# A Theoretical Investigation of the Polyaddition of an AB2+A2+B4 Monomer Mixture

## TL;DR

This paper presents a theoretical model to predict how the composition of a monomer mixture affects the properties of hyperbranched polymers formed through polyaddition.

## Contribution

A new structural kinetic model is introduced to predict polymerization outcomes in AB2+A2+B4 monomer mixtures, including gel point and branching.

## Key findings

- The model accurately predicts the gel point (pg) with up to 80% AB2 monomer content.
- The influence of monomer composition and substitution effects on polymer characteristics is quantified.
- An empirical formula for pg is proposed, combining Flory's equation with new parameters.

## Abstract

Hyperbranched polymers (HBPs) are widely applied nowadays as functional materials for biomedicine needs, nonlinear optics, organic semiconductors, etc. One of the effective and promising ways to synthesize HBPs is a polyaddition of AB2+A2+B4 monomers that is generated in the A2+CB2, AA′+B3, A2+B′B2, and A2+C2+B3 systems or using other approaches. It is clear that all the foundational features of HBPs that are manufactured by a polyaddition reaction are defined by the component composition of the monomer mixture. For this reason, we have designed a structural kinetic model of AB2+A2+B4 monomer mixture polyaddition which makes it possible to predict the impact of the monomer mixture’s composition on the molecular weight characteristics of hyperbranched polymers (number average (DPn) and weight average (DPw) degree of polymerization), as well as the degree of branching (DB) and gel point (pg). The suggested model also considers the possibility of a positive or negative substitution effect during polyaddition. The change in the macromolecule parameters of HBPs formed by polyaddition of AB2+A2+B4 monomers is described as an infinite system of kinetic equations. The solution for the equation system was found using the method of generating functions. The impact of both the component’s composition and the substitution effect during the polyaddition of AB2+A2+B4 monomers on structural and molecular weight HBP characteristics was investigated. The suggested model is fairly versatile; it makes it possible to describe every possible case of polyaddition with various monomer combinations, such as A2+AB2, AB2+B4, AB2, or A2+B4. The influence of each monomer type on the main characteristics of hyperbranched polymers that are obtained by the polyaddition of AB2+A2+B4 monomers has been investigated. Based on the results obtained, an empirical formula was proposed to estimate the pg = pA during the polyaddition of an AB2+A2+B4 monomer mixture: pg = pA = (−0.53([B]0/[A]0)1/2 + 0.78)υAB2 + (1/3)1/2([B]0/[A]0)1/2, where (1/3)1/2([B]0/[A]0)1/2 is the Flory equation for the A2+B4 polyaddition, [A]0 and [B]0 are the A and B group concentration from A2 and B4, respectively, and υAB2 is the mole fraction of the AB2 monomer in the mixture. The equation obtained allows us to accurately predict the pg value, with an AB2 monomer content of up to 80%.