Conforming nanoparticle sheets to surfaces with Gaussian curvature

TL;DR

This study explores how nanoparticle monolayer sheets can conform to surfaces with complex Gaussian curvature, revealing their deformation limits and the transition from full coverage to fractured caps with folds.

Contribution

It demonstrates the ability of nanoparticle sheets to adapt to highly curved surfaces and analyzes the deformation mechanisms involved, extending understanding beyond traditional thin sheets.

Findings

Nanoparticle sheets conform to surfaces with Gaussian curvature through three morphological stages.

Strain-induced dislocations are observed as the sheets deform to accommodate curvature.

Theoretical analysis captures the energy balance governing sheet morphology transitions.

Abstract

Nanoparticle monolayer sheets are ultrathin inorganic-organic hybrid materials that combine highly controllable optical and electrical properties with mechanical flexibility and remarkable strength. Like other thin sheets, their low bending rigidity allows them to easily roll into or conform to cylindrical geometries. Nanoparticle monolayers not only can bend, but also cope with strain through local particle rearrangement and plastic deformation. This means that, unlike thin sheets such as paper or graphene, nanoparticle sheets can much more easily conform to surfaces with complex topography characterized by non-zero Gaussian curvature, like spherical caps or saddles. Here, we investigate the limits of nanoparticle monolayers' ability to conform to substrates with Gaussian curvature by stamping nanoparticle sheets onto lattices of larger polystyrene spheres. Tuning the local Gaussian curvature by increasing the size of the substrate spheres, we find that the stamped sheet morphology evolves through three characteristic stages: from full substrate coverage, where the sheet extends over the interstices in the lattice, to coverage in the form of caps that conform tightly to the top portion of each sphere and fracture at larger polar angles, to caps that exhibit radial folds. Through analysis of the nanoparticle positions, obtained from scanning electron micrographs, we extract the local strain tensor and track the onset of strain-induced dislocations in the particle arrangement. By considering the interplay of energies for elastic and plastic deformations and adhesion, we construct arguments that capture the observed changes in sheet morphology as Gaussian curvature is tuned over two orders of magnitude.