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. +
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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
