Anal. Chem. 1991, 63,73-75
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CORRESPONDENCE Exchange of Comments on Data Acquisition for Chromatographic Peaks Sir: In a recent paper, Rowlen et al. (I) described an interesting instrumental implementation of the original work by Tswett (2). In the early applications of chromatography, the analyst was looking at the column and he could actually see the dye zones migrating along the column and separating from each other. This observation let him decide when to start and stop fraction collection. Rowlen et al. appear to have underestimated the importance of the data acquisition problem which has to be solved in order to handle properly the chromatograms obtained in HPLC (high-performance liquid chromatography). In their experimental section, they write “Toadequately sample a Gaussian peak (base line width go), a minimum of eight points must be acquired” (italics ours). On a purely theoretical basis, this is true (see Shannon theorem). Indeed, three points would be enough, since a Gaussian curve depends on three parameters, its mean, standard deviation, and height. Maybe then a data point density of one point per standard deviation over an 80 range gives enough information to permit accounting properly for a Gaussian curve shaped band, although we cannot expect the first and last data points to be significantly different from zero (i.e., they are 0.033% of peak height). Real chromatograms, however, are always noisy and exhibit base line drift. There is no way to synchronize the data acquisition and the chromatogram so that a data point may be measured at the peak maximum ( 3 , 4 ) . Furthermore, real Gaussian profiles are exceptional in chromatography. Almost all band profiles we have analyzed are at least slightly skewed. For all these reasons, a much higher data point density is needed in order to account properly for the band area, its lower moments, and its profile. The errors made in the data acquisition process have been investigated in detail by Chesler and Cram (3) and by Goedert et al. (4). They concluded that a density of 10 data points per standard deviation over a centered 6u range was a minimum. This density is 10 times as large as what is deemed sufficient by Rowlen et al. (I). Although it is conceivable that, when few data points are acquired during the elution of a chromatographic band, each of these points is the result of the integration of the signal over a short period of time, data acquisition is rarely performed this way in practice. In their work, Rowlen et al. (I) averaged the signal over 650-ms integration times. They do not elaborate on their data handling algorithm. As shown by Schmauch (5) for analog signal and according to results from the work of Chesler and Cram (3), this frequency permits the correct estimate of the properties of peaks which have a standard deviation of 6.5 s and a 4a bandwidth
of 26 s. At the column exit ( L = 15 cm), this bandwidth corresponds to peaks having an efficiency less than 8500 theoretical plates for a retention time of 10 min, which is reasonable. However, bands are expected to be much narrower when they are detected in the column, as they are in the cited reference, than at its outlet. After 2 min, for example, the same band should have migrated by 3 cm and exhibit 1700 plates with a base line width of only 11.6 s. Under these conditions, the time constant of the data acquisition system is too long to permit a correct determination of the band profile. The band spreading due to an excessively long averaging time may contribute to explain the result seen in Figure 3 of ref 1, where the band width does not seem to change significantly during its isocratic migration. This is in contradiction with basic chromatography theory. In agreement with eq 5 of ref 1,we would have expected a2 to increase linearly with the migration distance. The simple calculations reported above seem to show that whole-column detection (WCD) would benefit from a data acquisition system more sophisticated than the one described in ref 1. It might also require that the columns used be highly homogeneous along their length. In classical HPLC, it does not matter much whether the packing density or the local HETP varies along the column, as long as their average value is acceptable. WCD is probably more demanding from this point of view.
Sir: Guiochon and Sepaniak (I) have questioned the adequacy of the sampling rate used in our recent implementation of whole-column detection (WCD) chromatography (2).
In our paper, we state that a Gaussian peak is adequately sampled if a sample is taken at least once every standard deviation. This sampllng rate is derived from signal processing
LITERATURE CITED (1) Rowlen, K. L.; Duell, K. A,; Avery, J. P.; Birks, J. W. Anal. Chem. 1989, 61, 2624. (2) Tswett, W. Ber. Deufsch. Bofan. Ges. 1906, 2 4 , 316, 384. (3) Chesler, S.; Cram, S. P. Anal. Chem. 1971, 43, 1922. (4) Goedert, M.; Guiochon, G. Chromatographie 1973, 6, 76. (5) Schmauch, L. J. Anal. Chem. 1959, 31, 225. To whom correspondence should be sent at the University of Tennessee. University of Tennessee. +
’
Georges Guiochon* Michael J. Sepaniak’ Department of Chemistry University of Tennessee Knoxville, Tennessee 37996-1600 and Division of Analytical Chemistry Oak Ridge National Laboratory Oak Ridge, Tennessee 37831-6120
RECEIVED for review March 23,1990. Accepted September 28, 1990.
0003-2700/91/0363-0073$02.50/00 1990 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 1, JANUARY 1, 1991
theory ( 3 , 4 )and has been reported frequently in the literature. For example, Kelly and Horlick (5) state that to sample a Gaussian peak with less than 0.1% error (percent of peak height), a t least nine samples must be taken. Thus, if the entire peak is defined to be 80 wide, then the required sampling time, to,is to 5 0 . 8 9 ~ .Similarly, Massart et al. (6) state that eight samples per 60 width of a Gaussian peak are required. This corresponds to to< 0.75~.Indeed, Goedert and Guiochon (8)also derive this result as one of their criteria for setting the sampling rate. Differences in these derived sampling rate requirements reflect small differences in the criteria chosen for adequate sampling. A sampling frequency of one point per standard deviation corresponds to twice the frequency at which the Fourier transform of a Gaussian peak decays to 0.01 times its maximum amplitude. This rate differs by 1 order of magnitude from the results of Cheder and Cram (7)and from the final results of Goedert and Guiochon (8). The rates in the latter (7,8) references are coincidentally the same but are derived from different premises, and each is flawed in that the rate required for adequate sampling is confused with the rate required for adequate reconstruction. The rate required for adequate sampling (2, 5, 6), over which there can be no real controversy, is determined by information theory. The required reconstruction sample density is, however, strongly dependent upon the reconstruction technique used. Thus in Chelser and Cram (7), a rectangular approximation technique is used for reconstruction that indeed requires more than 10 times the samples needed for adequate sampling. However, sampling theory (3, 9, 10) assures us that by use of digital filtering interpolation techniques the additional points can be generated at whatever density is required. The problem in the Goedert and Guiochon paper (8)goes beyond problems with recontruction techniques. The authors make an approximate derivation of the sampling rate required by sampling theory and produce a result in rough agreement with the references cited above. They conclude, however, that this rate is too low by about a factor of 10. The additional factor of 10 comes from neither noise considerations, nor skewedness of peaks, nor baseline drift-as might be inferred from the comment (1)-but from an attempt to reduce errors resulting from inadequate modeling and characterization of their measurement system. In their method, the transfer function of the measurement system is characterized as a first-order system with time constant 7. They recognize that the transfer function is probably of higher than first order but suggest that the errors caused by the approximation and measurement of 7 amount to about 0.17. In their method, T must be subtracted from the apparent peak positiop to recover the retention time. In order to make the error in 7 contribute negligibly to the error in the retention time, they require that 0.17 be essentially the same as the error in the measurement of the apparent peak position. They thus empirically determine, for their particular system, that they must use a filter with a time constant some 10 times less than that required for the antialiasing filter dictated by sampling theory. But this filter is not an adequate antialiasing filter a t the theoretically correct sampling rate. As a result, to minimize noise aliasing, they must sample 10 times too fast. The factor of 10 is entirely dependent upon the presumed error in 7: were the error reduced to 0.017, the optimum would be at a 7 value 10 times as long, which would correspond to the rate derived from sampling theory. In contrast it is possible to rigorously compensate for the effects of our filter, because we have an adequate representation of our signal and complete knowledge of the parameters of our measurement system. The statement of Guiochon and Sepaniak that sampling rates must be increased to compensate for baseline drift is
not correct. Baseline drift is a frequency component and will be adequately sampled if the superimposed peaks are adequately sampled. Noise, of course, must be dealt with in any measurement system. Unless one is interested in the character of noise a t frequencies beyond what is significant in the signal, it is better to filter the signal and sample at a rate that captures the signal and rejects higher frequency noise. (We note that the higher sampling rate proposed by Goedert and Guiochon (8) must capture additional noise a t frequencies at which there is no significant signal.) In our method the filtering is performed by integrating over the period set by the sampling theorem. This approach is superior to first-order low-pass RC filters conventionally used in postcolumn detection. In addition to eliminating 60-Hz noise, integrating in this manner distorts the signal less than an RC filter with equivalent noise variance at the filter output. Note that, regardless of what fiter is used, noise at frequencies below the cutoff frequency are adequately sampled and remain in the samples. The skewing of chromatographic peaks generally broadens them; thus, if we sample adequately for the narrowest (unretained) peak, subsequent wider and skewed peaks will be adequately sampled. We found that our peaks fit with excellent precision the y peak model derived from plate theory by Smit et al. (11):
where K represents the amplitude of the peak, t , is the retention time, 7 is a measure of the peak width, and n is the asymmetry factor. In all our WCD experiments where accurate peak parameters were required, we have used this four-parameter asymmetric function, rather than the symmetric Gaussian function, to model our peaks. We found that an asymmetry factor n = 6 accounts for skewedness of peaks in our system. It can be shown that, for this value of n, no higher sampling rate is needed for this function than for a reasonable Gaussian approximation of it. The sampling rate we chose for our WCD experiments was based upon the above considerations and not upon any instrumental limitations. Real sampling is never a perfect operation, so in our work we chose to sample 2.5 times the minimum rate, which for peaks with widths greater than 13 s works out to be 1.538 Hz or 650 ms/point. As stated in our paper, the sampling time of the instrument is variable between 50 and lo00 ms, dowing sampling rates up to 13 times greater than what we chose to use. For the narrowest peak measured, an unretained peak having a baseline width (8u)of 13 s at the inlet of the column, 20 data points were obtained. Although it can be removed by subsequent processing, the contribution to the variance of the unretained peak by the 650-ms integration time is calculated to be approximately 3% of the total variance. Guiochon and Sepaniak suggest that the variance of the peaks in Figure 3 of our paper does not increase linearly with time as theory would predict. The widths displayed in Figure 3 are baseline widths determined manually and do not represent accurate variance measurements by curve fitting. Also, peak broadening as a function of column position is difficult to assess from this figure because of a relatively large extracolumn contribution to the peak width from the tubing connecting the injector to the column in this experiment. As discussed above, the extracolumn contribution to peak width by the electronic integration time is quite small. In fact, as shown in a paper submitted for publication (12),the variance of all peaks does increase linearly with column position, and the slope of a plot of total variance vs column position provides an accurate measurement of plate height, H. Our submitted
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Anal. Chem. 1991, 63,75-78
paper (12) completely characterizes the variance contributions of the column, injector, connecting tubing, detectors, and electronic integration time for the three isomers of nitroaniline as a function of solvent composition. We disagree with the statement that WCD might require that the columns used be highly homogeneous along their length. None of the conclusions we arrived at demand a high degree of column homogeneity. Perhaps an advantage of WCD is that discontinuities in the column could be readily recognized as sudden changes in the higher moments of the peaks as they elute. In summary, we certainly agree that WCD chromatography places greater demands on the data acquisition system than does ordinary chromatography. The WCD data acquisition system we designed meets all of those demands.
LITERATURE CITED Guiochon, G.; Sepaniak, M. J. Anal. Chem., previous correspondence in this issue. Rowlen, K. L.; Dueli. K. A.; Avery, J. P.; Birks, J. W. Anal. Chem. 1969, 67, 2624-2630. Roberts, R. A.; Mullis, C. T. Dig/&/ Signal Processing; Addison Wesley: Reading MA, 1987. Bracewell, R. N. The FoWier Transform and Its Applicatbns; McClawHili Book Co.: New York, 1966. Kelly, P. C.; Horlick, G. Anal. Chem. 1973, 45, 518-527. Massart, D. L.; Vandeginste, B. G. M.; Deming, S. N.; Michotte, Y.; Kaufman, L. Chemometrics: a Textbook; Eisevier: New York, 1988; p 240. Chesler, S.; Cram, S. P. Anal. Chem. 1971, 43, 1922-1933. Goedert, M.; Guiochon, G. Chromatographia 1973, 6 . 76-83. Crochiere, R. E.; Rabiner, L. R. Multirate Processing of Digital Signals. I n Advanced Topics in Signal Processing; Lim. J. S.. Oppenheim, 0.
V., Eds.; Prentice Hall: Englewood Cliffs, NJ, 1988. (10) Oppenheim, A. V.; Schafer, R. W. Discrete-Time Signal processing; Prentice Hall: Englewood Cliffs, NJ, 1989. (11) Smit, H. C.; Smit, J. C.; de Jager, E. M. Chromatographia 1966, 22, 123. (12) Rowlen, K. L.; Dueil, K. A.; Avery, J. P.; Birks, J. W. Accurate Measurements of Column Efficiency in Whole-Column Detection Chromatography. Unpublished work.
Kenneth A. Duel1 Department of Electrical and Computer Engineering and Optoelectronic Computing Systems Center University of Colorado Boulder, Colorado 80309 James P. Avery* Department of Electrical and Computer Engineering and Cooperative Institute for Research in Environmental Sciences (CIRES) University of Colorado Boulder, Colorado 80309 Kathy L. Rowlen John W. Birks Department of Chemistry and Biochemistry and Cooperative Institute for Research in Environmental Sciences (CIRES) University of Colorado Boulder, Colorado 80309 RECEIVED for review June 4,1990. Accepted September 28, 1990.
Single-I njection Liquid Chromatographic Separation of a Mixture of Transition Metals, Neutral Organics, and Inorganic Anions on a Bonded 8-Quinolinol Stationary Phase Sir: Bonded alkyl phases such as C18and C8 have proven extremely successful for liquid chromatographic separation of a wide variety of both organic and inorganic analytes. Selectivity is typically provided in the mobile phase, an approach which makes it somewhat difficult to separate a mixture of analytes belonging to different classes of compounds, such as neutral organics and transition metals, anions and cations, and so forth. A number of approaches have been developed to enhance column or stationary-phase versatility to address situations such as these. Stationary phases with selective functionality have been used in conjunction with mobile-phase manipulation to effect separation of various analyte classes. For example, a bonded dithizone phase was converted from a chelating to an anion-exchange column by changing the mobile-phase pH (1). Likewise, an amino acid column was taken from a cation exchanger a t a pH above the isoelectric point to a neutral metal-complexing material near this pH to an anion exchanger at pH values below the isoelectric point (2). Although pH control yields some versatility, generally only one class of compounds has been separated at one time with this approach. Several studies have been reported, however, where more than one class of analytes have been separated in one run. An EDTA-containing mobile phase yields anion complexes of transition metals and permits anion-exchange separation of these metals along with inorganic anions on a protonated amino phase ( 3 , 4 ) . Connecting anion- and cation-exchange columns in series likewise can resolve mixtures containing both of these classes of compounds (5,6). This idea was extended 0003-2700/9 1/0363-0075$02.50/0
by Issaq and co-workers who packed two different types of bonded-phase material in the same column, yielding a mixed-bed C18//3-cyclodextrin column (7). Issaq and Gutierrez studied serial, mixed-bed, as well as mixed-ligand C8/cation-exchange columns (8). They found the best efficiency on the mixed-ligand column, where both ligands were present on the same silica particle. Research in our laboratory over the last several years has focused on providing multimode character by developing bonded phases in which different functionalities are present on the same ligand molecule. Most of our work has involved a phenylazo-8-quinolinol phase that is bonded to the silica surface by a propylamido backbone from the para position of the phenyl ring. We have successfully used this phase to separate transition metals via the chelating 8-quinolinol group (9),as well as a variety of organic analytes using the bonded phase uas is (10) and loaded with a metal ion in the ligand-exchange mode (10, 11). The purpose of the present study was to employ this stationary phase to effect separation of a mixture of organic and inorganic analytes in one run without a change in mobile phase. Several 8-quinolinol silica gel (QSG) columns were employed, of both low and relatively high capacity, prepared via two different synthetic routes (12, 13).
EXPERIMENTAL SECTION Apparatus. The chromatographic system consisted of an SSI
Model-300 pump, a Perkin-Elmer TriDet detector, and a Rheodyne Model-7010 injection valve fitted with a 10-pL sample loop. 0 1990 American Chemical Society
