Translational and rotational Brownian displacements of colloidal particles of complex shapes

The exact analytical expressions forthe time-dependent cross-correlationsof the translational and rotational Brownian displacements of a particle with arbi-trary shape were derived by us in [3, 4]. They are in this work applied to constructa method to analyze the Brownian motion of a particle of an arbitrary shape, andto extract accurately the self-diffusion matrix from the measurements of the cross-correlations, which in turn allows to gain some information on the particle structure.As an example, we apply our new method to analyze the experimental results ofD. J. Kraftet al.for the micrometer-sized aggregates of the beads [8]. We explicitlydemonstrate that our procedure, based on the measurements ofthe time-dependentcross-correlations in the whole range of times, allows to determine the self-diffusion(or alternatively the friction matrix) with a much higher precision than the methodbased only on their initial slopes. Therefore, the analytical time-dependence of thecross-correlations serves as a useful tool to extract information about particle struc-ture from trajectory measurements.