Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram

Abstract

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle–particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system’s variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network’s resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid–liquid phase boundary using a single volume fraction of particles well beyond this phase boundary.

Transport coefficient approach for characterizing nonequilibrium dynamics in soft matter

“…Real-time measurements serve as a valuable tool to unravel the kinetics and mechanisms governing these transitions, facilitating improved control and predictability ( 26 , 27 ). Consequently, it becomes imperative to develop robust in situ tools and analysis models that enable us to investigate the dynamic behavior of complex materials ( 28 , 29 ), validate theoretical constructs ( 30 , 31 ), and engineer functional materials for a variety of applications within these soft matter systems.…”

Small variations in particle-level interactions lead to large structural heterogeneities in colloidal gels

“…By comparing colloidal structures formed with [slightly] non-uniform interactions to those with ideally uniform ones, we isolate the influence of spatial interaction variation on the overall gel structure morphology. Previous studies have shown that at the very weak attraction limits of u 0 = 3–4 k B T , inherent structural heterogeneities of the colloidal gels are most visible; 11,26,32,33 however, there also exist inconsistencies between the experimentally observed structures and computationally modeled ones at these limits. Thus, here, we conduct simulations at two average attraction strengths, u 0 = 6 k B T and 12 k B T , representing weak and strong gels.…”

“…6–9 Emergence of elasticity in colloidal gels is believed to be directly governed by the characteristics of their underlying particulate structure. 10–12 Recent work on the characterization of the mesoscale description of colloidal gels shows that the size and inter-connectivity of clusters play a major role in the load-bearing ability of the overall structure. 11 Hence, different factors that change the cluster-level characteristics of the particle network can potentially impact the overall mechanics of the gel.…”

“…15,20–24 While the role of hydrodynamic interactions in large-scale structural heterogeneities and shear-induced structuration of these colloidal networks is quite established, 15,24–27 there remains a significant deviation between the gel structure under the quiescent conditions observed in experiments and that resulted from large scale particle simulations. 11…”