Slow-sound propagation in aerogel-inspired hybrid structure with backbone and dangling branch
It has been almost 30 years after Gross and Fricke found the ultra-slow sound propagation in the aerogels (J Non Cryst Solids 1992, 145: 217–222). Although a qualitative model of elastic nonlinearity of bar-like skeletons was given, microscopic understanding is still unclear. Brinker’s group mentioned that the large value of exponent between density and modulus is due to the unconnected dangling arms, showing a microscopic hypothesis of sound wave-aerogels interaction (Nat Mater 2007, 6, 418–423).
Inspired by this hypothesis, recently, Yuhan Xie, Bin Zhou and Ai Du developed a simple model composed of a hybrid structure with backbone and dangling branch to study the interaction between aerogels and sound wave semi-quantitatively.
Fig. 1 (a). The modified model. Brown connecting rods between the dangling particles are added to adjust the modulus ratio of the dead-ends to the backbone particles. (b). The schematic graph of the analytical model of the hierarchical oscillator system.
They found an indirect interaction among density, dangling branch ratio and sound velocity by using DLCA (diffusion-limited cluster aggregation) and COMSOL simulations, explaining the scaling law between sound speed and aerogel density.
(a). The scaling law relation between the transport velocity of sound propagation and the proportion of backbone particles (1-Nde/Ntotal). Inset is the relation between the speed and the number of particles on a single dangling branch. (b). The rate of transport velocity v/vr against the mass fraction of backbone particles (details along the white line in Fig.2 (a). where the Ede∕Ebone = 0.01)
Interestingly, when introducing the sound wave via an acoustic-structure coupling, the energy could transfer from the backbone into dangling branch and back, inducing an obvious delay or even backflow. A versatile model of a hierarchical oscillator system was established.
Fig. 2 (a). The evolution of energy in the first dangling branch. (b). The evolution of energy in the tenth dangling branch. (c). The numerical simulation of the energy transfer in the constructed structure (zoom-in view from a repeated structure of 320 mm including 24 pairs of dangling branches)
Theoretical analysis indicate that the sound speed should be in direct proportion to mass fraction of backbone particles, which agrees well with experiment results. This work explained why the silica aerogels with low density and deep subwavelength structure could interact strongly with the sound wave. They unlocked the puzzle of density-sound speed scaling law and gave a convincing microscopic mechanism of ultraslow sound propagation in aerogels.
This work has been published in Advanced Composites and Hybrid Materials (2021, 4, 248–256) accompanied with a cover story.