Driving Frustrated Lattices of Active Droplets

Self-organization is the process by which interacting building blocks arrange themselves into an ordered structure. While there are many examples of self organization, there are no examples which explore the use of external fields to drive self-organizing particles in a geometrically frustrated environment. Here, we explore frustrated self-organization in a novel system comprised of self-propelled droplets. Ensembles of these droplets interact with one another, via a vapor-mediated and long-ranged potential, displaying dynamic behavior that resembles chemotaxis. We present an experiment that confines droplets to hexagonal lattice sites, using gravity to drive the system away from equilibrium. Hence, we study the relationship between single particle dynamics and the statistics of ensemble organization. In this geometrically frustrated environment we observe a phase transition of droplet self-assembly as a function of the driving from equilibrium. Comparison to simulation allows us to connect our experimental results to statistically relevant distributions, thereby connecting observations of single particle dynamics and local accommodation of frustration to statistical physics.