I. INTRODUCTION III. EXPERIMENTAL WORK II. SAMPLES. A. Actuator response

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1 New piezoelectric polymer for air-borne and water-borne sound transducers Reiner Kressmann a) Institute for Telecommunications, Darmstadt University of Technology, Merckstr. 25, D Darmstadt, Germany Received 13 September 2000; accepted for publication 18 January 2001 Acoustic transducers made of a charged cellular polymer called EMFi have been designed and investigated with respect to air-borne and water-borne sound. The longitudinal transducer constant is around 90 pc/n, strongly exceeding the values of other piezoelectric polymers. This is mainly attributed to the very low Young s modulus of about 2 MPa. The acoustic impedance is only kg/ m 2 s) and results in good matching to air but strong loading under water. Due to this strong loading, a pronounced reduction of resonance frequency from 300 khz in air down to 17 khz under water is observed. The experiments indicate that fluid loading is not only mass-like but also compliant, reducing the transducer s sensitivity below the resonance frequency of about 63 db re 1 V/Pa 0.7 mv/pa in air to 71 db re 1 V/Pa under water. This compliance is attributed to the medium s compressibility. Piezoelectricity of EMFi films is limited to temperatures below 70 C; above, irreversible discharge of trapped charges takes place. Furthermore, a second type of EMFi, called OS was investigated, having a piezoelectric constant of 15 pc/n and a Young s modulus of 6 MPa. In quasi-static sensor measurements, the piezoelectric constant increases with the applied load. This nonlinearity explains the higher values reported in other publications on the same materials Acoustical Society of America. DOI: / PACS numbers: Fx, Yj, Jd, Jx SLE I. INTRODUCTION Polymers are well-known materials for acoustic transducers, both for air-borne and water-borne sound applications. The most important ones are Teflon due to its charge storing capabilities and piezoelectric polyvinylidene fluoride PVDF. In the last few years, scientific interest on charge retention in cellular and porous polymers 1 8 and inorganic porous electrets 9 has grown rapidly. In this paper, the properties of transducers fabricated with two types of a novel polymer, the so-called electro-mechanical film EMFi, provided by the Finnish company VTT, are presented and explained by a simple model. The two types are called HS high sensitivity and OS ordinary sensitivity. II. SAMPLES The EMFi film is a foam based on polypropylene which is biaxially stretched during fabrication. 1 This results in the formation of lens-like air bubbles with diameters of about 10 to 70 m and a thickness of about 5 m resulting in a quite soft material. The manufacturer reports for the HS high sensitivity type of the material a thickness of 70 m, a density of 330 kg/m 3, a Young s modulus of around 1 MPa, a relative permittivity of 1.2 and a sensitivity of 160 pc/n. The respective values for the OS type are thickness, 37 m; density, 550 kg/m 3 ; Young s modulus, 9 MPa; relative permittivity, 1.6, and sensitivity, 30 pc/n. 1 The piezoelectricity is induced by means of corona charging resulting in charge storage inside the film. a Electronic mail: kre@nt.tu-darmstadt.de EMFi films of several cm 2 size metallized on one side have been cut, glued on brass electrodes and mounted in aluminum housings to assure good shielding. Transducers with diameters of 20 and 35 mm active size were fabricated. For the underwater measurements, only carried out with the HS type, they have been covered with a thin waterproof film to protect them from contact with the water. A schematic of a transducer is given in Fig. 1. III. EXPERIMENTAL WORK Air-borne sound measurements have been carried out in an anechoic chamber under free-field conditions and a coupler. For the water-borne sound experiments an approximately cubic plastic tank of 1 m 3 size was used. The problems caused by its small opening of only 20 cm diameter are discussed together with the results in the following section. Calibrated sensors were from Brüel and Kjær quarterinch microphone 4135, eighth-inch microphone 4138 and hydrophone Since the transducers active capacitances are between 44 and 400 pf, a charge amplifier 2635 from Brüel and Kjær was used in the sensor experiments. Furthermore, an audio analyzer UPD from Rohde and Schwarz was used for signal generation and analysis. A. Actuator response The radiated sound pressure of a circular EMFi-HS actuator of 35 mm diameter driven sinusoidally with 100 V is shown in Fig. 2. The actuator was baffled slightly unsymmetrically with a wooden plate of cm 2 size. The microphone was placed 60 cm apart from the sample on the main axis. The sound pressure increases with the square of frequency as expected below the resonance since in this 1412 J. Acoust. Soc. Am. 109 (4), April /2001/109(4)/1412/5/$ Acoustical Society of America 1412

2 FIG. 1. Schematic of EMFi transducers with diameter 2R. range the deflection of the piezoelectric does not change with frequency. From interferometric measurements of dynamic deflection and dielectric measurements, a resonance frequency of about 300 khz is known. 10 For the linear response, the transmitting sensitivity at 1 m distance is 4.7 mpa/v at 100 khz. The resonance frequency changes drastically, if the transducer is driven under water. The result shown in Fig. 3 is for an actuator of 35 mm diameter driven with 80 V at a distance of 20 cm. Though the boundary of the tank is strongly reverberant, it has been proved at a frequency of 10 khz with gated actuation that the echoes from the walls are 10 db weaker than the direct sound. The projector was mounted with its back close to the water surface to prevent contact at the electrical connectors with water. Therefore, the projector is baffled by the sound-soft water surface. Unfortunately, the adjustment of the reference hydrophone on the main axis of the sample was not very successful. This mainly results from the limited space for mounting transducers due to the small opening of the tank of just 20 cm diameter. Furthermore, the tank s upper wall does not allow the usage of heavy supports. Hence, the high frequency response of the sample can only be explained by assuming a deviation of 25 degrees off axis. Since this coincides with a 3 db loss at 53 khz it does not corrupt the data at lower frequencies. The resonance shifts down to around 17 khz which is attributed to the medium load. The transmitting sensitivity in water at 1 m distance is 8 mpa/v at 10 khz. FIG. 3. Sound pressure level of an EMFi-HS projector (2R 35 mm) at 20 cm distance 25 off axis. This unusual orientation results from the geometrical limitations of the small opening of the tank. The transmitting sensitivity in air of an EMFi-OS actuator not shown of 20 mm diameter is 0.32 mpa/v at 100 khz. Both in water and in air, a quite strong second harmonic is present in the actuator experiments, whereas other harmonics do not occur. The second harmonic is due to an electrostatic effect as shown later in Eq. 7. Unpoled films only radiate the second harmonic and no fundamental. Poled films, too, show a similar behavior after thermal discharge. In this experiment, an EMFi actuator was placed inside an oven, and the radiated fundamental and second harmonic were recorded. The result is depicted in Fig. 4. The acoustic signals have not been very stable due to refraction caused by temperature gradients in the air between sample and microphone. Discharge takes place between 70 C to 100 C and is irreversible. 1,3 This is not surprising, since also solid polypropylene is known to show weak charge storage capabilities. 11 The slight decrease of the sound pressure level during cooling is attributed to the lower Young s modulus at elevated temperature. After the experiment it could be seen at the first view that the sample could not further be used. B. Sensor response The sensitivity to air-borne sound of a transducer of 20 mm diameter is depicted in Fig. 5. At low frequencies, a three-port coupler with a diameter of 20 mm and a volume of 3cm 3 was used. It guarantees a constant sound pressure up to 6 khz. In the ultrasonics range, the substitution method in FIG. 2. Sound pressure level of an EMFi-HS actuator in air (2R 20 mm) at 60 cm distance. FIG. 4. Radiated sound pressure level in arbitrary units a.u. at 50 khz fundamental and 100 khz second harmonic versus temperature. Arrows indicate heating and cooling, respectively. The heating rate was 200 K/h J. Acoust. Soc. Am., Vol. 109, No. 4, April 2001 R. Kressmann: Piezoelectric polymer transducers 1413

3 From Fig. 6 it can be seen that the resonance is shifted down to 17 khz as it appears in the actuator mode as well. Furthermore, the sensitivity below the resonance frequency is 0.3 mv/pa, i.e., it is 8 db lower in water than in air. IV. THEORY A. Mechanical acoustical conversion FIG. 5. Sensitivity of EMFi transducers to airborne sound (2R 20 mm). The low-frequency sensitivity was recorded with a three-port coupler with constant pressure up to 6 khz. The sensitivity with respect to ultrasound was measured in free field using the substitution method. The difference of the values is attributed to the uncertainties of the measurements. free field 12 using a baffled EMFi transducer as an actuator was used. The reference microphone and the EMFi sensor have been placed in the actuator s far field on the main axis and carefully adjusted with respect to inclination. The frequency response of the EMFi-HS sensor is quite flat between 4 Hz and 6 khz at about 0.7 mv/pa. This corresponds to a longitudinal piezoelectric charge constant of about 100 pc/n, exceeding the data of PVDF, for instance, by about 10 db. EMFi-OS sensors have a sensitivity of about 60 V/Pa yielding a piezoelectric constant of about 15 pc/n. In the ultrasonics range, the sensors still work, but show strong directivity due to their size. The equivalent A-weighted noise level of the EMFi-HS microphone is 52 db with the present setup. Even for sound pressure levels of up to 144 db at 300 Hz, the total harmonic distortion THD of both sensor types does not exceed that of the eighth-inch reference microphone B & K 4138, which is just 3% at 168 db. No change in the piezoelectric constant is observed for applied pressures between 20 mpa and 340 Pa. The sensitivity of the EMFi-HS transducer used as hydrophone was measured with the comparison method and is shown in Fig. 6. Owing to the large reverberation time inside the tank, several frequency responses under various geometric configurations have been monitored. In this way, it is possible to average over the various spatial modes inside the tank. Below 6 khz, the sound pressure level produced by the projector is too low to permit an accurate measurement of the sensitivity, and the number of modes inside the tank is too small to guarantee a successful spatial averaging. 1. General remarks In both air-borne and water-borne sound experiments the actuator can be modeled as a circular piston mounted in an infinite baffle 13 radiating the power N Re Z m v 2 with the radiation impedance 2 Z m c R 1 J 1 2kR j S 1 2kR kr kr 1 and having a directivity ratio of kr 2 D 1 J 1 2kR /kr. 2 In these equations, v is the velocity of the vibrating piston, c is the characteristic impedance of the medium, R is the piston s radius, k is the wave number, and J 1 (x) and S 1 (x) are the Bessel and Struve function of first order, respectively. 14 Then, the sound pressure amplitude on the main axis at distance r can be computed: p r 2 cnd 2r R2 2 x, 3 where x is the deflection of the surface. The 2 increase of the pressure is confirmed experimentally up to about 100 khz see Fig. 2. The strong decrease of sound pressure of the second harmonic at frequencies above 150 khz is mainly attributed to a decrease in sensitivity of the reference microphone. The following calculations have been carried out for the HS type of EMFi films: The 2 increase with frequency holds from infra-sonic frequencies up to the mechanical resonance, above which x in Eq. 3 decreases. The mass per area is calculated from the geometry and the density of the film to be M kg/m 2, in which it is considered that the dynamic mass is only one-third of the static one since the layer is clamped on one side. Any kind of impact of the backing on the resonance frequency can be excluded. The compliance is calculated from Young s modulus Y 2 MPa to be F m 3 /N. These data result in a resonance frequency of 307 khz. FIG. 6. Sensitivity of EMFi-HS under water hydrophone, 2R 35 mm. Below 6 khz the data are corrupted by insufficient signal to noise ratio and unsuccessful spatial averaging. 2. Fluid loading For the water-borne sound measurement, carried out with transducers of 35 mm diameter, an additional mass load per area computed from the imaginary part of Eq. 1 using a power expansion being valid for low frequencies M s 8R 14.4 kg/m J. Acoust. Soc. Am., Vol. 109, No. 4, April 2001 R. Kressmann: Piezoelectric polymer transducers 1414

4 data for the EMFi-OS actuator are d 1 23 m, d 2 14 m, d pm/v. A Young s modulus of Y 2 MPa EMFi-HS and Y 6 MPa EMFi-OS was calculated from the electrostatic force per area A, FIG. 7. Schematic of simplified model of EMFi film. F el A 2d 2 U 2 Y d x 7 has to be considered. The shifted resonance frequency would be 7 khz. Therefore, a further effect must be present, resulting in a slightly higher resonance and reduced sensor sensitivity at low frequencies. This effect seems to be an additional restoring force due to the medium: Considering that the same volume which is moved as a mass M s is also compressed, the medium s compliant load times the area is F s 8R m 3 /N, 5 using the compressibility of water Pa 1.Asa consequence, the total compliance is reduced by a factor of about 5 which yields a resonance frequency of 18 khz being in fair agreement with the experiment. Stiffness terms in radiation impedances of fluid-loaded vibrating plates are well known in the literature for certain vibration modes In these experiments, however, we have no reason to assume any kind of mode distribution on the transducer s surface, and it must be premised that the surface vibrates piston-like. Furthermore, radiation impedances with negative imaginary part only appear in a small frequency range, 15 whereas the present experiments show, that both mass and compliant loading from the fluid take place over a broader frequency range. This effect might not have been observed in the past since its impact was small. From Eq. 4, it can be seen that mass loading increases with increasing sensor area. B. Electro-mechanical conversion The electro-mechanical coupling of a stack of two dielectrics of different elasticity with a charge layer in between which is similar to an electret microphone 18 has been already investigated 19 and extended to charged cellular polymers. 2 The latter model assumes a material composed of alternating air and solid layers with a finite charge density at the boundary. It can be further simplified as shown in Fig. 7. The following transducer constant, identical both for sensor and actuator mode, is deduced: d 33 d Y d 1 d 1 d 2 2 x U. In this equation, for HS-type transducers, d 1 26 m is the total thickness of the solid layers, 2.35 is their permittivity, and d 2 44 m is the total thickness of the air layers. d 1 and d 2 are calculated from the total thickness d of 70 m and the density of the film. From the measured sound pressure at the fundamental, a transducer constant of about 80 pm/v is computed from Eqs. 3 and 6. The respective 6 which results for the actuating mode in radiation of the second harmonic due to the nonlinearity with respect to the driving voltage Fig. 2. Inserting these data into Eq. 6, a charge density of C/m 2 for EMFi-HS and of C/m 2 for EMFi-OS are computed. The actuator constant has been also deduced from interferometric measurement of deflection to be between 85 and 100 pm/v. From this experiment a resonance frequency of about 300 khz was obtained 10 resulting in a Young s modulus of 2 MPa. V. DISCUSSION The obtained piezoelectric constants vary up to 20% from sample to sample, but are, on average, much smaller than the data reported in the literature. 2,20 These published higher values are observed by applying a static load of about 10 4 Pa to the sample, whereas in the present sensor experiments, the load was between 20 mpa and 340 Pa. The author s experiments with static loading have shown, that in this method a nonlinearity with respect to the loading appears. Furthermore, in the large-signal regime, the piezoelectrically induced charge increases, if just a small area of the film is loaded. In this case, the air can flow from the bubbles of the loaded area into the unloaded neighborhood resulting in an apparently softer film. This also explains the slow relaxation reported in Ref. 20 which was also observed in our experiments with quasi-static loading. The nonlinearity with respect to loading will be discussed in more detail in a future publication. A similar low value of 110 pm/v is reported in Ref. 21 for the actuating mode monitoring the sample s deflection under electrical load with an accelerometer. Since the nonlinearity appears in the stress strain relation, it affects both the measurement of piezoelectric constant and Young s modulus. But, the product of both, related to the surface charge at the interface see Eq. 6 is independent of this effect. Therefore, the lower Young s modulus of about 1 MPa reported in Refs. 2 and 20 leads to the same surface charge. Charged porous polymers show longitudinal piezoelectric constants being much larger than those known for other polymers, e.g., polyvinylidene fluoride PVDF. This follows mainly from the very low Young s modulus of EMFi-HS layers which also results in a very low acoustic impedance of about Z Y kg/ m 2 s. Therefore, cellular layers are matched better to air than to water. It should be clearly stated, that EMFi films are no piezoelectrics in the classical sense. Polypropylene does not contain any dipoles, and our measurement of the transversal coefficient yielded 1415 J. Acoust. Soc. Am., Vol. 109, No. 4, April 2001 R. Kressmann: Piezoelectric polymer transducers 1415

5 the very low value of d 31 2 pc/n. The same value is reported in Ref. 10. Hence, EMFi films have been called pseudo-piezoelectrics. 2 The observed low stability of EMFi films against heating is insufficient for many applications; it is inferior to that of other common piezoelectrics, e.g., PVDF and PZT. This problem might be overcome by using Teflon as a basic material known to have excellent charge storage properties. 11 Charge retention in porous polytetrafluorethylene has been already investigated, 4,5 and the piezoelectricity of various solid double layers with charge layer at the boundary was reported, 6 8 but no experiments on temperature dependence and transducers are reported up to now. In the latter publication, piezoelectric coefficients up to 600 pc/n are reported for double layers, obtained from quasi-static measurements. It should be remembered that our own measurements were all obtained on the simpler and mechanically more stable single layers. VI. CONCLUSIONS The presented acoustic experiments on transducers for water-borne and air-borne sound show that charged cellular polymers are promising candidates for several applications, mainly as hydrophones in shallow water or in air as ultrasonic sources or broadband sensors. The flexibility of the polymer allows the fabrication of large-scale transducers with almost arbitrary directivity pattern e.g., a true omnidirectional transducer at high frequencies, if the film is fixed on a curved substrate which can also contain a more or less sophisticated electrode pattern. The underwater experiments seem to indicate that a low impedance material as the EMFi film is loaded by the medium simultaneously mass-like and compliant. The very weak transversal piezoelectricity of 2 pc/n see above and Ref. 10 avoids bending of actuators glued on a substrate. For narrow-band applications, the resonance frequency can be tuned by applying an additional mass on top of the film which might be also desirable for protection against any kind of environmental influence. The main future scope is to fabricate layers with higher temperature stability. Furthermore, the interaction between EMFi films and water should be investigated more deeply. Finally, the microscopic structure both mechanically and electrically of cellular polymers is of great interest to improve material properties and to understand the nonlinear behavior. Higher piezoelectric constants are possible by further softening films through enhanced gas content and higher charge density. ACKNOWLEDGMENTS The author thanks Professor G. M. Sessler, H. Berger, M. Fischer, J. Meyer, and F. Steffens for stimulating discussions and help with some of the experiments. Brüel and Kjær, Copenhagen, Denmark, is gratefully acknowledged for providing the hydrophone, and VTT, Tampere, Finland, for making the EMFi films available. Financial support of the Deutsche Forschungsgemeinschaft DFG is also acknowledged. 1 J. Lekkala and M. Paajanen, EMFi New electret material for sensors and actuators, Proceedings of the 10th International Symposium on Electrets, Delphi IEEE, Piscataway, NJ, 1999, pp G. M. Sessler and J. Hillenbrand, Electromechanical response of cellular electret films, Appl. Phys. Lett. 75, J. v. Turnhout, R. E. Staal, M. Wübbenhorst, and P. H. de Haan, Distribution and stability of charges in porous polypropylene films, Proceedings of the 10th International Symposium on Electrets, Delphi IEEE, Piscataway, NJ, 1999, pp Z. Xia, J. Jian, Y. Zhang, Y. Cao, and Z. Wang, Electret properties for porous polytetrafluorethylene PTFE Film, CEIDP, 1997 Annual Report IEEE, Piscataway, NJ, 1997, pp R. Schwödiauer, G. Neugschwandtner, S. Bauer-Gogonea, S. Bauer, J. Heitz, and D. Bäuerle, Dielectric and electret properties of novel Teflon PTFE and PTFE-like polymers, Proceedings of the 10th International Symposium on Electrets, Delphi IEEE, Piscataway, NJ, 1999, pp R. Gerhard-Multhaupt, Z. Xia, W. Künstler, and A. Pucher, Preliminary study of multi-layer space-charge electrets with piezoelectric properties from porous and non-porous Teflon films, Proceedings of the 10th International Symposium on Electrets, Delphi IEEE, Piscataway, NJ, 1999, pp W. Künstler, Z. Xia, T. Weinhold, A. Pucher, and R. Gerhard-Multhaupt, Piezoelectricity of porous polytetrafluoroethylene single- and multiplefilm electrets containing high charge densities of both polarities, Appl. Phys. A: Mater. Sci. Process. 70, G. Neugschwandtner, R. Schwödiauer, S. Bauer-Gogonea, and S. Bauer, Large piezoelectric effects in charged, heterogeneous fluoropolymer electrets, Appl. Phys. A: Mater. Sci. Process. 70, Y. Cao, Z. Xia, Q. Li, L. Chen, and B. Zhou, Study of porous dielectrics as electret materials, IEEE Trans. Dielectr. Electr. Insul. 5, G. S. Neugschwandtner, R. Schwödiauer, M. Vieytes, S. Bauer-Gogonea, S. Bauer, J. Hillenbrand, R. Kressmann, G. M. Sessler, M. Paajanen, and J. Lekkala, Large and broadband piezoelectricity in charged polypropylene foam electrets, Appl. Phys. Lett. 77, R. Kressmann, G. M. Sessler, and P. Günther, Space-charge electrets, in Electrets, 3rd ed., edited by R. Gerhard-Multhaupt Laplacian, Morgan Hill, 1999, Vol. 2, Chap. 9, pp V. Nedzelnitsky, Calibration of pressure and gradient microphones, in Encyclopedia of Acoustics, edited by M. J. Crocker Wiley, New York, 1997, Vol. 4, Chap. 157, pp H. F. Olson, Acoustical Engineering van Nostrand, New York, M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 9th ed. Dover, New York, M. Lax, The effect of radiation on the vibrations of a circular diaphragm, J. Acoust. Soc. Am. 16, P. W. Smith, Jr., The imaginary part of input admittance: a physical explanation of fluid-loading effects on plates, J. Sound Vib. 60, D. G. Crighton, The 1988 Rayleigh medal lecture: Fluid loading The interaction between sound and vibration, J. Sound Vib. 133, G. M. Sessler and J. E. West, Applications, in Electrets, 3rd ed., edited by G. M. Sessler Laplacian, Morgan Hill, 1999, Vol. 1, Chap. 7, pp R. Kacprzyk, E. Motyl, J. B. Gajewski, and A. Pasternak, Piezoelectric properties of nonuniform electrets, J. Electrost. 35, M. Paajanen, H. Välimäki, and J. Lekkala, Modelling the electromechanical film EMFi, J. Electrost. 48, J. Hillenbrand and G. M. Sessler, Piezoelectricity in cellular electret films, IEEE Trans. Dielectr. Electr. Insul. 7, J. Acoust. Soc. Am., Vol. 109, No. 4, April 2001 R. Kressmann: Piezoelectric polymer transducers 1416