Staff involved and contact person : Olivier Mondain-Monval
The concept of metamaterial can be directly extended from electromagnetic to acoustic waves. In that case, the physical quantities that drive the wave propagation are the mass density ρ and the compressibility χ of the materials. In a tightened partnership with the I2M institute, the Laboratory of the Future and, initially, the LOMA, our approach consists in trying to modulate the effective properties (and more specially the effective mass density and compressibility ρeff and χeff respectively) of materials. To do so, small resonating inclusions, further called micro-resonators, are suspended in a continuous matrix. This strategy is known as the “locally resonant materials” approach. These micro-resonators should present the following features : i) be synthesizable in fluid phases in order to fully profit of our skills in soft matter techniques such as emulsion templating and microfluidics ii) be calibrated objects with a rather narrow size distribution around typically 100 µm in order to remain smaller than the typical ultrasound wavelength (λ 1 mm) used in our experiments iii) present a maximal sound speed contrast with the matrix for the resonance amplitudes to be as intense as possible. Following this strategy, we were able to propose (Brunet, Leng & Mondain-Monval, Science 342, 323 (2013)) different types of resonators in order to obtain metamaterials exhibiting exotic values of ρeffand χeff (Figure 1).
Figure 1 : Schematic representation of a metamaterial exhibiting a negative effective mass density ρeff (A) or a negative effective compressibility χeff (B). (C), (D), (E) and (F) : resonators of various morphologies leading to either simple negative ((C) and (F)) or double negative metamaterials
1) Soft 3D acoustic metamaterials with negative index
Coll. : Jacques Leng (LOF), Olivier Poncelet, Christophe Aristégui, Thomas Brunet (I2M)
Staff : Artem Kovalenko, Kévin Zimny, Simon Raffy, Aurore Merlin, Benoit Mascaro
Porous materials appear to be the best candidates to shape acoustic metamaterials for they present a very high sound speed contrast with a water-based matrix. They indeed present a rather high compressibility due to the large proportion of gas in the material (assuming that the skeleton is soft enough) while still having a non zero density related to the materials skeleton. Using an emulsion-templating formulation technique and microfluidics, we synthesized several types of porous beads, and especially silicon macroporous polymer beads and silica xerogels porous beads. In such systems, the sound speed can decrease to attain very low values (typically less than 100 m/s). Thus, intense resonance phenomena occur as these particles are introduced in the water-based matrix. Recent measurements proved that meta properties could thus be attained. We realized the first soft 3D acoustic metamaterial with negative index in a frequency range around typically 100 kHz. These results will soon appear in Nature Materials. (Brunet, Merlin, Zimny, Mascaro, Poncelet, Aristégui, Leng & Mondain-Monval, Nature Materials 2015).
Figure 2 : SEM picture of (a) macroporous silicon polymer beads (b) porous xerogel silica beads (c) Phase velocity and (d) acoustic index of a suspension of porous silicon beads as a function of frequency and for 3 different volume fractions : green 0.2 %, red 15 %, black 20 %
You can listen to the Radio postcast of January 22nd 2015 ! ...Or look at the TV spot !
This part of our work was widely described in high impact vulgarization newpapers and websites :
2) Tunable acoustic materials
Coll. : Jacques Leng (LOF), Olivier Sandre (LCPO), Olivier Poncelet, Christophe Aristégui, Thomas Brunet (I2M)
Staff : Kévin Zimny, Simon Raffy, Benoit Mascaro
Our first study showed that suspensions of fluorinated droplets (Fig 3a) with a very narrow size distribution (Fig 3b) synthesized using a robotic approach have a sufficient sound speed contrast with the surrounding water-based yield stress fluid to give birth to the expected resonance phenomena. This could be evidenced on the attenuation and phase velocity spectra (Fig 3c), which exhibit characteristic resonance peaks of different orders (T. Brunet, S. Raffy, B. Mascaro, J. Leng, R. Wunenburger, O. Mondain-Monval, O. Poncelet & C. Aristégui, Applied Physics Letters 101, 011913 (2012)). We also could study the impact of the system polydispersity on the acoustic spectra (B. Mascaro, T. Brunet, O. Poncelet, C. Aristégui, S. Raffy, O. Mondain-Monval & J. Leng, Journal of the Acoustical Society of America 133 (4), 1996 (2013)).
We could turn these passive systems into tunable acoustic materials under an external magnetic field by doping the fluorinated oil droplets with iron oxide particles (in collaboration with O. Sandre, LCPO, Pessac). A fluorinated ferrofluid was synthesized and emulsified in the water-based yield stress fluid (Kevin Zimny, Benoit Mascaro, Thomas Brunet, Olivier Poncelet, Christophe Aristégui, Jacques Leng, Olivier Sandre, and Olivier Mondain-Monval, Journal of Materials Chemistry B 2, 1285 (2014)). Resonances also appear on the acoustic spectra but their positions can be tuned by the application of an external magnetic field. This is due to the deformation of the ferrofluid droplets under the external magnetic field (Fig 4). As a result, a tunable acoustic material is obtained, which exhibits acoustic spectra strongly dependent on the magnetic field intensity and orientation with respect to the wave propagation vector (Fig. 5). These results were recently published in Physical Review Letters (T. Brunet, K. Zimny, B. Mascaro, O. Sandre, O. Poncelet, C. Aristégui & O. Mondain-Monval, Physical Review Letters 111, 264301 (2013)).
Figure 3 : (a) Optical microscopy picture of a fluorinated oil emulsion in the water-based yield stress fluid (b) Corresponding size histogram (c) Evolution of the attenuation and phase velocity as a function of frequency (blue : gel only ; red : gel + emulsion ; solid line : fitting to the Independent Scattering Approximation model with no polydispersity ; dashed line : same with polydispersity.
Figure 4 : Evolution of a ferrofluid droplet ( 200 µm) aspect ratio as a function of the applied magnetic field
Figure 5 : (a) Evolution of the frequency spectra as a function of the angle between the applied magnetic field B and the acoustic wave propagation vector k. Optical microscopy pictures of the emulsion droplets ( 100 µm) with (b) k // B and (c) k ┴ B.
3) Spring-mass resonators
Coll. Jacques Leng (LOF) and Régis Wunenburger (Institut Jean Le Rond d’Alembert, UPMC)
Former staff : Rawad Tadmouri, Lyuba Lukyanova, Lionel Bos
In this study, we aimed at the realization of core-shell resonators constituted of a rigid core embedded in a soft shell synthesized using a microfluidic technique. The first step is to realize a rigid and dense core, for example using a bismuth-based alloy with a high mass density value (R. Tadmouri, M. Romano, F. Guillemot, O. Mondain Monval, R. Wunenburger & J. Leng, Soft Matter 8, 10704 (2012)). Then, the second step is to encapsulate it in a soft shell (here an agarose gel), still using microfluidics. Core-shell particles could thus be realized such as those presented on figure 6 (L. Lukyanova, L. Séon, A. Aradian, O. Mondain-Monval, J. Leng & R. Wunenburger, Journal of Applied Polymer Science 128 (6), 3512 (2013)). However, a parametric study showed that getting “meta” properties with such materials requires very specific materials in terms of shear elastic moduli of the shell and the matrix.
Figure 6 : Optical microscopy picture of a core-shell system obtained using microfluidics.