Origin of the Acoustic Bandgaps in Hypersonic Colloidal Phononics: The Role of the Elastic Impedance

How phonons propagate in nanostructures determines the flow of elastic and thermal energy in dielectric materials. However, a reliable theoretical prediction of the phonon dispersion relation requires experimental verification both near to and far from the Brillouin zone of the nanostructure. We report on the experimental hypersonic phonon dispersion of hard (SiO2) and soft (polymer) fcc colloidal crystals infiltrated in liquid polydimethylsiloxane with different elastic impedance contrast using Brillouin light spectroscopy. We discuss the distinct differences with first-principles full elastodynamic calculations involving a multiple-scattering theory. Interparticle contacts strongly impact the long-wavelength speed of sound and the nature of the particle vibration resonance-induced hybridization hypersonic bandgap. The absence of the order-induced Bragg bandgap in SiO2 and its presence in soft opals cannot be fully accounted for by the theory, limiting its predictive power. Bridging the elasticity of the two colloidal crystals with suitable SiO2 core-shell (polymer) particles reveals an unprecedented crossover behavior in the dispersion relation. In view of many conversational parameters, the control tuning of phonon propagation in soft matter-based hypersonic phononics remains challenging.