The single-particle dynamics of square platelets on an inner spherical surface

The diffusion of colloidal particles on curved surfaces is crucial for understanding mass transport in a wide range of biological and physical systems. To date, most experimental studies on colloid diffusion on curved surfaces have focused on the behavior of isotropic colloids diffusing on soft oil-water interfaces. However, there has been no experimental work reported on how anisotropic colloids diffuse on hard spherical surfaces.

Herein, we report a first experimental study of the single-particle dynamics of micro-sized Brownian square platelets on solid spherical surfaces with four different curvatures. Utilizing video microscopy and particle-tracking techniques, we investigated both the translational and rotational motion of the square platelets. An analytical model based on Smoluchowski equations was developed to explain the observed diffusion behaviors.

The translational motion of the square platelets was found to be sub-diffusive at time scales comparable to their relaxation time, with the power-law exponent of the mean square displacement (MSD) decreasing as the curvature increased. In contrast, the rotational diffusion of the platelets exhibited minimal variation with changes in curvature. The developed analytical model based on Smoluchowski equations could explain the observations in both translational and rotational diffusion, highlighting the crucial role of surface geometry in determining the diffusion dynamics. This research provides new insights into the diffusion of anisotropic particles on hard spherical curved surfaces, which will pave the way for understanding mass transport problems on curved surfaces in various fields.