Anal. Chem. 1982, 5 4 , 2126-2127
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Minimizing Flow-Associated Noise in Electrochemical Detectors for Liquid Chromatography Stephen G. Weber Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Liquid chromatographic detectors which are flow rate sensitive (e.g., electrochemical detectors) are plagued by the fluctuations in the flow rate caused by the piston pump mechanics. The fluctuations themselves are an inconvenience, and the irreproducibility of the fluctuations is a major noise source under many conditions. Of course the best way to reduce noise is at its source, and methods for pulse dampening have been given (I). If elaborate pulse dampening is not desired (e.g., in gradient elution one wishes to minimize preinjector dead volume) or if one wishes to further minimize the fluctuations after hydrodynamic pulse dampening has been employed, some method of signal processing is required. Both digital and analog routes are available; the Fourier transform (FT)is especially useful. Smith (2)has pioneered the use of FT data processing in electrochemistry.
EXPERIMENTAL SECTION The liquid chromatograph consisted of a Waters M-45 pump, a Rheodyne 7125 loop injector, a 25 cm X 0.5 cm (id.) column packed with 10 pm Spherisorb O.D.S. by HPLC Technology and a Bioanalytical Systems TL-8A electrochemicaldetector cell. The auxiliary and reference electrodes were downstream from the detector in a Kel-F cylinder. The potentiostat was a PAR 174-A. The current was filtered with a time constant of RC = 0.3 s cf3a = 0.53 Hz). The solute used as an example was 2,4-toluenediamine which was eluted with a mobile phase of 25% methanol/75% 0.1 M pH 5.5 phosphate buffer, 10“ M EDTA at 1.0 mL/min. The column generated a back-pressure of 1200 psi which is often large enough to decrease flow fluctuations to a sufficient degree. The detection was performed amperometrically at a potential of 0.900 V (vs. Ag/AgCl, 3 M NaC1). Data were collected at 10.0 Hz by a DEC LSI 11/03 microcomputer and stored on floppy disks for further processing. The Fourier transformations (FT) were carried out by using the International Mathematical and Statistical Library subroutines (FORTRAN) FFTRC and FFTCC on the University’s DEC-10. These are fast Fourier transform routines which use the technique of Singleton (3) to separate the data file into groups of points containing numbers of pointa equal to the prime factors of the total number of points in the file. Although the use of the F T is fairly simple, there are two caveats: one must ensure that there is no signal power at any frequency greater than half the sampling frequency to avoid aliasing (Nyquist’s criterion), and one must minimize abrupt changes in signal at the beginning or end of a time series (2, 4-7). In our experiment, the power spectrum from zero to 100 Hz was inspected and found to contain only the prominent low-frequency signal and noise and some 60-Hz noise. By using a 0.3-5 filter we ensure that less than 1%of the 60-Hz noise is aliased (it would be aliased t o 0 Hz). For this exploratory investigation this is satisfactory. For routine work in which one would not necessarily survey the power spectrum over a much wider range than the sampled frequency range, it is imperative that one use an antialiasing filter so that very little power can be measured at f = 0.5f,, f, = sampling frequency. Abrupt beginnings or ends on a time series are obviated if the beginning and end points of the file are at the same value. If this is not the case, then the data file appears as a superposition of a ”flat” signal base line plus a saw-toothed wave. The transform of the saw-tooth leads to oscillations in the inverse transform. This has been shown dramatically by Hayes et al. (7). Our liquid chromatography signal’s base lines are reasonably “flat” in time; thus no rotation (7) or window procedure [ ( 5 )(pp 140-146)] was undertaken. The FT of a real time domain signal will yield as the first point in the (complex)transform the value (A, 0.0) where A is the sum
over all the points in the time domain signal. Alterations in the value of A alter the base line of the time domain signal of the inverse transform. Since the base line value is not critical, we have arbitrarily altered A in various data files to control the scale in the plotting routines wed to view the FT of the frequency series.
RESULTS AND DISCUSSION If one is to separate signal from noise by simple band-pass filtering, then the signal information must be in a different frequency range than the noise. A portion of a chromatogram containing a typical chromatographic peak is shown in Figure 1. The peak had a k’ = 2 and the number of theoretical plates was about 5000. The peak width a t half-height for the range of k ’ = 2-5 would be in the range of about 15-20 s. The pump used was a Waters M-45 which has two cylinders, one with a 50-pL volume and one with a 100-pL volume. At 1.0 mL/min the slowest pump cycle occurs once every 6 s. Thus the signal and noise occur in different regions of the frequency domain. Fourier transformation confirms this (see Figure 2), in fact the large degree of separation in the frequency domain is a bit surprising. One can take advantage of this by removing the higher frequency components and inverse transforming the result. The high frequencies were removed by multiplying the complex frequency spectrum by a sigmoidal filter function given in eq 1. In eq 1fo is the center frequency of the filter and gain = (lO-Vod’/s
+ 1)-1
(1)
s is a slope term representing the sharpness of the cutoff. The sign in the exponent may be changed from minus (low pass filter) to plus (high pass filter). The slope term s is easily determined. For a low pass filter choose the lower frequency limit (fJ for which a gain of 0.99 is required (or an upper frequency limit for which a gain of 0.01 is required). For a high pass filter choose f,,for which a gain of 0.99 is required (or fi for which a gain of 0.01 is required). Then s = (fo- f1)/2. Considering Figure 2, one might choose fo = 0.10 Hz, fi = 0.07 Hz which would require f, = 0.13 Hz. When these parameters are used and the inverse transform is taken, the signal in Figure 3 results. Note, since the filter did not appreciably attenuate the frequency components of the signal, that there is no noticeable peak distortion. It is interesting to point out the actual quantitative accuracy which is more easily achieved after filtering. From figure 1 one may estimate an average base line a t about 160 pA (at 8 s). The peak height is about 420 pA yielding a signal of 260 PA. Turning to Figure 3 and repeating the procedure, one finds an interpolated (8 s) base line of 350 pA and a peak height of 570 PA, yielding a signal of 220 PA. The apparent discrepancy may be resolved by measuring Figure 1 in an internally consistent fashion, Le., from flow-induced peak tops. Thereby one obtains an interpolated base line of about 190 pA and a peak top of 420 pA yielding a peak height of 230 PA. The direct cause of the apparent discrepancy is the presence of the flow-induced peak a t the very top of the signal peak. Not everyone has or will have the digital computing capabilities required for this smoothing. There are two other options to pursue to make this available. (1)Buy or build a cross correlator which cross correlates the analog data with a time domain representation of eq 1.
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0 1982 American Chemical Society 0003-2700/82/0354-2126$01.25/0
2127
Anal. Chem. 1982, 54. 2127-2129
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Flgure 1. A 20-s portion of a chromatogram wtth a peak due to 100 pg of 2,440luenediamine. The current Is In pucoamperes and the time is in seconds.
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Flgure 3. The same data as Figure 1, after smoothing using eq 1. The same scales as in Figure 1 apply.
f l = 0.18 €32. A filter may be built with a variable frequency cutoff simply by switching in various values of a set of resistors. The filter may be simply realized using the tables of Horowitz and Hill (11). It must be appreciated that the Butterworth filter design may not always be appropriate. This filter has a flat frequency response where the gain is near 1, and a sharp "knee" in the log gain vs. log frequency plot. It does, however, alter the phase relationship %ong the various frequency components of the signal even when the gain is near 1. This leads to a "ringing" output from a step input. One may anticipate that rapid changes in the detector output (filter input) will lead to a distorted filter output. The Bessel configuration may be used if this proves to be a problem, though we have never found it to be a problem with normal chromatographic peaks.
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Flgure 2. The Fourier transform of .Figure 1. The real and imaginary components are the oscillating traces, while the absolute value of the spectrum is the top CUWB whlch demonstrates three peaks, one at 0 Hz (the chromatographic peak), one at 0.18 Hz, and one at 0.36 Hz representing the pulse fluctuations.
Horlick and Hieftje have written an excellent chapter on correlation (8). (2) Buy or build a high order classical RC filter (9-11). The former is more expensive, but will be versatile. The latter will be inexpensive to build at the cost of versatility. The second option may be implemented with a Butterworth or Bessel Filer. Using an eight-pole Butterworth filter, one can achieve fo = 0.08 142,f, = 0.14, and f1 = 0.06 Hz. These conditions would be apipropriate for the conditions described. If one were working routinly at 3.00 mL/min using the same hardware, one would require fo = 0.24 Ilz, f, = 0.42 Hz, and
Nikeily, J. G.; Ventura, D. A. Anal. Chem. 1979, 57, 1585-1568. Smith, D. E. Anal. Chem. 1976, 4 8 , 517A-526A. Singleton, R. C. Coqmun. ACM 1967, IO, 647-654. Bracewell, R. N.; Roberts, J. A. Aust. J. fhys. 1954, 7 , 615-640. BrlQham, E. 0. "The Fast Fourier Transform": Prentlce Hall: Enqlewood Cllffs, NJ, 1974. Bloomfield, P. "Fourier Analysls of Time Series"; Wiley: New York, 1976. . .
Hayes, J. W.; Glover, D. E.; Smith, D. E.; Overton, M. W. Anal. Chem. 1973. 45. 2771284. Horllck, G.; Hieflje, G. M. In "Contemporary Toplcs in Analytical and Clinical Chemistry"; Hercules, D. M., Hiefljd, G. M., Snyder, L. R., Evenson, M. A., Eds.; Plenum: New York, 1978; Vol. 3, pp 153-216. Graeme, J. G.; Tobey, G. E.; Huelsman, It. D. "Operational Ampliflers, Deslgn and Applications"; McGraw-Hill: New York, 1971; Chapter 8. Johnson, D. E.; Hllburn, J. L. "Rapid Practical Designs of Actlve Fllters"; Wiley: New York, 1975. Horowltz, P.; hill, W. "The Art of Electronics"; Cambridge University Press: Cambridge, 1960; p 158.
RECEIVED for review April 30, 1982. Accepted July 2, 1982. It gives me great pleasure to acknowledge the support of Grant GM-28112 from the National Institute of General Medical Sciences.
Phase Separator for Flow Injection Analysis Koreharu Ogata, Klyomi Taguchi, and Toshio Imanari" Faculty of Pharmaceutical1 Sciences, Chiba lJniversity, Yayoi-cho 1-33, Chiba-shi, Chiba 260, Japan
Flow injection analysis (FIA), first developed by Ruzicka and co-workers ( I ) , is a versatile technique in the field of 0003-2700/82/0354-2127$01.25/0
analytical chemistry. Recently, the concept of solvent extraction was coupled with FIA ( 2 , 3 )to enhance its versatility. 0 1982 American Chemlcal Society
