Resolution of Quenched Fluorescence Mixtures of Two Conformers of trans-1-(2-Anthryl)-2-phenylethene by Constrained and Unconstrained Methods of Principal Component Analysis: a Comparative Study

Two different methods of principal component analysis (PCA) were applied to resolve pure component spectra in the two-component spectral mixture of gradually quenched fluorescence. The two approaches differ by that in the first method one uses an additional physical constraint to arrive at the desired solution, while none of this but simple matrix transformations are used to this aim in the other. Both methods are classified as the approaches of Principal Component Analysis with Self-Modeling (PCA-SM). The first technique is known as PCA-SM-SV, where SV stands for a constraint related to the Stern-Volmer equation, the second method is known as Kubista's approach to two same-sized correlated sets of spectral data matrices. The methods were applied to resolve the pure component fluorescence spectra in the fluorescence mixture of two conformers of trans-1-(2-anthryl)-2-phenylethene (t-APE) quenched by fumaronitrile in toluene. The results of the application of both methods to precisely measured spectra appear practically equivalent and eventually dispel the controversy existing in the literature about the fluorescence spectral profiles of the t-APEA and t-APEB conformers in favour of the PCA-SM-SV method which results were earlier questioned by the outcome of other methods.