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Anal. Chem. 1984, 56, 1268-1272
LITERATURE CITED (1) Small, Famish; Stevens, Timothy S.; human, William C. Anal. Chem. 1875, 47, 1801-1809. (2) Smith, F. C., Jr.; Chang, R. CRC, Crlt. Rev. Anal. Chem. 1980, 9(3), 197-217. (3) Wang, Chung-Yu; Bunday, Scott D.; Tarter, James 0.Anal. Chem. 1883, 55, 1617-1619. (4) Dlonex Applicatlon Note 7R. “Separation Of Large Polarizable Anions”; Dionex: Sunnyvale, CA, 1982. (5) Rockiin, Roy D.; Johnson, Edward L. Anal. Chem. 1983, 55, 4-7. (6) Hansen, L. E.; Richter, E. E.; Rollins, D. K.; Lamb, J. D.; Eatough, D. J. Anal. Chem. 1979, 51, 633-637. (7) Trujillo, F. J.; Mlller, M. M.; Skogerboe. R. K.; Taylor, H. E.; Grant, C. L. Anal. Chem. 1981, 53, 1944-1946.
(8) Igawa, Manabu; Saito, Kimlko; Tsukamoto, Jun; Tanaka, Masao Anal. Chem. 1881, 53, 1942-1944. (9) Willard, Hobart H.; Merritt, Lynne L., Jr.; Dean, John A,; Settle, Frank A., Jr. “Instrumental Methods of Analysis”, 6th ed.; Van Nostrand: New York, 1981; pp 520-521. (10) Sunden, Thomas; Lindgren, Mats; Cedergren, Anders; Siemer, Darryl D. Anal. Chem. 1983, 55, 2-4. (11) Tarter, J. G. LC, Llq. Chramatogr. HPLC Mag. 1983, 1, 508-509.
RECEIVED for review November 14, 1983. Accepted March 12,1984. This work was funded by a grant from the North Texas State University Faculty Research Fund.
Comparison of Methods for Reconstructing Chromatographic Data from Liquid Chromatography/Fourier Transform Infrared Spectrometry Ching Po Wang, Daniel T. Sparks,’ Stephen S. Williams? and Thomas L. Isenhour*
Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27514
Integrated spectral absorbance, Gram-Schmidt, and factor analysis chromatographic reconstruction methods are used in analyzing LC/FT-IR data. The SNR values of these methods are compared. Simplex optimization results of the Gram-Schmidt and factor analysis reconstructions of LC/FTI R are compared with those obtained from GC/FT-IR. Quantitative analyses are performed from Gram-Schmidt and factor analysis reconstruction intensities.
Analytical systems that couple separation instrumentation with identification devices offer powerful analytical capabilities. Gas chromatography/Fourier transform infrared spectrometry (GC/FT-IR), one coupling of this kind, has proven to be a very useful analytical system (1). Since more than 70% of all organic compounds are too nonvolatile for direct gas chromatographic analysis, liquid chromatography/Fourier transform infrared spectrometry (LC/FT-IR) is a natural extension of GC/FT-IR. Hundreds to thousands of interferograms may be collected in one LC/FT-IR run. A method is needed to differentiate between those interferograms corresponding to analyte absorption and those containing only chromatographic background information. To use another chromatographic detector along with the FT-IR spectrometer is one solution. However, a chromatographic reconstruction method using the collected FT-IR information is more desirable. Besides saving another interface, using an infrared reconstruction method can avoid ambiguous information provided by another chromatographic detector. If a component cannot be detected by some infrared reconstruction method, there is little chance that the infrared spectra from the LC/FTIR experiment will exhibit any useful qualitative information. Therefore even if another detector is able to detect more peaks by giving a higher signal-to-noise ratio (SNR), it still does not offer any practical advantages in utilizing the LC/FTIR data.
The integrated spectral absorbance reconstruction (“chemigram”)and the Gram-Schmidt reconstruction are the two reconstruction methods most often employed for GC/ FT-IR chromatographic reconstructions. The Gram-Schmidt and factor analysis reconstruction methods have been proven to be superior methods in both speed and SNR ( 2 , 3 ) . Both integrated spectral absorbance and Gram-Schmidt reconstructions ( 4 , 5 )have been applied to LC/FT-IR. However, no attempt has been made to optimize the Gram-Schmidt reconstruction parameters and to compare these parameters with those obtained from optimizing GC/FT-IR GramSchmidt reconstruction. This paper compares the capabilities of the time domain and the spectral domain reconstruction methods when applied to LC/FT-IR data. Differences in applying the GramSchmidt to LC/FT-IR vs. GC/FT-IR are discussed. The quantitative capabilities of the Gram-Schmidt and factor analysis reconstruction are also explored for LC/FT-IR applications. EXPERIMENTAL SECTION Calculations. Absorbance spectra were generated from interferograms by first applying triangular apodization, then performing 2K fast Fourier transforms (FFT), Mertz phase corrections, and finally ratioing to a coadded reference spectrum which was generated by the same procedure. The integrated spectral absorbance reconstructions were calculated by numerically summing the absorbances of the Fourier transformed spectra (in 8 cm-’ resolution) over selected windows. The Gram-Schmidt reconstruction is essentially the same as that developed by de Haseth and Isenhow (6). The reconstruction considers a certain segment of the interferogram as a vector in a multidimensional hyperspace. A reference subspace is formed by using several vectors drawn from a known base line region of the chromatogram, and orthonormal basis vectors which describe this subspace are calculated by using the Gram-Schmidt orthogalization method. Reconstructed sample intensities are then calculated as the orthogonal distance from each vector to this reference subspace by using eq 1 distance =
‘Present address: IBM Instruments, Inc., P.O. Box 332, Danbury,
CT 06810.
*Present address: Varian Instrument Division, 2700 Mitchell Drive, Walnut Creek, CA 94587.
-..
[i-i- X(I~Bn)21’/2 n=1
(1)
where i is the interferogram vector, Bn is the nth orthonormal basis vector, and m is the total number of basis vectors. The SNR advantage of the Gram-Schmidt reconstruction results from the
0003-2700/84/0356-1268$01.50/00 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
orthonormal basis vectors of the reference subspace which are able to dynamically map the changing GC/FT-IR background. Owens et al. (3) have demonstrated that by applying factor analysis to a set of reference interferograms, fewer basis vectors are needed to effectively describe the background in GC/FT-IR. In the factor analysis basis set calculation, an n by m reference matrix B is formed by taking m reference vectors, each vector with n points, from the set of reference interferograms. The m by m covariance matrix C is then calculated by premultiplying the reference matrix B by its transpose. The eigenvectors (v's) of the covariance matrix form an orthonormal basis set. The final basis vectors (u's) are each calculated by premultiplying the individual eigenvectors by the original reference matrix, u = B X v. Because the eigenvectors corresponding to the smaller eigenvalues only describe the noise in the reference space, a smaller number of basis vectors are needed to describe the reference space. The distance from each subsequent sample vector to the reference subspace is then calculated by using eq 1. The SNR values were calculated as follows: (i) 15 points on either side of each peak were linearly fitted to generate a base line equation (linear fitting provided enough correction for the data used in this paper); (ii) the intensity values of the base line and peak segment were corrected by removing the offset of the base line according to the calculated base line equation; (iii) the signal was defined as the highest intensity value after the base line correction; (iv) the root mean square value for the 30 base line points was defined as noise. LC/FT-IR System. The LC/FT-IR data were supplied by IBM Instruments, Inc. The chromatographic system employed consisted of the following: an IBM Instruments 9521 isocratic HPLC pump, Rheodyne 7125 injector with a 20-pL loop (the loop was completely filled for each injection),and an IBM Instruments silica gel column (45 mm X 25 cm with 5-pm particles). Methylene chloride was used as the mobile phase, pumped at 20 pL/min. An IBM Instruments IR-85 FTIR with a ZnSe flow cell (0.2-mm path length with a volume of about 25 pL, connected to the column by 12 in. of Teflon tubing) was used to detect components eluting from the chromatographic system. The data were collected at 5 scans/s at 8 cm-l resolution and coadded four times. Sample Preparation. A solution of four components having the following concentrations in methylene chloride was made: m-xylene, 5 pg/pL; methyl benzoate, 5.2 pug/& phenol, 4.9 pg/pL; and aniline, 5.5 fig/pL. This was also the elution order. Four more solutions were made by performing successive 1:2 dilutions of the original mixture. Solutions of the following approximate concentrations resulted: 100 pg per component per injection (LCl), 50 pg per component per injection (LC2), 25 fig per component per injection (LC3), 13 pg per component per injection (LC4),6.5 pg per component per injection (LC5). AU five solutions were chromatographed under identical conditions. Data Handling. Data were collected on hard disk and then transferred via tape to a VAX 11/78@computer for data reduction. All programs were written in Fortran 77 and IMSL subroutines were used for t,he FFT and eigenvector calculations.
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RESULTS AND DISCUSSION The integrated absorbance, Gram-Schmidt, and factor analysis chromatographic reconstruction techniques were each initially optimized fro the LC/FT-IR data. This was done in order to determine if previously reported GC/FT-IR reconstruction optimization (7) could be directly applied to LC/FT-IR analyses. The integrated absorbance reconstructions were optimized by testing 11different integrated absorbance windows. Figure 1A depicts the optimum reconstructed chromatogram for peaks 1, 3, and 4 obtained from using a 1600-1650-~m-~ window. Unfortunately, this window does not identify peak 2, whose optimum window was found to be in the 17001750-cm-' region as shown in Figure 1B. Figure 1C represents the optimum absorbance reconstruction for all peaks. This was obtained by using only the single absorbance point at 1615 cm-'. Although in this case all four peaks can be detected by using only the 1615-cm-' point, in most cases it would not be
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Figure 1. Integrated absorbance of LC1 for the following windows: (A) 1600-1650 cm-', (B) 1700-1750 cm-', (C) 1615 cm-'.
practical to use a single frequency. Absorbance window reconstructions always involve a trade-off between SNR and generality of detection. The Gram-Schmidt and factor analysis reconstructions require the selection of several parameters which affect chromatographic SNR. Both reconstruction techniques were optimized by using a modified simplex optimization algorithm (8)to maximize SNR as a function of these parameters. For both techniques these parameters are the displacement from
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
Table I. Modified Simplex Optimization Result of LC1 Data peak number DISP
NPTS
NBV
68 84 83 50 -35 44
99 84 97 85 100 91
16 6 36 20 36
27 103 97 40 33 77
75 62 74 82 94 83
NEV
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4
av
19.51 25.33
84.60 120.75
147.73 64.14
32.38
21
38 48 46 25 24 22
3
125.95 12 9 5 12 9 10
factor analysis 40.79 428.55 46.68 57.96 497.37
22.08 22.77
103.09 129.17
148.63 66.20
40.68 110.58
--
Table 11. SNR Comparison of FFT, Gram-Schmidt, and Factor Analysis SNR values
(1600-1650)" (1615)" Gram-Schmid t factor analysis
peak 1 9.82 24.37 39.40 40.79
peak 2 (62.85) 3.18 447.41 428.55
peak 3 5.21 10.68 19.51 22.08
peak 4 10.70 12.57 84.60 103.09
av 8.58c 12.70 147.73 148.63
a Integrated absorbance window for 2K FFT reconstruction. Value for 2K FFT integrated absorbance reconstruction using point at 1715 cm-'. Average value for peaks 1, 3, and 4 only.
the centerburst (DISP), the number of data points used to form each vector (NPTS), and the total number of basis vectors used (NBV). Additionally, the factor analysis technique requires optimization of a fourth parameter, the number of eigenvectors (NEV) used in reconstructing chromatograms. Details of the modification of the simplex algorithm can be found in ref 7. Table I depicts the simplex optimization results for GramSchmidt and factor analysis reconstructions. Due to the extreme complexity of the SNR response surface for these reconstruction techniques, the modified simplex algorithm did not apparently determine a global optimum. For different sets of start and step parameters, different simplex optima often resulted. Each simplex optimization was performed a number of times starting at different points on the response surface. The values listed in Table I are those corresponding to the highest SNR's for the peak(s) optimized. The instrument used to collect the LC/FT-IR data stored only 38 points before the burst for each interferogram collected. Therefore the simplex optimization could only effectively investigate the positive displacement side. However, certain differences between the nature of the GC/FT-IR and LC/FT-IR data were clearly evident. With GC/FT-IR data collected on a similar instrument, the chromatographic SNR in the Gram-Schmidt reconstruction was found to drop sharply with DISP values greater than about +40. A local optimum was found between the DISP values of +10 to +20 (7). From Table I, most of the optimal DISP values for LC/FT-IR were found further away from the burst. This difference between the LC/FT-IR and GC/FT-IR data may be due to the fact that the mobile phase in LC is highly IR absorbing while the carrier gas in GC is almost totally IR transparent. Therefore the reference subspaces of these two complementary techniques for both factor analysis and Gram-Schmidt reconstructions are quite different. White et al. (9) determined that the optimal parameters for the Gram-Schmidt reconstruction of GC/FT-IR data exhibit a component dependence. In LC/FT-IR, the optimal param-
eters should also vary with different mobile phases. Even for the same LC/FT-IR conditions and components, the optimal parameters were found to vary with component concentrations for these data. This increases the difficulty in optimizing the factor analysis and Gram-Schmidt parameters for LC/FT-IR reconstructions. Parameter optimization is not, however, necessarily required to obtain good factor analysis and Gram-Schmidt reconstructions. Figure 2A and Figure 2B are Gram-Schmidt and factor analysis reconstructions for data set LC1 using unoptimized parameters. The Gram-Schmidt reconstruction was obtained with a DISP = 30, NPTS = 100, and NBV = 10. The factor analysis reconstructed chromatogram used the following parameters: DISP = 25, NPTS = 100, NBV = 25, NEV = 10. The reconstructed chromatograms using these two sets of arbitrarily chosen parameters clearly identify all peaks. From the optimization results in Table I, it appears that factor analysis and Gram-Schmidt reconstructions exhibit comparable SNRs. However, in virtually all cases the number of factor analysis eigenvectors was significantly lower than Gram-Schmidt basis vectors. Since the calculation time has been shown to be proportional to the number of these vectors (3), the factor analysis reconstruction technique appears to be more computationally efficient. The SNR's for the integrated absorbance, the factor analysis, and the Gram-Schmidt reconstructions of the LC1 data are summarized in Table 11. At all concentrations, the factor analysis and the Gram-Schmidt reconstructions give higher SNR than the integrated absorbance technique. However, at concentrations lower than those in Table 11, the difference decreases. The S N R s for the Gram-Schmidt and factor analysis reconstructions are approximately the same, with the factor analysis SNRs slightly higher for most peaks. From these results, it is clear that the integrated absorbance technique, even when optimized for a particular data set, does not match the chromatographic sensitivity of the factor analysis and Gram-Schmidt reconstruction techniques. Additionally, optimization is necessary for integrated absorbance
ANALYTICAL CHEMISTRY, VOL. 56,NO. 8, JULY 1984
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Flgure 2. Chromatographic reconstruction of LC1: (A) Gram-Schmidt with DISP = 30, NPTS = 100, NBV = 10; (B) factor analysis with DISP = 25,NPTS = 100, NBV = 25,NEV = 10; (C) Gram-Schmidt with the same parameters as (A) only including a reference vector from the end
of the chromatographic run (interferogram number 300) in the reference subspace: (D) factor analysls with the same parameters as (B) only including a reference vector taken 20 interferograms before each peak and 20 interferograms after last peak In the reference subspace. reconstructions, while it has been previously shown that it is not necessary for factor analysis and Gram-Schmidt reconstruction techniques. The optimization process is a lengthy one and should be avoided if possible. Thus, for maximum chromatographic sensitivity and universality of detection, the factor analysis and Gram-Schmidt reconstruction techniques offer several inherent advantages over integrated absorbance methods. Small background changes during the LC/FT-IR experiment can result in a sloping base line for both Gram-Schmidt (Figure 2A) and the factor analysis (Figure 2B) reconstructed chromatograms when all reference vectors (NBV) are taken from the beginning of a run. One method to minimize or eliminate the sloping base line is to include some reference interferogram(s) from base line positions later in the chromatographic run. Figure 2C is the Gram-Schmidt reconstructed chromatogram of LC1 using a reference subspace that includes a vector from the end of the chromatographic run (interferogram number 300). Figure 2D is the factor analysis reconstructed chromatogram of LC1 using a reference subspace that includes one reference vector taken from between each peak. The sloping base line is effectively eliminated by using both methods. Sparks et al. (IO) have recently used Gram-Schmidt reconstruction intensities to attain on-the-fly quantification in GC/FT-IR analyses. A pseudolinear relationship between the Gram-Schmidt intensities and a limited concentration range
Figure 3. Quantitative plot for reconstructions of methyl benzoate: Gram-Schmidt, squares and solid line; factor analysis, triangles and dashed line.
was derived in theory and demonstrated by examples. Since this technique gives quantitative results directly from interferometric data, it is a computationally efficient method and its application to the analysis of LC/FT-IR data would prove to be useful. Figure 3 illustrates the potential of this technique for LC/FT-IR analyses. Figure 3 was generated by plotting
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Anal. Chem. 1984, 56, 1272-1277
the peak area vs. the “absolute” concentration for the methyl benzoate peaks. The peak area was numerically integrated by Simpson’s method over the entire peak after the reconstruction intensity values had been base line corrected. The plots in Figure 3 exhibit good linearity although no internal standard was used. Similar results were obtained by using different sets of reconstruction parameters. Additionally, Figure 3 illustrates that similar results were obtained by use of factor analysis reconstruction intensities. As in GC/FT-IR, a positive x intercept occurs which is caused by the forced positive error introduced by Gram-Schmidt and factor analysis calculations. Compared with the results from ref 10, the linearity of LC/FT-IR appears to extend to higher concentrations than GC/FT-IR. The successful application of the Gram-Schmidt and factor analysis methods to GC/FT-IR and LC/FT-IR indicates that they should also be applicable to associated techniques such as supercritical fluid chromatography (SFC)/FT-IR.
ACKNOWLEDGMENT The authors thank Dennis Gerson and Sharon Smith of
IBM Instruments, Inc., for supplying the LC/FT-IR data.
LITERATURE CITED (1) Erickson, Mitchell, D. Appl. Spectrosc. Rev. 1070, 75,261-325. (2) Hanna, D. Alan; Hangac, Greg; Hohne, Bruce A.; Small, Gary W.; Wiebok, Richard C.; Isenhour, Thomas L. J. Chromatogr. Scl. 1979, 17, 423-427. (3) Owens, Patrick M.; Lam, Richard B.; Isenhour, Thomas L. Anal. Chem. 1082, 54,2344-2347. (4) Johnson, Charles C.; Taylor, Larry T. Anal. Chem. 1083, 55, 436-441. (5) Brown, Robert S.; Taylor, Larry T. Anal. Chem. 1083, 55,723-730. (6)De Haseth, James A.; Isenhour, Thomas L. Anal. Chem. 1077, 4 9 , 1977-1981. (7) Sparks, Daniel T.; Owens, Patrick M.; Williams, Stephen S.;Wang, Ching Po; Isenhour, Thomas L., submltted to Appl. Spectrosc. (8) Nelder, J. A.; Mead, R. Computer J. 1065, 7, 308. (9) White, Robert L.; Giss, Gary N.; Brissey, Gregory M.; Wiikins, Charles L. Anal. Chem. 1083, 55, 998-1001. (IO) Sparks, Daniel T.; Lam, Richard E.; Isenhour, Thomas L. Anal. Chem. 1082, 54, 1922-1926.
RECEIVED for review July 8,1983. Accepted February 17,1984. This work was supported by National Science Foundation Grant No. CHE 8026747.
Determination of Lipid Class Concentrations in Seawater by Thin-Layer Chromatography with Flame Ionization Detection Roger P. Delmas,’ Christopher C. Parrish,2 and Robert G . Ackman*
Canadian Institute of Fisheries Technology, Technical University of Nova Scotia, P.O. Box 1000, Halifax, Nova Scotia B 3 J 2x4, Canada
A three-step separatlon on silica-coated Chromarods Is used to resolve dissolved and partlculate seawater llplds Into flve neutral and two polar lipid classes. The Chromarods are conditioned before development by equlllbratlon with an atmosphere of constant humidity and by equiilbratlon with the developing solvent. The response obtalned from Iatroscan flame Ionization detection of llplds on Chromarods Is usually curvlllnear In the range 0.2 to 20 pg. Indlvldual Chromarods glve 5-15 % preclslon for a range of llpld classes at low loads (3 pg). Land-based and shipboard analyses of seawater samples indicate conslderable spatlal varlablllty In llpld class composltlon In the top 100 m of the water column over the Scotlan Shelf.
Chromarod thin-layer chromatography with Iatroscan flame ionization detection (TLC-FID) has been used to analyze lipid classes from diverse sources (1-9). The composition of the solvents required for certain TLC separations on the S or S-I1 silica-coated Chromarods and the FID responses from burning numerous compounds on them both indicate that there are distinct peculiarities to the Iatroscan system. Separations proved to be different from those obtained on TLC plates (1, 2, 10, II), FID response factors were found (3, 12) to be different to those obtained in gas chromatography (GC), and calibration curves either showed some deviation from linearity Present address: Universite de Bretagne Occidentale, 6 Av. Le Gorgeu, 29283 Brest, France. Present address: Department of Oceanography, Dalhousie University, Halifax, Nova Scotia B3H 451, Canada.
or did not extrapolate through zero-zero (4-8,13). From these considerations it is now apparent that Iatroscan TLC-FID is not a simple combination of plate TLC and GC-FID. I t is an analytical system in its own right requiring a careful consideration of parameters affecting both separations and quantification. We have been studying various qualitative and quantitative aspects of this system to assess its usefulness in the analysis of lipid classes present in seawater. Marine lipids are important biological energy sources and have been used as tracers in food-web studies (14-17).Some lipids, however, are pollutants (18,19) and all lipids can potentially act as solvents, transporters, or sinks for pollutants (18, 20-22). There have been few studies of the total distribution of lipid classes in the oceans. GC has been the usual means of measuring the components of these classes, and this normally necessitates a relatively time-consuming and complicated sample workup procedure (14,23-26), which is often carried out long after sample collection. The rapidity with which the Iatroscan TLC-FID system provides synoptic lipid class data from small samples suggested that it would be useful for screening seawater samples prior to performing more detailed chromatographic analyses. The lipid class concentrations obtained by TLC-FID would provide reference values for the concentrations of the individual components obtained by other techniques. In particular, shipboard TLC-FID analyses would help in deciding sampling strategies for more detailed investigations. In addition, the TLC-FID technique alone could provide an overall picture of spatial or temporal variations in the distribution of a complete range of lipid classes without a large financial ob-
0003-2700/84/0356-1272$01.50/00 1984 American Chemical Society
