Characterization of the unimodality constraint as an effective chemistry-based condition in resolving of chemical processes data

Abstract

Multivariate curve resolution (MCR) techniques are powerful methods for qualitative and quantitative analyses of spectral data. However, MCR methods suffer from non-unique solutions - instead of a unique solution usually a continuum of possible pure component decomposition exists. This ambiguity is covered in a low-dimensional way by the so-called area feasible solutions (AFS). In the quantitative purpose, the rotational ambiguity has a negative effect on the accuracy of the results. By applying additional constraints on the profiles the range of feasible solutions can considerably improve the reliability of quantitative results. Another approach to analyze the size of the continuum of possible pure component profiles is to compute the extrema of the signal contribution function (SCF). The SCF can also be applied under additional constraints.In this study we analyze the restriction of the AFS and the change of the SCF-extrema under additional unimodality constraints. An interesting effect is stated for two examples namely that the unimodality constraint can divide a single subset of the AFS into two parts. In such cases the SCF cannot resolve the ambiguity completely. The effect of the unimodality constraints has been systematically investigated on two- and three-component simulation data sets. This phenomenon are also studied for an experimental data set related to the spectrophotometric titration of a mixture of ligand (3,7-diazanonanedioic acid diamide) and Cu2+ with varying degrees of acidity. Imposing of unimodality constraints as an effective chemically meaningful limitation on the feasible solutions of MCR methods is strongly recommended.