A simple self modelling curve resolution (SMCR) method for two-component systems

Highlights: • By applying different constraints, Self-modeling curve resolution (SMCR) techniques produce a range of feasible solutions for every component in a system. It is important to determine the range of all feasible solutions of SMCR methods. • A simple procedure for determining the boundaries of feasible solutions of two-component systems using the micro-structure of data is proposed. • The proposed method is based on the fact that the solutions of non-negative bilinear decomposition of two-component systems are always present as two rows and columns of the measured data. Multivariate self-modeling curve resolution (SMCR) methods are the best choice for analyzing chemical data when there is not any prior knowledge about the chemical or physical model of the process under investigation [[1Q3: The reference '1' is only cited in the abstract and not in the text. Please introduce a citation in the text.]]. However, the rotational ambiguity is the main problem of SMCR methods, yielding a range of feasible solutions. It is, therefore, important to determine the range of all feasible solutions of SMCR methods. Different methods have been presented in the literature to find feasible solutions of two, three, and four component systems. Here, a novel simple SMCR method is presented for calculating the boundaries of feasible solutions of two-component systems. At first, the simple strategy is presented for calculating the feasible solutions of two-component systems. Next, four different experimental two-component systems are analyzed in detail for calculating the boundaries of feasible solutions in both spaces, including complex formation equilibrium, keto-enol tautomerization kinetic, lipidomics data, and a case for quantification of an analyte in gray systems. In all cases, the boundaries of range of feasible solutions are properly determined by the proposed simple strategy.