Effect of self-propulsion on equilibrium clustering

In equilibrium, colloidal suspensions governed by short-range attractive and long-range repulsive interactions form thermodynamically stable clusters. Using Brownian dynamics computer simulations, we investigate how this equilibrium clustering is affected when such particles are self-propelled. We find that the clustering process is stable under self-propulsion. For the range of interaction parameters studied and at low particle density, the cluster size increases with the speed of self-propulsion (activity) and for higher activity the cluster size decreases, showing a nonmonotonic variation of cluster size with activity. This clustering behavior is distinct from the pure kinetic (or motility-induced) clustering of self-propelling particles which is observed at significantly higher activities and densities. We present an equilibrium model incorporating the effect of activity as activity-induced attraction and repulsion by imposing that the strength of these interactions depend on activity superlinearly. The model explains the cluster size dependence of activity obtained from simulations semiquantitatively. Our predictions are verifiable in experiments on interacting synthetic colloidal microswimmers.