Mesophases as stepping stones to enhance crystallization kinetics in nanoparticle self-assembly

Manipulation of kinetic pathways is essential to self-assemble nanoparticle building blocks into complex ordered structures, as the emergence of intermediate metastable states could either facilitate or hinder crystallization of the target lattice. Molecular simulations and Markovian and transition state theory are used to validate our conjecture that intermediary mesophases, with partial but long-range translational or orientational structural ordering, accelerate crystallization kinetics from the disordered structure. Using four representative models, two lyotropic single-component and two thermotropic binary mixture systems, we demonstrate that mesophases with intermediate entropies, such as nematic fluid, rotator solid, and microsegregated mesophases, speed up the overall crystallization rate. This enhancement occurs by effectively splitting a larger isotropic-to-crystal free energy barrier into two smaller barriers corresponding to isotropic-to-mesophase and mesophase-to-crystal transitions, with mesophase "bulk" macrostates being kinetically more favorable than microscopic fluctuations. The single-step isotropic-to-crystal transition occurs through a composite-cluster pathway that includes mesophase microdomains; an isotropic-crystal interfacial energy greater than or comparable to the sum of the isotropic-mesophase and mesophase-crystal interfacial energies is associated with enhanced two-step crystallization rate. Overall, our findings validate the conjecture, which offers additional guidance for selecting nanoparticle designs and conditions that promote efficient crystallization pathways.