Component Concentrations, Known Spectra

Assuming we know the two rate constants ki and fc that allow the computation of C. Assuming further, we only have measured spectra between time = 200 and 1200 (fast reaction with significant dead time of the instrument). The task is to determine the three absorption spectra of the pure compounds A, B and C. All three are not accessible directly in the range of available spectra because of severe overlap. 

A calc=C p Y p % component spectra via multivariate linear regression 

---

The instrument uses three recordings stored in memory a spectrum of the sample (composed of the two compounds to be analysed) and a spectrum of each of the pure components in the same spectral domain (reference solutions of known concentrations). 

Raman spectroscopy is a scattering, not an absorption technique as FTIR. Thus, the ratio method cannot be used to determine the amount of light scattered unless an internal standard method is adopted. The internal standard method requires adding a known amount of a known component to each unknown sample. This known component should be chemically stable, not interact with other components in the sample and also have a unique peak. Plotting the Raman intensity of known component peaks versus known concentration in the sample, the proportional factor of Raman intensity to concentration can be identified as the slope of the plot. For the same experimental conditions, this proportional factor is used to determine the concentration of an unknown component from its unique peak. Determining relative contents of Si and Ge in Si—Ge thin films (Figure 9.38 and Figure 9.39) is an example of quantitative analysis of a Raman spectrum. 

For overlapping peaks the data matrix contains linear combinations of the pure spectra of the overlapping components in its rows, and combinations of the pure elution profiles in its columns. Multivariate analysis of the data matrix may allow extraction of useful information from either the rows or columns of the matrix, or an edited form of the data matrix [107,116-118]. Factor analysis approaches or partial least-squares analysis can provide information on whether a given spectrum (known compound) or several known compounds are present in a peak. Principal component analysis and factor analysis can be used to estimate the maximum number of probable (unknown) components in a peak cluster. Deconvolution or iterative target factor analysis can then be used to estimate the relative concentration of each component with known spectra in a peak cluster. 

Relation (10) allows to obtain the elements of matrix E[AJd] as well, values which are proportional to the absorbances of the pure components measured at the selected A wavelengths. Relation (10) allows thus to obtain the spectrum of the M individual components. This is important if a sufficiently large number of standard solutions are available with known concentrations of components, but individual components are not available for recording their individual spectra. 

In order to perform an analysis, one must establish a correlation between the molecular species present and the peaks observed in the mass spectrum. The gas may consist of known components, whose relative concentrations are to be determined, or alternatively it may be required to identify unknown species. 

In some cases, components in a mixture can be determined quantitatively without prior separation if the mass spectrum of each component is sufficiently different from the others. Suppose that a sample is known to contain only the butanol isomers listed in Table 10.17. It can be seen from Table 10.17 that the peak at miz = 33 is derived from butanol, but not from the other two isomers. A measurement of the miz = 33 peak intensity compared to butanol standards of known concentration would therefore provide a basis for measuring the butanol content of the mixture. Also, we can see that the abundances of the peaks at m z = 45, 56, and 59 vary greatly among the isomers. Three simultaneous equations with three unknowns can be obtained by measuring the actual abundances of these three peaks in the sample and applying the ratio of the abundances from pure compounds. The three unknown values are the percentages of butanol, 2-butanol, and 2-methyl-2-propanol in the mixture. The three equations can be solved and the composition of the sample determined. Computer programs can be written to process the data from multicomponent systems, make all necessary corrections, and calculate the results. 

We may now deal with some of the procedures employed in quantitative spectrographic analysis. In the comparison sample method, the spectrum of an unknown sample is compared with the spectra of a range of samples of known composition (e.g. those supplied by the US Bureau of Standards) with respect to a particular component or components. The spectra of the unknown and of the various standards are photographed on the same plate under the same conditions. The concentrations of the desired constituent can then be estimated by comparing the blackening of the lines of the particular constituent with the same lines on the standards visual or photometric comparison of blackening may be used. 

To produce a calibration using classical least-squares, we start with a training set consisting of a concentration matrix, C, and an absorbance matrix, A, for known calibration samples. We then solve for the matrix, K. Each column of K will each hold the spectrum of one of the pure components. Since the data in C and A contain noise, there will, in general, be no exact solution for equation [29]. So, we must find the best least-squares solution for equation [29]. In other words, we want to find K such that the sum of the squares of the errors is minimized. The errors are the difference between the measured spectra, A, and the spectra calculated by multiplying K and C ... 

Assume also that a validation sample has been collected with concentrations for Sj, Sy, and ij of 1, 3, and 2 respectively (c = [1 3 2]). Assuming linear additivity holds, the resulting response vector for this mixture sample is r= (12 8 10]. When validating tire models using this sample, the known information is the measured spectrum, r= [12 8 10], and the component amcentrations for the known analytes c = [1 3]- The steps for validating the CLS model arc shown in Figure 5.62 and include (a) formulating... 

The classical approach to the analysis of mixtures by use of infrared spectroscopy consists in identifying specific, strong bands that belong to a suspected component, obtain a pure spectrum of the suspected component, and then remove those in the spectrum of the mixture that are due to the identified compound. The process is repeated for the remaining bands in the mixture spectra. Once the component spectra are known for a mixture, a series of calibration curves is produced. These curves relate concentration to absorbance, using Beer s law. The concentration of the components of the mixture are then obtained by interpolation. The advantage of Fourier-transform, infrared spectroscopy is that components of a mixture may be... 

---