Pair Interaction of Catalytically Active Colloids: From Assembly to Escape

Abstract

The dynamics and pair trajectory of two self-propelled colloids are reported. The autonomous motions of the colloids are due to a catalytic chemical reaction taking place asymmetrically on their surfaces that generates a concentration gradient of interactive solutes around the particles and actuate particle propulsion. We consider two spherical particles with symmetric catalytic caps extending over the local polar angles $θ^1_{cap}$ and $θ^2_{cap}$ from the centers of active sectors in an otherwise quiescent fluid. A combined analytical-numerical technique was developed to solve the coupled mass transfer equation and the hydrodynamics in the Stokes flow regime. The ensuing pair trajectory of the colloids is controlled by the reacting coverages $θ^j_{cap}$ and their initial relative orientation with respect to each other. Our analysis indicates two possible scenarios for pair trajectories of catalytic self-propelled particles: either the particles approach, come into contact and assemble or they interact and move away from each other (escape). For arbitrary motions of the colloids, it is found that the direction of particle rotations is the key factor in determining the escape or assembly scenario. Based on the analysis, a phase diagram is sketched for the pair trajectory of the catalytically active particles as a function of active coverages and their initial relative orientations. We believe this study has important implications in elucidation of collective behaviors of auotophoretically self-propelled colloids.