Defect Structure around Two Colloids in a Liquid Crystal

This Letter investigates the defect structures that arise between two colloidal spheres immersed in a nematic liquid crystal. Molecular simulations and a dynamic field theory are employed to arrive at molecular-level and mesoscopic descriptions of the systems of interest. At large separations, each sphere is surrounded by a Saturn ring defect. However, at short separations both theory and simulation predict that a third disclination ring appears in between the spheres, in a plane normal to the Saturn rings. This feature gives rise to an effective binding of the particles. The structures predicted by field theory and molecular simulations are consistent with each other.

Figure 1

Two spheres dispersed in a liquid crystal, with homeotropic (perpendicular) anchoring at the spheres’ surface and the confining walls. Periodic boundary conditions are applied in the $x$ and $y$ directions. Colors (online only) indicate orientations, from vertical (blue) to horizontal (red). This snapshot from one of our simulations shows a layer of molecules anchored at both spheres.

Figure 2

New three-ring disclination structure around two spheres at a separation $s/R=0.3$: (a) Contour plot $S=0.26$; (b) Size of the rings: $a$ (radius of the Saturn rings), $b$ (radius of the third ring along the $y$ axis), and $c$ (radius of the third ring along the $z$ axis).

Figure 3

Director and scalar order parameter maps obtained from (a) field theory and (b) Monte Carlo simulations.

Figure 4

Ring radii obtained from field theory calculations as a function of the sphere separation. The lines are guides to the eye.