Trilinear self‐modeling curve resolution using Borgen‐Rajkó plot

Abstract

AbstractModern analytical instruments provide measurement data arrays with full of hidden and redundant information. Multivariate curve resolution (MCR) techniques decompose data set to physic‐chemically meaningful abstract profiles. On the other hand, for such data matrices, Borgen‐Rajkó self‐modeling curve resolution (SMCR) techniques reveal all possible solutions analytically under the minimal assumption. Although Lawton‐Sylvestre (LS) and Borgen methods have been proposed for the non‐negative curve resolution of two‐component and three‐component systems, there is still a great deal of interest to include further restrictions on the Borgen‐Rajkó SMCR. As modern hyphenated analytical instruments produce multiway (eg, three‐way) arrays, multiway analysis (eg, trilinear decomposition) was received much more popularity by chemists.This contribution is decicated to the extension of the Borgen algorithm to the trilinear data sets. The Borgen method incorporating trilinearity constraint is approached in an analogy to the trilinear Lawton‐Sylvester method. The proposed analytical triadic decomposition is applied to the simulated three‐way arrays with full rank and rank overlap (a type of rank deficiency) loadings. Finally, the proposed algorithm is further exemplified with a three‐component spectrofluorimetric study of acid‐base equilibrium of the pyridoxine. Investigating feasible regions of the simulated and experimental three‐component arrays reveal interesting additional information.