Hierarchical self-assembly of nematic colloidal superstructures

We show that colloidal superstructures could be assembled in mixtures of large and small colloidal particles dispersed in a nematic liquid crystal. Using elastic interaction of small colloidal particles with the disclination lines we succeed to demonstrate how one can decorate with small particles a topological matrix of defect rings and loops formed by an array of large colloidal particles. Our simulations show that this concept of colloidal self-assembly in nematics could be extended down to the nanoscale particles.

Figure 1

(Color online) (a) Small colloidal particle of $1.5\mu \text{m}$ diameter is attracted into the Saturn ring of a $19\mu \text{m}$ colloidal particle, following the black dashed path. (b) Binding potential of the small colloidal particle along the trapping path. (c) Numerical calculation: a 100 nm nanoparticle is attracted into the Saturn ring around a $1\mu \text{m}$ colloidal particle. (d) The calculated binding potential of the small particle as a function of the particle-particle separation for trajectories at different off-centeredness ‘‘$z$’’ from the central $xy$ plane. Note the qualitative matching between the theory and experiments.

Figure 2

(Color online) (a) Smaller colloidal particles of $2.32\mu \text{m}$ are also strongly attracted into the figure eight defect loop. (b) The potential of smaller colloidal particles in the vicinity of the figure eight. (c) Trapping sequence of smaller 100 nm particles into the figure eight defect formed around a pair of $1\mu \text{m}$ particles. Step 0 corresponds to the initial configuration and step 24 to the final configuration in the quasidynamical relaxation.

Figure 3

(Color online) (a) Smaller colloidal particles are trapped into the topological defect loop, twisting around a larger colloidal pair (diameter $10\mu \text{m}$). Images were taken at different heights of the microscope focus. (b) Microscope image of birefringence, showing nematic distortion around the colloidal superstructure.

Figure 4

(Color online) (a) Possible split ring resonator superstructure, formed of small colloidal particles trapped into the Saturn ring of the large particle. (b) A calculated stable colloidal ring superstructure of small 100 nm and a large $1\mu \text{m}$ particle. The inset shows a schematic electrical circuit corresponding to a Saturn ring filled with conductive colloidal particles. (c) Calculated binding energy of a small particle with diameter $d$ into the core of the Saturn ring, formed around a $1\mu \text{m}$ colloidal particle for two different anchoring strengths $W$ at the particle surfaces. Lines are parabolic fits.