A theory for the flow of chemically-responsive polymer solutions: equilibrium and shear-induced phase separation

TL;DR

This paper develops a comprehensive theory for chemically-responsive polymer solutions, predicting equilibrium and shear-induced phase separation driven by solute-polymer interactions, with implications for biological and smart material systems.

Contribution

It introduces a novel modeling framework using Onsager's formalism that captures the coupling between solute distribution and polymer conformation changes, including phase separation phenomena.

Findings

Predicts equilibrium phase separation in polymer-solute mixtures.

Identifies shear-induced phase separation under flow conditions.

Demonstrates the importance of solute-polymer interactions in rheological behavior.

Abstract

Chemically-responsive polymers are macromolecules that respond to local variations of the chemical composition of the solution by changing their conformation, with notable examples including polyelectrolytes, proteins and DNA. The polymer conformation changes can occur in response to changes to the pH, the ionic strength or to the concentration of a generic solute that interacts with the polymer. These chemical stimuli can lead to drastic variations of the polymer flexibility and even trigger a transition from a coil to a globule polymer conformation. In many situations the spatial distribution of the chemical stimuli can be highly inhomogeneous, which can lead to large spatial variations of polymer conformation and of the rheological properties of the mixture. In this paper, we develop a theory for the flow of a mixture of a solute and chemically-responsive polymers. The approach is valid for generic flows and inhomogeneous distributions of polymers and solutes. To model the polymer conformation changes introduced by the interactions with the solute, we consider the polymers as linear elastic dumbbells whose spring stiffness depends on the solute concentration. We use the Onsager's variational formalism to derive the equations governing the evolution of the variables, which unveils novel couplings between the distribution of dumbbells and that of the solute. Finally, we use a linear stability analysis to show that the governing equations predict an equilibrium phase separation and a distinct shear-induced phase separation whereby a homogeneous distribution of solute and dumbbells spontaneously demix. Similar phase transitions have been observed in previous experiments using stimuli-responsive polymers and may play an important role in living systems.