Reduction of the rotational ambiguity of curve resolution techniques under partial knowledge of the factors. Complementarity and coupling theorems

Multivariate curve resolution techniques allow to uncover from a series of spectra (of a chemical reaction system) the underlying spectra of the pure components and the associated concentration profiles along the time axis. Usually, a range of feasible solutions exists because of the so‐called rotational ambiguity. Any additional information on the system should be utilized to reduce this ambiguity. Sometimes the pure component spectra of certain reactants or products are known, or the concentration profiles of the same or other species are available. This valuable information should be used in the computational procedure of a multivariate curve resolution technique. The aim of this paper is to show how such supplemental information on the components can be exploited. The knowledge of spectra leads to linear restrictions on the concentration profiles of the complementary species and vice versa. Further, affine–linear restrictions can be applied to pairs of a concentration profile and the associated spectrum of a species. These (affine) linear constraints can also be combined with the usual non‐negativity restrictions. These arguments can reduce the rotational ambiguity considerably. In special cases, it is possible to determine the unknown concentration profile or the spectrum of a species only from these constraints. Copyright © 2012 John Wiley & Sons, Ltd. The rotational ambiguity of curve resolution techniques can successfully be reduced if additional knowledge on the chemical system is available. Complementarity and coupling theorems are presented, which provide affine–linear restrictions on the admissible concentration profiles and on the spectra. Numerical results are given for a three‐component model problem as well as for a catalytic system, namely, the formation of hafnacyclopentene.