Ligand-induced incompatible curvatures control ultrathin nanoplatelet polymorphism and chirality

Abstract

The ability of thin materials to shape-shift is a common occurrence that leads to dynamic pattern formation and function in natural and man-made structures. However, harnessing this concept to rationally design inorganic structures at the nanoscale has remained far from reach due to a lack of fundamental understanding of the essential physical components. Here, we show that the interaction between organic ligands and the nanocrystal surface is responsible for the full range of chiral shapes seen in colloidal nanoplatelets. The adsorption of ligands results in incompatible curvatures on the top and bottom surfaces of the NPL, causing them to deform into helicoïds, helical ribbons, or tubes depending on the lateral dimensions and crystallographic orientation of the NPL. We demonstrate that nanoplatelets belong to the broad class of geometrically frustrated assemblies and exhibit one of their hallmark features: a transition between helicoïds and helical ribbons at a critical width. The effective curvature κ ¯ is the single aggregate parameter that encodes the details of the ligand/surface interaction, determining the nanoplatelets’ geometry for a given width and crystallographic orientation. The conceptual framework described here will aid the rational design of dynamic, chiral nanostructures with high fundamental and practical relevance.

Ligand Tail Controls the Conformation of Indium Sulfide Ultrathin Nanoribbons

“…We now examine the possible physical origin of this trend in the framework of incompatible elasticity theory, which is relevant for ribbons covered with a monolayer of surfactants. 20 We showed that ribbons display an effective curvature given by…”

“…A similar trend was observed previously for CdSe in experiments 19 and simulation. 20 This physical parameter impacts all the terms in eq 1 directly or indirectly. First, it appears through the…”

“…More recently, the conformation of CdSe NPL was shown to depend on thiol ligand chain length 18,19 and branching. 20 The concept of principal curvature is helpful to describe how NPL bend, curl, and adopt in fine their 3D shape. The two principal curvatures of a surface are the maximum and minimum values of the curvature at a given point along two orthogonal directions.…”

“…These interactions can be encompassed in an effective curvature parameter whose value and the NPL's geometrical features dictate the NPL's geometry. 20 Due to the symmetry elements of the crystalline core, the ligand-induced curvatures at the top and bottom layers of the NPL can be orthogonal. This is the case for CdSe, whose zinc-blende crystal structure contains a 4̅ symmetry axis.…”

“…This is the case for CdSe, whose zinc-blende crystal structure contains a 4̅ symmetry axis. An interplay between geometry and energy then dictates the shape of a thin NPL and can be accurately described using the incompatible theory framework, 20 which has been used to describe macroscopic objects such as seedpods 25,26 or surfactant self-assemblies. 26,27 Beyond cadmium chalcogenides, few ultrathin NPLs have been shown to adopt various conformations.…”