Anal. Chem. 1980, 58,2195-2199
2195
Maximum Absorbance Algorithm for Reconstruction of Gas Chromatograms from Gas Chromatography/ Infrared Spectrometry Data I a n C. Bowater,’ Robert
S.Brown, J o h n R. Cooper, and Charles L. Wilkins*
Department of Chemistry, University of California, Riverside, California 92521
A new algorithm for generation of chromatograms in gas chromatography/Fourier transform infrared spectrometry Is described. This “maximum absorbance” aigorlthm is compared with both the integrated absorbance method and the Gram-Schmidt reconstructiontechnique. Such comparisons establish that maximum absorbance reconstruction Is more senslthre than the Integrated absorbance method for Selective detection reconstructbns. For universal (Le., wide frequency window) reconstructions, the maximum absorbance algorithm is as SenSnive as the Gran+Schmkn reconstruction. Because of its simplicity and its ability to create both universal and selective reconstructions with good sensltivities, it is suggested the new algorithm should replace the integrated absorbance method and be considered as an alternative to the Gram-Schmidt method.
The two algorithms most widely used to reconstruct chromatograms in gas chromatography1Fourier transform infrared spectrometry are the Gram-Schmidt (1) and the integrated absorbance methods (2). The Gram-Schmidt method, which operates on time domain interferograms, is preferred for universal reconstructions (i.e., wide frequency window) because it is computationally faster ( 1 ) and, when optimized, gives reconstructions with greater signal to noise ratios (SIN) than integrated absorbance reconstructions (3,4). The integrated absorbance method, however, can be used to create selective chromatograms by integrating over a narrow frequency range, characteristic of a particular functional group. Both methods have been implemented to reconstruct chromatograms in real time. To use the Gram-Schmidt method, one first collects a series of base line interferograms that contain no sample absorption. These interferograms are then used to construct a set of orthonormal basis vectors (NBV), using a number of consecutive data points (NPT) from each of the original interferograms, starting at some positive or negative displacement (DISP) from the interferogram centerburst. For chromatogram reconstruction, each interferogram collected following the start of chromatography is used to compute a resultant vector orthogonal to the basis vectors. The magnitude of this orthogonal vector increases from the noise level when an absorbing compound elutes from the gas chromatograph. This magnitude is a measure of the total infrared absorbance of the sample. These operations were fully described in the original paper by de Haseth and Isenhour ( I ) . Values, which optimize the S I N of the resulting reconstructions, must be chosen for the parameters NBV, NPT, and DISP. The values of NTP = 100 and NBV = 10-30 were shown to give close to the maximum S I N ( I , 3,4). However, several studies demonstrated that the optimal value of DISP Present address: Department of Chemistry, Swinburne Institute of Technology, Melbourne 3122, Australia. 0003-2700/86/0358-2195$01.50/0
depends on both the spectral characteristics of the compound (5,6)and interferometer stability (4,6). Signal due to sample absorption is greatest a t the centerburst and decays with increasing distance from the centerburst, with the rate of decay dependent on the bandwidths of the peaks. Noise behaves in the same manner; however, the magnitude of centerburst noise is smallest for stable interferometers. Brissey et al. (6) and Sparks et al. (4)suggested that values from +10 to +20 for DISP would be a good compromise for most compounds and interferometers. Sparks et al. (4)also concluded that use of double-sided vectors would increase the SI N and reduce the dependence of SIN upon choice of DISP. The integrated absorbance method calculates the total absorbance in a selected frequency window of the transformed spectra. Universal reconstructions can be formed by selecting a wide frequency window. However, the S I N values thus obtained were shown to be poorer than those obtained using the Gram-Schmidt methoid (4,7). A major reason for poorer SIN is that the choice of a wide frequency range includes substantial regions of base line containing only noise. More selective reconstructions with improved S I N can be formed by selecting a frequency window characteristic of part of the infrared spectrum. For example, choice of the window 1800-1700 cm-’ gives a reconstruction characteristic of compounds in the sample which contain the C=O bonds with absorbances in that frequency range. This paper describes and evaluates an alternative method of reconstructing chromatograms, which has been previously applied in liquid chromatography1UV spectrometry (8). This method, called maximum absorbance reconstruction, is based upon the magnitude of frequency-domain data values within a selected frequency window. The frequency window may contain one or several ranges of contiguous points. A similar method that involved monitoring the frequency of a single spectral peak (similar to selected ion monitoring in GCImass spectrometry) was advocated by Krishnan and co-workers in an early paper (9). The maximum absorbance algorithm presented here is a more general implementation of the same fundamental concept. In practice, following the start of chromatography, interferograms are collected and Fourier transformed and the maximum absorbance value within the selected frequency window is used as the Y coordinate value for the corresponding time (X coordinate) value in the reconstruction. For base line regions, this procedure results in low values and, as absorbing compounds elute, the values rise and fall to reflect their absorbance behavior, producing the desired reconstruction. It is shown that this method can be used to create selective reconstructions that are superior to those obtained from the integrated absorbance method and universal reconstructions with similar S I N to those obtained from the Gram-Schmidt method. EXPERIMENTAL SECTION Two samples were analyzed with a GC/FTIR system that consisted of a Varian 3700 gas chromatopaph coupled to a Nicolet 60SX IT-IR spectrometer. For sample 1,the gas chromatograph 0 1986 American Chemical Society
2196
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986 UNIVERSAL
Table I. Identities of Compounds in Order of Elution sample la 1 hydrocarbon impurity 2 3-methylpentane 3 ethyl acetate
methylcyclopentane 5 diethyl ketone 6 3-heptene 7 toluene 8 hydrocarbon impurity 9 hydrocarbon impurity 10 p-xylene 11 hydrocarbon impurity 12 hydrocarbon impurity 13 isobutyl methacrylate 4
sample 2h
?I*
3100-2850.
16300-1000 Cn-1
ni
1 1,1,2-trichloroethane 2 o-xylene
3 o-dichlorobenzene 4 nitrobenzene
SELECllVE
3000-2900 Ctl-L
"Hexane was eluted between peaks 2 and 3. bChloroform was eluted before peak 1. was equipped with a 25 m X 0.33 mm i.d. capillary column coated with a 1.0 pm thick coating of Carbowax 20M. For sample 2, a 60 m X 0.32 mm i.d. capillary column coated with a 1.0 Km thick coating of DB-5 was used. Each column was connected directly to the light pipe entrance and enclosed in a short transfer line, which was heated to 250 OC. The gold-coated light pipe was 15 cm long with a 1.0 mm i.d. and was heated to 200 "C. For sample 1, a narrow-range MCT detector with a 1mm2 element was used (D*= 42.5 X lo9 cm Hz'/* W at 10 kHz). For sample 2, a medium-range MCT detector with a 0.5 mm2element was used (D* = 48 X lo9 cm Hz'l2 W at 10 kHz). The low-frequency cutoffs for these detectors were about 750 cm-' and 640 cm-', respectively. Sample 1 consisted of 100 pL each of ethyl acetate, isobutyl methacrylate, diethyl ketone, 3-heptene, toluene, and p-xylene diluted to about 2 mL with hexanes (predominately n-hexane). Sample 2 contained 100 pL each of 1,1,2-trichloroethane,o-xylene, o-dichlorobenzene,and nitrobenzene diluted to about 1.5 mL with chloroform. About 0.4 pL of each sample was injected onto the column via a split (301) injection. In sample 1,two of the three peaks, which eluted near the large n-hexane peak, were identified as 3-methylpentane and methylcyclopentane, using the Nicolet search software (IO)and the EPA Vapor Phase Library. The other peak and the four weak impurity peaks, which eluted near pxylene, could not be identified. However, all the unidentified compounds had their strongest absorbance in the range 3000-2900 cm-', so they were presumed to be hydrocarbons. These impurities were retained in the analysis, as they showed trends at concentrations near the detection limit. The compounds in both samples are listed in Table I in order of elution. Data acquisition was controlled by a Nicolet 1280 data system employing standard GC-FTIR software. For sample 1, the physical velocity of the interferometer was 0.733 cm s-', and 10 scans were coadded and saved to disk every 1.7 s. For sample 2, the physical velocity of the interferometer was 1.626 cm s-l, and 12 scans were coadded and saved to disk every 1.2 s. For both samples, 2048 point interferograms were collected. The 1024-pointFourier transformations were performed in real time, so that the eluents could be monitored by use of a series of selective reconstructions called chemigrams (2). The 512-, 1024-, and 20Gpoint interferograms were transformed with one level of zero filling and Happ-Genzel apodization after data collection, to produce 32,16, and 8 cm-' resolution infrared spectra, respectively. All data manipulation programs were written in Fortran. The Gram-Schmidt program provided by Nicolet was altered to allow the value of DISP to be altered and double-sided vectors to be chosen. Programs were written to produce maximum absorbance and integrated absorbance reconstructions and S I N analyses of reconstructions. After a linear least squares fit through sections of the base line where there was no evidence of eluting compounds, the root mean square noise and then S I N for the peaks were calculated. These sections of base line contained 140 points for sample 1and 123 points for sample 2. This method of calculating the root mean square noise was preferred to the calculation of the local root mean square noise near each peak (4), aa variations in the local root mean square noise, due to a smaller number of base line points, obscured some trends in S I N values.
n 1
'130
470
510
$50 590 830 O R l R POINlS
SELECTIVE
SELECTIVE
Figure 1. Reconstructions using the for sample 1 at 16-cm-' resolution.
870
)lo
$50
1766-1736 c n - l
1250-1149 C M - 1
maximum absorbance method
RESULTS AND DISCUSSION The strongest absorbances of the majority of organic compounds are in the frequency ranges 3100-2850 and 1 ~ 1 O O O crn-'. A universal maximum absorbance reconstruction for sample 1using this frequency window (3100-2850,1800-1000 cm-l) is shown in Figure 1A. There are larger noise spikes below lo00 cm-' than in the selected ranges, due to decreased sensitivity of the narrow range MCT detector from lo00 cm-' to 750 cm-I, the low-frequency cutoff. However the S I N is
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
2197
Table 11. Effect of Resolution on SIN of Gas Chromatographic Peaks in the Universal Maximum Absorbance Reconstruction SIN for compounds in sample lb
resolution
rms noise (A" x 103)
1
2
3
4
5
6
7
8
9
10
11
12
13
32 cm-' 16 cm-' 8 cm-' 8 cm-', 3 points 8 cm-', 5 points
0.28 0.30 0.37 0.40 0.41
30 32 28 25 24
49 52 47 43 41
555 640 587 525 502
115 127 121 108 102
138 140 119 108 104
51 52 45 39 38
58 59 49 46 45
6.2 6.0 5.1 5.0 4.8
9.5 10.6 8.4 7.6 7.1
63 67 61 56 53
6.6 6.4 5.5 5.0 5.2
7.0 8.2 5.3 5.1 5.2
322 395 375 324 303
resolution
rms noise (Ao X lo3)
1
32 cm-' 16 cm-' 8 cm-'
0.17 0.17 0.25
75 124 99
SIN for comDounds in samDle 2c 2 3 25 41 41
27 54 53
4 81 127 92
Absorbance. Frequency window 3100-2850, 1800-1000 cm-'. cFrequency window 3100-2850, 1800-700 cm-l. only 15% lower when the low frequency end of the window is extended down to 800 cm-'. Selective maximum absorbance reconstructions using the ranges 3000-2900,1766-1736, and 1250-1149 cm-' are shown in Figure 1, parts B, C, and D, respectively. For some compounds the strongest absorbance is outside the range 3100-1000 cm-'. Sometimes it is also below 750 cm-l, the low-frequency cutoff of the narrow range MCT detector. For example, many aromatic compounds and halogenated compounds absorb most strongly below 750 cm-'. This will only cause a substantial loss in sensitivity for compounds where the most intense infrared peak is much greater than those in the selected frequency window (e.g., polyhalogenated compounds). Each compound in sample 2 was chosen because it has a strong infrared absorbance below 750 cm-', but above 640 cm-', the low-frequency cutoff of the medium range MCT detector. A universal maximum absorbance reconstruction for sample 2 using the frequency window 3100-2850,1800-700 cm-' is shown in Figure 2A. A representative selective maximum absorbance reconstruction using the range 771-677 cm-' is shown in Figure 2B. The corresponding integrated absorbance reconstruction for this region is shown in Figure 2C. As the resolution of the infrared spectrum was improved from 32 cm-' to 8 cm-', both the maximum absorbance of the peak, and the noise in the reconstruction increased. Although the S I N was relatively insensitive to the resolution, the S I N was best at 16 cm-' for both samples. Averaging the absorbance value a t the selected maximum point with the absorbance value of the points on either side of the maximum did not improve the SIN. These changes in the S I N of the universal reconstructions are shown in Table 11. Selective reconstructions for sample 1, using both the maximum absorbance and the integrated absorbance methods, were compared over the ranges 3000-2900, 1766-1736, and 1250-1149 cm-l. The S I N values at 16 cm-' resolution are listed in Table IIIA. The S I N values, using the maximum absorbance method, are slightly better in the range 3000-2900 cm-', and much superior in the other two ranges. The integrated absorbance method is at its best in the 3000-2900 cm-l range because the position of the band in this range is relatively constant, and the band is sufficiently broad to occupy most of the range. However, in the other ranges, the characteristic bands are narrower and their frequencies less constant. The frequency windows used for these two ranges in Table IIIA were selected to give the maximum values of the S I N for the integrated absorbance method. If the windows had been larger, the S I N would have been worse, as shown in Figure 3. On the other band, the S I N obtained by using the maximum absorbance method is relatively independent
A
UNIVERSAL
3100-2650. 1800-700 Cfl-1
SELECTIVE 771-677
CPl-1
771-677 Cfl-1
7
200
525
$50
575 Boo 625 OATA POINTS
B50
875
300'
Figure 2. Reconstructions using the maximum absorbance and Integrated absorbance methods for sample 2 at 16-cm-' resolution.
of the size of the window, provided that the tops of all the selected infrared absorptions are included in the window. For sample 2, selective windows using both methods were com-
2198
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
Table 111. Comparison of S/N for Sample 1
algorithm
frequency range, cm-'
S I N for compounds
rms noise (A" X lo3)
2
1
3
4
5
6
7
8
9
10
11
13
12
A. Comparison of S I N for the Selective Maximum Absorbance and Selective Integrated Absorbance Reconstructions for Sample 1 at 16-cm-' Resolution
maximum integrated maximum integrated maximum integrated
3000-2900 3000-2900 1766-1736 1766-1736 1250-1149 1250-1149
0.35 0.27 0.26 0.27 0.30 0.28
29 23
46 39
83 65 464 325 649 238
45 39
121 120 162 93 27 14
111 77
30 24
5.3 5.0
9.3 7.4
58 48
5.7 7.1
7.2 5.7
134 96 268 155 402 161
47 42
6.3 7.4
5.6 5.4
107 85
B. Comparison of S I N for Sample 1 Using Real Time Transforms with 1024 Points
maximum integrated
3000-2900 3000-2900
0.50 0.31
23 21
32 36
63 57
95 70
91 109
21 20
31 34
4.7 4.9
6.0 7.0
Absorbance. Table IV. Comparison of S/Nfor the Selective Maximum Absorbance and Selective Integrated Absorbance Reconstructions for Sample 2 at 16-cm-' Resolution
algorithm maximum integrated maximum integrated maximum
integrated maximum
integrated maximum integrated
frequency range, cm-'
rms noise
S I N for compounds
(A" X lo3)
1
3000-2900 3000-2900 1600-1500 1600-1500 1500- 1400 1500-1400 1400- 1300 1400-1300 771-677 771-677
0.19 0.18 0.13 0.12 0.13 0.12 0.11 0.11 0.25 0.20
9 3 10 2 86 43
2
3
5 4 53 21
29 13
37 14
STRETCH
REGION
0
0
300.
0
s/n
e
200'
0
4
0
. .
*
100'
24 20 18 5 19 12
C.0
A
*
.
'
i
6
.
172 72 17 7 156 54 34 17
" Absorbance. pared over the ranges 3000-2900, 1600-1500, 1500-1400, 1400-1300, and 771-677 cm-'. The S I N values are listed in Table IV. The maximum absorbance method is again superior for all frequency windows. When 1024-point real-time transforms are used instead of the 16-cm-' postrun transforms, noise is greater, and S I N is lower for both maximum absorbance and integrated absorbance reconstructions, as shown in Table 111. This is because with the real-time transforms, time is saved by using boxcar apodization, no zero-filling, and magnitude-mode phase correction. However, computer advances, such as the use of array processors or coprocessors, should make these compromises unnecessary in the near future. When these compromise real time transforms are used, the maximum absorbance method still gives similar S I N to the integrated absorbance method over the range 3000-2900 cm-', and better S I N over the other ranges. Universal reconstructions using the Gram-Schmidt method were optimized prior to comparison with the results from the maximum absorbance method. With N P T = 100 and NBV = 10, DISP was altered by using both single-sided and double-sided vectors to select the parameters that give the best S I N , under the prevailing interferometer conditions. All the hydrocarbons in sample 1gave the best SIN using single-sided vectors across the centerburst (DISP = -50), whereas the esters and the ketone gave the best S I N using double-sided vectors with DISP = +20. Each of these values of DISP agree with a recommendation in the literature (3, 4 ) and suggest that the spectrometer used has a stable interferometer. In Table V, the S I N of the gas chromatographic reconstruction peaks obtained by using the Gram-Schmidt method with these two sets of parameters are compared with those obtained by using the maximum absorbance method at 16-cm-' reso-
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~
-
12
14
1242
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m 1157 l
1149
-
10
20
22
24
la?
1265
1273
1281
1200
1142
1134
1126
1119
Ill1
IS
Flgure 3. Variation of S I N with the number of points in the window for the integrated absorbance method for sample 1 at 16-cm-' resolution. All windows include the top of each band in Figure 4: (0) ethyl acetate, ( X ) isobutyl methacrylate, (+) diethyl ketone.
lution. The maximum absorbance method gives a better SIN for GC peaks 1,2,4,6,8,and 9 (all hydrocarbons) and a poorer SIN for GC peaks 5 (diethyl ketone) and 10 @-xylene). These differences reflect variations in the relative maximum absorbance when compared to the total integrated area of these compounds. At the extremes, the maximum absorbance method should be better for a compound with one narrow absorption, and the Gram-Schmidt method should be better for a compound with many broad absorptions of equal intensity. For the four solvent impurity peaks near the detection limit, the maximum absorbance method gives a similar S I N for peaks 11 and 12, but a much larger S I N for peaks 8 and 9.
The compounds in sample 2 gave the best S I N using double-sided vectors with NBV = 10, NPT = 100, and DISP in the range +40 to +80. Increasing NBV to 20 and 30 did not increase the SIN values. The compounds in sample 2 were expected to have an optimum value of DISP further from the centerburst, because their major bands are narrower than the major bands of the compounds in sample 1. However, these optimum values of DISP may also result from the interferometer being less stable at the higher velocities employed for sample 2. The universal maximum absorbance and optimized
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
2199
Table V. Comparison of SIN for Universal Maximum Absorbance and Gram-Schmidt Reconstructions S I N for compounds in sample 1 reconstruction method
1
2
3
4
5
6
7
8
9
10
11
12
13
G.S.,” DISP = -50, single sided GS.,” DISP = +20, double sided M.A.,*16 cm-’
20 14.5 32
39 32 52
434 652 640
79 75 127
157 191 140
44 32 52
58 41 59
3.0 2.1 6.0
4.6 1.9 10.6
82 57 67
8.2 3.6 6.4
7.1 2.8 8.2
243 400 395
S I N for compounds in sample 2 M.A.,C 16 cm-’ G.S.,”DISP = +60, double sided G.S.,” DISP = +lo, double sided
1
2
3
4
124 68 33
41 35 24
54 55 23
127 193 89
“ N T P = 100, NBV = 10. *Frequency window 3100-2850 cm-’, 1800-1000 cm-’. cFrequency window 3100-2850 cm-’, 1800-700 cm-’.
Flgure 4. Universal Gram-Schmidt reconstruction for sample 2 using double-slded vectors and DISP = +60.
Gram-Schmidt reconstructions are shown in Figures 2A and 4, respectively. The SIN of the GC peaks obtained by using the Gram-Schmidt method are compared with those obtained with the maximum absorbance method in Table V. The results at DISP = +10 have been included to show how sensitive the Gram-Schmidt method is to the value of DISP. Again, the S I N is better using the maximum absorbance method for some compounds and worse for others. However, the selection of the optimum values of parameters was easier using the maximum absorbance method than the GramSchmidt method. From the Gram-Schmidt results obtained in this study, it appears that any universal compromise set of parameters could involve a loss in sensitivity of up to a factor of 2 for some compounds.
CONCLUSIONS The maximum absorbance algorithm can be used to create both universal and selective reconstructions. The best sensitivity is obtained at a resolution of 16 cm-l for most compounds. At present, the full sensitivity is not available in real time, due to compromises used in the calculations. However, improvements in computer speed and structure should make the full sensitivity available in the near future. The maximum absorbance method should replace the integrated absorbance method of creating chemigrams, because it is more sensitive, even in real time with the current reduction in sensitivity. In contrast to the integrated absorbance method, the sensitivity does not decrease when the size of the frequency window is increased to include sections of base line. This results because the maximum absorbance method employs an extremely narrow window, which can move within a larger window to find the peak maximum, and ignore the rest of the larger window. Thus, the maximum absorbance method is sub-
stantially more sensitive than the integrated absorbance method for universal reconstructions and selective reconstructions where the frequency window is much larger than the bandwidth of the peak within the window. With the maximum absorbance method, it is possible to select a wide window to include infrared peaks at different frequencies without the penalty of a loss of SIN. This will often be necessary, because many characteristic frequencies vary significantly from compound to compound. The best senstivity obtained by using the maximum absorbance method for universal reconstructions is better than that obtained by using the optimized Gram-Schmidt for some compounds, and worse for others. This variation arises because the maximum absorbance method utilizes peak height, whereas the Gram-Schmidt method uses the total integrated area. When the full sensitivity for the maximum absorbance method is available in real-time, it should be considered an alternative or supplement to the Gram-Schmidt method. The Gram-Schmidt method has the advantage that it involves fewer computations, although advances in computer technology should render this aspect less important in the future. The maximum absorbance method has the advantage that it is easier to understand, less sensitive to the values of parameters, and can be used to create both universal and selective reconstructions with good sensitivities.
ACKNOWLEDGMENT We wish to thank P. R. Griffiths for the loan of the medium-range MCT detector. LITERATURE CITED
(6) (7) (8) (9) (IO)
de Haseth, J. A.; Isenhour, T. L. Anal. Chem. 1977, 49, 1977-1981. Coffey, P. J.; Mattson, D. R.; Wright, J. C. Am. Lab. (FalrfleM, Conn.) 1978, IO, 126-129. Hanna, D. A,; Hangac, G.; Hohne, B. A,; Small, G. W.; Wiebolt, R. C.; Isenhour, T. L. J. Chfomatogr. S d . 1979, 17,423-427. Sparks, D. T.; Owens, P. M.; Williams, S.S.;Wang, C. P.; Isenhour, T. L. J. Chromatcgr. Sci. 1985, 3 9 , 288-296. White, R. L.; Giss. G. N.; Brissey, G. M.; Wilkins, C. L. Anal. Chem. 1983. 55. 998-1001. Brissey, G. M i H&y, D. E.; Giss. G. N.; Yang, P. W.; Griffiths, P. R.; Wilkins, C. L. Anal. Chem. 1984. 56, 2002-2006. White, R. L.; Giss, G. N.; Brissey, G. M.; Wilkins, C. L. Anal. Chem. 1981, 5 3 , 1770-1782. Drouen, A. C. J. H.; Billiet, H. A. H.; De Galan, L. Anal. Chem. 1985, 57,962-968. Krishnan, K.; Curbelo, R.; Chiha, P.; Noonan, R . C. J. Chromatogr. Sci. 1979, 17,413-416. Lowry, S. L.; Huppler, D. A. Anal. Chem. 1981, 5 3 , 889-893.
RECEIVED for review December 30,1985. Resubmitted March 31, 1986. Accepted May 20, 1986. Support of this research under National Science Foundation Grant CHE-82-08073 is gratefully acknowledged.
