  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.
