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Attractive colloidal gels exhibit solid-like behavior at vanishingly smallfractions of solids, owing to ramified space-spanning networks that form due toparticle-particle interactions. These networks give the gel its rigidity, andas the attraction between the particles grows, so does the elasticity of thecolloidal network formed. The emergence of this rigidity can be describedthrough a mean field approach; nonetheless, fundamental understanding of howrigidity varies in gels of different attraction strengths is lacking. Moreover,recovering an accurate gelation phase diagram based on the system's variableshave been an extremely challenging task. Understanding the nature of thesefractal clusters, and how rigidity emerges from their connections is key tocontrolling and designing gels with desirable properties. Here, we employwell-established concepts of network science to interrogate and characterizethe network of colloidal gels. We construct a particle-level network, havingall the spatial coordinates of colloids with different attraction levels, andalso identify polydisperse rigid fractal clusters using a Gaussian MixtureModel, to form a coarse-grained cluster network that distinctly shows mainphysical features of the colloidal gels. A simple mass-spring model then isused to recover quantitatively the elasticity of colloidal gels from thesecluster networks. Interrogating the resilience of these gel networks show thatthe elasticity of a gel (a dynamic property) is directly correlated to itscluster network's resilience (a static measure). Finally, we use the resilienceinvestigations to devise [and experimentally validate] a fully resolved phasediagram for colloidal gelation, with a clear solid-liquid phase boundary usinga single volume fraction of particles well beyond this phase boundary.

Network physics of attractive colloidal gels: Resilience, Rigidity, and Phase Diagram