# Swelling thermodynamics and phase transitions of polymer gels

## TL;DR

This paper reviews the thermodynamics and phase transitions of polymer gels, highlighting how shear rigidity influences phase behavior and introduces the concept of extreme thermodynamics for large shape changes.

## Contribution

It provides a comprehensive analysis of gel phase transitions, emphasizing the role of shear rigidity and introducing the novel concept of extreme thermodynamics for shape change.

## Key findings

- Volume phase transition resembles mean-field binary mixture models
- Shear rigidity causes failure of analogy at critical point
- Phase separation can induce macroscopic shape change

## Abstract

We present a pedagogical review of the swelling thermodynamics and phase transitions of polymer gels. In particular, we discuss how features of the volume phase transition of the gel's osmotic equilibrium is analogous to other transitions described by mean-field models of binary mixtures, and the failure of this analogy at the critical point due to shear rigidity. We then consider the phase transition at fixed volume, a relatively unexplored paradigm for polymer gels that results in a phase-separated equilibrium consisting of coexisting solvent-rich and solvent-poor regions of gel. Again, the gel's shear rigidity is found to have a profound effect on the phase transition, here resulting in macroscopic shape change at constant volume of the sample, exemplified by the tunable buckling of toroidal samples of polymer gel. By drawing analogies with extreme mechanics, where large shape changes are achieved via mechanical instabilities, we formulate the notion of extreme thermodynamics, where large shape changes are achieved via thermodynamic instabilities, i.e. phase transitions.