  The complete orientational ordering tensor of quasi-ideal colloidal rods is
obtained as a function of shear rate by performing rheo-SANS (rheology with
small angle neutron scattering) measurements on isotropic fd-virus suspensions
in the two relevant scattering planes, the flow-gradient (1-2) and the
flow-vorticity (1-3) plane. Microscopic ordering can be identified as the
origin of the observed shear thinning. A qualitative description of the
rheological response by Smoluchowski, as well as Doi--Edwards--Kuzuu theory is
possible, as we obtain a master curve for different concentrations, scaling the
shear rate with the apparent collective rotational diffusion coefficient.
However, the observation suggests that the interdependence of ordering and
shear thinning at small shear rates is stronger than predicted. The extracted
zero-shear viscosity matches the concentration dependence of the self-diffusion
of rods in semi-dilute solutions, while the director tilts close towards the
flow direction already at very low shear rates. In contrast, we observe a
smaller dependence on the shear rate in the overall ordering at high shear
rates, as well as an ever-increasing biaxiality.
