Theory of Elastic Microphase Separation

TL;DR

This paper presents a theoretical model explaining elastic microphase separation in gels, linking pattern formation to nonlocal elasticity and predicting how pattern period depends on material properties.

Contribution

It introduces a combined model of phase separation and nonlocal elasticity to explain experimental observations of pattern formation in elastic gels.

Findings

Pattern period is determined by the geometric mean of elasto-capillary and microscopic lengths.

The model predicts a continuous phase transition from homogeneous to patterned states.

Nonlocal elasticity is crucial for understanding microphase separation in soft materials.

Abstract

Elastic microphase separation refers to equilibrium patterns that form by phase separation in elastic gels. Recent experiments revealed a continuous phase transition from the homogeneous phase to a regularly patterned phase, whose period decreased for stiffer systems. We here propose a model that captures these observations. The model combines a continuous field of the elastic component to describe phase separation with nonlocal elasticity theory to capture the gel's microstructure. Analytical approximations unveil that the pattern period is determined by the geometric mean between the elasto-capillary length and a microscopic length scale of the gel. Our theory highlights the importance of nonlocal elasticity in soft matter systems, reveals the mechanism of elastic microphase separation, and will improve the engineering of such systems.