Non-equilibrium Theory of Arrested Spinodal Decomposition

TL;DR

This paper applies a non-equilibrium theory to describe spinodal decomposition in deeply quenched liquids, predicting a complex interplay between phase separation, glass transitions, and gel formation.

Contribution

It extends the non-equilibrium self-consistent Langevin equation theory to predict the relationship between spinodal decomposition, ergodicity breaking, and glass transitions in model liquids.

Findings

Spinodal curve marks the boundary between ergodic and non-ergodic states.

Glass-glass transition line intersects the spinodal curve at lower temperatures.

Two distinct domains are identified: phase separation and gel formation.

Abstract

The Non-equilibrium Self-consistent Generalized Langevin Equation theory of irreversible relax- ation [Phys. Rev. E (2010) 82, 061503; ibid. 061504] is applied to the description of the non- equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermo- dynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass tran- sition and from above by the spinodal dynamic arrest line we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the for- mation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.