The self-assembly of finite clusters of colloidal particles into crystalline objects is a topic of technological interest, as a route to produce photonic crystals and other meta-materials. Such assembly problems are also of fundamental scientific interest because they involve thermodynamically small systems, with number of particles (10 – 1000) that is far below the bulk limit. The assembly methods include the use of thermodynamic variables (e.g. temperature, depletant concentration) or external fields as actuators, to tune the level of interparticle attraction. The phase behavior of these small clusters is qualitatively different from typical behavior observed in bulk systems. For example, at a fixed temperature a small cluster may exhibit coexistence between fluid-like and solid-like phases over a range of osmotic pressure values, rather than at a single value. In this paper we report the phase behavior of thermodynamically small colloidal clusters interacting via the Asakura-Oosawa depletion pair potential.
To quantify the phase behavior, we have conducted Monte Carlo simulations of these small colloidal clusters and generated potential energy histograms for various levels of the osmotic pressure that controls the strength of the interactions. We have used potential energy as the histogram variable to identify the fluid-like and solid-like phases. By carefully tuning the osmotic pressure, we observed bimodal distributions in the potential energy space that is indicative of coexistence between fluid-like and solid-like configurations. We report comparisons of phase behavior for these colloidal clusters obtained from the thermodynamic approach outlined here with previous results from a Fokker-Planck order parameter approach and also investigate the differences with phase diagrams of their bulk counterparts.