Rotational motions of repulsive graphene oxide domains in aqueous dispersion during slow shear flow

In our earlier work Lee et al., Soft Matter 15, 4238–4243 (2019), we demonstrated that mutually attractive graphene oxide (GO) domains were under a tube-rolling motion with a vorticity alignment at low shear rates. In this work, we prepared repulsive GO domains, which were dispersed in water. The distinct stress wave-prints were measured using a cone and plate rheometer at low shear rates. All possible Jeffery orbits were calculated for input into the Leslie–Ericksen theory. The Tikhonov regularization method was used to determine the orientation probability density function at the start of an orbit cycle from the experimental stress wave-print and the calculated stress matrix using the Leslie–Ericksen theory. Therefrom, it was concluded that at a shear rate of 0.03 s−1, the orientation dynamics were “twist-tumbling,” whereas at 0.06 s−1 the domains underwent “twist-tumbling” and “kayaking.” Finally, the orientation probability density function was used to evaluate the orientation tensors in the Larson–Doi model for polydomain liquid crystals and susequently to reconstruct the stress evolution, which compares reasonably well to the experiment. In addition, a calculation method for estimating the b/a ratio, where the trajectory is different from the prolate in the case of the triaxial ellipsoid shape (c > b > a), has been presented.