  We study how the three-dimensional shape of rigid filaments determines the
microscopic dynamics and macroscopic rheology of entangled semi-dilute Brownian
suspensions. To control the filament shape we use bacterial flagella, which are
micron-long helices assembled from flagellin monomers. We compare the dynamics
of straight rods, helical filaments, and shape diblock copolymers composed of
seamlessly joined straight and helical segments. Caged by their neighbors,
straight rods preferentially diffuse along their long axis, but exhibit
significantly suppressed rotational diffusion. Entangled helical filaments
escape their confining tube by corkscrewing through the dense obstacles created
by other filaments. By comparison, the adjoining segments of the rod-helix
shape-diblocks suppress both the translation and the corkscrewing dynamics, so
that shape-diblocks become permanently jammed at exceedingly low densities. We
also measure the rheological properties of semi-dilute suspensions and relate
their mechanical properties to the microscopic dynamics of constituent
filaments. In particular, rheology shows that an entangled suspension of shape
rod-helix copolymers forms a low-density glass whose elastic modulus can be
estimated by accounting for how shear deformations reduce the entropic degrees
of freedom of constrained filaments. Our results demonstrate that the
three-dimensional shape of rigid filaments can be used to design rheological
properties of semi-dilute fibrous suspensions.
