3D rotational diffusion of micrometric wires using 2D video microscopy

Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université Paris Diderot 10, rue A. Domon et L. Duquet, 75205 Paris Cedex 13, France, EU

^a remy.colin@univ-paris-diderot.fr

Received: 16 September 2011
Accepted: 4 January 2012

Abstract

We propose a simple way to measure the three-dimensional rotational diffusion of micrometric wires, using two-dimensional video microscopy. The out-of-plane Brownian motion of the wires in a viscous fluid is deduced from their projection on the focal plane of an optical microscope objective. An angular variable reflecting the out-of-plane motion, and satisfying a Langevin equation, is computed from the apparent wire length and its projected angular displacement. The rotational diffusion coefficient of wires between 1 and 100 μm is extracted, as well as the diameter distribution. Translational and rotational diffusion were found to be in good agreement. This is a promising way to characterize soft visco-elastic materials, and probe the dimension of anisotropic objects.