We demonstrate how gold nanoparticle monolayers can be curled up into hollow scrolls that make it possible to extract both bending and stretching moduli from indentation by atomic force microscopy. We find a bending modulus that is two orders of magnitude larger than predicted by standard continuum elasticity, an enhancement we associate with nonlocal microstructural constraints. This finding opens up new opportunities for independent control of resistance to bending and stretching at the nanoscale.

Ultrathin sheets comprised of a few layers of atoms, such as graphene, or a few layers of close-packed, ligated nanoparticles have attracted much interest because of their unique properties. In terms of mechanical properties, most attention has focused on nominally flat sheets. These thin sheets have been found to be mechanically robust and remarkably stiff under extension, capable of forming large freestanding membranes. However, out-of-plane bending, while playing a key role in emerging fields such as the manipulation of thin films into three-dimensional structures, is just starting to be explored in systematic experiments for ultrathin sheets. With thicknesses on the order of or below 10nm, such sheets are expected to be highly flexible and responsive to out-of-plane bending. The questions we are addressing here are to what extent the resistance to bending can be derived from knowledge of the physical thickness of the sheet and its tensile strength, and how can one extract the bending modulus.

Our key results are a) that bending ultrathin sheets into scrolls, i.e., hollow tubes, makes it possible to extract both bending and stretching moduli from a single set of indentation measurements (previously two separate experiments were required) and b) the bending resistance of nanoparticle monolayers is unexpectedly large, effectively corresponding to the stiffness under bending of a sheet 10x as thick as its actual physical thickness!

1. •Yifan Wang, Jianhui Liao, Sean McBride, Efi Efrati, Xiao-Min Lin and Heinrich M. Jaeger, “Strong Resistance to Bending Observed for Nanoparticle Membranes”, Nano Letters 15, 6732−6737 (2015). link