On the extraction of spectra of components from spectra of mixtures. A development in factor theory—I

The theory of factor analysis is extended to permit the computer based extraction of the spectra of pure components from spectra of mixtures. A simultaneous linear, non-orthogonal transformation of the eigenspectra and eigenvectors is used to generate all positive absorbances and concentrations within noise level. Applications to actual spectra of mixtures of: (A) ethyl ethanoate, butan-2-one and oct-1-ene; (B) ethyl ethanoate, butan-2-one and cyclohexane; and (C) butan-2-one, cyclohexane and 2-methylpentane are presented. The effects of changes in signs of the constrained diagonal elements of the transformation matrix is investigated. To explore the ability of the software to cope with component spectra in which there are no wavenumbers at which one component dominates an artificial set of mixtures is examined. Recognizable spectra are extracted. It appears that, even when there are no wavenumbers at which one component dominates, the condition of finding “the sum of squares of negative absorbances/concentrations” near zero is adequate to yield useful spectra for library searches.