Modeling of the Inaccuracy Vector by the Number-Average Molecular Weight in the Basis Space of Nonlinear Parametric Functions for Unbreak Polymerization of Dienes

The paper proposes a mathematical model of the polymerization process on Ziegler-Natta catalysts of three elementary stages. The statements of direct and inverse kinetic problems are given, the latter of which consists in finding the regions of the chain growth stages and gears that are indeterminate for the rate constants. It is shown that for the process under consideration, the values of constants can be determined in a basis space constructed on vectors of constants. The basic space allows calculating and visualizing grid surfaces by the inaccuracy function for the number-average molecular weight. If the discrepancy is calculated as the maximum of deviations or the sum of the squares of deviations, different surfaces are obtained. It is shown how the superposition of surfaces on each other localizes the minimum regions, which can subsequently be characterized as the solution of inverse kinetic problems. At the same time, this approach allows us to evaluate the shape and appearance of “gully” minima and, in general, to determine the optimal set of constants identifying the minimum points.