Kinetics of nonideal hyperbranched polymerizations. 1. Numeric modeling of the structural units and the diads

The kinetics of reactions with nonuniform reaction rate constants leading to hyperbranched polymers has been examined and discussed. A matrix notation was developed, which has then been applied to the analysis of the kinetics of AB(2), AB(3), AB(n), and ABB' systems. All differential equations have been integrated numerically in order to obtain plots of the ratios of structural units as functions of the conversion. Three general situations for AB(2) systems and the kinetics of self-condensing vinyl polymerization as one example of an ABB' system are discussed. It was found that the influence of the first B group on the reactivity of the second B group has the largest effect on ratio of structural units and final composition. Thus, by varying the rate constants of these reaction steps in the model the resulting degree of branching ranges between 15 and 89%. Furthermore, the diad formation of the AB(2) system is analyzed.