Colloidal Diffusion on Curvature Landscapes

Ordered structures of self-assembled colloidal particles can form metasurfaces with exceptional properties (optical, electromagnetic, thermal, etc). Collective particle dynamics govern the transition between disordered and ordered states during self-assembly, and so are crucial for quickly achieving target structures. However, significant characterization has only occurred on planar and constant curvature surfaces, avoiding spatially varying curvature. In contrast, flexible and/or curved surfaces dominate potential use-cases including protein assembly on cell membranes, flexible quantum dot displays, and plasmonic particle assembly. Here, we study how curvature affects colloidal dynamics on surfaces of varying curvature up to the concentrated fluid regime. We simulate spherical colloids with short-range repulsive potentials using Brownian Dynamics from infinite dilution to a dense fluid and measure self-diffusion. We find that the apparently curvature-dependent mean-squared displacement can be accounted for using only local planar approximations, leaving the diffusivity itself independent of curvature up to freezing conditions. Our results demonstrate that curvature does not intrinsically affect dynamics in fluid systems. Understanding these fluid-state dynamics is critically important for guiding any self-assembly process which involves them and so we expect these findings to undergird further simulations of colloidal assemblies which transition between disordered and ordered states.