Theory of chemically driven pattern formation in phase-separating liquids and solids

TL;DR

This paper develops a theoretical framework combining reaction kinetics and diffusive transport to analyze pattern formation in driven phase-separating systems, with applications to energy materials and biological processes.

Contribution

It introduces a generalized model extending Cahn-Hilliard and Allen-Cahn equations to include chemical reactions and chemo-mechanical coupling, predicting conditions for phase separation control.

Findings

Driven autoinhibitory reactions suppress phase separation at high reaction rates and low diffusivity.

Autocatalytic reactions promote phase separation.

Model predictions align with numerical simulations and are applicable to energy and biological systems.

Abstract

Motivated by recent experimental and theoretical work on the control of phase separation by (electro-)autocatalytic reactions, we analyze pattern formation in externally driven phase separating systems described by a generalization of the Cahn-Hilliard and Allen-Cahn equations combining nonlinear reaction kinetics with diffusive transport. The theory predicts that phase separation can be suppressed by driven autoinhibitory reactions when chemically driven at a sufficiently high reaction rate and low diffusivity, while autocatalytic reactions enhance phase separation. Analytical stability criteria for predicting the critical condition of suppressed phase separation based on linear stability analysis track the history dependence of pattern formation and agree well with numerical simulations. By including chemo-mechanical coupling in the model, we extend the theory to solids, where coherency strain alters the morphology and dynamics of driven phase separation. We apply this model to lithium iron phosphate nanoparticles and simulate their rate-dependent electrochemical charging and discharging patterns, paving the way for a quantitative understanding of the effect of reaction kinetics, diffusion, and mechanics on the electrochemical performance of energy materials. The theory may also find applications to microstructure formation in hardening cement paste, as well as membraneless organelle formation in biological cells by chemically controlled liquid-liquid phase separation.