A conceptual view to the area correlation constraint in multivariate curve resolution

Multivariate curve resolution (MCR) techniques are widely employed to study chemical systems and unravel underlying physic-chemical information. Different constraints have been introduced to reduce the extent of uncertainty in the results of MCR-ALS. It is important to study the effect of each constraint on the range of feasible solutions in the curve-resolution studies. As each constraint uses specific information, constraints have different effects on the amount of uncertainty. In the present contribution, condition which resulted in uniqueness applying area correlation constraint (ACC) was illustrated. Additionally, the effect of area correlation constraint (relative known-value constraints) on the amount of uncertainty in the resolved profiles was investigated and visualized in detail. Besides, some rules were established for determining the required number and composition of calibration samples. To illustrate how ACC leads to the uniqueness of a MCR result in the presence of validation samples, the extent of rotational ambiguity was evaluated by analyzing different simulated and experimental data sets. The latter involves the quantification of Phenylalanine and Tyrosine in a second-order excitation-emission fluorescence data sets.