Brownian Motion of Stiff Filaments in Confined Media

The thermal motion of stiff filaments in a crowded environment underlies the behavior of such disparate systems as polymer materials, nanocomposites, and the cell cytoskeleton. Despite decades of theoretical studies, the fundamental dynamics of such systems remains a mystery. Using near-infrared video microscopy, we study the thermal diffusion of individual single-walled carbon nanotubes (SWNTs) confined in porous agarose networks. SWNTs are the ideal system to study confined dynamics of stiff filaments. SWNTs are slender (typical diameters  0.7-1.2 nm), sufficiently long to be visualized by optical microscopy (3-15 μm), stiff (20-150 μm, scaling with d³), and share many dynamical characteristics with polymers. Surprisingly, we find that even a small bending flexibility strongly enhances their motion: the rotational diffusion constant is proportional to the filament bending compliance and is independent of the network porosity. This study establishes conclusively the dynamics of individual stiff filaments in crowded environments, elucidating the fundamental physics of how backbone flexibility affects mobility and diffusion. In addition to their relevance for the fundamental physics of stiff polymers, our results can be exploited in biological and technological contexts.