We study the onset of clustering in low concentration fluids with competing short-range attractive and long-range repulsive (SALR) interactions. Our focus is on cluster fluids consisting of a dispersion of large, liquid-like droplets within a low-density background vapour. While it is known that large clusters can form for sufficiently strong attractive interactions as the particle density is increased, there is some uncertainty about the nature of this transition. Early grand canonical Monte Carlo (GCMC) simulations and Percus-Yevick (PY) integral equation results indicated that the transition can be first-order for sufficiently strong attractive interactions, whereas later work using a density functional theory model suggests instead that the transition is always continuous and similar to micelle formation in surfactant solutions. Here, we use integral equation methods to study this issue. We find that this transition is probably continuous and that earlier predictions that it can be discontinuous are likely caused by artifacts of the PY closure and finite-size simulation effects. However, further large-scale simulations are needed to confirm this. This insight could have repercussions for our understanding of the behaviour of many microphase forming systems.
Sweatman et al. (Mon,) studied this question.