[Paper Review] Phase Separation in Soft Matter: Concept of Dynamic Asymmetry

Hajime Tanaka|arXiv (Cornell University)|Jul 5, 2013

Material Dynamics and Properties4 citations

TL;DR

This paper introduces 'dynamic asymmetry'—a key concept in soft matter where differences in component dynamics (e.g., size or glass transition temperature) drive viscoelastic phase separation. It proposes that phase separation patterns emerge from a competition between deformation rate and slowest mechanical relaxation, unifying pattern formation and mechanical instability in soft and glassy materials through a viscoelastic model incorporating concentration, velocity, and stress coupling.

ABSTRACT

Phase separation is a fundamental phenomenon that produces spatially heterogeneous patterns in soft matter. In this Lecture Note we show that phase separation in these materials generally belongs to what we call "viscoelastic phase separation", where the morphology is determined by the mechanical balance of not only the thermodynamic force (interface tension) but also the viscoelastic force. The origin of the viscoelastic force is dynamic asymmetry between the components of a mixture, which can be caused by either a size disparity or a difference in the glass transition temperature between the components. We stress that such dynamic asymmetry generally exists in soft matter. The key is that dynamical asymmetry leads to a non-trivial coupling between the concentration, velocity, and stress fields. Viscoelastic phase separation can be explained by viscoelastic relaxation in pattern evolution and the resulting switching of the relevant order parameter, which are induced by the competition between the deformation rate of phase separation and the slowest mechanical relaxation rate of a system. We also discuss an intimate link of viscoelastic phase separation, where deformation fields are spontaneously generated by phase separation itself, to mechanical instability (or fracture) of glassy material, which is induced by externally imposed strain fields. We propose that all these phenomena can be understood as mechanically-driven inhomogeneization in a unified manner.

Motivation & Objective

• To address the limitation of classical phase separation theories that assume dynamic symmetry between components.
• To explain how dynamic asymmetry—arising from size or Tg differences—alters phase separation dynamics in soft matter.
• To unify the understanding of viscoelastic phase separation, gelation, and mechanical fracture in soft and glassy materials.
• To develop a phenomenological viscoelastic model that captures the coupling between concentration, velocity, and stress fields.
• To establish a framework for mechanically driven inhomogeneization in materials under deformation or phase separation.

Proposed method

• Introduces dynamic asymmetry as a fundamental feature in soft matter, arising from large size or relaxation time disparities between components.
• Develops a viscoelastic model that couples the Cahn-Hilliard equation for concentration evolution with momentum and stress balance equations.
• Incorporates both bulk and shear stress contributions to describe mechanical relaxation in phase-separated systems.
• Uses scaling arguments to relate characteristic timescales of phase separation (τd) and mechanical relaxation (τts) to classify system behavior.
• Applies the model to predict pattern evolution and instability switching, including the role of viscoelastic length scale ξve in nonlocal transport.
• Draws analogy between phase separation and mechanical fracture by comparing the competition between deformation and relaxation rates.

Experimental results

Research questions

• RQ1 How does dynamic asymmetry between components affect phase separation dynamics in soft matter?
• RQ2 What is the role of viscoelastic forces in determining the morphology of phase-separated structures?
• RQ3 How can viscoelastic phase separation be described using a unified model that includes concentration, velocity, and stress fields?
• RQ4 In what way does the competition between deformation rate and mechanical relaxation rate govern pattern evolution?
• RQ5 Can mechanical instability and fracture in glassy materials be understood as part of the same framework as viscoelastic phase separation?

Key findings

• Dynamic asymmetry—caused by size or Tg differences—leads to non-trivial coupling between concentration, velocity, and stress fields, breaking the assumption of dynamic symmetry in classical models.
• Viscoelastic phase separation is governed by the competition between the domain deformation time τd and the slowest mechanical relaxation time τts, leading to switching of the relevant order parameter.
• The viscoelastic model, incorporating both bulk and shear stress, provides a universal description of isotropic phase separation across soft matter, from gels to glasses.
• Phase separation can spontaneously generate deformation fields, which are linked to mechanical instability and fracture in glassy materials under strain.
• The analogy between phase separation and mechanical fracture holds because both are governed by the same rate competition: deformation vs. relaxation.
• The model identifies the viscoelastic length scale ξve as critical for capturing nonlocal transport effects in dynamically asymmetric mixtures, which are not accounted for in standard hydrodynamic models.