# Polymerization of Branched Polyetherimides: Comparison between Monte Carlo Simulation and Flory-Stockmayer Theory

## TL;DR

This study develops a Monte Carlo simulation method to model the polymerization of branched polyetherimides and compares its predictions with Flory-Stockmayer theory, highlighting the conditions under which each method is accurate.

## Contribution

The paper introduces a Monte Carlo simulation approach based on the Gillespie algorithm for branched polyetherimide polymerization and compares its accuracy to Flory-Stockmayer theory across different system states.

## Key findings

- MC simulation accurately predicts molecular weight distribution below gel point.
- Flory-Stockmayer theory fails near or above gel point.
- MC simulations are computationally efficient for small systems with large-scale implications.

## Abstract

A Monte Carlo (MC) simulation method based on the Gillespie algorithm is developed for the polymerization of branched polyetherimides from two back-bone monomers [4,4'-bisphenol A dianhydride (BPADA) and m-phenylenediamine (MPD)], a chain terminator [phthalic anhydride (PA)], and a branching agent [tris[4-(4-aminophenoxy)phenyl] ethane (TAPE)]. This polymerization involves 4 reactions that all can be reduced to a condensation reaction between an amine group and a carboxylic anhydride group. By comparing the MC simulation results to the predictions of the Flory-Stockmayer theory on the molecular weight distribution, we show that the rates of the 4 reactions in the MC simulations should be set based on the concentrations of the functional groups on the monomers involved in each reaction. Using the MC simulations, we show that the Flory-Stockmayer theory predicts the molecular weight distribution well for systems below the gel point that is set by the functionality of the branching agent but starts to fail for systems around or above the gel point. However, for all the systems the MC simulations can be used to reliably predict the molecular weight distribution. Even for a macroscopic system, a converging distribution can be quickly obtained through the MC simulations on a system of only a few hundred to a few thousand monomers but with the same molar ratios of monomers as in the macroscopic system.