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

The connection between shear thinning and biaxial orientation for quasi-ideal rods