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

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.

Shape anisotropic colloidal particle fabrication using 2-photon polymerization.

HYPOTHESIS: Our ability to dictate the colloid geometry is intimately related to self-assembly. The synthesis of anisotropic colloidal particles is currently dominated by wet chemistry and lithographic techniques. The wet chemical synthesis offers limited particle geometries at bulk quantities. Lithographic techniques, on the other hand, provide precise control over the particle shape, although at lower yields. In this respect, two-photon polymerization (2PP)1 has attracted growing attention due to its ability to automatically fabricate complex micro/nano structures with high resolution. EXPERIMENTS: We manufacture precisely designed colloids with sizes ranging from 1 µm to 10 µm with 2PP and optimize the process parameters for each dimension. Moreover, we study the shape dependent Brownian motion of these particles with video microscopy and estimate their diffusion coefficients. FINDINGS: We observe that increasing the geometrical anisotropy leads to a pronounced deviation from the analytically predicted diffusion coefficient for disks with a given aspect ratio. The deviation is attributed to stronger hydrodynamic coupling with increasing anisotropy. We demonstrate, for the first time, 2PP manufacturing of colloids with tailored geometry. This study opens synthesis of colloidal building blocks to a broader audience with limited access to cleanrooms or wet-chemistry know-how.