Metadynamics Simulations of Three-Dimensional Nanocrystals Self-Assembled from Triblock Janus Nanoparticles: Implications for Light Filtering

Self-assembly of colloidal particles into 3D lattices, with potential applications as single crystals with promising optical properties, has received considerable attention. The superior bandgap properties of open colloidal lattices over their more easily self-assembling close-packed counterparts make them more demanding for this purpose. However, due to the mechanical instability of low-coordination open lattices, their self-assembly has proven to be challenging. Here, we employ a model of triblock Janus nanoparticles, which includes their surface chemistry (hydrophobic patches at the poles and surface charges in the equator) to simulate their self-assembly to three-dimensional nanocrystals. The solvent is explicitly included in the simulation, and hydrodynamic interactions are taken into account by dissipative particle dynamics. Biased sampling simulations are conducted to drive the simulations between different phases. The phase diagrams represent a competition between the liquid phase, open (pyrochlore, perovskite, and diamond), and close-packed body-centered cubic (bcc) and face-centered cubic (fcc) nanocrystals, whose stabilities depend on the patch width, temperature, and density. Patch widths allowing for three contacts per patch stabilize the pyrochlore nanocrystal at low densities and the fcc phase at high densities, and those allowing four contacts per patch stabilize the perovskite nanocrystal at low densities, the bcc lattice at higher densities, and upon further compression, the fcc lattice. The diamond nanocrystal is stabilized by wide enough patches that provide strong enough bonding between nanoparticles. Increasing the density converts the diamond nanocrystal to bcc and, subsequently, to a higher-density fcc lattice. The calculated free energies for conversion of liquid to crystalline phases reveal that the barrier height for nucleation of open lattices (within their stability domains) is lower than that for denser lattices.