The Importance of Unbound Ligand in Nanocrystal Superlattice Formation.

Significant experimental and theoretical work has been devoted to understanding why colloidal nanocrystals (NCs) self-assemble into such a diverse array of structures. Previous research has focused on factors such as nanocrystal charging, the ratio of ligand length to core radius, core faceting, and ligand coverage among many controllable parameters. Here, we demonstrate that the presence of unbound/free ligand in colloidal suspension plays a pivotal role in determining NC superlattice (SL) structure and orientation. We investigated the structure of PbS NC SLs with grazing-incidence small-angle X-ray scattering (GISAXS) while using nuclear magnetic resonance (NMR) to quantify the bound and unbound ligand populations. Through a series of controlled additions of unbound oleic acid to solutions of identically sized oleate-capped NCs with different bound ligand coverages, we mapped the continuous evolution of the final SL structure from body-centered cubic (BCC) to face-centered cubic (FCC) through a series of body-centered tetragonal (BCT) intermediate phases. Strikingly, this phase transformation pathway is identical to the uniaxial contraction observed when evaporating solvent, suggesting that unbound ligand and solvent occupy a similar space within the SL unit cell. Molecular dynamics simulations of single NCs confirm that unbound ligand readily swells the bound ligand shell over all exposed NC facets-even without explicit rebinding to the NC surface-and we establish limitations on the range of tunability via this approach based on Flory-Rehner gel-swelling theory. Furthermore, we explain the effect of high free ligand fraction on the early time dynamics of spin coating concentrated colloidal dispersions, which can disrupt the formation of long-range SL order. The controlled addition of unbound ligand represents a novel mechanism for directing superlattice structure and highlights the experimental importance of fully characterizing bound and unbound ligand populations.