Predictive Modeling of Nanocrystal Orientation in Superlattices: Insights from Ligand Entropy.

The self-assembly of nanocrystals (NCs) into close-packed, ordered superlattices (SLs) is of broad, engineering interest. The coherent orientation of polyhedral nanocrystals within NC SLs enhances electronic, magnetic, and vibrational coupling, leading to a variety of emergent phenomena. Here, we show that coherent orientation of polyhedral NCs in many SLs can be understood simply by considering its effect on the conformational entropy of surface ligands. We report the predicted nanocrystal orientations and entropic driving force to orient for a broad range of nanocrystal shapes and superlattice unit cells, and we show that ligand entropy is sufficient to reproduce a host of reported experimental and computational observations. We additionally use this framework to predict the expected distribution of interstitial species such as solvent or unbound ligands in an oriented NC SL. This work offers intuition for understanding the orientation of NCs in superlattices and a future framework for analyzing multinary structures.