Coupling between the translational and rotational brownian motions of rigid particles of arbitrary shape I. Helicoidally isotropic particles

It is demonstrated that coupling exists between the translational and rotational Brownian movements of rigid macroscopic particles possessing screwlike geometric properties. The theory is developed for the case of helicoidally isotropic particles, these being the class of bodies for which the theory adopts its most elementary form. In addition to the classical translational and rotational diffusion coefficients characterizing the intensity of the Brownian motion, it is shown that there exists yet a third independent pseudoscalar diffusivity, which quantitatively describes the degree of coupling. The cross-effect associated with this coupling coefficient manifests itself by the appearance of cross-terms in the expressions for the components of the diffusion flux vector in a six-dimensional “configuration” space when projected onto its respective three-dimensional physical and orientation subspaces.