Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

Joep Rouwhorst,Peter Schall,Alessio Zaccone,Simeon Stoyanov,Christopher Ness

doi:10.1038/s41467-020-17353-8

Abstract

The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents ~1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents −3/2 and −5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.

Highlights

The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking
At effective interparticle attractions of many kBT, the thermal energy, the detailed balance in the particle attachment and detachment processes is broken, and the system falls out-of equilibrium; in this case, a description based on an underlying equilibrium phase diagram may no longer apply
This regime, which is most relevant for biological network formation, is often modeled by cluster kinetic equations, but there is no theory that describes the formation of these out-of-equilibrium structures and that is able to explain or predict, from first-principles, the fractal dimension of the growing clusters, and its relation to the cluster-mass distribution

Summary

Introduction

The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. At effective interparticle attractions of many kBT, the thermal energy, the detailed balance in the particle attachment and detachment processes is broken, and the system falls out-of equilibrium; in this case, a description based on an underlying equilibrium phase diagram may no longer apply This is demonstrated by a recent experimental study on the intermittent dynamics of colloidal gels[18], revealing a marked asymmetry in the cooperative bonding and de-bonding processes. Recent two-dimensional simulations suggest that the jamming of attractive spheres falls into a distinct universality class[21]: the continuous growth of clusters is reminiscent of a continuous phase transition with a diverging length scale, different from the more familiar repulsive jamming Such framework of critical phenomena has been sought as a possible connection between physical, colloidal, and chemical gelation, as it would offer a unifying description[22,23]. All approaches uniquely converge to show that the observed short-range attractive colloidal gelation is related to a nonequilibrium second-order phase transition, with critical exponents of cluster growth in agreement with percolation theory

Methods

Results

Conclusion