Multivariate curve resolution

The challenge is to determine which components are changing and their concentration at any point in time. Collecting a large number of spectm corresponding to the various compositions generates a large data set that can allow this to be achieved. Modem FT-IR spectrometers come with chemometric routines for this data analysis, and stand-alone systems that can perform these computations in real time as spectra are collected are also available. The main issue is the quality of the spectral data when quantitative analysis is required. 

This is a statistical analysis of spectml data in order to reduce the data set to the minimum number of principal components which, with an appropriate weighting, can explain all of the variations in the spectra that have occurred throughout the process. 

The total spectral output from the reaction sequence may be expressed as a series of linear combinations of these components, so the outputs from a PCA analysis of a data set are 

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R. Tauler, A.K. Smilde and B.R. Kowalski, Selectivity, local rank, three-way data analysis and ambiguity in multivariate curve resolution. J. Chemom., 9 (1995) 31-58. 

DOSY is a technique that may prove successful in the determination of additives in mixtures [279]. Using different field gradients it is possible to distinguish components in a mixture on the basis of their diffusion coefficients. Morris and Johnson [271] have developed diffusion-ordered 2D NMR experiments for the analysis of mixtures. PFG-NMR can thus be used to identify those components in a mixture that have similar (or overlapping) chemical shifts but different diffusional properties. Multivariate curve resolution (MCR) analysis of DOSY data allows generation of pure spectra of the individual components for identification. The pure spin-echo diffusion decays that are obtained for the individual components may be used to determine the diffusion coefficient/distribution [281]. Mixtures of molecules of very similar sizes can readily be analysed by DOSY. Diffusion-ordered spectroscopy [273,282], which does not require prior separation, is a viable competitor for techniques such as HPLC-NMR that are based on chemical separation. 

Tauler R., Smilde A.K., Hemshaw J.M., Burgess L.W., Kowalski B.R., Multicomponent Determination of Chlorinated Hydrocarbons Using a Reaction-based Chemical Sensor. Part 2. Chemical Speciation Using Multivariate Curve Resolution, Anal. Chem. 1994 66 3337-3344. 

Terrado M, Barcelo D, Tauler R (2009) Quality assessment of the multivariate curve resolution alternating least squares method for the investigation of environmental pollution patterns in surface water. Environ Sci Technol 43 5321-5326... 

Terrado M, Barcelo D, Tauler R (2010) Multivariate curve resolution of organic pollution patterns in the Ebro River surface water-groundwater-sediment-soil system. Anal Chim Acta 657 19-27... 

Keywords Chemometrics, Contamination sources, Ebro River, Multivariate curve resolution, Principal component analysis... 

MCR-ALS Multivariate curve resolution alternating least squares... 

Multivariate Curve Resolution Alternating Least Squares... 

Multivariate curve resolution methods (MCR [17]) describe a family of chemometric procedures used to identify and solve the contributions existing in a data set. These procedures have been traditionally applied for the resolution of multiple chemical components in mixtures investigated by spectroscopic analysis techniques [18]. 

Tauler R, Maeder M, De Juan A (2009) Multiset data analysis extended multivariate curve resolution. In Brown S, Tauler R, Walczak R (eds) Comprehensive chemometrics, vol 2. Elsevier, Oxford, pp 473-505... 

Multivariate curve resolution, 6 54—56 Multivariate linear regression, 6 32—35 Multivariate optical elements (MOE), 6 68 Multiwalled carbon nanotubes (MWCNTs), 77 48, 49 22 720 26 737. See also Carbon nanotubes (CNTs) Multiwall nanotubes (MWNTs) synthesis of, 26 806 Multiwall fullerenes, 12 231 Multiwall nanotubes (MWNTs), 12 232 Multiwall paper bags, 78 11 Multiway analysis, 6 57-63 Multiyear profitability analysis, 9 535-537 Multiyear venture analysis, 0 537-544 sample, 9 542-S44 Mummification, 5 749 Mumps vaccine, 25 490 491 Mumps virus, 3 137 Municipal biosolids, as biomass, 3 684 Municipal distribution, potential for saline water use in, 26 55-56 Municipal effluents, disposal of, 26 54 Municipal landfill leachate, chemicals found in, 25 876t... 

Literature examples include one-, two-, and three-step hydrogenation reactions, hi each case, the reactant and product concentrations were monitored, as were intermediates or side reaction products as necessary. Simple peak height or area measurements were sufficient to generate reaction profiles for the reduction of cyclohexene [116] and of l-chloro-2-nitrobenzene [117]. However, for more spectrally complex systems, such as the reduction of carvone and of 2-(4-hydroxyphenyl) propionate, multivariate curve resolution (MCR) was required [117]. 

Earlier, it was mentioned that due to the orthogonality constraints of scores and loadings, as well as the variance-based criteria for their determination, it is rare that PCs and LVs obtained from a PC A or PLS model correspond to pure chemical or physical phenomena. However, if one can impose specihc constraints on the properties of the scores and or loadings, they can be rotated to a more physically meaningful form. The multivariate curve resolution (MCR) method attempts to do this for spectral data. 

Figure 12.23 Example of multivariate curve resolution (MCR). (A) A series of 210 FTIR. spectra obtained during the course of a chemical reaction (B) the pure spectral profiles obtained using MCR. and (C) the corresponding pure concentration profiles obtained using MCR.

A. de Juan and R. Tauler, Multivariate curve resolution (MCR) from 2000 progress in concepts and applications, Crit. Rev. Anal Chem., 36, 163-176 (2006). 

R. Tauler, B. Kowalski and S. Fleming, Multivariate curve resolution applied to spechal data from multiple runs of an industrial process. Anal. Chem., 65, 2040-2047 (1993). 

Figure 4.43 Background correction based upon multivariate curve resolution following hyperspectral scans. (From Martinez, M.J. et al.. Nucleic Acid Res., 31(4), 1-8,2003. With permission.)...

Tauler, R. (1995), Multivariate curve resolution applied to second order data, Chemomet. Intell. Lab. Syst., 30,133-146. 

Tauler, R., Kowalski, B. and Fleming, S., Multivariate Curve Resolution Applied to Spectral Data from Multiple Runs of an Industrial Process Anal. Chem. 1993, 65, 2040-2047. 

In the ATR FTIR study of the synthesis of cyclopentyl silsesquioxane 7F3, in situ ATR FTIR spectra of the reaction mixture were collected every 2 min during the reaction. The spectra obtained were plotted as a function of reaction time (Fig. 9.11). Pure component spectra and relative concentration profiles were subsequently recovered using a multivariate curve resolution (MCR) [59] technique based on a modified target factor analysis algorithm [60]. 

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