Verification of Perrin's theory of the motion of dilute spheroidal colloids

Brownian motion is of central importance for understanding diffusive transport in biology, chemistry, and physics. For spherical particles, the theory was developed by Einstein, whereas a theoretical description of the motion of spheroids was given by F. Perrin. Here, we report the systematic verification of Perrin's theory 90 years after its publication. To this end, we synthesized oblate and prolate core-shell spheroids with different aspect ratios and tracked their three-dimensional diffusive motion in high dilution using confocal fluorescence microscopy. The experimental data for the dependence of translational and rotational diffusion on aspect ratio are in excellent agreement with the theoretical predictions. The crossover dynamics from anisotropic to isotropic diffusion as a hallmark for translation rotation coupling are also found as predicted. This verifies Perrin's theory as a cornerstone for understanding diffusive transport and underlines the excellent suitability of the particle system for testing more detailed theory.