Normal Incidence Acoustic Absorption Characteristics of a Carbon Nanotube Forest

Transcription

1 Normal Incidence Acoustic Absorption Characteristics of a Carbon Nanotube Forest M. Ayub a,, A. C. Zander a, C. Q. Howard a, B. S. Cazzolato a, D. M. Huang b, V. N. Shanov c, N. T. Alvarez c a School of Mechanical Engineering, The University of Adelaide, SA 55, Australia b Department of Chemistry, The University of Adelaide, SA 55, Australia c Department of Biomedical, Chemical and Environmental Engineering, University of Cincinnati, Cincinnati, OH 45221, USA Abstract The acoustic absorption of carbon nanotube (CNT) absorbers made of vertically aligned CNT forests is investigated experimentally in an impedance tube using the two-microphone method with normal incidence. Results show that a 3 mm thick forest of CNTs can provide upto 1% acoustic absorption within the frequency range 125 Hz 4 khz. Theoretical predictions of the acoustic absorption properties of CNTs made using classical acoustic theories, including the Biot-Allard and Johnson-Allard models, agree reasonably well with the experimental results in terms of the general trends, although there are significant difference at specific frequencies. This suggests that nanoscopic acoustic absorption mechanisms are important and are not accurately represented within the classical models developed for conventional porous materials. In addition, theoretical studies of the acoustic absorption potential of CNT forest indicate that they may provide better acoustic absorption than conventional porous materials of equivalent thickness and mass, and that the absorption could be enhanced significantly with a lower forest density of CNTs than the samples tested in this study. Keywords: Carbon nanotube, CNT forest, acoustic absorption coefficient, porous absorption material, impedance tube 1. Introduction Advances in nanotechnology have provided acoustic researchers with a number of new materials, with features such as nanofibres and nanopores, that can potentially be implemented as porous acoustic absorbers. The molecular behaviour of these new nanoscopic Corresponding author. md.ayub@adelaide.edu.au Preprint submitted to Applied Acoustics June 14, 217

2 materials may have a significant influence on their sound absorption properties. In addition, their properties could play an important role in reducing the thickness and mass of absorbers compared with currently available materials. In the current era of nanotechnology, a variety of nanotube constituents are available that can be formed into nanoscopic fibres, for instance carbon nanotubes (CNTs) [1, 2], boron nitride nanotubes (BNTs) [3] and titania nanotubes (TNAs) [4]. Although carbon nanotubes are the most widely studied materials for nanofibres and composite foams [5], other nanotube types have a similar ability to form nanoscopic fibres and composites [3, 6]. Since the discovery of the carbon nanotube (CNT) structure by Iijima [1], numerous potential applications for CNTs have been suggested in the fields of electronics, energy, mechanics, field emission and lighting [5, 7]. Although a number of applications of CNTs in noise control engineering have also been suggested [5], they have not been widely used as sound absorbers. In one application, a lightweight CNT foam was fabricated by exploiting the extraordinarily strong inter-tube interaction between the carbon nanotubes, which could be used in shock absorbing and acoustic damping materials [5]. Recent developments in nanotechnology have also made it possible to construct CNT structures with unique alignment of the tubes in a particular direction (i.e. vertical or horizontal), which allows for the creation of structures with various desired fibre orientations [8 1]. In a study by Qian et al. [11], it was shown that super-aligned carbon nanotubes grown on the surface of a micro-perforated panel (MPP) can improve the acoustic absorption performance of MPP absorbers at low frequencies. Investigations were also conducted for nano-integrated polyurethane foam using multi-walled carbon nanotubes [12]. Test results showed that the incorporation of carbon nanotubes improved the acoustic absorption performance by 5-1% in the frequency range 8-4 Hz. Several other studies on the use of carbon nanotubes for enhancement of the acoustic absorption of conventional porous materials have been reported [13 15]. The use of carbon nanotubes for reducing airplane noise by encapsulating the carbon nanotubes in a polymer nanocomposite to create electrospun fibres has also been proposed [16]. It has been suggested that the nanotubes may improve the sound absorption performance of the polymer nanocomposites as the individual nanotubes would oscillate with the sound waves, helping to absorb sound energy [16]. Moreover, vertically aligned CNT arrays was investigated for optical absorption capability. It was observed that low-density vertically aligned CNT arrays can be engineered to make a near-perfect (an ideal black) optical absorption materials that 2

3 absorbs light at all angles and over all wavelengths [17]. Similarly, an analogues porous lamella structure were fabricated that behaves like a true deaf body [18]. Experimental observations showed that porous lamellas arranged into a low-density crystal backed by a reflecting support can absorb incident sound at all angles for a frequency range exceeding two octaves [18 2]. These developments in nanotechnology offer exciting possibilities for developing acoustic absorption materials using carbon nanotubes. Carbon nanotubes can be produced with an average diameter in the range of 3 to 5 nm and typical lengths of 1 µm to hundreds of micrometres [21] and more recently even millimetre lengths [22, 23] and thus can be used to produce absorbers with nanopores [5]. In general, for absorber materials, the lower the diameter of the fibre, the greater the acoustic absorption, as a reduction of the fibre diameter entails more fibres to achieve an equal volume density for a given absorber thickness, therefore creating a more tortuous path and higher airflow resistance [24 26]. Moreover, thin fibres can move more easily than thick fibres in the presence of sound waves, inducing vibration in air and increasing airflow resistance by means of friction through the vibration of the air [26]. Hence, absorbers with thin fibres such as CNTs have the potential to provide good acoustic absorption at low frequencies for a given absorber thickness. Moreover, advanced nanostructuring technologies can facilitate the tailoring of open cell structures in CNT arrays [5]. Open pore structures, together with the nanopores of the tubes, can potentially have a significant influence on the enhancement of acoustic absorption of CNT absorbers. Recent improvements [22, 23] in the fabrication of CNT absorbers with various CNT forest densities suggests that the investigation of the acoustic absorption of CNT arrays will guide the development of effective acoustic absorbers that make use of various arrangements of carbon nanotubes. However, a fundamental understanding of the physical mechanisms associated with the use of nanotubes as acoustic absorbers has not been developed, and their potential benefits have not been quantified. Furthermore, measurements of the acoustic absorption properties of nano-materials on their own have not been reported to date. The experimental investigation of the acoustic absorption characteristics of a CNT forest reported in this paper is a first step towards the establishment of a fundamental understanding of acoustic absorption at the nanoscale. Development of this understanding will advance the knowledge base of the discipline, and will also lay the ground work for other novel arrangements of acoustic absorbers to be investigated. This paper presents the acous- 3

4 tic absorption characteristics of a CNT forest based on experimental measurements and theoretical predictions using classical methods. Characterising the acoustic absorption behaviour of the CNT forest will allow researchers to determine the degree to which the acoustic absorption mechanisms of nano-materials are likely to deviate from continuum phenomena and the modelling approaches applicable to conventional porous materials. This paper examines the absorption coefficient of a forest of CNTs using an impedance tube with a normal incidence sound source. Details of experimental measurement methods and the corrective measures implemented to account for microphone phase mismatch error and tube attenuation are also discussed in this paper. Theoretical predictions of the acoustic absorption behaviour using the Biot-Allard [27, 28] and Johnson-Allard [28] models are described and compared with the experimental results. The results highlight the necessity for the existing theoretical models to be adjusted for nanoscale acoustic behaviour. A comparison of the absorption coefficient of a composite absorber made of a CNT absorber component and a conventional porous material is described and the results show the potential acoustic absorption benefits of CNT materials. In addition, a detailed description of the verification procedure of the measured results, including repeatability, reproducibility, and error analysis, is presented. It should also be noted that this article is an extended and a substantially new version of the paper[29] presented in the Inter-noise (214) conference. 2. Materials and Methods The acoustic absorption coefficient of the CNT forest was measured in an impedance tube using two microphones [3, 31] in accordance with the ASTM E15 standard [32]. It should also be noted that the research presented here forms a foundational study, with experiments performed on a few CNT samples of a limited size that are not intended to be commercial-grade acoustic absorbers Impedance Tube Method and Apparatus A schematic of the setup for the two-microphone impedance tube method is illustrated in Figure 1(a). A specimen to be tested is placed in a sample holder at the end of the tube. A sound source generates a plane wave inside the tube, which propagates through the sample and is reflected back from the rigid termination. Thus, a standing wave develops inside the tube. The transfer function between the two microphones located at positions 4

5 1 and 2 was measured as H12 = G12 /G22, where G12 is the averaged cross-spectrum between the two microphones and G22 is the averaged auto-spectrum of the microphone at location 2. The reflection coefficient, R, and absorption coefficient, α, at the face of (a) Schematic of impedance tube set up (b) Photograph of impedance tube arrangement Figure 1: (a) Schematic and (b) photograph of impedance tube and instrumentation used to measure the absorption coefficient of the CNT samples. the sample can be evaluated as [3, 31, 33] R = e2ikl1 H12 e ikd, e+ikd H12 α = 1 R 2, (1) (2) where e ikd = Hi and e+ikd = Hr represent acoustic transfer functions associated with the incident and reflected wave components, respectively [31], l1 is the distance of the microphone that is further from the surface of the termination, d is the separation distance between the two microphones and k is the wavenumber. The specific surface acoustic impedance Zs of the sample can also be determined from the measured reflection coefficient using the relation [3, 31, 33] Zs /ρc = 1+R, 1 R (3) where ρ is the density of air and c is the sound speed in air. A custom-made 22.1 mm internal-diameter steel impedance tube was used to measure the normal incidence absorption coefficient of the CNT acoustic absorber. The impedance tube was constructed from a number of pipe lengths, a horn driver, and a pipe section which holds the two microphones that measure the acoustic pressure in the 5

6 tube. A photograph of the experimental apparatus is shown in Figure 1(b). Overall, four microphone spacings of 2.43 mm, mm, 5.13 mm, and 14 mm were available to conduct the measurements with different operating frequency ranges, as determined by the upper and lower frequency limits [34 36], f u <.45c/d and f l >.5c/d, respectively. A list of the the upper and lower frequency limits for each of the microphone spacings of the impedance tube calculated using these equations is given in Table 1. It should be noted that the impedance tube has a cut-on frequency of 4.2 khz for the first higher order acoustic mode based on the tube diameter of 22.1 mm. This sets up the upper limit of the useful frequency range of the impedance tube. Table 1: Operating frequency range for different microphone spacings. Microphone spacing Frequency range d (mm) (khz) The instrumentation comprised two 1 -inch Brüel & Kjær (B&K) type 4958 array 4 microphones, a four-channel B&K Photon+ TM data acquisition system, and LDS Dactron software [37]. The B&K microphones have a free-field frequency response (re 25 Hz) of ±2 db within the frequency range 5 to 1 khz. A B&K type 4231 acoustic calibrator was used to calibrate the microphones to 94 db at 1 khz. Measurement data was acquired to give a 4 Hz frequency resolution, with a sampling interval of 7.6 µs (with 128 lines and points) and sample records of finite duration of approximately 16 s for 3 averages using a Hanning window. A B&K type 3545 sound intensity probe was used to verify the phase difference between the microphone pairs by placing them in an identical sound field generated in a B&K type UA914 sound intensity coupler with a B&K type ZI55 broadband sound source Correction for Microphone Phase Mismatch Error and Tube Attenuation The acoustic impedance was measured using the two-microphone method [3, 31]. When the transfer function between two microphones is measured, a phase error between the microphones is unavoidable and must be corrected. The standard sensor-switching technique [3] was used to calibrate the microphones used in the impedance tube. Each transfer function H 12 measured between the microphones was corrected (e.g., H corrected 12 = 6

7 H 12 /H cal ) by a calibration transfer function H cal = H 12 H 21 [38], which ensured that any variation in the magnitude and phase of the measured transfer function due to differences in the two sensors was eliminated. The transfer functions H 12 and H 21 were obtained by switching the locations of microphone 1 and microphone 2 shown in Figure 1(a), then measuring the transfer function. An additional correction was applied to account for the tube attenuation due to viscous and thermal losses at the tube walls, as well as damping and leaks using a method developed by Han et al. [33]. The real valued wavenumber k in the wave equation is replaced by a complex wavenumber, k = k ik, (4) where k = 2πf/c, with f and c the frequency and sound speed, respectively, and k the attenuation constant, which can be predicted theoretically using an empirical relationship provided in the standards ASTM E15 [32] and ISO [36] [33] as f k = A cd, (5) where D is the diameter of the tube and A is a constant. Values of A =.223 [32] and A =.194 [36] have been specified previously. As an alternative to Equation (5) the attenuation constant k can also be measured directly from the measured transfer function for an assumed rigid termination. The attenuation constant is estimated based on the relationship between reflection coefficient R and transfer function H 12, with the assumption of R = 1 for the rigid termination [33], where H 12 = cos[(k ik )(l 1 d)]. (6) cos[(k ik )l 1 ] Equation (6) can be solved numerically for k using the Newton-Raphson iteration scheme [33, 39]. Estimation of k from Equation (5) and from the measured transfer function using Equation (6), as detailed in Appendix A.3.2, shows that the tube has significant attenuation, which indicates this tube behaved as a lossy waveguide. Hence the tube attenuation correction was necessary for this arrangement. The estimated complex wavenumber k can also be used to predict the acoustic impedance Z i of the closed tube normalised to the characteristic impedance of air (ρc) 7

8 Acoustic impedance, Re[z i ] Acoustic impedance, Im[z i ] Theoretical: Re(z t i ) Experimental: Re(z e i ) Theoretical: Im(z t i ) Experimental: Im(z e i ) Figure 2: Experimental and theoretical estimates of the normalised internal acoustic impedance of the closed tube terminated with a rigid wall. Here superscripts e and t indicate the experimental and theoretical estimates of the impedance, respectively. using the analytical expression [4, 41] z t i = Z i ρc = i cot k L, (7) where L is the tube length ( 984 mm) and z t i is the normalised surface acoustic impedance. Figure 2 presents the analytical estimates of the real and imaginary components of the normalised acoustic impedance. The analytical estimate of the acoustic impedance of the closed tube was also compared with the experimental value estimated using the load impedance of the rigid termination. The normalised acoustic impedance z e i of a closed tube can be calculated from the measured surface acoustic impedance of the rigid termination using the expression [4] z e i = z r + i tan k L 1 + iz r tan k L, (8) where z r (= Z r /ρc) is the normalised surface acoustic impedance of the rigid wall termination. The real and imaginary parts of the normalised impedance are displayed in Figure 2 as dashed lines. It can be observed that both plots show consistency between the numerical and experimental results. The impedance measurement below 5 Hz is limited by poor signal to noise ratio due to low sound pressure levels from the horn driver and 8

9 (a) Fabricated CNT sample (b) CNT forest and sample holder Figure 3: Fabricated sample of 3 mm CNT forest. (The total thickness in (a) include the attached.5 mm substrate.) the non-flat amplitude response of the microphones at low frequencies Sample Preparation and Configuration The CNT samples were manufactured by a research team in the Nanoworld Laboratories at the University of Cincinnati, USA. A vertically aligned CNT forest was grown on a silicon wafer substrate to produce the absorber sample as exhibited in Figure 3. Each sample was 3 mm thick and cut to a diameter of 22.1 mm to match the internal diameter of the impedance tube. The vertically aligned CNT array was grown in a 5.8 mm (2 inch) quartz tube reactor (ET 1 by FirstNano) using a water-assisted chemical vapor deposition (CVD) process. The substrates were prepared as follows: (1) deposition of 2 nm Al (aluminum) film on a 11.6 mm (4 inch) Si wafer (1) coated with a (5 nm) SiO2 layer by electron beam evaporation, (2) oxidation of the Al film to form an Al2 O3 buffer layer, and (3) deposition of (1.5 nm) Fe/Gd thin film on the formed Al2 O3 /SiO2 /Si substrate structure by e-beam evaporation. The growth parameters were 4 SCCM (standard cubic centimetres per minute) Ar, 1 SCCM H2, 75 SCCM C2 H4 and 9 ppm H2 O vapor. The deposition temperature was maintained at 78 C. Details are presented in previously published works [22, 23]. The micro-morphological surface features and material characteristics of a CNT sample can be examined using scanning electronic microscopy (SEM) and transmission electron microscopy (TEM). SEM and TEM images of this type of sample can be found in previous works [22, 23]. The absorption coefficients of the CNT samples were measured using sample mounting configurations shown in Figure 4. The CNT samples were held in an annular mounting plate as shown in Figure 4(b). Several orientations of the CNT sample were tested in 9

10 (a) Mounting schematic for substrate only (b) CNT array (c) Composite absorber Figure 4: Arrangement of (a) the sample configuration for the substrate only, (b) the sample mounting plate to orient the CNT facing towards the acoustic source and (c) the sample configuration for a composite absorber panel. Note that components are shown as separated for illustrative purpose. The numbers on the mounting plates indicate that the configurations were adjusted accordingly for each orientation of the sample (such as blank tube, substrate, CNT and conventional absorber) by replacing the corresponding holding plates in the mounting arrangement shown in (a). order to separate the influence of the substrate material and the acoustic characteristics of the impedance tube. Figure 4(a) shows a configuration with only the substrate, in which the incident acoustic wave strikes the substrate material. This configuration was used to quantify the acoustic absorption coefficient of the substrate material. Figure 4(b) shows a similar mounting configuration used to measure the acoustic absorption coefficient of the sample for the case of an incident acoustic wave striking the CNT forest and substrate. The CNT forest was oriented (by replacing the substrate holding plate 3 with the CNT sample holding plate in the configuration shown in Figure 4(a)) such that the long axis of the CNTs was perpendicular to the substrate and aligned with the direction of propagation of the incident acoustic wave. To determine the absorption coefficient of the impedance tube apparatus in which no sample was installed in the sample holder (blank impedance tube), a configuration was made by removing sample mounting annular plate 3 and sample supporting plate 4, as shown in Figure 4(a). These configurations allowed the mounting condition of the CNT forest and substrate material to be the same for tests with and without the CNT forest exposed to the incident acoustic wave, without having any effect on the insertion loss during the measurements. Figure 4(c) shows a configuration in which a conventional absorber material was installed in the impedance tube along with the CNT sample, as used to determine the absorption coefficient of a composite absorber made of a conventional material and the CNT sample. 1

11 3. Results and Observations The experimental investigation of the test samples using the impedance tube comprised measurements of the normal incidence sound absorption coefficient of the CNT forest up to a maximum frequency of 4.2 khz. The measured coherence between the acoustic source and the microphone signals for the tests conducted here, as displayed in Figure A.24(a), was found to be close to 1 for the majority of the frequency range from 125 Hz to 4 khz. Hence, results are presented here for only that frequency range. The results were compared with those of the substrate (Si) material alone, a blank impedance tube, and conventional absorptive materials. The accuracy and reliability of the test results were also verified by conducting repeated measurements and by evaluating the errors in the measurements and calculations. A detailed description of the verification procedure can be found in Appendix A Experimental Results Measurements were conducted for several orientations of the sample to yield the acoustic absorption capability of the CNT forest. The mounting configurations shown in Figures 4(a) and 4(b) were used for the measurement of the absorption coefficient of the substrate material and the CNT forest, respectively. The measurement for the substrate material alone was conducted to determine the influence of the substrate material on the CNT forest absorption measurements. The absorption coefficient of the blank impedance tube was also measured using a similar mounting configuration to that shown in Figure 4(a) (by removing the sample holder and supporting plates 3 and 4) to estimate the acoustic absorption by the impedance tube itself. Comparison of the acoustic absorption coefficient for these three configurations is necessary to determine the absorption of the CNT forest alone. The acoustic absorption coefficient α of the CNT forest, the substrate material, and the blank impedance tube were estimated from the transfer function (H 12 ) measured between the two microphones placed with a separation distance of mm (where the measured distance was corrected using the frequency null method [38], as discussed in Appendix A.3). The assumed rigid termination consisted of a 5 mm thick mild steel blanking plate. Figure 5 shows the measured absorption coefficient of the blank impedance tube (with the rigid termination) and that of the substrate material for the sample configurations shown in Figure 4(a), with and without the implementation of the correction for tube attenuation. It may be observed that both the substrate and 11

12 Absorption Coefficient, α Rigid wall, α mes Rigid wall, α corr Substrate, α mes Substrate, α corr Figure 5: Measured and corrected normal incidence sound absorption coefficient of substrate material and tube with rigid termination. Here, α mes and α corr correspond to the measured and corrected absorption coefficients, respectively the rigid wall termination show almost the same amount of absorption, which indicates that the substrate material can be considered as a rigid wall for the comparison of the absorption behaviour with that of the CNTs. As shown in Figure 5, the impedance tube exhibits an absorption of less than 25%, which occurs predominantly due to the attenuation associated with the small tube diameter [33], as well as sound leakage around the tube end and background noise. However, the expected result of zero absorption for the rigid wall termination is nearly achieved once the correction for tube attenuation [33] is applied. Figure 6 shows the measured absorption coefficient of the CNT forest for the sample configuration shown in Figure 4(b). The absorption coefficient was estimated by applying the correction to the measured results, which was also comparable with the difference of absorption coefficients between that of the CNT forest and the bare tube with rigid termination. It can be seen that the CNT forest shows a 5 1 % normal incidence acoustic absorption coefficient over the mid and high frequency range and less than 5% absorption at low frequencies below 1 Hz. It is acknowledged that an absorption coefficient of 5% is unremarkable compared with conventional acoustic absorption materials that have values of 5%. However, it will be shown in Section 4 that when equivalent material weights are used, the CNT samples have comparable acoustic absorption. The thickness of the sample used in this test was very thin compared with the wavelength and there was a concern that the incident noise had little chance to dissipate before being reflected back from the rigid wall [42]. Hence, it was anticipated that the acoustic 12

13 Absorption Coefficient, α CNT, α mes Rigid Wall, α mes CNT, α corr Rigid Wall, α corr Differences, α corr = α corr diff CNT - αcorr Rigid wall Figure 6: Measured and corrected normal incidence acoustic absorption coefficient of CNT forest sample compared with that of the tube with rigid termination. The differences curve was obtained by taking the difference between the measured absorption coefficient of the bare rigid walled tube and that with the CNT forest present. behaviour of the CNT forest could be more accurately captured if the sample was combined with conventional materials and an air gap to increase the absorber thickness. This method would also increase the acoustic absorption coefficient above the noise floor of the lossy waveguide (impedance tube) and the effect of losses (by the rigid walled tube) on the results would be avoided. Therefore, additional measurements were conducted with the CNT forest combined with conventional porous materials to check the reliability of the previously obtained acoustic absorption coefficient of the CNT forest. In addition, an improvement in the acoustic absorption of a conventional absorber can be observed if the CNT forest is combined with conventional porous materials to create a composite absorber panel. A conventional absorptive material of 14.5 mm polyurethane (PU) foam (.1176 g, 21.1 kgm 3 ) was placed in front of the CNT forest as shown in Figure 4(c). The previously used arrangements shown in Figure 4 were again used to carry out the measurements for the composite absorber panels for three different mounting conditions of the CNT forest, substrate material, and rigid wall. To isolate the contributions of the CNT to the acoustic absorption, the following configurations were experimentally measured: Panel A mm PU (polyurethane foam) + 37 mm AG (air gap) + 3 mm CNT + RW (rigid wall) Panel B mm PU + (37 mm + 3 mm) AG + ST (substrate) 13

14 Panel C mm PU + (37 mm + 3 mm) AG + RW Panel D mm PU + (37 mm + 3 mm) AG + 3 mm CNT + RW The configurations of Panel A, Panel B, and Panel C were chosen to represent arrangements (combined with the PU foam) equivalent to that of the CNT forest, substrate material, and rigid wall, respectively. The schematic shown in Figure 4(c) represent the mounting configuration for Panel A. A photograph of the test sample of polyurethane foam and the estimated absorption coefficient results from the measurements are shown in Figures 7(a) and 7(b), respectively. As expected, Panel A comprising the polyurethane.6.5 Absorption Coefficient, α Panel A: PU + 37 mm AG + CNT Panel B: PU + 4 mm AG + ST Panel C: PU + 4 mm AG + RW Panel D: PU + 4 mm AG + CNT α diff : Panel A - Panel C α corr : Panel A - Panel C diff (a) Polyurethane foam sample (b) Measured absorption coefficient of composite absorber Figure 7: Comparison of the absorption coefficient for combinations of polyurethane foam and the CNT forest. Here, α diff and αdiff corr correspond to the difference between the measured and corrected absorption coefficients of the CNT and rigid wall. PU, CNT, AG, ST and RW stand for the polyurethane foam (14.5 mm), CNT forest (3 mm), air gap, substrate, and rigid wall, respectively. foam backed by the CNT forest (solid bold line in the figure) exhibits a higher acoustic absorption coefficient than Panel B and Panel C which incorporate the substrate material and rigid wall, respectively. Replacing the 3 mm air gap with the 3 mm CNT forest in the composite Panel C comprising 14.5 mm PU foam, 4 mm air gap and the rigid wall decreased the surface impedance above a frequency of 15 Hz. It reduced the mismatch between the impedance of the absorber and the characteristic impedance of air, resulting in higher acoustic absorption by the composite Panel A. Similarly, a fourth type of composite panel with the 14.5 mm PU foam, 4 mm air gap, and 3 mm CNT forest (Panel D) increased the acoustic absorption coefficient at the low and high frequencies. This result supports the veracity of the earlier assessment of the absorption capability of CNTs. The 14

15 findings also highlight the ability of CNTs to enhance the acoustic absorption coefficient of conventional porous materials as was shown by previous researchers [13 15]. In order to demonstrate the significance of the absorption performance of nanoscopic fibres, the absorption characteristics of a CNT forest were also compared with those of conventional porous materials for samples of equivalent thickness and equivalent mass. A detailed analysis of this comparison is presented in Section 4. The estimated acoustic absorption coefficient of the CNT forest samples used in this study as shown in Figures 6 and 7 is very small and not sufficient to consider the CNT forests in the form investigated as beneficial as sound absorbers. However, neither the arrangement of the CNTs, their density nor the thickness of the specimen had been optimised in any way for acoustic absorption considerations. Advanced manufacturing methods are allowing CNTs in the range of centimetres (cm) in length scale to be fabricated [22, 23, 43 46]. It is anticipated that a forest of CNTs of greater length (in the cm range), lower density, and possibly with a different arrangement of the nanotubes could be used to provide enhanced acoustic absorption. Advances in nanotechnology show that centimetre-long CNT forests can be grown efficiently using water-assisted thermal CVD (chemical vapour deposition) with a controlled growth time [22, 23]. In addition, it has been shown that a wide range of forest densities can be synthesised by controlling the catalyst nano-particle formation process [47]. Long CNT arrays with low forest density may permit the CNTs to vibrate more with the sound waves, resulting in additional absorption. Furthermore, patterned CNT arrays can currently be fabricated with various densities of CNTs, for example, CNT arrays in which the nanotubes are bunched together in 1 mm-diameter post-like structures [22] and for which the density of the forest could be optimised to increase acoustic absorption. Several other arrangements of CNT are also possible [22, 23], including super-aligned arrays [11]. The experimental study conducted here on a CNT forest of a limited size supports that potential. Further experiments are needed to measure the absorption coefficient of a CNT sample of greater length and possibly lower forest density with the aim of observing an increased absorption coefficient sufficient for practical application as a CNT-based acoustic absorber. Theoretical estimates of the absorption coefficient for different length of CNTs and bulk density of the CNT forest, presented in Section 5, show that the absorption performance could be improved significantly with a lower forest density of CNTs. Overall, these results indicate that it is worthwhile pursuing further study of CNTs as acoustic absorbers. 15

16 3.2. Theoretical Prediction using Classical Methods The acoustic absorption mechanisms and the acoustic behaviour of CNTs are expected to differ with those of conventional porous materials based on considerations of the physical structure and size of the CNTs. Thus, the classical methods applicable for conventional materials might not be able to characterise the acoustic behaviour of the CNTs. Therefore, it is of interest to analyse the acoustic behaviour using classical methods to explore whether experimental estimates of the absorption coefficient of the CNTs deviate from theoretical predictions. Table 2: Measured parameters and estimated physical properties of the CNTs and CNT forest that were used to predict the acoustic absorption characteristics using classical methods. Parameters Value Sample thickness, t (mm) 3. Fibre diameter, d f (nm) 12 Mass of the sample, m (g).499 Bulk density, ρ b (kg m 3 ) 43.4 Nanotube (Multi-walled) density, ρ m (kg m 3 ), [21] 21 Shear modulus, N (GPa), [48] 1.4 Poisson s ratio, ν, [49].2 Predicted properties Flow resistivity, σ (Pa s m 2 ): 9 ρ1.53 b (a) σ Bies-Hansen = d 2, [5 52] f Developed for fibre glass products with d f < 15 µm, Range of d f used for experimentation: 1 2 µm (b) σ Ballagh = 49 ρ1.61 b df, [53] Developed for wool with mean d f = 29 µm, Range of d f used for experimentation: µm (c) σgarai-pompoli modified = ρ1.44 b d 2, [54] f Developed for polyester fibre with mean d f = 33 µm, Range of d f used for experimentation: µm Porosity: φ = 1 ρ b ρ m, [51].979 Tortuosity: α φ 1, [55] 1.15 Viscous characteristic length, Λ (µm): Λ = 1, where l = 4ρ b πd f, [28, 56].145 l ρm πd 2 f Thermal characteristic length, Λ (µm): Λ = 2Λ, [28].29 The simple empirical and classical methods of the Bies-Hansen (see [5], p623, Appendix C), Garai-Pompoli [54] (both are actually a modified Delany-Bazley model [58]), 16

17 Absorption Coefficient, α 3 mm CNT Experimental, α corr 3 mm CNT Biot-Allard, σ Garai-Pompoli Garai-Pompoli, σ Ballagh Delany-Bazley, σ Ballagh Biot-Allard, σ Ballagh Biot-Allard, σ Bies-Hansen Garai-Pompoli, σ Garai-Pompoli Bies-Hansen, σ Ballagh Johnson-Allard, σ Garai-Pompoli Biot-Allard, σ Optimum Figure 8: Theoretical prediction of the absorption coefficient of the CNT forest using the classical models of Biot-Allard [28, 57], Johnson-Allard [28, 51] and Bies-Hansen [5]. The predicted absorption coefficient of the Biot-Allard and Johnson-Allard models using the flow resistivity value of σ Garai-Pompoli and of the Bies-Hansen and Delany-Bazley empirical models using the flow resistivity value of σ Ballagh are identical and coincide with each other in the figure. Biot-Allard [27, 28] and Johnson-Allard [28] models were used to predict the acoustic absorption behaviour of the CNT forest. The estimated non-acoustical parameters of the CNTs used here to calculate the theoretical acoustic absorption coefficient are listed in Table 2. The geometrical and physical properties given in Table 2 were measured by the research group in the Nanoworld Laboratories at the University of Cincinnati, USA, and the details have been presented previously [22, 23]. The predicted absorption coefficient of the CNT forest based on the estimated non-acoustical properties using the five theoretical methods is shown in Figure 8. It can be noticed that the predicted acoustic absorption coefficients are significantly influenced by the value of the estimated flow resistivity parameters. As listed in Table 2, the flow resistivity relationships by Bies- Hansen [5] and Ballagh [53] give two significantly different values of the flow resistivity of Pa s m 2 and Pa s m 2, respectively. The effect of these estimates is reflected in the predicted absorption coefficient using the Biot model (σ Bies-Hansen and σ Ballagh ) shown in the figure. It can be seen that the use of a flow resistivity value of Pa s m 2 (σ Ballagh ) overestimates the acoustic absorption coefficient of the CNT 17

18 forest compared with that of the experimental measurement. On the other hand, the Biot model with a flow resistivity value of Pa s m 2 (σ Bies-Hansen ), severely underpredicts the absorption coefficient of the CNT forest. Similarly, other empirical models such as the Delany-Bazley [58] and Bies-Hansen [5] models under-predict the acoustic absorption coefficient with the flow resistivity value σ Ballagh, whilst the Garai-Pompoli [54] model over-estimates. This kind of inconsistency among the empirical models is expected considering the flow resistivity value of the CNT sample is six orders of magnitude larger than the applicable flow resistivity range of 1 3 to Pa s m 2 for accurately predicting the absorption coefficient using these models [5]. In addition, the predicted flow resistivity value in the range of 1 9 to 1 1 Pa s m 2 is excessively high for an absorber material of 3 mm thickness. Hypothetically, an absorber material with a very high flow resistivity will have a high surface acoustic impedance for a small thickness of the material; thus it will result in a high impedance mismatch with the characteristic impedance of air and reduce the chance of incident sound waves entering the absorber and being dissipated. Hence, the classical models using a flow resistivity value of Pa s m 2 given by σ Bies-Hansen predict a low absorption coefficient. However, the two estimates of the flow resistivity value given by σ Ballagh and σ Bies-Hansen may be taken as representative of extreme values for theoretical estimates of the flow resistivity of a CNT forest, considering their effect on the predicted absorption coefficient, as shown by the Biot-Allard model. Furthermore, it can be demonstrated that a flow resistivity value chosen between these two extreme values of σ Ballagh and σ Bies-Hansen can be used to predict an acoustic absorption coefficient similar to that of the experimental measurements. A modified equation of σ Garai-Pompoli [54], given in Table 2, was used to predict the new flow resistivity value to be Pa s m 2. It can be seen that a flow resistivity of Pa s m 2 (σ Garai-Pompoli ) in the Biot-Allard [27, 28] and Garai-Pompoli [54] models predicts acoustic absorption coefficients similar to the experimental values for the CNT forest, except for the uneven pattern of the curve. Nevertheless, an optimum value of flow resistivity, σ Optimum = Pa s m 2 gives a better prediction. Consequently, it is evident from Figure 8 that most of the classical methods based on phenomological models and microscopic mechanisms fail to accurately predict the acoustic absorption behaviour of the CNT forest. The reason for the discrepancies between the theoretical and experimental estimates of the acoustic absorption coefficient can be attributed to the significantly different values for the flow resistivity and characteristic 18

19 lengths of the CNT forest compared with conventional materials. Compared with conventional porous materials, the estimated flow resistivity of the CNT forest is very high given the small thickness of the material. The large material density (43.4 kg m 3 ) and the thin fibres (nanotube diameter = 12 nm) of the CNT forest, may contribute to the high flow resistivity, which influences the viscous and thermal losses substantially. Moreover, as listed in Table 2, the estimated characteristic length (viscous length = 145 nm) is only one order of magnitude larger than the fibre (nanotube) diameter of 12 nm, whereas typical porous materials have characteristic lengths many orders of magnitude larger than the CNT fibre diameter [53]. For example, the typical fibre diameter of 6.1 µm and 5.58 µm of glass wool and melamine foam has characteristic lengths of 132 µm and 199 µm, respectively [51]. These factors will affect the thermal and viscous layer thicknesses, and as a result, the relative influences of the various mechanisms are expected to change for CNTs or materials with pores or fibres at the smaller nanoscale (down to 1 nm). Despite having thin fibres (12 nm), CNTs have another extraordinary feature in the natural hollow structure of the fibre (i.e. nanotube), which potentially provides increased frictional resistance between the sound waves and the nanotubes and will also transfer the air particle vibrations into fibre vibrations more easily [59]. As a result, CNTs may provide a different mechanism for structural vibration and heat transfer interaction with the gas molecules, which would contribute in a different manner to the viscous and thermal boundary layers of conventional materials. Thus, accurate estimates of the viscous and thermal effects during the interaction between the material and the sound wave would be crucial to predict the acoustic absorption of a CNT acoustic absorber. Although these are plausible explanations of the acoustic behaviour of CNTs based on the experiments conducted on limited samples, further investigations and measurements of the non-acoustical parameters are required to confirm these concepts. Overall, it can be concluded that the microscopic absorption mechanism applicable to conventional materials is not applicable to nanoscopic fibres such as CNTs. In order to develop an understanding of the nanoscopic acoustic absorption mechanisms, acoustic modelling in the nanoscale range using molecular simulation is essential. Further research on modifications to the analytical methods is required as well. An overview of potential simulation methods such as Molecular Dynamics (MD), Direct Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) can be found in the authors review article [6, 61]. 19

20 4. Comparison with Conventional Materials The significance of the acoustic absorption performance of CNT forests can be demonstrated by considering the absorption characteristics of conventional materials such as melamine foam and glass wool for an equivalent thickness or mass of the material. The analytical framework applied here was adapted from Kino and Ueno [51] to predict the normal incidence acoustic absorption coefficient of a reference thickness of 25.5 mm melamine foam and 25 mm of glass wool using the relevant non-acoustical parameters. Thereafter, the model was used to predict the acoustic absorption coefficient of both materials by reducing the material thickness to 3 mm, equivalent to that of the CNT forest. Comparison of the absorption coefficient of the 3 mm CNT forest and conventional porous materials of equivalent thickness is displayed in Figure 9(a), which shows that both conventional materials exhibit lower absorption than the CNT forest for an equivalent thickness. A g of 3 mm CNT forest (43.4 kg/m 3 ).499 g of mm Melamine foam (1.3 kg/m 3 ).499 g of 4.9 mm Glass wool (31.8 kg/m 3 ) Absorption Coefficient, α Absorption Coefficient, α mm CNT forest (.499 g, 43.4 kg/m 3 ).1 3 mm Melamine foam (.119 g, 1.3 kg/m 3 ) 3 mm Glass wool (.366 g, 31.8 kg/m 3 ) (a) Equivalent thickness (b) Equivalent mass Figure 9: Comparison of experimentally measured acoustic absorption coefficient of CNT forest with theoretical estimates for two conventional porous materials, melamine foam and glass wool, of equivalent (a) thickness and (b) mass. Note that the mass of CNTs (without the substrate) here is an estimate from the sample configuration shown in Figure 3(a), in which the CNTs were attached to the substrate. similar comparison of the acoustic absorption coefficient of the CNT forest and the porous materials is presented in Figure 9(b) for an equivalent mass to the CNT sample (.499 g). It can be observed that 4.9 mm of glass wool of equivalent mass (.499 g) may provide similar absorption to a 3 mm CNT forest. On the other hand, mm of melamine foam of equivalent mass may yield a maximum absorption of 5% (at 4 khz) over the measured frequency range, which is significantly higher than the CNT forest. As shown in Figure 9(b), even though an equivalent mass of melamine foam may produce significantly higher sound absorption than that of a CNT forest, it is four times as thick as the 2

21 CNT forest. These results highlight the significance of the absorption ability of CNTs and their potential for implementation in CNT acoustic absorbers. High flow-resistivity porous materials may exhibit similar or even higher absorption than a CNT forest. For instance, the sound absorption coefficient of a 3.5 mm Refrasil (produced from amorphous silica) sample (.224 g and kg m 3 ) was measured and the result is presented in Figure 1. As shown in the figure, this conventional porous material with a high flow resistivity shows higher absorption (by almost a factor of two) than the CNT forest. However, considering the flexibility available in fabricating CNT structures with different density and tube arrangements, it could be possible for a CNT absorber with lower forest density to achieve a similar or higher absorption than that of high flow-resistivity porous materials for an equivalent thickness. The effect of forest density is discussed in the following Section mm CNT forest (.499 g, 43.4 kg/m 3 ) 3.5 mm Refrasil (.224 g, kg/m 3 ) Absorption Coefficient, α (a) Refrasil sample (b) Measured absorption coefficients of 3.5 mm Refrasil and the 3 mm CNT forest Figure 1: Comparison of the sound absorption coefficient of the CNT forest with a high absorption coefficient specimen, Refrasil (3.5 mm), measured using the impedance tube. Refreasil is a commercial name for silica-based insulation products[62]. 5. Effects of CNT Length and Bulk Density The effects of CNT length and the bulk density of the CNT forest on the acoustic absorption performance of CNT absorbers were explored using the theoretical estimates of absorption coefficients based on the classical acoustic absorption model of Biot-Allard [28, 57] and the flow resistivity model of Garai-Pompoli [54] which gave a reasonable estimates of experimentally measured absorption coefficients of the CNT forest as shown 21

22 in Figure 8. The acoustic absorption performance of a 3 mm CNT forest was compared with that of CNT forests of varying thickness in the range of 3 5 mm and varying density in the range of kg m 3 (which are in the range of densities of melamine foam and glass wool [51]) to determine the effects on the absorption of CNT absorbers. Figure 11 shows the estimates of acoustic absorption coefficients for varying bulk density of the 3 mm CNT forest in the frequency range of 125 Hz 4. khz. It can be seen that Absorption Coefficient, α Experiments ρ b = 43.4 kg/m 3 ρ b = 2.7 kg/m 3 ρ b =1 kg/m 3 ρ b =7 kg/m 3 ρ b =5 kg/m Figure 11: Comparison of theoretical estimates of acoustic absorption coefficient of a 3 mm CNT forest with varying bulk density. absorption increases significantly as the bulk density of the CNT forest decreases. A 5 % reduction in the bulk density of the 3 mm CNT forest from its measured bulk density of 43.4 kg m 3 exhibits a 5 % increase in the absorption coefficient. Similarly, a 9 % reduction in the bulk density increases the absorption coefficient by as much as a factor of 4. This suggests that the absorption performance of CNT absorbers can be improved significantly with a lower CNT forest density and that the density may be optimised to tailor a CNT absorber with absorption capabilities suitable for commercial noise control applications. The result also implies that the bulk density of the 3 mm CNT sample used for the experiments was excessively high, which created a congested internal structure of the CNT forest and reduced the effect of the torturous path that allows the sound to travel inside the absorber. Thus, it is likely most of the incident sound waves were reflected back from the CNT surface instead of being absorbed, resulting in the relatively low absorption of the sample investigated in this study. The acoustic absorption performance of the CNT forest with a bulk density of 43.4 kg m 3 22

23 was calculated for varying thickness of CNTs and the results are presented in Figure 12(a). It can be observed that the length of the CNTs has a very small and subtle effect (at Absorption Coefficient, α.1.5 Experiment, 3 mm CNT 3 mm CNT 6 mm CNT 2 mm CNT 5 mm CNT Absorption Coefficient, α mm CNT 6 mm CNT 2 mm CNT 5 mm CNT (a) CNT forest with a bulk density of 43.4 kg m (b) CNT forest with a bulk density of 1 kg m 3 Figure 12: Comparison of theoretical estimates of the acoustic absorption coefficient of CNT forests with bulk densities of (a) 43.4 kg m 3 and (b) 1 kg m 3 for varying thickness. low frequency) on the absorption performance of the density of the CNT forest investigated here, which is in contrast to conventional materials, for which the thickness is a dominating factor for enhancing the absorption. This can be attributed to the high bulk density of the sample, as mentioned earlier. Hence, the absorption performance of CNT forests with varying thickness were also estimated for a much lower bulk density of the sample. For instance, the acoustic absorption of a 3 mm CNT forest with a bulk density of 1 kg m 3 shown in Figure 12(b) indicates that the absorption of the CNT forest increases at low frequency as the thickness increases from 3 to 5 mm. However, the effect of the thickness is not as significant as that of the bulk density. 6. Absorption of Sound at Oblique Incidence Although only the normal incidence acoustic absorption has been experimentally measured here, in order to observe the effect of the angle of incidence of sound on the absorption behaviour of CNT forests, the absorption coefficient of the 3mm CNT forest at oblique incidence was estimated using the plane wave assumption based on the classical absorption model of Biot-Allard [28, 57] and the flow resistivity model of Garai-Pompoli [54]. Figure 13 shows the absorption behaviour of the CNT forest at angles of incidence of 3, 45, 6 and 8 degrees and at random incidence. It can be seen that the acoustic absorption coefficient varies with the angle of incidence and increases with more oblique 23

24 angles of incidence. The results also indicate that the trends (i.e., the absorption curves) remain almost the same as for normal incidence except for having larger absorption values. In addition, estimate of random incidence acoustic absorption coefficient (also known as statistical absorption) of the CNT forest shows higher values compared with the normal incidence absorption coefficient indicating enhanced absorption at diffuse field. This observation also suggest that changing the alignment of the CNT forest with respect to the angle of incidence may affect the absorption coefficient of CNT absorbers. Hence, the sound absorption by CNTs at oblique incidence and with different orientation of the CNT forest is of interest for future study. Absorption Coefficient, α 3 mm CNT θ = θ = 3 θ = 45 θ = 6 θ = 8 Measurement Statistical absorption Figure 13: Comparison of theoretical estimates of acoustic absorption coefficient of a 3 mm CNT forest at normal (θ = ), oblique angles of incidence (θ = 3, 45,6, 8 ) ) and random incidence. Estimate of acoustic absorption at random angles of incidence is exhibited as statistical absorption of sound, which is evaluated using the method described by Bies and Hansen [5] based on specific acoustic normal impedance. Here, the measurement data is the absorption coefficient obtained at normal incidence (θ = ) using the impedance tube method. 7. Conclusion This paper presents the acoustic absorption characteristics of a CNT absorber based on an experimental investigation of the acoustic absorption coefficient of a forest of aligned CNTs within the frequency range of 125 Hz to 4.2 khz. It was found that a CNT forest with a material thickness of 3 mm can provide up to 1% acoustic absorption and can enhance by 5 1 % the acoustic absorption of a combined composite acoustic panel consisting of the CNT forest and a conventional porous material. Although only a small 24

25 enhancement in absorption was demonstrated for the CNT samples investigated, it was achieved by a small mass (.499 g) and thickness (3 mm) of the CNT forest. It was also shown that the absorption is reproducible. This investigation exposes the limitations of classical methods, based on phenomological models and microscopic mechanisms, to accurately predict the performance of the CNTs for acoustic absorption. Although the theoretical predictions using the models developed for conventional acoustic materials do agree reasonably well in terms of the general trends, they do not agree well with the experimentally measured acoustic absorption coefficient of the CNT forest at specific frequencies. The results also suggest that the acoustic absorption mechanisms are likely to deviate from those for continuum phenomena. In addition, a comparison of the absorption ability between the CNT forest and conventional porous materials shows that the CNT absorber of lower thickness and mass can achieve the equivalent (or significantly higher) absorption coefficient to a conventional material. Moreover, a theoretical study on the effect of bulk density of the CNT forest indicates that the absorption performance could be improved with a lower forest density of CNTs. These results demonstrate the significance of the absorption capability of CNT absorbers. The overall findings also highlight the necessity of acoustic modelling at the nanoscale to develop an understanding of the nanoscopic absorption mechanisms of CNTs. 8. Acknowledgement This research was supported under Australian Research Council s Discovery Projects funding scheme (project number DP ). The authors would like to thank Prof. Mark Schulz of Nanoworld Laboratories (University of Cincinnati, USA) for providing the carbon nanotube samples. The assistance of Mr Hywel Bennett with the experiments is greatly appreciated. References [1] Iijima, S.. Helical microtubules of graphitic carbon. Nature (London) 1991;354: [2] Koziol, K., Vilatela, J., Moisala, A., Motta, M., Cunniff, P., Sennett, M., Windle, A.. High-performance carbon nanotube fiber. Science 27;318(5858):

26 [3] Cohen, M.L., Zettl, A.. The physics of boron nitride nanotubes. Physics Today 21;63(11): [4] Peng, H., Li, G., Zhang, Z.. Synthesis of bundle-like structure of titania nanotubes. Materials Letters 25;59(1): [5] Ajayan, P., Carrillo, A., Chakrapani, N., Kane, R.S., Wei, B.. Carbon nanotube foam and method of making and using thereof. US Patent No. 11/5474, Rensselaer Polytechnic Institute; 26. [6] Yuan, Z.Y., Su, B.L.. Titanium oxide nanotubes, nanofibers and nanowires. Colloids and Surfaces A: Physicochemical and Engineering Aspects 24;241(1-3): [7] Endo, M., Strano, M.S., Ajayan, P.M.. Potential applications of carbon nanotubes; vol Berlin/Heidelberg: Springer-Verlag; 28, p [8] Yang, Y., Huang, S., He, H., Mau, A., Dai, L.. Patterned growth of wellaligned carbon nanotubes: A photolithographic approach. Journal of the American Chemical Society 1999;121(46): [9] Huang, S., Mau, A., Turney, T., White, P., Dai, L.. Patterned growth of wellaligned carbon nanotubes: A soft-lithographic approach. The Journal of Physical Chemistry B 2;14(1): [1] CSIRO - Breakthrough for carbon nanotube materials. Media release, The Commonwealth Scientific and Industrial Research Organisation, Australia, Reference: 5/153,; 25. URL: psh5.html. [11] Qian, Y.J., Kong, D.Y., Liu, Y., Liu, S.M., Li, Z.B., Shao, D.S., Sun, S.M.. Improvement of sound absorption characteristics under low frequency for microperforated panel absorbers using super-aligned carbon nanotube arrays. Applied Acoustics 214;82: [12] Cherng, J.. Smart acoustic materials for automotive applications. Tech. Rep.; Henry W Patton Center for Engineering Education and Practice, The University of Michigan-Dearnborn;

27 [13] Bandarian, M., Shojaei, A., Rashidi, A.M.. Thermal, mechanical and acoustic damping properties of flexible open-cell polyurethane/multi-walled carbon nanotube foams: Effect of surface functionality of nanotubes. Polymer International 211;6(3): [14] Verdejo, R., Stämpfli, R., Alvarez-Lainez, M., Mourad, S., Rodriguez- Perez, M., Brhwiler, P., Shaffer, M.. Enhanced acoustic damping in flexible polyurethane foams filled with carbon nanotubes. Composites Science and Technology 29;69(1): [15] Basirjafari, S., Malekfar, R., Khadem, S.E.. Low loading of carbon nanotubes to enhance acoustical properties of poly(ether)urethane foams. Journal of Applied Physics 212;112: [16] Crawford, M.. Reducing airplane noise with nanofibers. Aerospace and Defense Topics, ASME; 212. URL: aerospace-defense/reducing-airplane-noise-with-nanofibers. [17] Yang, Z.P., Ci, L., Bur, J.A., Lin, S.Y., Ajayan, P.M.. Experimental observation of an extremely dark material made by a low-density nanotube array. Nano Letters 28;8: [18] Christensen, J., Romero-García, V., Picó, R., Cebrecos, A., García de Abajo, F.J., Mortensen, N.A., Willatzen, M., et al. Extraordinary absorption of sound in porous lamella-crystals. Scientific Reports 214;4:1 5. doi:1.138/srep4674. [19] Christensen, J., Willatzen, M.. Acoustic wave propagation and stochastic effects in metamaterial absorbers. Applied Physics Letters 214;15:1 4. doi:1.163/ [2] Christensen, J., Mortensen, N.A., Willatzen, M.. Modelling the acoustical response of lossy lamella-crystals. Journal of Applied Physics 214;116:1 5. doi:1.163/ [21] Seetharamappa, J., Yellappa, S., DSouza, F.. Carbon nanotubes: Next generation of electronic materials. The Electrochemical Society Interface 26;15(2):

28 [22] Cho, W., Schulz, M., Shanov, V.. Growth and characterization of vertically aligned centimeter long CNT arrays. Carbon 214;72: [23] Cho, W., Schulz, M., Shanov, V.. Growth termination mechanism of vertically aligned centimeter long carbon nanotube arrays. Carbon 214;69: [24] Sun, F., Banks-Lee, P., Peng, H.. Sound absorption in an anisotropic periodically layered fluid-saturated porous medium. Applied Acoustics 1993;39(1-2): [25] Lee, Y., Joo, C.. Sound absorption properties of recycled polyester fibrous assembly absorbers. AUTEX Research J 23;3: [26] Nor, M.J.M., Ayub, M., Zulkifli, R., Amin, N., Hosseini Fouladi, M.. Effect of different factors on the acoustic absorption of coir fiber. Journal of Applied Sciences 21;1(22): [27] Biot, M.. Generalized theory of acoustic propagation in porous media. Journal of the Acoustical Society of America 1962;34(9): [28] Allard, J.. Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials. Elsevier Applied Science, London; [29] Ayub, M., Zander, A.C., Howard, C.Q., Cazzolato, B.S., Shanov, V.N., Alvarez, N.T., Huang, D.M.. Acoustic absorption behavior of carbon nanotube arrays. In: 43rd International Congress on Noise Control Engineering (Inter-Noise 214); vol , p [3] Chung, Y.J., Blaser, D.A.. Transfer function method of measuring in-duct acoustic properties. I. theory. Journal of the Acoustical Society of America 198;68(3): [31] Chung, Y.J., Blaser, D.A.. Transfer function method of measuring in-duct acoustic properties. II. experiment. Journal of the Acoustical Society of America 198;68(3): [32] ASTM E15: Standard test method for impedance and absorption of acoustical materials using a tube, two microphones, and a digital frequency analysis system

29 [33] Han, J., Herrin, D., Seybert, A.. Accurate measurement of small absorption coefficients. Tech. Rep.; SAE Technical Paper ; 27. doi:1.4271/ [34] Oldfield, R., Bechwati, F.. Accurate low frequency impedance tube measurements. In: Proceedings of the Institute of Acoustics; vol , p [35] ISO : Acoustics - Determination of sound absorption coefficient and impedance in impedance tubes, part 1: Standing wave method. 21. [36] ISO : Acoustics - Determination of sound absorption coefficient and impedance in impedance tubes, part 2: Transfer-function method. 21. [37] LDS-Dactron RT Pro Dynamic Signal Analysis, User Guide, Rev. 7.1; 213. [38] Katz, B.F.G.. Method to resolve microphone and sample location errors in the two-microphone duct measurement method. Journal of the Acoustical Society of America 2;18(5): [39] Bhat, R.B.. Numerical Analysis in Engineering. Alpha Science International; 24. [4] Kinsler, L., Frey, A., Coppens, A., Sanders, J.. Fundamentals of Acoustics. 4th ed.; John Wiley & Sons, Inc., New York; 2. [41] Boonen, R., Sas, P., Desmet, W., Lauriks, W., Vermeir, G.. Calibration of the two microphone transfer function method with hard wall impedance measurements at different reference sections. Mechanical Systems and Signal Processing 29;23: [42] Choy, Y.S., Huang, L., Wang, C.. Sound propagation in and low frequency noise absorption by helium-filled porous material. Journal of the Acoustical Society of America 29;126(6): [43] Zhang, R., Zhang, Y., Zhang, Q., Xie, H., Qian, W., Wei, F.. Growth of half-metre long carbon nanotubes based on schulz-flory distribution. ACS Nano 213;7(7): [44] Hooijdonk, E.V., Bittencourt, C., Snyders, R., Colomer, J.F.. Functionalization of vertically aligned carbon nanotubes. Beilstein Journal of Nanotechnology 213;4:

30 [45] Beckman, W.. UC researchers shatter world records with length of carbon nanotube arrays. Media Release; 27. URL: [46] Berger, M.. Researchers grow half-meter long carbon nanotubes. Nanowerk; 213. URL: [47] Sakurai, S., Inaguma, M., Futaba, D.N., Yumura, M., Hata, K.. A fundamental limitation of small diameter single-walled carbon nanotube synthesis - A scaling rule of the carbon nanotube yield with catalyst volume. Materials 213;6: [48] Guhados, G., Wan, W., Sun, X., Hutter, J.L.. Simultaneous measurement of Young s and shear moduli of multiwalled carbon nanotubes using atomic force microscopy. Journal of Applied Physics 27;11(3): [49] Hall, L.J., Coluci, V.R., Galvo, D.S., Kozlov, M.E., Zhang, M., Dantas, S.O., Baughman, R.H.. Sign change of Poisson s ratio for carbon nanotube sheets. Science 28;32(5875): [5] Bies, D.A., Hansen, C.H.. Engineering Noise Control: Theory and Practice. 3rd ed.; London, UK.: Spon Press; 23. [51] Kino, N., Ueno, T.. Comparisons between characteristic lengths and fibre equivalent diameters in glass fibre and melamine foam materials of similar flow resistivity. Applied Acoustics 28;69: [52] Beranek, L.L., Ver, I.L.. Noise and Vibration Control Engineering: Principles and Applications. New York, USA: John Wiley and Sons; [53] Ballagh, K.. Acoustical properties of wool. Applied Acoustics 1996;48(2): [54] Garai, M., Pompoli, F.. A simple empirical model of polyester fibre materials for acoustical applications. Applied Acoustics 25;66: [55] Attenborough, K.. Models for the acoustical characteristics of air filled granular materials. Acta Acustica 1993;1: [56] Allard, J.F., Champoux, Y.. New empirical equations for sound propagation in rigid frame fibrous materials. Journal of the Acoustical Society of America 1992;91:

31 [57] Hosseini Fouladi, M., Ayub, M., Nor, M.J.M.. Analysis of coir fiber acoustical characteristics. Applied Acoustics 211;72(1): [58] Delany, M.E., Bazley, E.N.. Acoustical properties of fibrous absorbent material. Applied Acoustics 197;3(2): [59] Xiang, H.F., Wang, D., Liu, H.C., Zhao, N., Xu, J.. Investigation of sound absorption properties of kapok fibres. Chinese Journal of Polymer Science 213;31(3): [6] Ayub, M., Zander, A.C., Howard, C.Q., Cazzolato, B.S.. A review of acoustic absorption mechanisms of nanoscopic fibres. In: Proceedings of Acoustics. Gold Coast, Australia; 211, p [61] Ayub, M., Zander, A.C., Howard, C.Q., Cazzolato, B.S., Huang, D.M.. A review of MD simulations of acoustic absorption mechanisms at the nanoscale. In: Proceedings of Acoustics. Victor Harbor, Australia; 213, p [62] REFRASIL: Silica-based insulation products, Hitco Carbon Composites. 28. URL: [63] Wayman, J.L.. New methods of measuring normal acoustic impedance. Tech. Rep.; Naval Postgraduate School, Monterey, California; [64] Bodén, H., Åbom, M.. Influence of errors on the two-microphone method for measuring acoustic properties in ducts. Journal of the Acoustical Society of America 1986;79(2): [65] Seybert, A.F.. Two-sensor methods for the measurement of sound intensity and acoustic properties in ducts. Journal of the Acoustical Society of America 1988;83(6): [66] Hou, K., Bolton, J.S.. A transfer matrix method for estimating the dispersion and attenuation of plane waves in a standing wave tube. Tech. Rep.; Publications of the Ray W. Herrick Laboratories. Paper 54 (Abstract published in the Journal of the Acoustical Society of America, 125, 2596);

32 [67] Chu, W.T.. Extension of the two-microphone transfer function method for impedance tube measurements. Journal of the Acoustical Society of America 1986;8(1): [68] Seybert, A.F., Soenarko, B.. Error analysis of spectral estimates with application to the measurement of acoustic parameters using random sound field in ducts. Journal of the Acoustical Society of America 1981;69(4): [69] Ghan, J., Cazzolato, B., Snyder, S.. Statistical errors in the estimation of timeaveraged acoustic energy density using the two-microphone method. Journal of the Acoustical Society of America 24;115(3): [7] Bendat, J.S., Piersol, A.G.. Random Data: Analysis and Measurement Procedures. Wiley-Interscience; [71] Zou, Q., Hay, A.E.. The vertical structure of the wave bottom boundary layer over a sloping bed: Theory and field measurements. Journal of Physical Oceanography 23;33:

33 Appendix A. Verification Procedure for the Experimental Results Appendix A.1. Repeatability Test The repeatability and accuracy of the experimental measurements were checked by conducting repeated tests and varying parameters such as the amplitude and phase compensation of the microphones [63]; tests were also repeated with the samples inserted and removed from the apparatus a number of times. The results exhibited similar absorption trends over the measured operating frequency range for the variation of different parameters. For instance, Figure A.14(a) shows the repeatability of test results for the same CNT forest sample. These results were obtained by repeating the same test four times, Absorption Coefficient, α Repeated Test 1 Repeated Test 2 Repeated Test 3 Repeated Test 4 Mean Value (a) Absorption of CNT for repeated test data (b) Zoomed CNT sample surface Figure A.14: Comparison of absorption coefficients of a CNT forest for four repeated tests with the same sample. each time calibrating the microphone pairs, inserting and removing the sample, and rotating the sample to different surface positions each at approximately 9 to the previous one. As illustrated in Figure A.14(a), the test results indicate that the mean variation of the sound absorption coefficient results is within 2% for measurement frequencies above 125 Hz. It also confirms that the results are repeatable, even though the measured acoustic absorption coefficient is very small. The discrepancy and variation in the absorption curve at certain frequencies are due to irregularities in the tests and slight variations in the mounting conditions of the sample [31], as low absorption (high reflection coefficient) materials are very sensitive to the consistency in the mounting conditions [38, 64]. In addition, difficulty in maintaining a uniform wall contact with the rigid termination in the case of single layer samples did not help to create consistent mounting conditions of the sample inside the impedance tube. The sample mounting configuration as shown in 33

34 Figure A.14(b) is a somewhat manual setup with a flange-like system for the tube-end termination assembled technology using a number of nuts and bolts. Hence it is difficult to maintain consistency among repeated tests for the mounting conditions and perfect positioning of the annular plates aligned with the tube. This type of setup was required to accommodate the method by which the CNT sample was prepared. Hence a simpler and more convenient method for mounting sample configurations and the CNT sample arrangement will be the subject of future work. Appendix A.2. Reproducibility Tests A reproducibility test was performed using a separate 3 mm CNT sample in an impedance tube of diameter 25.4 mm (a different tube was used here). This test result offers systematic experimental data on the reproducibility of the impedance tube measurements on a similar material with different circular size (previous results presented in Section 3 were for a sample of diameter 22.1 mm), which would also provide a general idea of the variance in the measured absorption coefficient data obtained for two different samples (in regard to the circular dimension) of approximately equal thicknesses. Figure A.15 shows the absorption coefficient results for repeated tests of a 3 mm CNT forest of 25.4 mm circular diameter. Absorption coefficient, α Test 1 Test 2 Test 3 Test 4 Test Figure A.15: Comparison of absorption coefficients of a 3 mm long CNT forest of circular diameter 25.4 mm for five repeated tests with the same sample. The tests were conducted following the procedure described earlier in Appendix A.1. As shown in Figure A.15 the test results exhibit a consistent absorption trend among the repeated tests for the 3 mm CNT forest and show a 5-1% absorption. Similar to 34

35 α corr, tested in Φ25.4 mm impedance tube 3mm CNT α corr, tested in Φ22.1 mm impedance tube 3 mm CNT Absorption coefficient, α Figure A.16: Comparison of absorption coefficients of 3 mm long CNT forest samples of circular diameters 25.4 mm and 22.1 mm with a similar sample arrangement. the previous test results presented in Figure A.14(a), the variation in the results of the 3 mm CNT forest of 25.4 mm circular diameter is attributable to inconsistencies in the mounting conditions. An additional comparison of the test results obtained from the two impedance tubes (of diameters 25.4 mm and 22.1 mm) is presented in Figure A.16. It can be seen that both results show a similar trend in terms of the absorption coefficient. The variance in the absorption results for the two different tests are due to the non-uniformities of the materials. The dips in the absorption curve shown in Figure A.15 at frequencies around 11 Hz, 2 Hz, 29 Hz, and 34 Hz are due to the tube resonance, which occurs at frequencies corresponding to kl = mπ/2, m = 1, 3, 5,.... They can also be observed in the absorption curve of the blank impedance tube of diameter 25.4 mm, as displayed in Figure A.17. The extent of the ill-conditioning in the measured results due to the tube resonance can be explained using the wave spectra in the tube. The wave spectra can be evaluated using the decomposition theory of Seybert [65]. Any small measurement errors occurring in the neighbourhood of the tube resonance frequencies will cause large errors in the decomposition and hence in the evaluation of acoustic properties using this theory [65]. Figure A.18 shows estimates of the decomposed incident and reflected wave spectra, S AA and S BB, respectively, in the tube for the rigid termination. It can be seen that the spectra of the waves are strongly influenced by the resonances of the tube at the corresponding frequencies where the dips appear in the absorption curve shown in Figure A.15 35

36 .15 Measured, α blank tube (Φ25.4mm) Corrected, α corr blank tube (Φ25.4mm) Absorption coefficient, α Figure A.17: Absorption coefficient of an empty impedance tube of diameter 25.4 mm with rigid termination. Corrected absorption coefficient (α corr ) in the figure indicates the result obtained with the implementation of the correction for tube attenuation. [65]. The effect of this ill-conditioning extends to either side of the frequency region near the resonance peaks in the measured reflection coefficient of the rigid termination, as shown in Figure A.19, which was evaluated using the decomposed wave spectra. Appendix A.3. Error Analysis For the accurate estimation of the results over the measurement frequency range using the impedance tube method, several standard verification procedures were performed to eliminate the effect of errors associated with the following factors: sensor mismatch; waveguide damping; uncertainty in the separation distance between the microphones, and the distance of the furthest microphone from the termination; and bias and random errors. These are explained in the following sections. Appendix A.3.1. Sensor Mismatch. As discussed in Section 2.2, the effect of phase and magnitude mismatch on the measured transfer function between two microphones was eliminated using the standard sensor-switching technique [31, 38]. Prior to each measurement session, a separate calibrated transfer function H cal was calculated for each data set, which was used to calculate 36

37 16 Incident wave spectra S AA 14 Reflected wave spectra S BB Sound Pressure Level (db) Figure A.18: Decomposed wave spectra of the two microphones in the tube, showing the effect of tube resonances Reflection coefficient, R Calculated using cross-spectrum S AB Figure A.19: Measured reflection coefficient in the empty tube for the rigid termination using the decomposition theory of Seybert [65]. the corrected transfer function H corrected from the measured data. Figure A.2 displays the overlay of the magnitude and phase of the measured (H 12 ) and corrected (H corrected ) transfer function. It can be observed that the magnitude and phase mismatch of the transfer function at low frequencies below 5 Hz were eliminated in the corrected transfer function. However, the overall deviation between the magnitude and phase of the two transfer functions remained very small. Appendix A.3.2. Waveguide Damping. Standards for the impedance tube method recommend correcting for tube attenuation when the distance from the specimen to the nearest microphone exceeds three tube 37

38 Magnitude (db), H 12 Phase (deg), H H measured 12 H measured 12 H corrected 12 H corrected Figure A.2: Magnitude (top) and phase (bottom) of the transfer function measured between two microphones (dashed line) and the transfer function corrected using microphone switching technique (solid line). diameters [33, 66]. For all experiments conducted in this study, the nearest microphone was placed at a distance greater than 13 mm from the test specimen, which is approximately six tube diameters (22.1 mm) of the impedance tube. In addition, as determined by Chu [67], the effect of tube attenuation can be significant for a material of high reflection coefficient (similar to the case studied here), even though the tube attenuation appears to be small (Equation (5)). For instance, as estimated by Chu [67], a 1% error in the measured reflection coefficient ( R ) can result in an error of 8.5% in the absorption coefficient (α) for R =.9. Therefore, the correction for tube attenuation was applied as described in Section 2.2. The experimental estimates of the attenuation constant and the theoretical prediction using Equation (5) are presented in Figure A.21. It may be observed that the difference between these two estimates of the attenuation constant is small. The estimates of the attenuation constant indicate that the tube attenuation is very significant and that the effect is observed in the measured absorption coefficient of the impedance tube with a rigid termination. Figures 5 and 6 show the effect of the correction for tube attenuation in the estimation of acoustic absorption coefficient. It can be seen that the measured value of the absorption coefficient without the implementation of the correction for tube attenuation leads to an overestimate in the calculated absorption coefficient by a factor of two. Appendix A.3.3. Microphone Separation Distance. The measurement accuracy of the microphone separation distance d was verified with the frequency null method presented by Katz [38]. The distance from the acoustic centre 38

39 Attenuation constant, k" (1/m) Measured value for microphone spacing, d = mm Theoretical estimation for 22.1 mm duct Figure A.21: Comparison of the theoretical and measured attenuation constant for an empty impedance tube of diameter of 22.1 mm. The theoretical value was calculated from Equation (5) using the value of the constant A =.194 [33]. of the diaphragm of the microphone closest to the fixed termination can be determined from the frequency null of the transfer function measured between the measurement microphones (microphone 1 or microphone 2) and a microphone embedded in the rigid termination using the arrangement shown in Figure A.22(a). A separate set of measurements was conducted to obtain the transfer function for the measurement microphone (microphone 1 or microphone 2) and the termination microphone, an example of which is shown in Figure A.22(b). It can be observed that several frequency nulls existed over Magnitude (db) (a) Schematic of the setup of the microphone in the end plate. -3 Transfer Function, Ch1/Ch4 Transfer Function, Ch2/Ch (b) Measured transfer function using sensorswitching technique Figure A.22: Schematic of (a) the modified impedance tube setup with the additional termination microphone used to measure (b) the transfer function between the measurement microphones (Ch1: microphone 1, Ch2: microphone 2) and the embedded termination microphone (Ch4: microphone 4). Details of the setup and calculation procedure can be found in [38]. the selected measurement frequency range. A second-order polynomial fit was used to 39