Determination of rate constants from two-way kinetic-spectral data by using rank annihilation factor analysis

Rank annihilation factor analysis (RAFA) is applied to resolve the two-way kinetic-spectral data measured from spectroscopic reactions and acquire rate constants and the absorption spectrum of each component. A two-step first-order consecutive reaction is studied in this paper. When the first step rate constant acts as an optimizing object, and simply combined with the pure spectrum of reactant, the rank of the original data matrix can be reduced by one by annihilating the information of reactant from the original data matrix. The residual standard deviation (R.S.D.) of the residual matrix after bilineaization of the background matrix is regarded as the evaluation function. Owing to the correlation between kinetic functions of species in the reaction, two optimal resolutions, corresponding to the rate constants of the first and second step, respectively, can both be obtained in one computing process. Given the kinetic parameters, the absorption spectrum of each component including the intermediate can be obtained through least square regression. This approach can also be applied to reaction systems where the intermediate or the final product doesnot absorb. The performance of the method has been evaluated by using synthetic data. Electrodegradation of phenol solution and alkaline hydrolysis of dimethyl phthalate were also studied by the present method.