The ``Music" of Silica-Poly(methyl methacrylate) Core-Shell Spheres: Eigenvibrations and Mechanical Properties at the Nanoscale

We report on the measurement of elastic vibrational modes (eigenvibrations) in silica--poly(methyl meth\-acrylate) ($\mathrm{SiO}_2$--PMMA) core-shell spheres and corresponding spherical hollow capsules (PMMA) with different particle size (dia\-meter: 232~nm--405~nm) and shell thickness (25~nm--112~nm) using Brillouin light scattering, supported by numerical calculations.~[T.\ Still et al., Nano Lett.\ \textbf{8}, 3194 (2008)] These localized modes allow to access the mechanical moduli of core and shell material. We observe reduced mechanical strength of the porous silica core and for the core-shell spheres a striking increase of the moduli in both the $\mathrm{SiO}_2$ core and the PMMA shell. The peculiar behavior of the vibrational modes in the hollow capsules is attributed to antagonistic dependence on overall size and layer thickness. The present investigation of the acoustical properties of the individual core-shell particles can lead to the use of such nanoscale engineered particles in more eloborate systems to control hypersonic phonons.