Architecture Controls Phonon Propagation in All-Solid Brush Colloid Metamaterials

Brillouin light scattering and elastodynamic theory are concurrently used to determine and interpret the hypersonic phonon dispersion relations in brush particle solids as a function of the grafting density with perspectives in optomechanics, heat management, and materials metrology. In the limit of sparse grafting density, the phonon dispersion relations bear similarity to polymer-embedded colloidal assembly structures in which phonon dispersion can be rationalized on the basis of perfect boundary conditions, i.e., isotropic stiffness transitions across the particle interface. In contrast, for dense brush assemblies, more complex dispersion characteristics are observed that imply anisotropic stiffness transition across the particle/polymer interface. This provides direct experimental validation of phonon propagation changes associated with chain conformational transitions in dense particle brush materials. A scaling relation between interface tangential stiffness and crowding of polymer tethers is derived that provides a guideline for chemists to design brush particle materials with tailored phononic dispersion characteristics. The results emphasize the role of interfaces in composite materials systems. Given the fundamental relevance of phonon dispersion to material properties such as thermal transport or mechanical properties, it is also envisioned that the results will spur the development of novel functional hybrid materials.