On the use of aerogel as a soft acoustic metamaterial for airborne sound Matthew D. Guild,∗ Victor M. Garc´ıa-Chocano, and Jos´eS´anchez-Dehesay Wave Phenomena Group, Departamento de Ingenier´ıa Electr´onica, Universidad Polit´ecnica de Valencia, Camino de vera s/n (Edificio 7F), E-46022 Valencia, Spain Theodore P. Martin, David C. Calvo, and Gregory J. Orris U.S. Naval Research Laboratory, Code 7160, Washington DC 20375, USA (Dated: August 16, 2016) Soft acoustic metamaterials utilizing mesoporous structures have recently been proposed as a novel means for tuning the overall effective properties of the metamaterial and providing better coupling to the surrounding air. In this work, the use of silica aerogel is examined theoretically and experimentally as part of a compact soft acoustic metamaterial structure, which enables a wide range of exotic effective macroscopic properties to be demonstrated, including negative density, density- near-zero and non-resonant broadband slow sound propagation. Experimental data is obtained on the effective density and sound speed using an air-filled acoustic impedance tube for flexural metamaterial elements, which have previously only been investigated indirectly due to the large contrast in acoustic impedance compared to that of air. Experimental results are presented for silica aerogel arranged in parallel with either 1 or 2 acoustic ports, and are in very good agreement with the theoretical model. PACS numbers: 43.20.+g, 43.28.+h, 43.58.+z Keywords: acoustic metamaterials, silica aerogels, negative dynamical density, slow sound I. INTRODUCTION and exciting phenomena associated with effective proper- ties that are near zero, particularly those associated with Acoustic metamaterials have received interest in re- extraordinary transmission, which can be achieved when cent years by enabling macroscopic physical characteris- either the effective density or wave speed approaches tics which cannot be obtained with traditional materials, zero[4, 5]. In the case of a density-near-zero material, such as negative, near-zero or anisotropic dynamic ef- the effective wave speed increases dramatically and leads fective fluid properties. Acoustic metamaterials are able to a quasi-static field within a given structure, which to achieve such previously unattainable exotic properties can exhibit a supercoupling effect through long narrow through the careful design of the microstructure, which channels[6{8]. At the opposite extreme, there are also in- create microscale dynamics that result in the desired teresting effects which arise as the effective acoustic wave macroscopic properties. The reader is addressed to the speed approaches zero, which is referred to as slow sound, recent reviews on this topic where one can find many of the analogue of slow light in optics. Previous demonstra- the exciting applications of acoustic metamaterials[1, 2]. tions have utilized resonant effects using either sonic crys- Until recently, such acoustic metamaterials have relied tals or detuned resonators[9{11], resulting in slow sound on materials which are much harder than the surround- that occurs over a relatively narrow bandwidth. A novel ing fluid medium, often treated as acoustically rigid or application of slow sound propagation was recently pro- nearly-rigid structures for airborne sound. Alternatively, posed for the improved design of acoustic absorbers by soft acoustic metamaterials utilizing mesoporous struc- Groby et al.[12], in which slow sound in large slits filled tures have been proposed as a novel means for the mold- with absorptive foam were used to significantly increase ing and tuning of the overall properties of the resulting the low frequency absorption in air. metamaterial, while simultaneously providing better cou- One of the fundamental aspects that gives a meta- pling with the acoustic environment around it [3]. Build- material its exotic macroscopic properties is the ho- ing upon this concept, the use of silica aerogel as part mogenization of the microstructure, which has recently of a compact and conformal soft acoustic metamaterial been explored for elastic and flexural metamaterial structure is examined theoretically and experimentally, components[13, 14]. This is particularly important be- arXiv:1509.08378v1 [cond-mat.mtrl-sci] 28 Sep 2015 yielding an interesting suite of useful yet exotic proper- cause the effective macroscopic properties of an acoustic ties. metamaterial can be significantly different than those of In addition to extremely large and/or negative dy- the constituent microstructural elements. When there is namic properties, there are a wide range of interesting open flow through the structure, such as a sonic crys- tal lattice[15, 16] or transmission-line arrangement of Helmholtz resonators [17], it is relatively straightforward ∗ [email protected]; Current address: NRC Re- to extract effective properties experimentally due to the search Associateship Program, U.S. Naval Research Laboratory, relatively low acoustic impedance. Code 7160, Washington DC 20375, USA A formidable challenge, however, arises when obtain- y [email protected] ing the effective properties of a metamaterial sample con- 2 taining elastic elements, which have acoustic impedances are made possible by its unique microstructure. One that are orders of magnitude greater than the surround- of the most common types of aerogels, silica aerogel, ing fluid and at frequencies well below those typically consists of a high-porosity frame made of fused silica used to obtain acoustic properties through direct time- nanoparticles. The most notable characteristic of sil- of-flight measurements. As a result, previous works in ica aerogel is its extremely low static density which is air have either been restricted to theoretical and nu- directly related to the very high porosity of the struc- merical evaluation[4, 7, 18{20] or limited to an indirect ture, making it much closer to that of air compared with comparison of the metamaterial properties using experi- any other type of elastic solid. Due to the nanoscale mental results for the reflected and transmitted pressure pore size, however, the air is locked in place by vis- field[5, 21]. In this work we make the significant step cous effects producing a higher acoustic density than of experimentally extracting the effective dynamic prop- that compared to typical porous media used in acous- erties (density and sound speed) of these flexural meta- tic applications[26]. Furthermore, the small cross-section material elements, which has to the authors knowledge connecting the fused nanoparticles results in a very low never been accomplished previously for such a metama- elastic stiffness, compared with a rigid silica structure terial structure in air. of the same porosity[27]. This combination gives a rela- It is expected that the elasticity of the materials defin- tively low acoustic impedance (for an elastic solid), and ing the metamaterial structure might play a fundamental in particular yields an exceptionally low flexural wave role in order to understand the phenomena observed in speed, making it ideal for use as a subwavelength flexu- sound transmission and reflectance through the channels ral element for airborne sound. defined by the structure. In fact, the role of the elastic When the wavelength is much larger than the mi- properties is paramount for the case of structures embed- crostructure, negative effective properties are achieved ded in water, as it has been recently demonstrated [22]. via control of the microstructure arrangement and the Although some recent work has begun to incorporate the resulting dynamics. This feature in the microstructure elastic effects into the metamaterial structure, many of design is typically achieved with two main types of ar- these designs continue to have the primary dynamic ele- rangements: either as a mass-spring system, or in a ment consisting of mass-spring resonators which are af- transmission-line consisting of mass and stiffness ele- fixed to an elastic plate as structural support[19, 20]. ments. The mass-spring systems, which demonstrate ex- Alternatively, soft acoustic metamaterials represent a treme effective mass and stiffness in the vicinity of the paradigm shift beyond this framework by creating the mass-spring resonance, are therefore referred to as lo- dynamics from the structure itself. It is important to cally resonant acoustic metamaterials (LRAMs) [5, 28{ emphasize that such a soft acoustic metamaterial, real- 32]. Although such mass and spring elements can be ized with the unique properties of aerogels, can be tai- arranged in a compact configuration and are relatively lored to obtain a wide spectrum of desirable exotic prop- simple and robust, the resulting extreme effective prop- erties in a single versatile subwavelength acoustic meta- erties are inherently narrowband and subject to appre- material element. In this work, theoretical and experi- ciable loss due to the close proximity of the mass-spring mental results for a compact metamaterial configuration resonance[8, 33]. Alternatively, acoustic metamaterials are presented, enabling a thin, conformal configuration have been proposed using thin elastic plates as a means to be realized. In particular, these structures represent for operating as a positive stiffness element in acous- a soft acoustic metamaterial, which are realized using tic transmission-line arrangements [18], which has re- the flexural resonance of the zeroth-order anti-symmetric cently been applied to acoustic metamaterial leaky-wave