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 0.03s(-1), the orientation dynamics were twist-tumbling, whereas at 0.06s(-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.