Underwater Acoustic Measurements on Polyvinylidene Fluoride Transducers

Methods of making piezoelectric transducers from very thin sheets of polyvinylidene fluoride (PVDF) are discussed, 
together with techniques for calibrating these devices, particularly for underwater operation. Parameters measured 
include receiving response, source level, beamwidth, characteristic impedance and variation of impedance with 
frequency. Consideration is also given to the dependence of receiving response on the poling fields and temperatures 
used in making PVDF transducers. Because of their broadband response thin sheet PVDF transducers have been 
shown to be ideal for monitoring the true form of acoustic pulses underwater.


INTRODUCTION
Polyvinylidene fluoride (PVDF) has been studied intensively since 1969 when its piezooelectric properties were discovered in Japan. [1][2][3] The material has been used for a long time as a packing and insulating material, but now that it is obtainable in sheets as thin as 6/am there is a current interest in its possible application as a broadband piezo-electric transducer.
In this paper, emphasis is given to underwater measurements, and the dependence of the acoustic sensitivity of PVDF transducers on the poling fields and temperatures used during their construction. This area of study has arisen because PVDF has a characteristic acoustic impedance close to that of water, making it suitable for underwater use. Its acoustic impedance, measured here as 3.94 x 106 rayl, is quite close to the impedance of water (approximately 1.5 x 106 rayl), thereby ensuring good acoustic matching.
Of all the polymers which behave piezoelectrically, PVDF has the highest piezo-electric constants. 2 Although its relative dielectric constant is very low, varying between 9 and 15 depending on frequency and mechanical compliance, its piezoelectric g3a constant is very high. 4 Together with the good matching to water, this indicates that PVDF should be a potentially sensitive underwater transducer for broad band use.
PVDF is comparatively cheap, lightweight, transparent, flexible, resistant to mechanical and thermal shock and to chemical attack, and is available 149 in large area sheets, suitable for making cheap transducer arrays. Electrodes can be vapour-deposited onto its surface and it can be poled with much lower D.C. voltages than are used for poling conventional ceramic transducers. The piezoelectricity of PVDF is stable with time at temperatures below 80C, and its high capacitance, measured here as 500 pF cm -z makes it suitable for use at low frequencies when the signal is fed to a low input impedance instrument.

TRANSDUCER CONSTRUCTION
The PVDF samples used in this study were in the form of very thin sheets manufactured by the Kureha Chemical Industry Company, Japan. The sheets were 25/am thick and biaxially oriented (BO), i.e. during manufacture they were stretched both parallel and perpendicular to the direction of extrusion.
In principle, any dielectric contains electric charges that at a given temperature can be oriented by an electric field. If the dielectric is then cooled so that the charges are immobilised, it will act as the electrical equivalent of a permanent magnet and is called an electret, or more correctly, a thermoeleetret. If this treatment is applied to PVDF a piezoelectric device is obtained. to a specific temperature ( Figure 1). Typically, the oil was heated to between 60C and 105 C. The D.C.
voltage was applied only when the pre-determined temperature had been attained. This voltage, ranging from 1000 V to 3000 V, was applied for 15 minutes, then the sample was removed from the oil to cool to room temperature with the voltage still applied. For 25/am PVDF sheets, these voltages were equivalent to electric fields of 40 V/am-1 to 120 V/am-1.
Poling currents varied considerably for each transducer, and varied during poling, but were typically 500 nA or less.
The poling temperature cannot be increased much above 100C before the combination of temperature and field results in dielectric breakdown of the material. The highest temperature used in our work was 110 C. The poling field can, however, be increased but a transducer having good piezoelectric response can be obtained if the field is at least 100 V /am-. 6 The total time that the field was applied was between 15 and 30 minutes, but this could have been much longer. 7 An attempt was made to specify the type of material being used, since PVDF exists in three forms, referred to as phase (fl-form), phase II (a-form) and phase III (7-form), which can exist separately or together. Phase I, with dipoles in the polymer chains packed in a parallel array, can be described as noncentrosymmetric and polar, and largely determines the piezoelectric behaviour of PVDF. Phase II, with the dipoles packed in an anti-parallel array, is centrosymmetric and polar, and phase III is a sheared modification of phase 1. 6 The method of identifying these forms was from infra-red absorption spectra, obtained for wave numbers between 250 cmand 1000 cm -Comparison with spectra previously published a indicated that the material was predominantly phase II (aform). However, by a criterion 9 that the amount of each phase can be estimated from the absorbance ratio Dso/Dsao, it appears that the material consisted of approximately equal amounts of phase and phase II ( Figure 2).
There is evidence that the morphology of PVDF changes during poling. 8 This was briefly investigated by studying the infra-red spectra before and after poling two 25/am samples whose poling parameters were 80 V/am -x at 80C and 60 V/am -1 at 95C. Acoustic signals detected by the hydrophone (PVDF usually, a commercial type LC-10 for source level measurements) were amplified 40, 60 or 80 dB by a microphone amplifier (Brookdeal type 453).
The amplified signals were then fed to the receive side of the gating system, which gave two separate outputs for measurements. An a.c. output was used for monitoring the received train of pulses on an oscilloscope, triggered by the transmit gate. Alternatively part of the received train (say the first echo) could be gated, giving a d.c. output from a peak detector which could be monitored by an AVO meter. The second method was preferable since, it gave a more accurate measurement. Since the gating system had a high-frequency cutoff at 338 kHz, an alternative arrangement was used for measurements at higher frequencies. For measurements up to 3 MHz the oscillator and gating system were replaced by a Harwell (95 series) system, but the principle of operation was the same.
For beamwidth measurements, the stem of the PVDF transducer holder was supported by a turntable carrying a needle which moved across a sheet of polar graph paper. Variations of received signal amplitude with rotation of the PVDF transducer about its vertical axis were obtained from the gating system's d.c. output and were accurate to 0.5 No significant differences in any of the spectra could be detected.
The transducers made by the techniques described above were mounted in a nylon housing (Figure 3) for all underwater measurements. Each transducer was rigidly backed by carefully sticking it onto a perspex disc with quick-setting adhesive until it was perfectly flat, thus ensuring that it vibrated in only the thickness extension (TE) mode. Figure 4 shows the instrumentation used for most measurements of receiving response, source level and To obviate the problem of mains pick-up by the hydrophone, a simple high pass RC filter was designed. The cut-off frequency was determined by" f= 1/2 rRC 1/2 r(1000)(0.047 x 10 -6 ) f= 3.386 kHz This is well above the troublesome 50 Hz pick-up and was found to work perfectly.

INSTRUMENTATION
For velocity of sound measurements, a separate ultrasonic interferometer was used. The measuring technique is described in Section 4.5.
For impedance and admittance measurements a PVDF transducer was driven by the Marconi oscillator, and measurements of voltage and current were obtained with the arrangement shown in Figure 5. The oscilloscope (Telequipment type D63) had a single-ended input for voltage measurement, and a double-ended differential input for current measurement. The impedance IZlis given by" The admittance Y is given by Y IZ I-producing a PVDF piezoelectric transducer. A large combination of poling temperatures and poling fields, applied for a wide range of times, will result in a working device. Various piezoelectric constants have been shown to depend on the poling parameters, x but there are no known results showing how the open-circuit receiving response of an underwater PVDF transducer depends on them. This dependence was studied by measuring the relative receiving responses of a number of transducers at 3 MHz. A plot of receiving response (in mVpp) against temperature for electric fields of 40, 60, 80 and 108 V/am-1 is shown in Figure 6. The projector-receiver separation of 100 mm ensured that measurements were obtained in the far zone, which is defined as extending from axial distances of d z [4X, where d is the transducer diameter and X is the wavelength of sound in water. At 3MHz, is 0.5 mm and d 2/4 for a 10 mm diameter PZT-4 projector is 50 mm.
The best fit lines for fields of 40, 60 and 80 V /amwere obtained by regression analysis, and the equations of these lines are shown on Figure 6. Thus, for a given poling field there is an approximately linear dependence of response on temperature.
However, there appears to be little difference in response between those transducers poled at 80 V /am -1 and those poled at 108 V/am for which no best-fit line is drawn.
The maximum response (for poling parameters of 108 V/amat 105 C) is greater than the minimum response (40 V/am -x at 65C) by 11 dB. Figure 6 exhibits similar characteristics to some of our previous results for freely-mounted 20 mm diameter PVDF transducers, which were obtained for the same temperature range but with much lower fields. 4 The majority of results for freelymounted transducers were obtained for poling fields below 40 V #m -1 but a few that were obtained for fields up to 165 V/amshowed no levelling off of response with increase of field.
Since the PVDF was very thin and therefore receiving well below its thickness resonant frequency, 7 each point on Figure 6, representing the response of a particular transducer, could be expected to move only marginally for a broad band of frequencies. many metres out along the transmission axis. Thus, the pressure is often measured in the far zone and a value of source level is obtained by adding on the transmission loss due to geometrical spreading. For spherical law spreading, the transmission loss is 20 log r, where r is the range.
For the 10 mm diameter PVDF transducers the far zone started at approximately r 5 mm at 300 kHz, therefore source level could be measured directly at m and no transmission loss extrapolation was necessary. Figure 7 shows a linear-logarithmic plot of source level in dB relative to 1/aPa against r.m.s, electrical input power for a PVDF transducer having an effective resistance of 2.8 kohm at 300 kHz (from Figure 12). The source level for 100 Vpp drive voltage is 145.2 dB relative to 1/aPa. This source level is so low that it is unlikely that PVDF would be suitable as a sonar projector other than for very short range applications, such as medical diagnosis.

Beamwidth
The beamwidth of any circular disc transducer depends on the directivity function D  (Figure 9). We consider that these values are lower than the predicted values because of the collimating effect of the transducer holder.
At higher frequencies the theoretical beamwidth decreases, and for a diameter of 10 mm, the 3 dB beamwidths at MHz and 10 MHz are 8.75 and 0.875 respectively. However, measurements in this range, applicable to medical ultrasonics, were not made.

Characteristic Impedance
The characteristic impedance of a material is simply the product of its density and the velocity of sound through it.
A simple ultrasonic interferometer was used for velocity of sound measurements, but the instrument did not have the resolution for measurements with the thin sheets previously used. Instead, a 3 mm thick sample of Solvay PVDF, made by Solvay & Cie (Belgium), was used. This material had a measured density of 1.799 x 103 kg m-3, approximately the same as for the 25/am sheet.
The measurement arrangement is shown in Figure   10. A pulse was transmitted from the projector P to the reflector R with the PVDF sample, of thickness t, in contact with P. The round-trip transmission PVDF PROJECTOR p I: Next, the sample was removed and the reflector moved towards the projector by an amount d until the displayed transmission time was the same as before.
The two situations may be expressed mathematically as" 2t + 2x _ 2(t + x -d) Vp 2190 ms -1 By this method the velocity of sound was determined independently of the separation (t +x) of P and R, which in this experiment was about 100 mm.
The value of Vw was measured at 20C.
The product of density and velocity of sound gives the characteristic acoustic impedance (pc) for PVDF as 3.94 x 106 rayl. This is about 8% greater than the value of 3.64 x 106 rayl recently published for 25/am sheet.

6. Frequency Characteristics
One of the most significant finds in this study was the behaviour of PVDF transducers as low-frequency receivers. Because of their non-resonant response over a broad range of frequency, they were found to be excellent devices for monitoring the nature and length of acoustic waves in water. Normally, the nature of a pulse as it is transmitted can only be roughly inferred by observing the waveform of the electrical pulse applied to a transducer. If this transducer has a high Q an applied pulse causes it to ring up to a steady state vibration amplitude, then ring down again so that the acoustic pulse is longer than the applied voltage pulse.
A PVDF hydrophone such as the one shown in Figure 3 can be used to visualise acoustic pulses transmitted by high Q projectors over the entire frequency range up to near its fundamental resonance of approximately 20 MHz. This is illustrated by the oscilloscope photograph shown in Figure 11. The upper trace shows a 100/Js pulse applied to a foambacked PZT-4 projector at its series resonant frequency (fo) of 297.92 kHz. The lower trace shows the much longer, and completely distorted, pulse received by the PVDF hydrophone after a propagation delay of 250 gs. This is a true representation of the transmitted acoustic pulse.
The shape of the received pulse can in fact be calculated, for it is well known that a transducer  Since the transducer has a Q of 33.1 it takes 33.1 x 3.36 111.2/as to ring up to 0.9 of its steady state amplitude. This is 11.2/as longer than the applied electrical pulse showing that the transducer was still ringing up at the end of the electrical pulse.
If the transducer takes the same time to quiesce to 0.1 of its steady state amplitude then the actual length of the generated acoustic pulse, is at least 100 + 111.2 211.2/as, or more than twice as long as the electrical pulse. This is borne out by Figure 11.
Since the PVDF sheets used here were only 25 /am thick, measurements of their electrical impedance (or admittance) were necessary to describe their broadband response. This was done with the arrangement shown in Figure 5. The variation of impedance and admittance with frequency over the range kHz to 10 MHz is shown in Figure 12. The phase angle between voltage across the transducer and current flowing into the transducer is also shown. Figure 12 can be used to calculate the effective resistance of PVDF at any frequency. This was done earlier in obtaining source level and can be illustrated for a specific measurement. At 300 kHz the phase angle was 42.3 and the impedance IZl was 3.9 kohm; thus the resistance was R IZ cos 42.3 2.8 kohm.

CONCLUSIONS
A range of underwater measurements on polyvinylidene fluoride (PVDF) has been made to describe its performance as an underwater transducer material.
PVDF transducers made with a variety of poling parameters were found to have a receiving response dependent on the poling field, poling temperature and poling time. Their absolute response was 20 dB lower than that of the standard LC-10 hydrophone 157 used for calibrations, but this response could be considered constant up to about 20 MHz for 25 #m thick transducers.
PVDF transducers used as projectors were found to have very low source levels, and are likely to be of use only for very short range applications. Beamwidth measurements agreed only approximately with theoretically calculated values, but we consider that this was because of the particular design of our transducer holder. A value of 3.94 x 106 rayl was obtained for the characteristic impedance by measuring the velocity of sound and the density of Solvay PVDF. PVDF hydrophones were found to be ideal for characterising acoustic pulses underwater because of their fiat response over a wide frequency range. This led to a simple direct method of determining the Q of some source transducer by counting the number of cycles in the receiver waveform up to 0.9 of the peak amplitude.
The receiving response of PVDF is considered high enough for future development of a hydrophone by suitable poling techniques, and of a multi-element array for calibrating underwater acoustic fields.