Lattices by design: exploring long-ranged interactions with gradient sensing droplets

Many body interactions are ubiquitous and occur across length scales, giving rise to a vast diversity of phenomena ranging from frustration to pattern formation with important implications for the design of new materials. However, their behavior can be challenging to predict since the number of relevant configurations scales exponentially with the number of particles. Two-component Marangoni-contracted droplets have been shown to interact via long-ranged vapor mediated attractions, resulting in a dynamic behavior that resembles chemotaxis and a capacity to self-organize. Meanwhile, hydrophobic barriers can create well-defined potential energy wells that are impassable to droplets but transparent to a vapor gradient landscape. Here, we develop exotic lattice systems that exploit the tools of photolithography to fabricate arbitrary patterns of hydrophobic boundaries, enabling us to experimentally manipulate the geometry in which long-ranged degrees of freedom interact. The macroscopic nature of this system provides real time access to microstate configurations, providing the opportunity for mechanistic insights and the development of control strategies in complex, interacting systems.