Brownian motion is the random motion of (colloidal) particles due to collisions with the atoms and molecules of the solvents, which are moving due to temperature.

An arbitrary anisotropic particle will undergo Brownian motion along (translational) or around (rotational) its major axes, as well as motion that couples translational and/or rotational motion (e.g. translational motion in x direction is coupled to a rotation around the z axis).

By using anisotropic colloidal particles assembled from fluorescent, spherical PMMA beads, we can track and analyze their position and orientation in 3D using confocal microscopy.

The movies below are 2D projections of the 3D data of the motion of a triangular particle.

From this data we can extract the diffusion constant matrix, or - by dividing out temperature and solvent viscosity - the hydrodynamic friction matrix H using a short time expansion of the Langevin equation. It contains the full, shape-dependent information of the Brownian motion of the anisotropic colloidal particle!