# Beyond Flory’s principle: Cyclization and unequal reactivity in step-growth linear polymerization

## TL;DR

This paper improves the classical Flory model for polymerization by incorporating unequal reactivity and cyclization, offering better predictions and control over polymer structures.

## Contribution

The paper introduces a refined Flory model with individual reaction probabilities and cyclization, along with a top-down algorithm to decode polymer growth from molecular weight data.

## Key findings

- The extended Flory model accounts for unequal functional group reactivity and cyclization in step-growth polymerization.
- A top-down algorithm was developed to extract polymer growth and cyclization information from molecular weight data.
- The model reveals how concentration influences polymerization kinetics and provides insights for controlling polymer structures.

## Abstract

Step-growth polymerization (SGP) products are ubiquitous, but the theoretical understanding of SGP reactions has stagnated since the introduction of Flory’s classical theory. Flory’s model based on two key assumptions—equal reactivity of functional groups and the absence of cyclization—falls short in guiding real-world polymerization processes. In this work, we extend Flory’s model by accounting for individual reaction probabilities and cyclization tendencies, making it applicable to real SGP situations. Moreover, we have developed a top-down algorithm capable of extracting crucial information about polymer growth and cyclization from molecular weight data during the SGP process. By applying this expanded model to real SGP experiments, we reveal their kinetic mechanisms and demonstrate how concentration affects polymerization kinetics, offering valuable insights for predicting and controlling the polymer structure.

Flory’s model was refined by including reactivity and cyclization and decodes polymer growth kinetics from molecular weight.