Colloidal Diffusion on Curvature Landscapes

Simple material units arranged in hierarchical structures can exhibit complex emergent properties (e.g. optical, electromagnetic, and thermal). Colloidal particles, a relevant and generalizable subset of reconfigurable materials, can form multifunctional metasurfaces through the cheap and efficient method of self-assembly. Consistently achieving target material structures requires knowledge of the collective particle dynamics that govern the transition between disordered and ordered states during self-assembly. However, this understanding of particle self-diffusion on surfaces is only substantial for the planar and constant-curvature case. In contrast, spatially varying curved surfaces dominate potential use-cases including protein assembly on cell membranes, flexible quantum dot displays, and plasmonic particle assembly. Here, we simulate nearly hard disks constrained to curved surfaces with molecular dynamics to study how curvature affects colloidal dynamics on surfaces of varying curvature up to the freezing criterion. We find that the Euclidean mean-squared displacement of particles on curved surfaces compared to flat surfaces in fluid densities is slower while it is faster past the freezing criterion. Before the freezing criterion, the same self-diffusivity, D_L, of planes can be found on curved surfaces by accounting for curvature using local planar approximations to adjust the slower surfaced averaged diffusion value, D_SA. For denser systems, we found that defect density increases with surface curvature, and areas of high defect density have particularly mobile particles that drive diffusion in these systems compared to similarly dense flat surfaces. We demonstrate that curvature does not intrinsically affect dynamics until freezing and surface curvature adds another surface averaged diffusion, D_SA, regime to the typical model of short time, D₀, and long time, D_L employed on planes. Particle diffusion rates determine how assemblies behave and reconfigure between states, making our findings on these processes critical to designing more adaptable materials.