Polymer-Like Self-Assembled Structures from Particles with Isotropic Interactions: Dependence upon the Range of the Attraction.

We conduct Metropolis Monte Carlo simulations on models of dilute colloidal dispersions, where the particles interact via isotropic potentials of mean force (PMFs) that display a long-ranged repulsion, combined with a short-ranged and narrow attraction. Such systems are known to form anisotropic clusters. There are two main conclusions from this work. First, we demonstrate that the width of the attractive region has a significant impact on the type of structures that are formed. A narrow attractive well tends to produce clusters in which particles possess fewer neighbors than in systems where the attraction is wider. Second, metastable clusters appear to persist in the absence of specific simulation moves designed to overcome large energy barriers to particle accumulation. The so-called "Aggregation-Volume Bias Monte Carlo" moves were previously developed by Chen and Siepmann, and they facilitate particle exchanges between clusters via unphysical moves that bypass high energy intermediate states. These facilitate the progression of metastable clusters to equilibrium clusters. Metastable clusters are generally large with significant branching of thin filaments of aggregated particles, while stable clusters have thicker backbones and tend to be more compact with significantly fewer particles. This general behavior is observed in both two- and three-dimensional systems. In two dimensions, less anisotropic clusters with backbones possessing lattice structures will occur, particularly for systems where the particles interact with a PMF that has a relatively wide attractive region. We compare our results with PMF calculations established from a more specific model, namely weakly charged polystyrene particles, which carry a thin surface layer of grafted polyethylene oxide polymers in aqueous solution. We hope that our investigations can serve as crude guidelines for experimental research, aiming to construct linear or branched polymers in aqueous solution built up by colloidal monomers that are large enough to be studied by confocal microscopy. We suggest that metastable clusters are more relevant to experimental scenarios where the energetic barriers are too large to be surmounted over typical timescales.