Multivariate curve resolution technique

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. 

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]. 

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]. 

The results presented below were obtained by multivariate curve resolution-alternating least squares (MCR-ALS). MCR-ALS was selected because of its flexibility in the application of constraints and its ability to handle either one data matrix (two-way data sets) or several data matrices together (three-way data sets). MCR-ALS has been applied to the folding process monitored using only one spectroscopic technique and to a row-wise augmented matrix, obtained by appending spectroscopic measurements from several different techniques. 

Esteban, M., Anno, C., Dfaz-Cruz, J.M., Dfaz-Cruz, M.S., and Tauler, R., Multivariate curve resolution with alternating least squares optimization a soft-modeling approach to metal complexation studies by voltammetric techniques, Trends Anal. Chem., 19, 49-61, 2000. 

Multivariate curve resolution is widely applicable to separations data and is one of the most common approaches (Franch-Lage et al, 2011 Marini et al., 2011, de la Mata-Espinosa et al., 2011a). The aim of this technique is to determine the number of components present in a sample and the contribution of each component to the sample. In performing MCR, the concentration and response profiles for each analyte are obtained, providing a qualitative and semi-quantitative overview of the components in an unresolved mixture without a priori knowledge of the mixture composition. 

Abstract This chapter introduces an application of multivariate curve resolution (MCR) technique based on a factor analysis. Not only series of IR spectra but also two-dimensional data (series of nuclear magnetic resonance (NMR), mass spectrometry (MS), and X-ray diffraction (XRD)) can deal with same manner (further more two-dimensional data generated by hyphenated techniques such as gas chromatography/mass spectrometry (GC/MS) and liquid chromatography/ultravi-olet (LC/UV) analysis, which combine two functions based on different principles, namely, chromatography, which has a separating function, and spectrometry, which provides information related to molecular structure). By using MCR techniques appropriately, the mixture data is resolved into some essential elements (chemical components, transient states and phases). The results can reveal a true chemical characteristic in your study. 

In particular, if complex reaction mixtures have to be analyzed quantitatively in real time, time-consuming calibration and validation procedures have to be considered. Such sophisticated methods might be mainly the choice in cases of quality and process control during production, but also for long-term in-depth analysis in process optimization studies. However, recent progress in chemometric analysis might lessen this drawback in the future Modern techniques such as multivariate curve resolution (MCR) promise quantitative determination without any calibration procedure in the near future [23, 24]. 

Multivariate analysis techniques such as principal component analysis (PCA) and multivariate curve resolution (MCR) providing useful tools for gaining important information from large data sets, have been employed to interpret TOF-SIMS spectra of macromolecules [39 9]. PCA is especially useful to characterize the... 

Whenever the goals of curve resolution are achieved, the understanding of a chemical system is dramatically increased and facilitated, avoiding the use of enhanced and much more costly experimental techniques. Through multivariate-resolution methods, the ubiquitous mixture analysis problem in chemistry (and other scientific fields) is solved directly by mathematical and software tools instead of using costly analytical chemistry and instrumental tools, for example, as in sophisticated hyphenated mass spectrometry-chromatographic methods. 

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