Bond flexibility and low valence promote finite clusters of self-aggregating particles

Systems of complex particles such as proteins or colloidal particles have a widely observed tendency to form nonconnected nanometer-size clusters at steady state, but the underlying mechanisms remain poorly understood. We report here a numerical study on the self-aggregation of low-valence particles with flexible bonds (i.e., free bond orientations) in two dimensions and predict the formation of a stable cluster phase for average valences ranging from 2 to 3.6. For the intermediate case of trivalent particles, we show that a cluster phase is present over a wide range of concentrations and interaction energies. The clusters are polydisperse in size, have a fractal dimension of 1.5, and tend to fully saturate their bonds at high interaction energies. The number of unformed bonds scales linearly with the number of particles in a cluster, which implies the absence of phase transition in the explored region of interaction energies and concentrations. We discuss possible implications of our model for membrane protein clustering.