Predicting multidimensional distributive properties of hyperbranched polymer resulting from AB2 polymerization with substitution, cyclization and shielding

TL;DR

This paper introduces a deterministic mathematical model for hyperbranched polymerization that accounts for substitution, cyclization, and shielding effects, providing comprehensive multidimensional results validated by a novel approximation method.

Contribution

It presents the first full multidimensional model for hyperbranched polymerization considering multiple effects, with a novel approximation method validated against analytical solutions.

Findings

Model accurately predicts polymerization behavior

Novel approximation method shows perfect agreement with analytical solutions

Provides comprehensive multidimensional results for complex polymerization processes

Abstract

A deterministic mathematical model for the polymerization of hyperbranched molecules accounting for substitution, cyclization, and shielding effect has been developed as a system of nonlinear population balances. The solution obtained by a novel approximation method shows perfect agreement with the analytical solution in limiting cases and provides, for the first time in this class of polymerization problems, full multidimensional results.