Evaluation of the extension of rotation ambiguity associated to multivariate curve resolution solutions by the application of the MCR-BANDS method

Abstract

Multivariate Curve Resolution (MCR) methods have been widely used to resolve the spectra (instrumental responses) and concentration profiles of the unknown constituents of chemical mixtures especially when no prior information is available about the nature and composition of these mixtures. Based on the fulfillment of a bilinear model, like the multivariate extension of Beer's law, MCR solutions are affected by rotation ambiguity, which means that a range of feasible solutions can explain the observed data equally well fulfilling the same constraints. The MCR-BANDS method has been proposed to provide a measure of the extension of rotation ambiguity associated to a particular MCR feasible solution. In this work, the two extreme (maximum and minimum) feasible solutions obtained by the MCR-BANDS method are investigated and projected on to the area of feasible solution (AFS) obtained by other methods like the FACPACK method, and compared under the application of different constraints. In contrast to other methods that estimate the whole set of feasible solutions (i.e. the AFS), MCR-BANDS provides a simpler and flexible way to give an estimation of the extension of rotation ambiguity associated to a particular MCR solution (for instance using the MCR-ALS method) of systems with any number of components and under any type of constraints, in the concentration and spectral domains.