Rotation of topological defects by trapped micro-rods in the nematic phase of a liquid crystal

Abstract

The dynamics of rod-shaped micro-particles, trapped within a topological defect, was investigated. It is demonstrated that there is an attractive interaction force between particle and defect, which is of the order of F ≈ 30 pN, pulling the free micro-rod into the defect core, directing it along the direction of escape. Application of an electric field can induce motion of the trapped rod along the macroscopic path of a circular trajectory, which results in a circular drag motion of the defect's director field. The direction of circular motion can be clockwise or counter-clockwise with equal probability, independent of the sign of the defect. The electric field dependence of trajectory diameter and angular velocity are investigated, and it is found that these lead to a velocity, which is largely independent of electric field and particle-defect rotation direction.

Dynamical theory of topological defects I: the multivalued solution of the diffusion equation

“…Here, we show that, in addition to the static defect solution (3), an additional contribution given by the average defect angular momentum arises. This contribution is moreover orthogonal to (3), such that the solution (12) predicts that a defect with nonzero angular momentum generates spiraling field lines, as experimentally observed in a number of liquid crystal systems [40,41].…”

“…Despite the fact that equation (20) describes the orientation far field generated by a moving charge, it takes a quasi-static form when expressed in the reference frame of the defect, as it solves the Laplace equation: ∇ 2 θ(r, t) = 0. We conclude this section by noting that spinning topological defects have recently been realized in sandwiched liquid crystal suspensions [40]. By adding micro-rods to the suspension, the former are indeed attracted to the core of topological defects, whereas the application of an alternating electric field along the third dimension results in a spinning motion of the rods, which drives the defects along circular trajectories.…”

“…Schlieren textures of rotating defects then clearly show a characteristic spiral shape with an orientation set by the chirality of the defect trajectory (clockwise or counter-clockwise). To evaluate the strength of the angular momentum in equation (20), we note that it is expressed in units of the orientation diffusion coefficient D. [40] reports defect circular trajectories with typical radius R ≃ 7 µm and speed v ≃ 7 µm s −1 , leading to an angular momentum of the order of L ≃ 50 µm 2 s −1 . Because the value of D is expected to lie in the range 10 − 150 µm 2 s −1 [43], we conclude that in this experiment, L/D can easily take values of order one, leading to a clear spiraling of director field lines around the defect.…”

Annihilation dynamics of topological defects induced by microparticles in nematic liquid crystals

“…Topological defects are also of great interest from the standpoint of trapping and manipulation of colloidal inclusions [32][33][34][35] . Dispersions of microparticles in nematic LCs have been Please do not adjust margins Please do not adjust margins investigated since topological defects of LCs were studied in more detail.…”