Ligand mediated nanocrystal growth far from equilibrium leads to shape symmetry breaking

In crystal growth processes at the nanoscale, it has long been heuristically understood that ligands play a key role in producing and stabilizing thermodynamically unfavorable crystal shapes. A prototypical example of such a "far-from-equilibrium" growth process is the seed-based synthesis of asymmetric products, such as nanorods, within an isotropic environment. However, while this phenomenon is well-studied experimentally, there currently does not exist a theory of crystal growth that can explain the onset of persistent asymmetry without asymmetry in the initial conditions. We present a coarse-grained dynamical model that demonstrates the emergence of asymmetric growth due to thermal fluctuations in the coverage of ligands on the growing crystalline facets. Within this simple model, we study how the interplay of thermodynamic and kinetic factors affect both the onset of symmetry breaking and and the degree of asymmetry within the final products. We then map this coarse-grained model directly onto an atomistically resolved model of crystal growth to study how fluctuations at the atomic scale affect the stability of the asymmetric growth phases. The parameters within our model correspond to experimental observables such as the concentration, hydrophobicity, and binding strength of the ligands used in the synthetic protocol, which opens the door for leveraging insights from the model to optimize the yield of asymmetric products in colloidal nanoparticle syntheses.