  Topologically-engineered mechanical frames are important model constructs for
architecture, machine mechanisms, and metamaterials. Despite significant
advances in macroscopically fashioned frames, realization and phonon imaging of
nanoframes have remained challenging. Here we extend for the first time the
principles of topologically-engineered mechanical frames to lattices
self-assembled from nanoparticles. Liquid-phase transmission electron
microscopy images the vibrations of nanoparticles in self-assembled Maxwell and
hexagonal lattices at the nanometer resolution, measuring a series of otherwise
inaccessible properties such as phonon spectra and nonlinear lattice
deformation paths. These properties are experimentally modulated by ionic
strength, captured by our discrete mechanical model considering the complexity
of nanoscale interactions and thermal fluctuations. The experiment-theory
integration bridges mechanical metamaterials and colloidal self-assembly,
opening new opportunities to manufacture phononic devices with solution
processibility, transformability, light weight, and emergent functions, at
underexplored length, frequency, and energy scales.
