Collective dynamics and self-assembly of calcium-alginate motors of varying sizes

Self-propelling calcium-alginate motors exhibit complex interactions driven by attractive capillary and repulsive Marangoni forces, yet how motor size influences their collective dynamics remains unclear. Here we experimentally investigate the size-dependent oscillatory collisions, synchronization, and self-assembly of calcium-alginate motors ranging from two to fifteen units. Using high-speed imaging and a particle-based model incorporating pairwise interactions, we reveal that smaller motors sustain longer oscillations, while larger motors coordinate the motion of smaller ones, leading to vibrational-like dynamics. Assemblies of eight or more motors form clusters characterized topologically by Betti numbers, reflecting evolving connectivity and voids. Our findings elucidate how size-dependent forces govern the emergent spatiotemporal patterns and self-organization of active polymer motors, providing insights for designing intelligent collective systems with potential applications in micro-actuation and soft robotics.