Mathematical modeling of obtaining functionalized statistical butadiene-styrene copolymers

The article considers approaches to mathematical modeling of the synthesis of butadiene-styrene random copolymers (DSSK). These rubbers are obtained by solution polymerization in the presence of an alkyl lithium modifier initiating system. The object of the study was the functionalized random butadiene-styrene rubber DSSK-2560F. The rubber was obtained by copolymerization of butadiene-1,3 with styrene in a periodic manner. The initiating complex (n-butyl lithium + modifier) is formed in situ in the presence of monomers. The synthesis temperature was constant. The conversion of monomers was determined using the dry residue method. It was taken into account that the random distribution of styrene in the copolymer is determined by the Me/Li ratio in the initiating system. A kinetic scheme for the synthesis of random butadiene-styrene rubber has been developed. A system of infinite differential equations is presented for the proposed kinetic scheme. Using the method of moments, an infinite system of equations is reduced to a finite system of equations. The degree of monomer conversion, the values of the number-average and weight-average molecular weight, and the polydispersity coefficient are estimated depending on the synthesis conditions under batch conditions. The kinetic parameters of the model are estimated using nonlocal optimization procedures. The values of the rate constants of elementary reactions are calculated. Analytical dependences of the effect of polymerization temperature on the degree of conversion and molecular weight characteristics of the rubber are obtained. The developed mathematical model can be used in the technology of producing solution-based butadiene-styrene random copolymers, where sodium alcoholate and n-butyl lithium act as the initiating system. Application of the developed mathematical model will allow us to determine the influence of process parameters (temperature, ratio of components of the initiating system) on the molecular weight characteristics of the resulting rubber..