Stabilizing Nonequilibrium Structures in the Growth of Model Colloidal Nanocrystals

A chemically driven system allows for the formation of stable patterns that would vanish quickly in equilibrium. For instance, it is well-known to synthetic chemists that, under the appropriate conditions, one can reliably induce the growth of nanorods and other asymmetric structures from symmetric nano-crystalline precursors in solution. This growth process both fails to minimize the free-energetic cost of the interface between the growing solid and the surrounding solution, and breaks the symmetry of the isotropic environment. While the synthetic protocols are well-established, a rigorous and broadly applicable understanding of how and why asymmetric structures are formed during these growth processes is lacking. Our work employs a minimal model to characterize this nonequilibrium symmetry-breaking and identify the necessary conditions under which asymmetric structures can be consistently produced. To do so, we use a Kinetic Monte Carlo simulation scheme alongside a cloning algorithm to generate both typical and rare trajectories of growth from an ensemble of initial seeds. With this procedure, we are able to quantify the susceptibility of a nanoparticle to grow asymmetrically, and observe how this depends on both rates of surface diffusion and the densities of ligands on different crystalline facets.