Analysis multicomponent

The analysis of a component in a complex mixture presents special problems. In this section we will examine how to determine the concentrations of a number of components in a mixture. 

The use of infrared spectroscopy to provide quantitative information on multicomponent systems has blossomed in recent years, spurred on by the development of chemometric techniques which have revitalised NIR spectroscopy. The principle of multicomponent analysis is outlined below, but see the books by Martens and Naes [13] and Massart et al. [14] for more thorough developments of these ideas. 

In the same way that the absorbance at a single peak maximum for a single material is related to concentration through Beer s law, intensity across the whole spectrum is related to the concentrations of all infrared active ingredients in a mixture through the equation  

The above relation can be rearranged for the prediction of concentration from absorbance. However, we first need k  

Calculation of concentrations therefore requires two matrix inverse calculations. This method is often referred to in the literature as the k matrix method of multilinear regression. The advantage of the technique is that it uses more variables (absorbances) than there are reference samples. In this sense, the solution is said to over-determined. 

Perhaps a superior method of multilinear regression is the so-called p matrix method. Here, we assume that concentration is a function of absorbance, rather than vice versa  

In general under practical conditions it is very exceptional to find wavelengths at which just one reactant absorbs. For this reason methods have to be developed to extract the different concentrations out of the overall absorption spectrum. This is very difficult since absorption spectra in the UVA is are very broad band and most of the spectra of the reactants overlap. If the reactants and their absorptions are known, a method called multicomponent analysis can be used. 

Using eq. (4.1) and defining the path length of the cell as d and taking decadic units for the absorption coefficient, the absorbance can be given in general in decadic units by 

whereby the states can symbolise different reaction times, pH values, etc. 

Taking the photoreaction of rron -stilbene as an example, absorbances for three selected wavelengths at a chosen time of irradiation are given for an optical path-length of d-i cm by the following summation over the partial absorptions of three reactants  

In reality the linear equations contain a value which takes into account that the measured absorbance includes some error caused by noise or by errors in the determination of the absorption coefficients. These coefficients are obtained by calibration. The pure reactant is weighted many times and its absorption coefficient is determined by a calibration curve as a result of many measurements at different concentrations. The absorption coefficient has to be evaluated statistically and contains a variance in dependence on the number of measurements of the blank, the different concentrations, and the exactness of the calibration itself [39,42]. 

The Kerridge-Bongard model of information is of great importance in quality assurance, in particular for the assessment of interlaboratory studies. Examples of the information-theoretical evaluation of analytical results within the context of interlaboratory comparisons have been given by Danzer et al. [1987, 2001], Wienke et al. [1991] and Danzer [1993]. 

Multispecies analyses require two-dimensional analytical information y = f(x)y see Sect. 3.4, mostly in the form of spectra and chromatograms. By evaluation of various signals or the entire signal function, simultaneous information on several sample components can be obtained (in the extreme case on all the constituents contained in the sample). The relevant quantity that characterizes multicomponent analyses is the information amount, 

M(n) being the sum of the information contents of all the n components under consideration  

For the case that all the n constituents have similar expectation ranges, equally probable signal levels and are estimated with comparable precision, the maximum information amount becomes (Danzer et al. [1987]) 

In the concrete case of qualitative tests on n components, the maximum information amount is M(n)quai = n bit. 

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Selectivity Selectivity is rarely a problem in molecular absorption spectrophotometry. In many cases it is possible to find a wavelength at which only the analyte absorbs or to use chemical reactions in a manner such that the analyte is the only species that absorbs at the chosen wavelength. When two or more species contribute to the measured absorbance, a multicomponent analysis is still possible, as shown in Example 10.6. 

This experiment describes a standard multicomponent analysis for two analytes based on measuring the absorbance at two wavelengths. Hexacyanoruthenate(II) is used as a complexing agent, forming a purple-blue complex with Fe(III) and a pale green complex with Cu(II). 

Another nice example of a multicomponent analysis based on current research is presented in this experiment. Although the H-point standard addition is not discussed in this text, this paper provides adequate theory and references to the original literature. 

Raymond, M. Jochum, C. Kowalski, B. R. Optimal Multicomponent Analysis Using the Generalized Standard Addition Method, /. Chem. Educ. 1983, 60, 1072-1073. 

To see how cahbration can be extended to multicomponent analysis, the linear model of equation 10 can be generalized to accommodate several analytes in the same sample, and several measurements made on each sample. Expressed in matrix notation, this becomes... 

The sensitivity of the analytical system in the case of multicomponent analysis with a square K matrix may be defined as the absolute value of the deterrninant of K. 

SELECTION AND USE OF INTENSIVE PARAMETERS OF ANALYTICAL SIGNAL ON MULTICOMPONENT ANALYSIS BY NON-SELECTIVE METHODS... 

Multicomponent analysis by non-selective methods is based on the measurement of total analytical signal (AS) of mixture of components at several intensive parameters and on the constmction of combined equations and the solving of it. The difference of partial sensitivity of components determined in common defines uncertainty. 

Multicomponent analysis using spectra of second order develops mainly in spectrofluorometry and chromatography. 

To make the actual analysis simple and fast, a large amount of precomputed information is utilized. By using library spectra of pure molecular gases together with a special mathematical multicomponent analysis, it is possible to calculate the partial pressures of the gases in a gas mixture. 

Saarinen, Pekka, and Jyrki Kauppinen, Multicomponent Analysis of FT-IR Spectra. Applu ci Spectroscopy 45 (1991), pp. 953-963. 

Carey, W.P., Beebe, K.R., Kowalski, B.R., "Multicomponent Analysis using an Array of Piezoelectric Crystal Sensors", Anal. Chem. 1987(59 1529-1534. 

Maris, M.A., C.W. Brown, GJ. Kavamos, "Nonlinear Multicomponent Analysis by Infrared Spectrophotometry", Anal. Chem. 1983 (55) 1694-1703. 

Otto, M. et. al. "Spectrophotometric Multicomponent Analysis Applied to Trace Metal Determinations", Anal. Chem. 1985 (57) 63-69. 

The mercury film electrode has a higher surface-to-volume ratio than the hanging mercury drop electrode and consequently offers a more efficient preconcentration and higher sensitivity (equations 3-22 through 3-25). hi addition, the total exhaustion of thin mercury films results in sharper peaks and hence unproved peak resolution in multicomponent analysis (Figure 3-14). 

Mourzina YG, Schubert J, Zander W, Legin A, Vlasov YG, Schdning MJ (2001) Development of multisensor systems based on chalcogenide thin film chemical sensors for the simultaneous multicomponent analysis of metal ions in complex solutions. Electrochim Acta 47 251-258... 

All these methods give similar results but their sensitivities and resolutions are different. For example, UV-Vis spectrophotometry gives good results if a single colorant or mixture of colorants (with different absorption spectra) were previously separated by SPE, ion pair formation, and a good previous extraction. Due to their added-value capability, HPLC and CE became the ideal techniques for the analysis of multicomponent mixtures of natural and synthetic colorants found in drinks. To make correct evaluations in complex dye mixtures, a chemometric multicomponent analysis (PLS, nonlinear regression) is necessary to discriminate colorant contributions from other food constituents (sugars, phenolics, etc.). 

Studies conducted by Barenghi eta.1. (1990) and Lodge etal. (1993) independently have demonstrated the facile, multicomponent analysis of a wide range of PUFA-derived peroxidation products (e.g. conjugated dienes, epoxides and oxysterols) in samples of oxidized LDL by high-field H-NMR spectroscopy. Figure 1.9 shows the applications of this technique to the detection of cholesterol oxidation products (7-ketocholesterol and the 5a, 6a and 5/3,60-epoxides) in isolated samples of plasma LDL pretreated with added coppcr(Il) or an admixture of this metal ion with H2O2, an experiment conducted in the authors laboratories. 

Grootveld, M.C., Herz, H., Haywood, R, Hawkes, G.E., Naughton, D., Perera, A., Knappitt, J., Blake, D.R. and Claxson A.W.D. (1994). Multicomponent analysis of radio-lytic products in human body fluids using high field proton nuclear magnetic resonance (NMR) spectroscoopy. Radiat. Phys. Chem. 43, 445-453. 

In many cases, one may measure spectra of solutions of the pure components directly, and the above estimation procedure is not needed. For the further development of the theory of multicomponent analysis we will therefore abandon the hat-notation in K. Given the pure spectra, i.e. given K (pxq), one may try and estimate the vector of concentrations (pxl) of a new sample from its measured... 

When discussing the calibration and multicomponent analysis examples in previous sections, we mentioned that the parameters to be estimated are not necessarily constant but may vary in time. This variation is taken into account by... 

Fig. 41.5. Multicomponent analysis (aniline (jC ), azobenzene (xi), nitrobenzene (xi) and azoxy-benzene (X4)) by recursive estimation (a) forward run of the monochromator (b) backward run (k indicates the sequence number of the estimates solid lines are the concentration estimates dotted lines are the measurements z).

Fig. 41.6. Multicomponent analysis (see Fig. 41.5) with an optimized wavelength sequence.

Thus /(/ ) is a measure of the predictive ability of the model. For the calibration example discussed in Section 41.2, x(/ - 1) contains the slope and intercept of the straight line, and h (/) is equal to [1 c(/)] with c(j) the concentration of the calibration standard for the yth calibration measurement. For the multicomponent analysis (MCA), x(/ -1) contains the estimated concentrations of the analytes after y - 1 observations, and h (/) contains the absorptivities of the analytes at wave-lengthy. 

One of the earliest applications of the Kalman filter in analytical chemistry was multicomponent analysis by UV-Vis spectrometry of time and wavelength independent concentrations, which was discussed by several authors [7-10]. Initially, the spectral range was scanned in the upward and downward mode, but later on... 

P.C. Thijssen, L.J.P. Vogels, H.C. Smit and G. Kateman, Optimal selection of wavelengths in spectrophotometric multicomponent analysis using recursive least squares. Z. Anal. Chem., 320(1985) 531-540. 

H. N.J. Poulisse, Multicomponent analysis computations based on Kalman Filtering. Anal. Chim. Acta, 112 (1979) 361-374. 

It has proved to be very useful, providing both qualitative and quantitative information derived from mathematical processing of UV/VIS spectra. The principles of derivative spectrophotometry were discussed [15,16]. Obviously, derivatisation of spectra does not provide any additional information to that acquired during the measurement, but allows for easier interpretation. In particular, the possibility of resolving overlapping peaks makes derivative spectrophotometry a valuable tool for multicomponent analysis. Typically, derivative spectrophotometry is useful for the simultaneous determination of two additives in polymeric materials with very closely positioned absorption maxima. In quantitative analysis, derivative spectrophotometry leads to an increase in selectivity. 

Applications In contrast to El ionisation, ion-molecule reactions in IMR-MS usually avoid fragmentation [71]. This allows on-line multicomponent analysis of complex gas mixtures (exhaust gases, heterogeneous catalysis, indoor environmental monitoring, product development and quality control, process and emissions monitoring) [70], It should easily be possible to extend the application of the technique to the detection of volatiles in polymer/additive analysis. 

In polymer/additive analysis, spectroscopic methods are used for studying both molecular and atomic composition, usually as a detector for chromatographic techniques. Application of spectroscopic techniques to molecular additive analysis depends on the nature of the sample and its complexity (Table 10.26). Application of the intrinsically simple monocomponent analyses by means of UV/VIS and FUR is rather exceptional for real-life samples. Most industrial samples are complex. It is in the area of multicomponent analysis that most... 

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