# Flory-Huggins theory for the solubility of heterogeneously-modified polymers

## TL;DR

This paper develops a Flory-Huggins model to understand how heterogeneity in chemical modification affects the solubility of water-soluble polymers, revealing that increased heterogeneity decreases solubility and can lead to phase separation.

## Contribution

It introduces a theoretical model to analyze the impact of heterogeneity in polymer modification on solubility, including the transition to polymer-polymer demixing at high blockiness.

## Key findings

- Heterogeneity decreases polymer solubility.
- Increased blockiness enhances phase separation.
- Extreme blockiness causes polymer-polymer demixing.

## Abstract

Many water soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is found that heterogeneity leads to decreased solubility, with the effect increasing with increasing blockiness. In the limit of extreme blockiness, the nature of the phase coexistence crosses over to a polymer-polymer demixing transition. Some consequences are discussed for the synthesis of partially modified polymers, and the experimental characterisation of such systems.