The self-assembly of nanoparticles by an anisotropic fluid allows for the study of fascinating phenomena and the potential to assemble structures that can be used for a variety of industrial and biological applications. Here, we use a nematic liquid crystal to drive the self-assembly of quantum dots in confined geometries. The quantum dots have been modified with a special mesogenic ligand that aids in dispersion into the liquid crystal host.

By confining the liquid crystal to a certain geometry, we can assemble nanoparticle structures at defined locations, as the geometry forces the formation of topological defects in certain areas. Particles gather at topological defects to lower the free energy of the system, and so we utilize this fact to gain spatial control over the self-assembly process. We also use the isotropic-nematic phase transition of the liquid crystal to direct the self-assembly by forcing the particle to non-energetically favorable locations, as spatial control is one of the current hurdles in self-assembly research. Using droplet geometry, we successfully form nanoparticle cluster and hollow micro-shells at defined locations in the liquid crystal. The phase transition sweeps up the particles in a process to ballistic aggregation, so we characterize the fractal nature of these aggregates, quantifying their packing dimension to be 2.5.

Finally, we have developed a model that replicates the particle-rich domains in a phase-changing nematic liquid crystal. Using a spin model that exhibits a first-order phase transition combined with the Cahn Hillard equation adjusted with a new driving term proportional to the nematic order parameter, we study the effect of cooling rate of the liquid crystal and how that changes particle domain size. We recover a linear relationship, showing that as cooling rate is increased, particle domain size decreases. In conclusion, these simulations have helped further the understanding of phase-transition driven self-assembly.