Direct optimization of self-modeling curve resolution: application to the kinetics of the permanganate – oxalic acid reaction

A new procedure to extract spectral and concentration information for unknown components in a series of mixture spectra is described. The algorithm, a form of self-modeling curve resolution (SMCR), requires no assumptions about the mixture data except for linear additivity and non-negativity of component spectra, and non-negativity of concentrations. It provides permissible bands for the spectra and concentration profiles of individual components in the mixtures and is applicable to problems in chromatography, equilibrium studies, and kinetics, among others. The new method employs a nonlinear optimization procedure and is substantially more efficient than similar methods that have been previously reported. The SMCR algorithm is demonstrated by applying it to the autocatalytic oxidation of oxalic acid by permanganate in the presence of sulfuric acid. The reaction was monitored spectroscopically between 200 and 1000 nm under four different reaction conditions. Results verified the presence of two reaction intermediates previously proposed in the literature and confirmed their spectral properties. Concentration profiles for the intermediates are