsel, G. R.; Johnston, M. V. Anal. Chem. 1088, 60, 2084-2089. (14) Segar. K. R.; Johnston, M. V. Org. Mass Spectrom. 1989, 2 4 , 176- 162. To whom correspondenceshould be sent. Current address: University of Delaware, Department of Chemistry and Biochemistry, Newark, DE 19716.
’
LITERATURE CITED Feng, R.; Wesdemlotls, C.; Zhang, M.-Y.; Marchettl. M.; McLafferty,F. W. J . Am. Chem. Soc. 1989, 7 7 7 . 1986-1991. Hilbig, R.; HHber, G.; Lago, A.; Wolff, E.; Wallensteln, R. Comments At. Mol. Phys. 1988, 78. 157-180. Kung, A. H.; Young, J. F.; Harris, S. E. Appl. Phys. Lett. 1973, 22, 301-302; 1976, 2 8 , 294. Palilx, J. E.; Schijhle. U.; Becker, C. H.; Huestls, D. L. Anal. Chem. 1080, 67, 805-811. McLafferty, F. W.; Wesdemiotis, C. Org. Mess Spectrom. 1989, 2 4 , 663-668. Holmes, J. L. Mess Spectrom. Rev. 1989, 8 , 513-539. Adams, J. Mess Spectrom. Rev. 1990, 9 , 141-186. Adams, J.; Gross, M. J. J . Am. Chem. Soc. 1989. 1 7 1 , 435-440. Van Bramer, S.E.; Johnston, M. V. J . Am. Soc. Mess Spectrom., in press. Collin, G. J. A&. Photochem. 1988, 14, 135-176. Deslauriers, H.; Collin, G. H.; Slmard, E. J . Fhotochem. 1983, 2 7 , 19.
S. E. Van Bramer’
M. V. Johnston*J Department of Chemistry and Biochemistry Cooperative Institute for Research in Environmental Sciences University of Colorado Boulder, Colorado 80309-0216 RECEIVED for review May 25,1990. Accepted September 6, 1990. This research was supported by Grant No. CHI38918638 from the National Science Foundation. The delay generator and assembly of the Xe/Ar cell were partially funded by the Biomedical Support Research Grant Program (2S07RR07013).
Recovery of Voltammograms by Target Factor Analysis of Current-Time Data in Electrochemical Detection Sir: Recently, voltammetry and related techniques have been shown to be useful tools for increasing the information content in chromatography (1-12). This method of detection is analogous to array-based spectrophotometric detection in that a second dimension is added by virtue of the potential (wavelength) dependence of the signal. An advantage of such an information-rich detection scheme is that the confidence level in quantitative analysis of particular components increases, although the detection limit decreases. We have been working to understand the signal-to-noise (S/N) ratio problem in voltammetry (11,12) and have found that there are advantages to using a large-amplitude sine wave perturbation of the electrode-solution interface. This is in contrast with the usual approach of using a triangle wave, for which mathematical solutions of the current-voltage curve exist (13). The advantage of the sine wave that made us first consider its use was the simplicity of the Fourier transform of the background current; it is approximately a cosine wave in the time domain and a single peak in the frequency domain (11). In this correspondence we consider another advantage-the simplicity of target transformation in the factor analysis of a flow injection/voltammogram. EXPERIMENTAL SECTION The flow injection apparatus consisted of an LDC Constametric I11 pump, a Rheodyne 7125 injector with a 50-pL loop, and a homemade detector. The detector was simply a piece of 0.5 mm i.d. Teflon tubing in the floor of a cylindrical container fashioned after Kristensen et al. (14). The tubing, which is the conduit for fluid flow, was cut flush with the Teflon floor of the cell. A cylindrical piece of glass tubing served as the wall. Overflow was controlled by capillary action; a piece of string in contact with the contents of the beakerlike cell was draped over the edge and into a waste container. The voltammograms were acquired with an IBM-PC-controlled apparatus consisting of a Kiethley 427 current to voltage converter and a BAS Ag/AgCI reference electrode. The potential was
Table
I. Eigenvalues for Fe(bpy),2’ Data Matrices 1.4 X
1.4 X
concn f M 1.4 X IO4
1.4 X IO-’
factor 1 2 3 4 5 6 7 8 9 10
3.54343+01 3.96133+01 4.55793+00 3.67213-01 5.65213-03 1.85943-02 1.25953-03 5.18323-04 4.11233-04 4.29873-04 1.00973-04 2.62803-04 4.46633-05 1.04763-04 3.8039345 5.31933-05 3.24093-05 4.19333-05 2.76033-05 3.75903-05
3.99873+01 3.99973+01 1.24323-02 1.81433-03 6.97893434 4.51413-04 2.29653-04 2.17383-04 7.82413-05 1.11453-04 5.46913-05 7.11923-05 4.21573-05 5.72203-05 4.05443-05 4.29783-05 3.71913-05 4.09583-05 3.31273-05 3.93263-05
applied as a staircase to the two-electrode system. The working electrode was a 10-pm Union Carbide pitch-based carbon fiber epoxied (353 ND Epo-Tek) into a pulled soft-glass disposable pipet. The roughly 200-pm assembly was placed into the 500-pm conduit of the cell described above. The voltage was applied as a 256-point discrete approximation to a 0.400-Hz sine wave. The A/D (analog to digital) converter was a Data Translation DT2801. A Wavetek 852-01 eight-pole Bessel filter set at 40 Hz was used as an antialiasing filter. The acquisition frequency was 102.4 Hz. Control of the experiment was through ASYST software (Macmillan). The current was measured halfway between potential changes. Each voltammetric sweep began at 4.00 s after the last one began; thus a 40-voltammogramexperiment required 160 s plus the sweep time of 2.5 s, or 162.5 s. Many voltammograms have been acquired under a variety of conditions. The voltammograms presented here are represent1.5 ative. Adrenalin (Aldrich) (1.5 X lo-’, 1.5 X lo”, 1.5 X X lo4 M) and tris(2,2’-bipyridine)iron perchlorate (1.4 X 10-’-1.4 x M) were used as test solutes. The latter compound was prepared by heating a 5050 (v/v) methanol/water solution containing a 1:3 molar ratio of ferrous perchlorate hexahydrate (ICN Pharmaceuticals) and 2,2’-bipyridine (Strem Chemicals). The progress of the reaction was observed spectrophotometrically. Solutions were prepared in 0.05 M phosphate buffer, pH 7.0. The
0003-2700/90/0362-2643$02.50/0 0 1990 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 23, DECEMBER 1, 1990
buffer alone acted as the fluid stream in the flow injection experiments. The calculations have been carried out at the computer center of the University of Vienna on an JBM 3090-4OOVF.The program used was a modified version of FACTANAL (15).
a
RESULTS AND DISCUSSION
50
IO0
150
200
250
50
LOO
150
200
250
Figwe 1. (a) Second factor from 1 5 p m F e ( b p ~ ) ~injection. ~+ Abscissa is explained in the text: it corresponds to 0 to +1.0 and back to 0 V (vs AgIAgCI). Ordinate units are arbitrary but are linear with current on any single plot. (b) Same for 14-pm adrenalin injection. Flow rate of 50 mM pH 7.0 buffer is 0.20 mLlmin.
Target factor analysis (TFA) is a very useful tool for estimating simple data vectors, e.g. spectra, from measured data matrices of a time-varying signal (16). The variation in time can be the result of a chemical procem, for the determination of reaction products in a kinetic experiment for example, or from a flowing solution, like in flow injection analysis (FIA) or in chromatography. The measured data matrix is the product of two matrices. Both of these matrices have one vector for each component. The vector in one matrix represents a certain property of the component; in this work it is the electrochemical current a t different potentials. The corresponding vector in the second matrix consists of the variation of the component with the time, or the concentration-time profile. Factor analysis tries to estimate the two matrices from the measured data matrix. As this problem has an infinite number of solutions, additional criteria are necessary to find an interpretable solution. For chemical problems it has been demonstrated that TFA is the strategy of choice for giving these criteria. T o execute target testing, a test vector has to be known that is similar to the expected result. If this is not possible, an iterative adaption of the test vectors has to be done. To carry out a factor analysis on a given data set, one has a t first to determine the number of components (factors) included in the data set. This is done with a principal component analysis (PCA). T h e PCA gives two results, the eigenvectors and the eigenvalues. the eigenvectors represent the so-called abstract factors, which are usually not interpretable in terms of a given problem. The
I 10
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,
,
,
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,
,
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,
150 ~, 150
,
,
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200 200
60
30
d
i
z
i
20
250 250
Flgure 2. (a) Factors and (b) scores for 1.5 pM Fe(bpy),2+. (c) Factors and (d) scores for 1.4 pM adrenalin. The abscissa points for the score plots are each 4 s apart and would represent the separation axis in a chromatogram. The score ordinates are arbitrary Unlts, but these are comparable from plot to plot.
ANALYTICAL CHEMISTRY, VOL. 62, NO. 23, DECEMBER 1, 1990
eigenvalues are magnitudes that are a measure of the variance of the different uncorrelated component signals (factors) in the measured signal. The magnitudes of the eigenvalues allow one to estimate the number of components or factors responsible for the information content of the signal. A detailed description of the different kinds of factor analysis can be found elsewhere (16-18). In this application of factor analysis, the component property is the voltammogram measured with a sinusoidal potential waveform; the time-varying part comes from a flow injection system. The first part of the factor analysis is a principal component analysis, which yields eigenvalues and eigenvectors, as mentioned above. The eigenvectors are usually tabulated in decreasing order of the magnitude of the corresponding eigenvalue. The eigenvalues for the largest 10 eigenvectors are given in Tables I and 11. It can be seen that there is a large first eigenvalue and also a second eigenvalue that is larger than the other remaining values. Two significant eigenvectors are expected because there are two obvious independent sources of variance-the signal and the background. A plot of the eigenvectors confirms that only two factors are involved, because, beginning with the third eigenvector, all eigenvectors clearly show only noise, much of which results from the digitization of the signal. T o be able to calculate the voltammograms of interest, target testing has to be done. A sine wave corresponding to the applied potential can be used as a test vector for the first vector. For the second vector it is sufficient to define three points, two points a t the baseline before and after the peak in the voltammogram with a value of 0 and one point in the region of the maximum of the signal with a value of 1. This shape, an inverted V, is similar to the shape of a microelectrode voltammogram plotted as current vs time. The test vector with only three defined points can be used only because it is known there is only one signal component left after the background has been removed. If there would be more than one signal present, more data points with a greater similarity to the signal would have to be given. The advantage of using only three points is that any signal of that general shape can be found. The actual positions of the points need not be very accurate. The estimated voltammograms for the Fe(bpy)32+ and adrenalin at 15 and 14 pm, respectively, after the target testing has been applied, are shown in Figure l a and Ib, respectively. The eigenvectors in the rotated data matrix, after target testing, are different from the abstract factors, whose eigenvalues are presented in Tables I and 11. However, they are linear combinations of these abstract factors. The vectors representing the voltammograms in Figure 1 are the second largest eigenvectors in the rotated data matrix. These are the analytical signals that would have been measured if it would have been possible to measure them in the absence of a background. Note that the abscissa corresponds to index in the data array. The scan goes from 0 to 1.00 V in the first 128 points and back to 0 in the last 128, as a sine wave. Thus the potential, E (volts), is
E = 0.5 + 0.5 sin (27rn/255)
v
,
,
,
,
,
,
,
,
50
,
,
,
,
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,
, 150
100
2645
,
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b
# Figure 3. Background-subtracted voltammograms: (a) 1.5 pM Fe(bpy):'; (b) 1.4 pM adrenalin. 1.0 ordinate unit Is 100 pA (10 pA per division).
I
I
b
(1)
where n runs from 0 to 255. To convert potential, E , on the abscissa to index, use
n = [255 arc sin (2E - 1 ) ] / 2 ~
(2)
The detection limit is probably not the best figure of merit for these experiments; however, some discussion of it is warranted because it can be compared to other experiments. Figure 2 shows factors (voltammograms) and scores (voltammogram intensity versus time) for 1.4 pM Fe(bpy)32+and for 1.5 pM adrenalin. The signal-to-rms (root mean square) noise
50
100
150
zoo
250
Figure 4. Background-subtracted voitammograms: (a) 0.15 pM Fe(bpy);'; (b) 0.14 pM adrenalin. Other conditions are as in Figure 3.
ratios (rms noise is taken to be peak-to-peak noise/5) in Figure 2a and 2c (the voltammograms) are 50 and 80, respectively.
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ANALYTICAL CHEMISTRY, VOL. 62, NO.
23,DECEMBER 1 1990
This implies a voltammogram detection limit of about 80 nM (injected) ( S I N 3). The signal-to-noise ratio in the score is about a factor of 3 worse, being about 20 in Figure 2b and 2d. This implies a signal-time detection limit of about 250 nM (injected). However, when target factor analysis was performed as described above on solutions containing 1order of magnitude less analyte, the signals could not be recovered. This can readily be appreciated by consideration of the eigenvalues presented in the right-hand columns of Tables I and 11. Note that the second factor is only 4 times as large as the third. We presume, because of the correlation of the magnitude with the concentration of injected analyte, that the voltammogram makes up a significant portion of the second eigenvector and that the third eigenvector is noise. At a concentration of about M injected, then, there must be enough noise in the eigenvector(s) containing the voltammogram to obscure the pattern used as the target. Using the actual voltammogram shape instead of the three-point (0, 1, 0) target for the second factor did not recover the signals either. The experiment bears a practical resemblance to optical absorbance spectroscopy because a small signal is being found in a large background. In Figure 2 the voltammograms represent the fraction 3 X lo4 of the variance of the whole signal (which can be confirmed by reference to Tables I and 11). To compare this approach with a more classical method, a simple background subtraction has been carried out. The result for the same data as shown in Figure 2a and 2c is shown in Figure 3. The signal-to-rms noise for the backgroundsubtracted signal is approximately a factor of 4 less favorable. This is in agreement with the theory of error in factor analysis as given by Malinowski (18). The ratio of the extracted error (IE) (i.e. the error still in the data after the factor analysis) to the total error (RE) in the data is given as ( n / ~ ) ' /In~ this . term n is the number of extracted factors (2 in this example) and c is the original dimensionality of the data (40 for this data set).
-
IE = ( n / c ) l / * R E = (2/40)'/'RE = RE/4.5
(3)
The signals from the solutions with the lowest concentration have, after background subtraction, a S / N ratio of about 2 to 3. This does not seem to be sufficient for the factor analysis method to find it. However, examination of the background-subtracted data clearly shows digitization noise (Figure 4). This, could contribute to the failure of the factor analysis approach. An A/D converter with 16 bits, for example, would decrease this problem. It would appear that there is a contradiction: The TFAtreated data have a higher S/N ratio, but at low concentrations the background subtraction reveals the voltammogram while TFA does not. For TFA to succeed, there must be an adequate S / N ratio in the whole data matrix to resolve the signal. The S/N ratio required is apparently greater than that required for visual discrimination. Once the signal is recovered, the S / N ratio within t h a t eigenvector governs the precision of the data. This S / N ratio is apparently greater than that in background-subtracted data. The important conclusions are that voltammetric signals can be recovered from background with only an approximate knowledge of the background, at micromolar levels of injected analyte. The voltammetric shapes of the waves of the two compounds are very different, and this seemed to have no influence on the outcome. In this example the background is approximately constant over the measurement period.
T a b l e 11. E i g e n v a l u e s for A d r e n a l i n Data M a t r i c e s
1.5 X lo4 factor 1 2 3 4 5 6 7 8 9
10
3.50683+01 4.91763+00 8.26813-03 3.52743-03 7.84993-04 2.94913-04 1,17773-04 5.61053-05 4.22903-05 3.24853-05
1.5 X
concn/M 1.5 X 10"
3.92033+01 7.94173-01 2.11933-03 3.51793-04 1.36123-04 6.32673-05 4.25733-05 3.40253-05 3.12843-05 2.91763-05
3.99853+01 1.31433-02 1.56133-03 1.67523-04 8.89063-05 6.88633-05 4.58403-05 4.17263-05 3.93213-05 3.40593-05
1.5 x 10-7 3.99913+01 8.42233-03 6.59723-04 2.99183-04 1.14543-04 7.04663-05 5.28003-05 4.60973-05 4.51593-05 4.13543-05
However if there is a changing background overlapping the stationary background and the signal, for example when gradient elution is used, (19),the natural symmetric nature of the current-time curve allows easy rotation of the data matrix to reveal the true factors. Other slowly varying background signals, such as those caused by oxygen, could also be found and eliminated by using this method characterizing the changing background with a third factor. The quantitative information can be recovered by scaling the voltammograms for equal height. The scaling factor is multiplied by the peak area to give the quantitative result. The magnitude of the score (the "chromatogram") can be used for quantitative analysis as well.
LITERATURE CITED O'Dea, J.; Osyteryoung, J. Anal. Chem. 1980, 52, 2215. Reardon, P. A.; O'Brien, C. E.; Sturrock, P. E. Anal. Chim. Acta 1984, 162, 175. White, J. G.; Jorgenson, J. W. Anal. Chem. 1988, 5 8 , 2992. White, J. G.; St. Claire, R. L., 111; Jorgenson, J. W. Anal. Chem. 1968. 293. ..., 58. .., -. . Caudill, W.L.; Ewing, A. G.; Jones, S.; Wightman, R. M. Anal. Chem. 1983. 55. 1877. Gunasingham, H.; Tay, B. T.;Ang, K. P. Anal. Chem. 1987. 59, 262. Last, T. A. Anal. Chem. 1983, 5 5 , 1509. Barnes, A. C.; Nleman, T. A. Anal. Chem. 1983, 5 5 , 2309. Trubey, R. D.; Nieman, T. A. Anal. Chem. 1986, 58, 2549. Lunte, C. E.: Ridgway. T. H.; Heineman, W. R. Anal. Chem. 1987, 5 9 , 761. Long, J. T.; Weber, S. G. Anal. Chem. 1988, 60, 2309. Weber, S. G.; Long, J. T. Anal. Chem. 1988, 60, 903A. Nicholson, R. S.; Shain, I. Anal. Chem. 1984. 36, 706. Kristensen, E. W.; Wilson, R. L.; Wightman, R. M. Anal. Chem. 1988, 5 8 , 986. Malinowski, E. R.; Howery. D. G.; Weiner, P. H.; Soroka, J. M.; Funke, P. T.; Selzer, R. B.; Levinstone, A. FACTANAL. QCPE Program No. 320; Indiana University: Bloomington, IN. Maiinkowski, E. R.; Howery, D. G. Factor Analysis in Chemistry; J. Wiley: New York, 1980. Brown, S. D. Anal. Chem. 1990. 62, 84R-101R. Malinowski, E. R. Anal. Chem. 1977, 49, 606-612. Oates, M. D.; Jorgenson, J. W. Anal. Chem. 1989, 61, 1977.
Gregor Reich* Josef Wolf Institute for Analytical Chemistry University of Vienna Waehringerstrasse 38 A-1090 Vienna, Austria
John T. Long Stephen G. Weber* Department of Chemistry University of Pittsburgh Pittsburgh, Pennsylvania 15260
RECEIVED for review June 21,1990. Accepted September 10, 1990. The work at Pittsburgh was supported by Grant 28112 through the NIGMS. Dedicated to Josef F. K. Huber on the occasion of his 65th birthday.
