Nanoscale or colloidal particles are important in many realms of science and technology. They can dramatically change the properties of materials, imparting solid-like behaviour to a wide variety of complex fluids1,2. This behaviour arises when particles aggregate to form mesoscopic clusters and networks. The essential component leading to aggregation is an interparticle attraction, which can be generated by many physical and chemical mechanisms. In the limit of irreversible aggregation, infinitely strong interparticle bonds lead to diffusion-limited cluster aggregation3 (DLCA). This is understood as a purely kinetic phenomenon that can form solid-like gels at arbitrarily low particle volume fraction4,5. Far more important technologically are systems with weaker attractions, where gel formation requires higher volume fractions. Numerous scenarios for gelation have been proposed, including DLCA6, kinetic or dynamic arrest4,7,8,9,10, phase separation5,6,11,12,13,14,15,16, percolation4,12,17,18 and jamming8. No consensus has emerged and, despite its ubiquity and significance, gelation is far from understood—even the location of the gelation phase boundary is not agreed on5. Here we report experiments showing that gelation of spherical particles with isotropic, short-range attractions is initiated by spinodal decomposition; this thermodynamic instability triggers the formation of density fluctuations, leading to spanning clusters that dynamically arrest to create a gel. This simple picture of gelation does not depend on microscopic system-specific details, and should thus apply broadly to any particle system with short-range attractions. Our results suggest that gelation—often considered a purely kinetic phenomenon4,8,9,10—is in fact a direct consequence of equilibrium liquid–gas phase separation5,13,14,15. Without exception, we observe gelation in all of our samples predicted by theory and simulation to phase-separate; this suggests that it is phase separation, not percolation12, that corresponds to gelation in models for attractive spheres.
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P.J.L. thanks D. Maas, M. Christiansen and S. Raghavachary for assistance in producing the renderings and movies. This work was supported by NASA, the NSF, the Harvard MRSEC, MIUR-Prin and the Marie Curie Research and Training Network on Dynamical Arrested States of Soft Matter and Colloids.
Three dimensional reconstruction (56x56x56μm3) of a typical fluid phase sample, here with ø=0.045, ξ=0.059, and cp=3.20 mg/mL, also illustrated in Fig. 1c. The structure is a snapshot of a single configuration in time, in the long-time steady-state limit, rotating to demonstrate that the clusters are small (fewer than fifty particles) and do not span the sample. The fluid’s clusters are colored by their mass s (number of particles) according to the color bar, with monomers and dimers rendered in transparent grey.
Early-time evolution of a gel sample with ø=0.045, ξ=0.059 and cp=3.31 mg/mL, also illustrated in Fig. 1d. Time elapsed after mixing indicated by the counter in the upper left. Three-dimensional reconstruction (56x56x56μm3) shown at left, with a two-dimensional confocal microscope image at upper right. The static structure factor S(q) is shown as a function of scattering vector q at lower right. Clusters are colored by their mass, as in Figs. 1c-d and Supplementary Video 1. After mixing, the sample undergoes spinodal decomposition. Clusters in the sample grow, manifest in S(q) as the growth and narrowing of a peak, which moves to lower q as a function of time. After two hours, all clusters have merged into a single spanning cluster that arrests, forming a gel. The peak in S(q) no longer evolves, and while the spanning cluster fluctuates thermally and exchanges monomers with a sparse colloidal gas phase, no significant structural arrangements occur.
Long-time evolution of the gel sample at ø=0.045 and ξ=0.059 and cp=3.31 mg/mL, also illustrated in Fig. 1d and Supplementary Video 2. Time elapsed after mixing indicated by the counter in the upper left. Three-dimensional reconstruction (56x56x56μm3) shown at left, with two-dimensional confocal microscope image at upper right. The gel is in the steady state: the structure remains essentially unchanged throughout the entire 100,000 second observation period, even as the spanning cluster exchanges monomers with the surrounding dilute colloidal gas. This exchange is highlighted in the lower right-hand panel: new gel particles that appear for the first time in a frame are highlighted in green, indicating condensation onto the gel from the gas; monomers that disappear in the subsequent frame are highlighted in red, indicating evaporation from the spanning cluster into the gas phase.
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