Volume-shrinking kinetics of transient gels as a consequence of dynamic interplay between phase separation and mechanical relaxation

Abstract

Gels are very important states of matter in our life and can be classified into three types: chemical, stable physical, and transient gels. The first two are formed by the percolation of chemical and physical bonds, respectively, and practically have an infinite lifetime, meaning that they have nonzero static shear moduli and behave as soft solids. On the other hand, the last one is formed only transiently during demixing of a dynamically asymmetric mixture composed of large (slow) and small (fast) components. It emerges as a transient percolated network of the large components, and accordingly it has a finite lifetime (or, it eventually behaves as a liquid). Although the states of chemical and physical gels are reasonably well understood, the physical understanding of transient gelation has remained very poor; for example, a mechanical boundary condition originating from transient elasticity has not been considered before. The fundamental difficulty originates from the fact that transient gelation is a dynamically evolving nonequilibrium process as a consequence of complex dynamical interplay between phase separation and mechanical relaxation (or rheology), but there is no reliable theory for the rheology of a nonequilibrium system. To overcome this difficulty and elucidate the physical essence of transient gelation, we combine experimental and theoretical approaches to study the volume-shrinking kinetics of a transient gel and compare it with that of a permanent chemical gel undergoing a volume phase transition. We reveal that the volume-shrinking behavior of a transient gel is fundamentally different from that of a chemical gel. A permanent gel has static elasticity coming from its permanent network topology. In contrast, a transient gel is formed by hierarchical structure formation (polymers $\ensuremath{\rightarrow}$ globules $\ensuremath{\rightarrow}$ percolated network) and is stabilized only by weak van der Waals bonding between globules, and thus it does not have static elasticity and its elasticity decays with time: viscoelastic relaxation. This relaxational feature leads to the switching of the relevant order parameter during phase separation in the order of scalar (composition), tensors (volume and shear deformations), and scalar (composition). Depending on the relation of the deformation rate generated by phase separation itself to the bulk and shear mechanical relaxation rates, a transient network behaves liquid-like, viscoelastic, and elastic; leading to liquid-like, ductile, and brittle fracture of the network during shrinking, respectively. We also find that the emergence of elasticity during transient gelation is the reverse of its disappearance and there is a one-to-one correspondence between them, strongly indicating the key role of viscoelastic relaxation in transient gelation. We argue that these basic features should be generic to any demixing-induced transient gels of soft matter, including polymer solutions, colloidal suspensions, emulsions, and biological solutions such as protein solutions. Our finding not only sheds new light on the physical nature of this intrinsically nonequilibrium transient state of matter but also provides the physical basis for demixing of soft- and bio-matter.