Extended Data Fig. 10: Scaled diffusion coefficient for edgewise translational motion of a flake composed of a conglomerate of spheres arranged on a regularly shaped hexagon in an unbounded (bulk) fluid or close to a planar hard wall.

a, Comparison between the Rotne–Prager approximation employed in the present work (red squares) and the bulk diffusion coefficients obtained using the open-source software HYDROLIB (blue circles). b, The predictions for the scaled diffusion coefficient are obtained by using the Rotne–Prager approximation combined with the Blake solution for hydrodynamic interactions between the spheres near a hard wall. Three flake sizes of aspect ratio 16, 20, and 35 are considered, which correspond to total numbers of spheres of 817, 1261, and 3781, respectively. Horizontal dashed lines correspond to the scaled diffusion coefficient in an unbounded fluid medium, that is, in the absence of the confining wall given by the substrate. c, Hydrodynamic simulations of a regular hexagon with various particle sizes: simulated diffusion constant D for hexagonal particles with side length a = 700, 840, 1000, 1450 nm depending on their distance to the surface h. Solid lines represent the fitting of the simulation data. See Supplementary Information Section IV for additional details.