### Identification and informativity of models for quantitative analysis of multicomponent mixtures

#### S. I. Spivak1, O. G. Kantor2, D. S. Yunusova3

Annotation The products of radical polymerization in presence of fullerene can contain a wide variety of compounds depending on the monomer’s degree of conversion. Among them free fullerene, some products of its tailing and macromolecules may exist. Therefore, quantitative determination of the mixture’s composition resulting from chemical reactions of fullerene $C_{60}$, is a rather complicated problem. One approach involves determining concentrations of fullerene and its derivatives in a mixture on the basis of Firord equations’ system. These equations are written for the optical densities of the solution at the wavelengths that characterize the absorption maximums. The direct solution of such system may lead to conflicting results due to the fact that some concentrations may be negative. In addition, problems may arise related to errors in the experimental data of the extinction coefficients. The paper presents a method for the determination of component concentrations in mixtures of fullerene based on UV spectrometric data analysis that mitigates the above mentioned problems. The methodological basis of the approach was formed by the linear programming. It permitted to use the theory of duality to analyze the models’ information capability. The approbation results of this method for the model mixture of fullerene components and polystyrene are presented. Obtained results match requirements for the concentrations of mixture components, and are characterized by high accuracy. multicomponent mixture, molar concentration, measurement error, maximum permissible error, models’ information capability

1Head of Department of Mathematical Modelling, Bashkir State University, Ufa; semen.spivak@mail.ru

2Senior researcher, Institute of Social and Economic Research, Ufa Research Centre of Russian Academy of Sciences, Ufa; o_kantor@mail.ru

3Assistant lecturer, Department of Information Security, Bashkir State University, Ufa; kazakova_d_s@mail.ru

Citation: S. I. Spivak, O. G. Kantor, D. S. Yunusova, "[Identification and informativity of models for quantitative analysis of multicomponent mixtures]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:3 (2016) 153–163 (In Russian)