Translational and rotational Brownian displacements of colloidal particles of complex shapes
The exact analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape were derived by us in [J. Chem. Phys. 142, 214902 (2015) and 144, 076101 (2016)]. They are in this work applied to construct a method to analyze Brownian motion of a particle of an arbitrary shape, and to 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 of D. J. Kraft et al. for the micrometer-sized aggregates of the beads [Phys. Rev. E 88, 050301 (R) (2013)]. We explicitly demonstrate that our procedure, based on the measurements of the time-dependent cross-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 method based only on their initial slopes. Therefore, the analytical time-dependence of the cross-correlations serves as a useful tool to extract information about particle structure from trajectory measurements.