Nanoscale phonon dynamics in self-assembled nanoparticle lattices.

Geometry and topology endow mechanical frames with unusual properties from shape morphing to phonon wave manipulation, enabling emerging technologies. Despite important advances in macroscopic frames, the realization and phonon imaging of nanoscale mechanical metamaterials has remained challenging. Here we extend the principle of topologically engineered mechanical frames to self-assembled nanoparticle lattices, resolving phonon dynamics using liquid-phase transmission electron microscopy. The vibrations of nanoparticles in Maxwell lattices are used to measure properties that have been difficult to obtain, such as phonon band structures, nanoscale spring constants and nonlinear lattice deformation paths. Studies of five different lattices reveal that these properties are modulated by nanoscale colloidal interactions. Our discrete mechanical model and simulations capture these interactions and the critical role of effects beyond nearest neighbours, bridging mechanical metamaterials with nanoparticle self-assembly. Our study provides opportunities for understanding and manufacturing self-assembled nanostructures for phonon manipulation, offering solution processability, transformability and emergent functions at underexplored scales of length, frequency and energy density.