A new approach to the resolution of the excitation-emission spectra of multicomponent systems

Abstract

A method has been developed for the calculation of the emission, absorption, and concentration characteristics of chemical species from the fluorescence spectra recorded for a series of solutions of varying composition at different excitation wavelengths. The three-dimensional fluorescence-intensity array (whose ijkth element is the fluorescence intensity of the ith solution at the jth excitation and the kth emission wavelength) is assumed to be a trilinear product of the excitation ( X), emission ( Y), and concentration ( C) characteristics of the emitting species. The decomposition of experimental spectra is carried out in three steps. In the first step, an eigenvector analysis of the Gauss transform of the fluorescence array is performed, whose rank is the lower bound to the rank of the matrices X, Y, and C, and thereby to the number of independently emitting chemical species present in the system. In the second step, factorization of the eigenvectors of the Gauss transform of the fluorescence array is performed, which gives approximate factor matrices X, Y and C. The obtained factors correspond to exact decomposition, if there is no error in the data. In the third step, the factors are refined by means of a nonlinear least-squares method, which is directed at minimizing the sum of the squares of the differences between the elements of the observed and calculated fluorescence array. Application of the method to the fluorescence spectrum of mixtures of anthracene and 9-methylanthracene resulted in perfect resolution of the fluorescence spectra into the component excitation and emission spectra and correct profiles of component concentrations. It is also shown that if the numbers of absorbing and emitting species are not equal, as occurs for the β-naphtol-β-naphtolate system in acid and neutral aqueous solution, unambiguous decomposition of the spectrum is impossible to carry out.