Problem of mixtures with known compositions and IRONFLEA method for multivariate curve resolution

A special case of gray spectral data systems (a) F.-T. Chau, Y.-Z. Liang, J. Gao, X.-G. Shao (Eds.), Chemometrics: From Basics to Wavelet Transform, Chemical Analysis Series, vol. 164, John Wiley & Sons, Inc., 2004; (b) Y.Z. Liang, O.M. Kvalheim, R. Manne, Chemom. Intell. Lab. Syst. 18 (1993) 235-250] is discussed here and the least-squares method for the multivariate curve resolution (MCR) named IRONFLEA is proposed. The system under consideration is the bilinear spectral data of the samples with known chemical compositions and unknown concentration matrix. If the spectra of samples (A_i) and (Q + A_i) (i = 1, …, n, n ≥ 2) are available, then the spectrum and the concentrations of Q could be found and the solution is unique. A practical chemical model for this problem could be mixtures, polymers, peptides, oligosaccharides, or supramolecular formations made of a limited number of monomeric components. In the cases of polymeric or oligomeric samples the spectral contributions and the concentrations of the particular monomeric units are extracted. The method is capable of extracting chemically meaningful spectra of components. The method is implemented in SAS IML code and tested for the deconvolution of spectra of polymers made of styrene derivatives with known monomeric compositions (a) H. Fenniri, L. Ding, A.E. Ribbe, Y. Zyrianov, J. Am. Chem. Soc. 123 (2001) 8151-8152; (b) H. Fenniri, S. Chun, L. Ding, Y. Zyrianov, K. Hallenga, J. Am. Chem. Soc. 125 (2003) 10546-10560]. The method performs calculations fast enough to allow the incorporation of leave-one-out outlier removal procedure.