Equilibrium and non-equilibrium cluster phases in colloids with competing interactions.

The phase behavior of colloids that interact via competing interactions - short-range attraction and long-range repulsion - is studied by computer simulation. In particular, for a fixed strength and range of repulsion, the effect of the strength of an attractive interaction (ε) on the phase behavior is investigated at various colloid densities (ρ). A thermodynamically stable equilibrium colloidal cluster phase, consisting of compact crystalline clusters, is found below the fluid-solid coexistence line in the ε-ρ parameter space. The mean cluster size is found to linearly increase with the colloid density. At large ε and low densities, and at small ε and high densities, a non-equilibrium cluster phase, consisting of elongated Bernal spiral-like clusters, is observed. Although gelation can be induced either by increasing ε at constant density or vice versa, the gelation mechanism is different in either route. While in the ρ route gelation occurs via a glass transition of compact clusters, gelation in the ε route is characterized by percolation of elongated clusters. This study both provides the location of equilibrium and non-equilibrium cluster phases with respect to the fluid-solid coexistence, and reveals the dependencies of the gelation mechanism on the preparation route.