Gram-Schmidt reconstructions

Figure 2. Gram-Schmidt Reconstruction obtained from SFE/SFC/FTIR of hexane fraction of Day 25 sample.

As in a GC-IR experiment, all spectral information is displayed during the run (Fig. 6.8-25) and all spectra are stored on the hard disc for post running processing. The Gram Schmidt reconstruction of the spectral data can be analyzed in order to obtain the components which are cleaved during decomposition of the sample. Library search may fail in the case of technical products due to the more complex composition of the evolving gases, which, for example, contain monomers as well as additional compounds, such as plasticizers, etc. The use of special TGA/FT-IR libraries should be very helpful and is recommended therefore. 

Figure 2. a) FID chromatogram from capillary SFC separation of pesticide mixture, b) Gram-Schmidt reconstructed chromatogram of the same separation. 

Figure 6 is a Gram-Schmidt reconstructed chromatogram of a citrus oil components test mixture. The major peak in the chromatogram is due to limonene which is essentially a solvent. Note that the analysis time is extremely short, less than 5 minutes/ and is accomplished under mild temperature conditions, 50 C. The resolution is not superb on all the compounds present. However, infrared detection can be used to resolve overlapping chromatographic bands. For example, the peak prior to limonene in the chromatogram (denoted with an ) appears to be pure with no shoulders evident. Close examination of the infrared spectra of the peak shows that the peak actually consists of two compounds. 

Figure 6. Gram-Schmidt reconstructed chromatogram of citrus oil test mixture.

Figure 4.3 TGA-FTIR A schematic diagram of a TGA-FTIR interface B (a), weight-loss curve of a plasticised PVC ( 20 mg) by TGA (b), first derivative of weight-loss curve (c), Gram-Schmidt reconstruction calculated from spectral data acquired by FTIR analysis C Thermograms , specific reconstruction for three different functional groups, which are a chemoselective record of the evolving gas (a) carbonyl (1760-1740 cm ) (b) HCl (2831-2785 cm ) (c) benzene (684-664 cm ) D spectrum obtained from the middle of the first weight-loss region. Reproduced from R. C. Wieboldt, S. R. Lowry and R. J. Rosenthal (1988) Mikrochim. Acta /, Recent Aspects of Fourier Transform Spectroscopy, Vol. 2, Proc. 6th Int. Conf Four. Trans. Spec.), pp. 179-82, by...

Figure 2. Plot of a typical Gram-Schmidt reconstruction (GSR).

GC-FTIR requires a large number of spectra to be stored over a very short time interval. The gas phase exiting the column is sampled at very short time intervals throughout the elution. The resolution of the spectra is lowered in order to occupy less memory. The data are then used to reconstruct a pseudo-chromato-gram called Gram-Schmidt after the mathematicians whose method is used to treat the data. 

A sensitive technique used for real time reconstruction of chromatograms from the interferogram is the Gram Schmidt vector orthogonalization method. The Gram Schmidt method relies on the fact that the interferogram contains information on absorbing samples at all optical retardations less than the reciprocal of the width of each band in the spectrum. 

Figure 4a is the spectrum of supercritical CO2 (same as Figure 1) plotted to visually compare the two spectra. It is important to realize that the Gram-Schmidt Plus algorithm removes the CO2 interference from the reconstructed chromatograms only. It does not affect the actual FT-IR spectra in any way. 

Fig.4. The distribution of a contaminant is examined by reconstructing images of an acrylic fiber contaminant on a microcircuit die using various methods of visualization. Image generation methods include the use of a absorbance intensity at 2968 cm, b integrated absorbance between 2850 and 3000 cm"b C integrated absorbance from 1000 to 4000 cm , and d the Gram-Schmidt method, (reproduced from Ref. [31])...

After infrared spectra at low resolution (usually 4 cm ) have been recorded as a function of time and temperature, the further procedure is similar to GC/FT-IR (see Section 17.5.1.7) and, in fact, GC/FT-IR. software, such as Gram-Schmidt thermogram reconstruction and library search with a vapor-phase spectra database is commonly used. Helpful for the identification in the vapor phase is the virtual absence of interaction between molecules, and therefore the nondestructive IR detection enables in many cases an easy and fast interpretation of single and overlapping absorption bands. 

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