Ultralight graphene oxide/polyvinyl alcohol aerogel for broadband and tuneable acoustic properties

An ultralight graphene oxide (GO)/polyvinyl alcohol (PVA) aerogel (GPA) is proposed as a new class of acoustic materials with tuneable and broadband sound absorption and sound transmission losses. The interaction between GO sheets and PVA molecules is exploited in our environmentally friendly manufacturing process to fabricate aerogels with hierarchical and tuneable porosity embedded in a honeycomb scaffold. The aerogels possess an enhanced ability to dissipate sound energy, with an extremely low density of 2.10 kg m−3, one of the lowest values ever reported for acoustic materials. We have first experimentally evaluated and optimised the effects of composition and thickness on the acoustic properties, namely sound absorption and sound transmission losses. Subsequently, we have employed a semi-analytical approach to evaluate the effect of different processing times on acoustic properties and assessed the relationships between the acoustic and non-acoustic properties of the materials. Over the 400–2500 Hz range, the reported average sound absorption coefficients are as high as 0.79, while the average sound transmission losses can reach 15.8 dB. We envisage that our subwavelength thin and light aerogel-based materials will possess other functional properties such as fire resistance and EMI shielding, and will prove to be novel acoustic materials for advanced engineering applications.

. Comparison of density, porosity, and sound absorption properties between GPA-1 samples from this work and other porous absorbers with comparable thickness previously reported in the literature. A The average was calculated in the 400 -2500 Hz range. Methods used to measure acoustic properties.
The aerogels were acoustically characterised through measurements of two key parameters: the Normal Absorption Coefficient ( ) and the Normal Incident Sound Transmission Loss ( ). For the first, the standard test method ASTM E1050 6 was followed. Briefly, samples of the composite structure were placed in one end of a two microphone impedance tube having an internal diameter of 50.8 mm with a rigid back surface, while a loudspeaker generating a broadband random signal was mounted at the other end. The coefficient was then estimated as expressed in equation (S1): Where is the Complex Reflection Coefficient measured on the incident surface of the sample following the transfer function method 6 . The sound transmission losses were instead evaluated according to the standard test method ASTM E2611 7 . The procedure is similar to the determination of , but the transfer functions were calculated for four microphones, with two of them mounted each side of the sample, and two different terminations, anechoic and open. The was then estimated with equation (S2): where is the sound transmission coefficient.

Equivalent fluid model of porous absorbers.
The acoustic behaviour of GPA-1 samples, specifically in terms of sound absorption ability, was studied with a semi-phenomenological approach following the Johnson-Champoux-Allard (JCA) model for porous materials 8,9 . The effective density ( ) and effective bulk modulus ( ) relate the physical properties of the absorber to the sound propagation through it, and are calculated as expressed in equations (S3) and (S4): where 0 , , , and are density, dynamic viscosity, ratio of the specific heat capacities and Prandtl Number for air, respectively, while 0 is the atmospheric pressure. The remaining parameters (i.e., the non-acoustic properties of porous materials) are porosity ( ), flow resistivity ( ), tortuosity ( ∞ ), viscous (Λ) and thermal (Λ′) characteristic lengths.
Methods to measure the non-acoustic properties.
The porosity was calculated as expressed by equation (2) in the manuscript. The flow resistivity was indirectly measured from the low frequency acoustic behaviour of the samples in a standard impedance tube with two different terminations (i.e., anechoic and open), according to equation (S9) 10,11 where and were evaluated following the transfer matrix approach detailed in the standard test method ASTM E2611 7 .
The tortuosity was determined with ultrasonic wave speed measurements in a sample saturated by air, according to equation (S10) 12 : where the ratio of celerity in free air over velocity inside the porous material ( 0 ⁄ ) was calculated from the increase of the time of flight of a short ultrasonic pulse sent at 50 kHz between two transducers when a sample of the material was inserted. The loss angle ( ) was derived from the pulse signal damping. The viscous and thermal characteristic lengths were finally obtained using an inverse identification method 13,14 : The sound absorption coefficient predicted by the JCA model was fitted to the acoustical experimental data by varying Λ and Λ′ and keeping all the other non-acoustic properties fixed to the experimentally or indirectly derived values.