Vortexlike Topological Defects in Nematic Colloids: Chiral Colloidal Dimers and 2D Crystals

We show that chiral ordering of the underlying complex fluid strongly influences defect formation and colloidal interactions. Nonsingular defect loops with a topological charge $-2$ are observed, with a cross section identical to hyperbolic vortices in magnetic systems. These loops are binding spontaneously formed pairs of colloidal particles and dimers, which are chiral objects. Chiral dimer-dimer interaction weakly depends on the chirality of dimers and leads to the assembly of 2D nematic colloidal crystals of pure or “mixed” chirality, intercalated with a lattice of nonsingular vortexlike defects.

Figure 1

(a) In a 90° TN cell, two antiparallel dipolar colloidal particles spontaneously fuse into a dimer. (b) An isotropic droplet formed by the laser tweezers separates the particles. After switching off the light, the particles are attracted by two thin birefringent lines. Note the difference between final states in (a) and (b). (c) Separation dependence of the attractive potential determined from (a) (circles) and (b) (squares). (d) The corresponding forces. Cell thickness $h=8\mu \mathrm{m}$.

Figure 2

(a) Two colloidal dimers of different chirality in a 90° $R$-twisted cell. Energetically preferable $L$ dimer between crossed (a,b) and parallel polarizers (c). $R$ dimer between crossed (d,e) and parallel polarizers (f). The $R$-handed nematic twist is indicated in (a) and (d). Scale bar in (a–f) is $2\mu \mathrm{m}$. (g) Cross section of a nonescaped hyperbolic line. (h,i) Escaping into the third dimension. (j) The escaped hyperbolic rings are chiral. Dark solid lines show the local director. (k) Left-handed and (l) right-handed escaped colloidal dimer, calculated from LdG theory. Color arrows indicate handedness of rings.

Figure 3

(a) Anisotropy of attraction between two $L$-colloidal dimers in a 90° $R$-twisted cell. Starting positions are labeled 1–12, ending positions of the approaching dimer are drawn. (b) Separation dependence of the attractive potential between two colloidal dimers of opposite chirality, determined for trajectories starting from positions No. 3 and 5, presented in (a). Cell thickness $h=8\mu \mathrm{m}$.

Figure 4

2D colloidal crystals assembled from chiral dimers by laser tweezers. (a) $L$ dimers in $R$-TN cell between crossed and (d) parallel polarizers. $R$ dimers in $R$-TN cell between crossed (b) and parallel polarizers (e). (c) 2D mixed colloidal crystal from equal number of $R$ and $L$ dimers between crossed and (f) parallel polarizers. Note the color difference between $R$ and $L$ dimers. Scale bar in (a–f) is $5\mu \mathrm{m}$.(g) $L$ and (h) $R$ colloidal crystals, as obtained from numerical modeling in $R$-handed nematic [12]. The isosurface corresponds to the geometrical escape parameter $\tilde{S}=0.8$. Color arrows indicate handedness of the ring.