Non-crystalline colloidal clusters in two dimensions: Size distributions and shapes

Cluster formation in many-body systems is very common, yet still not fully understood. We employ direct confocal microscopy to measure the size distribution and reconstruct the shapes of permanent gel clusters formed by sticky colloidal spheres in a two-dimensional (2D) suspension; the linear dimensions of the clusters are then measured by their radii of gyration R _g. We compare these non-ergodic clusters with the short-lived clusters, which reversibly form and deform, in a thermodynamically-equilibrated system of spherical colloids which interact solely by repulsions. Surprisingly, a similar behavior is observed for both types of clusters. In both cases, the average R _g of large clusters consisting of M particles scales as 〈R _g〉 ∼ M ^1/2, which indicates that these clusters are solid, while the smaller clusters are much more ramified. A simple lattice model with a single free parameter quantitatively describes this complex behavior of 〈R _g(M)〉. The experimental size distribution P(M) of our clusters is a (truncated) power law M ^-α, where the index α scales with colloid density and depends on the interparticle interactions. Strikingly, the observed behavior cannot be described by the common theoretical models which predict shorter correlation lengths and a density-independent value of α; thus, further theoretical efforts are necessary to fully understand the physics of clustering in this simple and fundamental system.