NAT'L INST. OF STAND & TECH

AlllDb b1DM71

NBSIR 76-1078

Piezoelectric Polymer

Transducers for Dynamic

Pressure Measurements

Aime S. DeReggi, Seymour Edelman, and Steven C. Roth

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

June 1976

Final

Department of Transportation

National Highway Traffic Safety Administration

Washington, D. C. 20590

QC

100

.U56

76-1078

1976

NBSIR 76-1078

PIEZOELECTRIC POLYMER

TRANSDUCERS FOR DYNAMIC

PRESSURE MEASUREMENTS

Aime S. DeReggi, Seymour Edelman, and Steven C. Roth

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

June 1976

Final

Department of Transportation

National Highway Traffic Safety Administration

Washington, D. C. 20590

The opinions expressed in this report are those of the authors and not necessarily

those of the National Highway Traffic Safety Administration

U.S. DEPARTMENT OF COMMERCE. Elliot L. Richardson. Secretary

Edward O. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director

Introduction

This report covers work completed on December 31, 1975, on thin (approximately 50 ym or 0.002 in. thick) piezoelectric polymer transducers which were

developed at the National Bureau of Standards (NBS) for the National Highway

Traffic Safety Administration (NHTSA) for use in their studies of the impact

pressure transients which occur in motor vehicle crashes.

The active material of the transducers is semi-crystalline polyviny lidene

fluoride (symbolized by either PVF^ or ?YDF in the polymer literature) which

is available in non-piezoelectric sheets. These sheets can be made strongly

piezoelectric by first subjecting them to a treatment which enhances the content

of one of the crystal forms (a planar zig-zag form referred to as either g-phase

or Form I in the polymer literature) and then subjecting them to a poling procedure. For information about the mechanism at the molecular level and about

how the piezoelectric activity is affected by sample preparation, treatment,

and poling parameters, the reader is referred to a review of the subject [1].

The polymer transducers were developed with two promising applications in

mind: 1) the measurement of the normal pressure between two impacting bodies

over the interface of contact during impact (this pressure is referred to

hereafter as the interface pressure) such as the interface pressure between

an anthropomorphic dummy and the instrument panel of a motor vehicle, and 2)

the measurement of intracranial pressure in animal subjects, such as rhesus

monkeys, during tests of controlled impact to the head.
_ 2 -

When mounted to the skin of an anthropomorphic dummy, the thin polymer

transducer is not expected to perturb significantly the surface density and

mechanical compliance of the dummy. As a result, the interface pressure

measured in this application should be representative of the pressure which

would occur in the absence of the transducer. When implanted into the cranium

of a rhesus monkey, the polymer transducer is expected to move with, rather

than relative to, the cranial fluid during impact , because the density of the

polymer transducer is comparable to that of the cranial fluid. Thus, in this

application too, the pressure measured by the polymer transducer should be

representative of the pressure which would occur in the absence of the transducer.

An earlier report [2] covered the development of a polymeric interfacepressure transducer with a circular active area 1 cm in diameter. In this work,

it was found that the electrical output of the transducer under general and possibly

complicated impact conditions could be explained qualitatively in terms of an

output proportional to the pressure normal to the surface of the transducer and

an output presumed to depend on membrane strains. The membrane strains may

result from bending or stretching of the active area during impact. Measurements

described in the earlier report indicated that bending-induced membrane strains

could be reduced by lubrication.

The present report covers work performed since the earlier report. This

work has proceeded in two main directions, one with the objective of preparing

and calibrating 10 intracranial pressure transducers (hereafter referred to as

ICPT's) for implantation in rhesus monkeys, and the other with the objective of

preparing and calibrating 23 interface-pressure transducers (hereafter referred

to as IFPT's) for use on anthropomorphic dummies and other biomechanical subjects.
- 3 -

In the case of the ICPT ' s , the pressure to be measured is quasi-hydrostatic.

Calibration data obtained with a polymer transducer placed in an oil-filled cell

and subjected to a known pressure transient have been found to be reproducible

to with + 3%. At NHTSA's request, the ICPT's were made with much-reduced

(2-mm diameter)sensitive areas. These small transducers are thus suitable for

implantation in the cranium of small lab animals such as rhesus monkeys. Ten

or more ICPT's have been calibrated in an oil-filled cell and delivered to

NHTSA for use in their other research programs.

A matter which needs to be resolved by further experiments is whether the

calibration factor of an ICPT is affected by the thermal conductivity of the

fluid into which the transducer is placed. Calculations are given in Appendix B

which suggest that the response of a polymer transducer (which is both pyro- and

piezoelectric) should contain a significant pyroelectric component associated

with adiabatic-compression heating of the transducer under changing pressure.

Adiabatic- compress ion heating of the fluid or other substance in contact with the

transducer, if different from that of the transducer, could act as a source or

sink of heat for the transducer. Experiments bearing on this matter are suggested

in the Recommendations for Future Work at the conclusion of this report.

In the case of IFPT's the pressure to be measured is the normal pressure,

that is, the pressure perpendicular to the surface of the transducer. However,

the stress induced in the polymer by the impact of compliant bodies may have

components parallel to the surface as well. As a result, the response may

contain extraneous components. Twenty- three transducers were made with circular

active areas 1 cm in diameter and calibrated under transient normal-pressure
- 4 -

conditions while the transducer was sandwiched between a flat-faced, dry,

aluminum piston and a dry aluminum disk. These calibration data yielded

pressure-response coefficients which are reproducible to within + 3%.

However, the measured coefficients depend on the mechanical and thermal

properties of the piston and disk and of any other substance introduced with

the sample between the piston and disk. The dry rigid aluminum surfaces of

the piston and disk tend to pin the surfaces of the transducer and to keep

the temperature of the transducer constant. If the test conditions are changed,

the measured coefficients will also change. It has been found, for example,

that if the transducer was in frictional contact with compliant instead of

rigid surfaces, the output increased by a factor which hereafter will be

referred to as the output enhancement, or simply the enhancement. The

enhancement depends on the compliance and frictional properties of the

impacting bodies. A range of impact situations has been investigated to

establish qualitatively the range of variation of the enhancement. Based on

these experiments, it is judged that the accuracy with which the effective

pressure- response coefficient of a transducer can be predicted for an arbitrary

set of field conditions will depend on the accuracy with which the field

conditions are known.

Enhancement measurements were also performed on a reduced-area transducer

and it was found that the enhancement was vastly reduced. These results

suggest that, in the future, reduced- area transducers should be considered

not only for intracranial pressure measurements but also for interfacepressure measurements in situations where the enhancement is apt to be large

or unpredictable. Still, however, separate calibration methods would be

required for each of the two applications. Calibration accuracy for interface pressure measurements within + 10% seems within reach.

*The enhancement is defined arbitrarily as a (multiplicative) factor. The

experiments performed in this project can be discussed conveniently using this

definition. However, this definition may need revision as more experiments

are performed if it turns out that enhancement has additive as well as multiplicative character.
- 5 -

The fundamental question concerning whether or not mobile real charge

(Injected during poling as opposed to bound dipolar charge) Is present In

the polymer Is still not resolved and requires future attention. Real charge

will contribute to the response if the stress induced across the thickness of

the polymer is nonuniform. Nonuniform stresses could be induced in an IFPT during

the impact of two bodies which deform differently.

Improvements in Transducer Construction

The polymer transducers delivered to NHTSA since the last report [2] have

been improved in the method used to make electrical contact to the miniature

electrical connector. Previously, connection from the ground side of the

connector to the ground electrode of the polymer was established by a layer of

silver-bearing rubber paint in the manner described in Appendix D . Exposure

to oil and multiple flexing in time caused this contact to deteriorate and to

increase in resistance. This problem has been eliminated by adding a small

U-shaped metallic clamp which securely establishes contact with the ground

electrode on both sides of the polymer' . A wire connects this clamp to

the ground side of the connector. Silver-bearing epoxy is used to further secure

the clamp and the whole region, as before, is covered with a coat of silverbearing rubber paint. The silver- bearing rubber paint, as in the previous design,

serves as an extended ground from the miniature electrical connector and thus

shields the wire connecting the inner electrodes of the polymer transducer to

the center contact of the miniature connector. The external appearance of the

transducer is not changed appreciably by this modification.

*The clamp is made from a small (approximately 3 mm x 3mm) piece of brass sheet

(100 ym thick) which is bent into a U, and squeezed in a vise until the sides

of the U nearly touch. A gap of one-half the thickness of the polymer to be

contacted is used.
- 6 -

Reduced-Area Transducer Construction

The construction of the reduced-area transducer is identical to the

construction of the transducer with 1-cm diameter active area described

previously [2] except that the active area has been reduced from a 1-cm

diameter circle to a 2-mm diameter circle, and the electrical improvement

discussed in the previous paragraph has been incorporated in the construction.

Figure 1 shows the external appearance of a reduced-area transducer (upper)

and a regular transducer (lower). The circular sensitive area in each case

appears near the left end.

Oil-Cell Pressure Calibration of ICPT's

A hydraulic transient pressure cell, shown in Figure 2, has been constructed

as an accessory to the drop tester. The cell was machined from a massive iron

block. During calibration, the polymer transducer is oriented with its active

area toward the left end and is attached to a feedthrough electrical connector

on the flange shown on the right. A calibrated conventional pressure transducer,

which has a pressure-dependent resistance, is mounted through the flange shown

on the left with its sensitive face exposed to the pressure inside the cell.

The transducer is connected electrically to the mini-box shown in the foreground,

which houses a bridge circuit and a battery power supply. The cell is filled

with oil and is sealed by means of the piston shown at the top. Pressure transients are generated by impacting the piston. Controlled impact is conveniently

achieved by placing the cell in the drop-test machine.

The waveform of the pressure transient is affected by many factors, including

air in the oil or in the cell. Air dissolved or entrapped in the oil (which

reduces the bulk modulus of the mixture and thus affects the rise time of the
- 7 -

r"1
- 8 -
- 9 -

pressure transient) can be removed by pumping on the oil under a bell jar

until bubbling stops (this requires pumping for a minimum of 15 minutes). Entrapping air in the oil cell during the filling process can be avoided by performing the entire filling operation under vacuum. However, satisfactory

filling can be achieved in air using gas-free oil by overfilling the cell to

permit the piston to be put in place without trapping air, and then forcing

the excess oil through the side flanges. Each flange is loosened in turn

while the piston is being depressed. Placing crusbable or compliant materials

over the piston also affects the waveform. This is a convenient method of

shaping the waveform.

The transducer constants (as distinguished from the piezoelectric constants

of the polymer material), which are measured during the oil-cell calibration,

are either AQ/AP or AV/AP, where Q is the charge output measured by a charge

amplifier, V is the voltage measured by a high-impedance voltage amplifier,

and P is the pressure measured by the calibrated pressure transducer. The

2 force F over the active area of the transducer is F = PA , where A = (ir/A) d a a a and d is the active diameter, which is found to be greater than the 1-cm

a electrode diameter. Quantitative information about the effective active area

is given in Appendix A.

In terms of the effective piezoelectric constant for a single sheet defined

as d^ = AQ/AF, the transducer constants are

AO/AP E A AQ/AF = 2 d, A , a ^ ha'

and

AV/aP = A AV/AF = 2 d^ A /C.

a ' ha
- 10 -

The subscript h indicates that the constant d^ is measured under quasi-hydrostatic

conditions. The factor of 2 comes from the fact that the transducer is bilaminate

with two sections electrically connected in parallel so that the respective charge

outputs add. The capacitance C includes the capacitance of the active sections,

the capacitance of the electrical leads within the transducer and the cable

capacitance. If the lead and cable capacitances are negligible, C 2 e ^J^^

where e is the permittivity and t is the thickness of one section of the transducer. An alternate form of AV/AP with C eliminated is

d

AV/AP = -^t E g^ t

which is independent of the active area A^. The constant gj^ , appearing above is

equal to (AE/AP)^^, where E is the induced electric field ( E = V/t) and D is

the electric displacement. The subscript D means that D is held constant. The

area A can also be eliminated from the AQ/AP expression, by using the capacia tance formula. The expression then becomes

AQ/AP = C t g^ .

For a bilaminate transducer with d = 1 cm, t = 25 ym, e = 10 e where e is the

a o o permittivity of free space, the capacitance will be C ~ 1 nF. Using d = 10 pC/lsi , h

the transducer constants are AQ/AP = 2.5 X lO""^^ C/Pa (17.5 x lO"-*-^ C/psi)

. AV/AP = 2.8 yV/Pa (20 mV/psi)

Figure 3 shows an example of the transients measured during calibration using

the oil cell. The good correspondence of the transient waveforms produced by

the polymer and standard transducers (the latter being known to have a wide

frequency response) is indicative of the good frequency response of the polymer

transducer in the kHz range. Similar tests using longer and shorter transients

indicate similarly good frequency response down to 1 Hz and up to 10^ Hz.
- 11 -

Figure 3. Oscilloscope record of pressure waveform

obtained in the oil-cell.

Upper trace: Vertical axis Y^(Q) is proportional to

charge output of polymer transducer.

Lower trace: Vertical axis Y^CP) is proportional to

voltage output of standard pressure transducer.

Upper and lower trace: Horizontal axis x is proportional to time.
- 12 -

Normal- Imp act Pressure Calibration

The fixture shown in the center of Figure 4 was made as an accessory to

the drop tester to allow the application of normal pressure transients to the

active part of the polymer transducers with 1-cm diameter active areas. The

fixture consists of an aluminum piston with flat faces shown toward the top

of the fixture. The piston is centered on the fixture and is guided by the

fixed bracket, which has a clearance hole for the piston to pass through. A

flat disk beneath the piston, which is partly obscured by the polymer transducer, forms the mounting surface for the polymer transducer. In a test, the

transducer is inserted between the piston and disk, and the piston is impacted.

The disk is supported rigidly by a calibrated quartz force transducer which

is mounted to the disk-shaped base of the fixture. Impact of the piston produces

normal pressure transients with a waveform which can be controlled by the

placement of a pad beneath the fixture and/or a washer over the piston.

For the reduced-area transducers, the piston is replaced by the assembly

shown to the right of the fixture. The lower piece of this assembly serves as

a guiding sleeve for the upper piece of this assembly which in turn serves as

a reduced-area piston. The diameter of this piston is approximately 2 mm

(nominally the same diameter as the active area of the polymer transducer).

Thus, the force applied by means of this piston can be confined to the active

part of the polymer transducer provided only that the latter is correctly

positioned in the test fixture. This arrangement meets the calibration requirement that the force measured by the calibrated force transducer is the force

applied to the active area. To interpret the calibration data, it is necessary

that the diameter of the piston not exceed the diameter of the active area of

the polymer transducer.
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_ 14 -

The transducer constants measured under normal- impact conditions are either

AQ/AF or AV/AF, where Q is the charge output measured by a charge amplifier,

V is the voltage measured by a high- impedance voltage amplifier, and F is the

force measured by the force transducer. In terms of the defined piezoelectric

constant for a single sheet, d = AQ/AF, the transducer constants are

n

and

AQ/AF = 2 d , n

'

AV/AF = 2 d /C

n

where C is the total capacitance consisting of the transducer capacitance,

the cable capacitance and the capacitance of the amplifier-input circuitry.

The subscript n indicates that the piezoelectric constant d^ is obtained under

normal impact with dry aluminum surfaces contacting the polymer transducer.

If d =10 pC/N (44.5 pC/lbf), then AQ/AF ~ 20 pC/N (89 pC/lbf). If C = 1 nF,

n then AV/AF = 20 nV/N (89 mV/lbf).

It should be noted that although d^ (for quasi-hydrostatic pressure conditions')

and d (for normal pressure conditions) have both been taken as 10 pC/N for

n the purpose of illustrating the magnitude of the measured transducer constants,

they (d^ and d^) in fact are going to be different by approximately a factor of

2 because the conditions of loading are different. In the case of hydrostatic

pressure loading, all the dimensions of the active region are reduced, including

the diameter of the sensitive area. In the case of uniaxial loading in the

thickness direction, the diameter of the sensitive area will always tend to

increase. The increase will be greatest when the transducer is in frictional

contact with a high compliance material and smallest when its two surface are

perfectly pinned by nearly non-compliant impacting surfaces.
- 15 -

The pressure coefficients are obtained from the force coefficients

using the relations,

AQ/AP = A AQ/AF,

Si and

AV/AP = A AV/AF

a

As indicated in the oil-cell calibration discussion, relations exist between

the measured transducer constants and the piezoelectric constants of a single

polymer sheet. These relations are

AQ/AP = 2 d A - C t g , n a n and

AV/AP = 2 d A /C t g t. n a n

The transducer constants measured by normal impact have been found to be

roughly twice as great as those for quasi-hydrostatic loading. Figure 5 shows

examples of the transients obtained for normal-pressure calibration.

Output Enhancement Studies

The conditions under which the interface pressure transducers; were calibrated

were such that the surfaces in contact with the polymer transducer during impact

were nearly noncompliant and flat. Thus, to a degree, the active; area of the

polymer surface was pinned rather than free to slide.

Output enhancement is anticipated if compliant impacting bodies with finite

dimensions contact the surfaces of tlie transducer. The mechanism for this

enhancement is believed to be the following. There will be a tendency for

compliant material to flow radially outward from the center of impact. A

polymer transducer with its center coinciding with the center of impact and its
- 16 -

Figure 5: Oscilloscope record obtained with the pistonimpact fixture in Figure 4 fitted with a l~cindiameter polymer transducer. Polymer transducer

was sandwiched between dry aluminum piston above

it and dry aluminum disc beneath it.

Trace Y(Q) versus X(t) is the polymer- transducer

output versus time. Calibration of axes given

as "Y(Q) cal" and "X(t) cal" respectively.

Trace Y(0) versus X(F) is the polymer-transducer

output versus force-transducer output. Calibration of X(F) axis is given as "X(F) cal". The mean

slope of Y(0) versus X(F) gives a polymer transducer sensitivity of 23.3 pC/N (103.7 pC/lbf).
- 17 -

surfaces in frictional contact with the compliant material will be stretched

radially. The radial stretching, even if slight, may develop sizeable membrane

stresses and, hence, a corresponding component to the transducer response.

This component, not having a simple relationship with normal pressure, is

considered to be extraneous and to constitute a major source of output

enhancement.

While it is possible to reduce this enhancement by lubrication, there are

'

situations where lubrication may not be desired or practical. For example, there are

instances where it might be desirable to bond a polymer transducer directly to

a compliant body. Thus, it is of interest to find out how much the output

enhancement varies for impact surfaces having a wide range of compliance. It

is also of interest to find out the dependence of the enhancement on the

diameter of the active area of the transducer. Preliminary measurements

described later in this report suggest that the enhancement decreases as the

active area is decreased.

The response Q vs P for each of two transducers having active areas 1 cm

and 2 mm in diameter was measured under each of the following separate test conditions

a) Dry surfaces of aluminum piston and disk directly in contact with

polymer transducer surfaces (sandwich structure in the sequence

Al-IFPT-Al).

b) Oil-lubricated, aluminum piston and disk (Al-oil-IFPT-oil-Al)

.

c) Poly tetraf luo roe thy lene (PTFE) tape inserted between piston and IFPT

and disk (Al-PTFE-Poly-PTFE-Al) . The thickness of the PTFE tape was

76 ym (0.003").

d) Unvulcanized rubber sheets inserted between piston and IFPT and between

IFPT and disk (Al-Rubber-IFPT-Rubber-Al) . The thickness of the rubber

sheet was 760 \im (0.030"). The particular grade of rubber was sticky

to the touch and adhered to the polymer transducer surfaces after impact.
- 18 -

e) Rubber sheet as in d) inserted only between piston and IFPT

(Al-Rubber-IFPT-Al) .

Configurations b) and c) are believed to approximate field conditions where

a polymer transducer is provided with liquid (oil for instance) or solid

(graphite for instance) lubrication. Configurations d) and e) represent

conditions under which the polymer device is subjected to a considerable amount

of stretch and acts much like a strain gage.

The dry configuration (a), as expected, gave the smallest AO/AF for both

transducers. For the 1-cm diameter transducer, the oil- lubricated configuration

(b) gave an enhancement of approximately 50% over the dry case, accompanied by

a scatter of + 20% in the Q vs F data. The PTFE sandwich configuration (c) gave

an enhancement of approximately 15%. The Q vs F data had little scatter and

were found to remain linear. The rubber-sheet sandwich (d) was found to produce

considerable enhancement and the reproducibility was poor, probably because of

long relaxation times for the viscoelastic rubber material. The enhancement can

be given only roughly as a factor of up to 4 or 5. The configuration with

rubber on one side only (e) also was subject to reproducibility problems. The

enhancement in this case was a factor of around 2.

The above results show that, in order for 1-cm diameter polymer transducers

to yield reliable information about interface pressure, they will have to be

mounted in a manner which avoids or reduces membrane strains. With proper

mounting techniques, it is anticipated that the enhancement should be held within

acceptable limits, and the estimated predictability of the enhancement should

be around + 10%. Additional investigative work is indicated in the area of

mounting techniques to insure predictable enhancement for specific field conditions.
- 19 -

The enhancement for the reduced-area transducer was found to be much

smaller than that for the 1-cm diameter transducer. The largest enhancement

using the configuration Al-Rubber-ICPT-Rubber-Al was found to be only about

40%, a dramatic improvement over the 1-cm diameter transducer. Enhancement

is expected to decrease as the radius of the active part of the transducer

is decreased. Hence, the reduced-area transducers, which were originally

developed for cranial implantation, may be promising interface-pressure transducers for applications where enhancement problems are expected.

Summary of Accomplishments to Date

Since the inception of this two-year project, the following accomplishments

have been achieved. 1) Polymer- transducer configurations have been developed for

measuring interface pressure and quasi-hydrostatic pressure resulting from

impacts. 2) Two transducer versions differing principally in the size of the

active area (1-cm and 2-mm diameters respectively) have been evaluated in the

laboratory by NBS. The larger size (developed first) was originally intended

to measure interface pressure transients, i.e., normal pressure between colliding

bodies, and the smaller size (developed later) was intended to measure quasihydrostatic pressure transients in the cranial cavity of rhesus monkeys. 3) Normalpressure test methods have been developed, including a method in which curvature

is imparted to the transducer during impact. 4) A quasi-hydrostatic test method

has also been developed. The results in the laboratory show promise for

the transducers in both types of application. However, used between highly

compliant colliding bodies, the transducers, being as thin as they are, are prone

to being flexed and stretched, so that outputs not related directly to normal

pressure result. It appears that, by devising proper mounting techniques, these
- 20 -

extraneous outputs can be maintained within acceptable limits. However, to

establish this with greater certainty, the transducers need to be tested in

the field with a variety of mounting techniques. 5) It has also been established

in our most recent tests with reduced-area transducers that their extraneous

outputs are much smaller than those of the larger- area transducers. The smallarea transducers should therefore be considered for interface-pressure measurements

in situations where considerable flexing and stretching are anticipated. 6) Twentythree (23) transducers with 1-cm diameter active areas were delivered to the

NHTSA as well as ten (10) transducers with 2-mm diameter active areas. These

transducers were tested prior to delivery for ability to withstand pressures of

7 6

up to 10 Pa (-1000 psi) and were calibrated in the pressure range 0 - 2 x 10 Pa

( 0 - 300 psi) under either normal pressure, quasi-hydrostatic pressure, or both.
- 21 -

Recommendations for Future Work

The work to date has resulted in 1) the development of two versions of

a piezoelectric polymer transducer for two different applications in dynamic

pressure measurements, namely IFPT's for interface-pressure measurements and

ICPT's for intracranial-pressure measurements; 2) the development of test and

calibration methods appropriate for each of the two applications; 3) the

identification of possible physical mechanisms of piezo- and pyroelectric origin

which might give rise to undesirable components in the transducer response; and

4) the delivery to NHTSA of the contract-specified numbers of calibrated IFPT's

and ICPT's.

Because of the restricted scope of the work to date, several aspects of

the behavior of polymeric pressure transducers have been left in a preliminary

stage of investigation. This fact and the fact that the range of impact conditions (dynamic stresses other than normal pressure and dynamic temperature

excursions) which are likely to be met in practice are not clearly established,

suggest that further progress will be made most efficiently through the close

coordination of laboratory and field work. The laboratory work is to gain a

greater understanding of the spurious outputs due to both piezo- and pyroelectric

effects. The field work is to obtain a realistic knowledge about the range of

stress and temperature excursions over the considerable variety of foreseeable

field applications, and to identify specific problem areas the knowledge of which

can guide the laboratory work. Deficiencies in performance in a given field

application do not necessarily indicate an inherently fatal property of polymeric

transducers, but merely a weakness of one particular transducer design for that

specific application to be corrected by further development.
- 22 -

The following work is recommended with the broad aim in mind of arriving

at a pressure transducer with properties so well known that it can be used

effectively by any technically competent personnel provided only that they

consult the calibration report and follow simple, recommended mounting practices:

1) To minimize the spurious response of an IFPT due to stretching and

flexing relative to the response due to normal pressure, the diameter of the

active area should be made as small as is practical. Experiments described

in the Enhancement Studies section of this report have shown that the enhancement of a 2 mm diameter transducer is smaller than that of a 1 cm diameter transducer. The theory in Appendix C indicates that stretching effects under spherical

impacts can also be minimized by reducing the active area. The diameter cannot

be reduced indefinitely, however, as the voltage sensitivity, low-frequency

response and noise figure will be degraded if the capacitance of the active

region becomes comparable to or smaller than the capacitance of the electrical

leads and shunt capacitance of the amplifier input. The optimum transducer size

should be determined by performing a study of the dependence of the enhancement

on the radius of the transducer active area under controlled laboratory impact

conditions. This study would require constructing several transducers with

the same thickness but with different active areas.

2) To gain the benefits of reduced active area without prohibitive loss of

capacitance, an IFPT could be constructed with several small mechanically isolated,

but electrically connected active areas. Mechanical isolation could be achieved

by making the active regions stiff and resistant to stretching compared with the

intervening inert regions.
- 23 -

3) Special transducer configurations for special applications should

also be investigated. For example, a ring or washer-stabilized prestressed

membrane configuration may reduce the effects of membrane strains in situations

where the membrane remains plane.

4) To compensate both IFPT's and ICPT's for pyroelectric response, the

dynamic temperature change experienced by the active areas should be determined

under representative pressure-measuring conditions. These temperature transients

could be obtained by measuring the temperature-dependent resistance change of

one of the thin-film electrodes, or by measuring the thermoelectric voltage of

a thin-film thermocouple deposited on one of the electrodes.

5) The change in pressure sensitivity due to changes in ambient temperature

should be measured over a range of temperature spanning the extremes anticipated

in the field.

6) A field calibrator should be designed, built, calibrated, and field

tested. Such an instrument could measure the in-situ response of an IFPT to

a pressure transient produced by the calibrator. Many of the spurious effects

would thus be automatically compensated for, including those induced by variations

of mounting technique and those induced by variations of local conditions.

7) It would be of interest also to measure the effects of the response of

changing dynamically the surface charge on the external surfaces of the transducer. The motivation for this measurement is that there are plans to measure

seat-belt pressures against a restrained body. Seat-belt materials could be

triboelectric which could result in significant charging of the material in

contact with the polymer transducer.
_ 24 -

Appendix A. Effective Active Area

The effective active area of a polymer transducer of the type described in

this report appears to be somewhat greater than the area of the poling electrodes.

This can be demonstrated by measuring the piezoelectric response of a transducer

to piston pressure, as the piston radius, r, is varied over a range of values

including values in excess of the electrode radius, r^.

For r < r , the short-circuit charge output Q produced by force F, is given — e by Q(r < r^) = 2 d^F, which is independent of r. For r > r^ the charge output

with the assumption that the active area is limited to the electrode area is

""e 2 given by Q(r > r^) = 2 '^j^^^'^) > ^ decreasing function of r with maximum negative

slope at r = r . Thus, a sharp break in the r-dependence is predicted at r = r . e e Table 1 shows the results of a set of measurements performed on a typical

transducer, for which = 1 cm, for six pistons of different radii, together with

corresponding theoretical predictions for comparison. The results bear out the

predicted independence on r, for r < r^, but do not indicate a sharp decrease in

response starting at r = r^. Instead, the sharp decrease begins around r = 1.2 r^

suggesting that the effective piezoelectrically active area extends radially

approximately 20% beyond the electrode boundary.

The origin of the extended active area has not been established. However,

several factors could contribute. During poling, the poling voltage may extend

beyond the poling electrode boundary due to electrical breakdown of the air or

to charge leakage along the surface. Electrical fringe effects and real-charge
- 25 -

Table 1

Variation of Transducer Response with Piston Radius

r (electrode radius) r (piston Theory ^''"^ Experiment

^ radius)

1 cm 0.8 cm 1.0 1.06

0.9 cm 1.0 0.94

1.0 1.0

1.1 0.83 1.07

1.2 0.69 0.92

1.3 0.59 0.63

1.4 0.51 0.49

(1) This column lists normalized response Q(r)/Q(r<rg) where

Q(r<r ) = 2d Ffor r<r , and Q(r) = 2d Fr^/r^ for r>r . e n e n e e

(2) This column lists Q(r)/Q(r<r )when Q(r<r ) was taken as

e e the mean of 4 high readings.
- 26 -

injection will further influence the poling field distribution. Finally,

during piezoelectric response measurements, mechanical fringe effects giving

rise to inhomogeneous stresses around the edge of the piston can introduce a

real-charge component to the response. This component will be greatest when

r r , in which case the mechanical fringe volume coincides with the electrical

e fringe volume.

The effects of extended active area on the accuracy of the device calibration

and on the reliability of using laboratory calibration data in field measurements

have not been quantitatively established. The importance of these effects,

however, is expected to increase as the radius of the transducer is decreased.

Thus, there may be cause for concern in the case of reduced-area transducers.

One way to eliminate extended active area would be to make transducers with

active sections cut out of larger poled sheets. This procedure, however, increases

the complexity of the device construction.

<
- 27 -

Appendix B. Effects of Heating under Adiabatic Compression

The piezoelectric polymer transducers discussed herein are also pyroelectric

.

- 2 -1

The pyroelectric coefficient is in the neighborhood of 4 nC'cm • K , yielding

an open-circuit voltage response of 6.3 V/K for a 1-cm diameter bilaminate device with

1 nF capacitance. At low frequencies, a transducer in good thermal contact with

a metallic base plate will respond nearly isothermally . At high frequencies

the same transducer will respond nearly adlabatically . This appendix suggests

that the difference between the isothermal and adiabatic response is significant

because plastics heat up sufficiently during adiabatic compression.

The thermodynamic relation for the pressure- induced infinitesimal temperature

change under adiabatic compression is

dT

dP C

P

where T is the temperature, P is the pressure, v is the specific volume B is the

P themal expansion coefficient at constant pressure — (:r^) , and C is the

^ V dT p p

specific heat at constant pressure.

At T = 300 K, we have C ==1.3Jg K ,v = 0.6xl0 5-and3 :=3x 10~ K

P Kg p

for polyvinyl! dene fluoride. These data give

~ 4.2 X 10"^ K/Pa (0.3 x lO""^ K/psi)

The pyroelectric responsivity due to adiabatic compression heating is thus predicted

-3

to be 0.26 yV/Pa (1.8 x 10 V/psi). This is about 17% of the piezoelectric responsivity under hydraulic pressure which is around 1.5 yV/Pa (10 mV/psi), and is

of opposite sign.
- 28-

The above analysis suggests three possible environmental situations.

Case 1: dT/dP of surroundings is the same as dT/dP of the polymer transducer. The transducer exchanges no heat with its surroundings and its response

is adiabatic at all frequencies. •

Case 2: dT/dP = 0 for surroundings and surroundings act as a constant

temperature bath. The transducer exchanges heat with its surroundings with

a characteristic equilibration time t. Its response will be adiabatic at

high frequencies compared to l/x and isothermal at low frequencies compared

to 1/t. At intermediate frequencies, the frequency response should exhibit

a smooth decrease with increasing frequency corresponding to a change from

isothermal to adiabatic conditions.

Case 3: dT/dP of surroundings is much greater than dT/dP of polymer.

In this case, the response at low frequencies compared to l/x will be dominated

by the pyroelectric effect, while the response at high frequencies compared

to 1/t will be adiabatic.
- 29 -

Appendix C. Response due to Stretching Resulting from Impact by a Sphere

Consider a polymeric transducer with an active surface of radius r^ , which

is mounted on an initially flat, yielding material such as a foam-rubber pad.

The transducer and the pad are impacted at normal incidence by a spherical,

rigid object of radius R, where R > r^. Contact between impactor and transducer occurs first at the center of the transducer. The impactor indents the

pad to the extent that the initially plane surface of the transducer is forced

to conform to the shape of the spherical impactor. After the transducer has

fully conformed to the shape of the impactor, the impactor continues to indent

the pad, and the deforming pad causes the transducer to stretch further while

sliding over the surface of the impactor. The membrane-extensional response

of the transducer (short-circuit charge or open-circuit voltage), can be

considered an "error" response. For the purposes of computing this error

response, assume that the membrane-extensional deformation of the transducer

proceeds in two stages.

During the first stage, assume that the planar surface of the transducer

transforms into a spherical cap by orthographic projection (refer to Fig. 6).

Imagine a polar grid pattern printed on the active surface of the transducer.

Before deformation, the pattern which has its pole at the center, consists of

concentric circles centered on the pole which are intersected by lines radiating

from the pole. In the assumed deformation process, the circles map into latitude

circles without change in radius, while the radial lines map into meridians with

an increase in length. The membrane deformation is thus considered to be purely

radial in this stage.
- 30 -

a)

ds

b)

Figure 6. Impact of rigid sphere and initially flat, semi-infinite, compliant pad with

circular (thin sheet) polymeric transducer on its surface: a) before impact;

b) at the end of the first stage of indentation when the transducer has fully

conformed to the shape of the impactor.
- 31 -

The piezoelectric equation which applies [3] during the first staee^ is

E3 = I

= - h3^ S^, for D = 0 (1)

where = the electric field across the thickness of the polymer sheet under

conditions of constant electric displacement D.

V = the corresponding open-circuit voltage output,

t = the thickness of the polymer sheet.

^3r

" piezoelectric constant relating the appropriate component of

field across the thickness to radial strain.

S = the radial strain,

r

Referring to Fig. 6 (a), the radial differential element, dr, transforms into

the differential arc length ds = R d9. The strain at a general radius r is thus

The field at r is, according to Equation (1):

The charge induced on the electrodes of the transducer is, by Gauss's law:

Q

= e E3 dA, (4)

where e is the dielectric permittivity of the polymer sheet (typically, e 10

where is the permittivity of free space) , E^ is the position-dependent field

in Equation (3) and dA is the differential element of area with circumference

2TTr and width ds = R de = — = — . The integration gives

cos e ;— r- °
- 32 -

Q = 2-rT e ho ^ 3r '° [—^ 1] (5)

^ r 2 = 27T e R {- 1/2 In [1 -{-f^) ] + - 1}. (6) 3r R

1 -

The open-circuit voltage is V = Q/C, where C is the strain-dependent

capacitance. If, for simplicity, it is assumed that the deformation conserves

eA ETTr 2

polymer volume, and that e is independent of strain, then C = — = —

^

will not depend on strain. In that case, the effect on the capacitance of

increased area is compensated exactly by the effect of decreased thickness.

r 2 Result (6) can be condensed if o/R << 1 by approximating In [1 -(-r^)]

and V 2 by the leading terms of their respective series expansions to

obtain

3 TT £ h „ 9 ^

' Q

=

1 R (^). (7)

The voltage for polymer volume- conserving strains and constant e is

V = Q/C = 3/4 h3^ t |. (8)

This voltage is seen to depend on r. Thus, for a given R and t, V can be reduced

by reducing r.

During the second stage, the deformation is more complicated. If the transducer

surfaces were ideally lubricated, then this deformation would be zero. If the

transducer can slide freely over the surface of the impactor but cannot slide

relative to the pad, then the pad deformation will cause the grid pattern to

expand in area. In that case, both the latitude circles and meridians will stretch.
The error voltage In this stage Is probably going to depend on the integral

of the tangential component of the pad reaction pressure P over the transducer

surface. The evaluation of the integral requires a knowledge of the tangential

pressure distribution P^ (6) or some assumption to be made about its form.

The integral is straightforward if the pad reaction pressure over the contact interface is assumed to be directed oppositely to the motion of the impactor

as shown in Fig. 6 (b) and if the pressure is assumed to be either constant or

2 linearly dependent on the indentation. The area element is dA = 2tt R sin 6 d9

.

Under the constant-pressure asumption, the integral is

? 2 F^ = 27T P R I ^ sin 6 d 6

= 27T R^ P[^ - 7 sin 26 ] , 2 4 c

where 9 is the half- angle subtended by the contact interface,

c Under the assumption that the local pressure, P, and the local indentation,

6 = d - R (1 - cos 6), are linearly related, i.e. P = k6 , the integral is

2 (^2

F^ = 2t7R k (d - R) sin e d 6

o

+ 2ttR k

^ sin 6 cos 6 d 6

o

„ 6 sin 26

^ = 27rR^ k (d - R) (-75^ -) + 4^ R-^ k sin 6 . Z 4 J C

Under either assumption, F^ is seen to increase with 6^. This suggests

that the error voltage in the second stage of deformation, as in the first stage,

can be reduced by reducing the radius of the transducer.
- 34-

Appendix D. Details of Transducer Construction

This appendix is a reproduction of Section 3.2 of the earlier report

(NBSIR 75-740) which gave details of the construction of 1- cm- diameter transducers. The procedure produces bilaminate transducers in lots of nine.

(1) Two rectangular sheets, 13 cm x 16 cm, are cut from a roll of capacitorgrade PVF^ sheet 25-ym thick.

(2) Each sheet of PVF2 is sandwiched between two sheets of glass. This

assembly is placed in an oven and is heat-treated at 130 + 10°C for approximately

two hours. This annealing treatment serves to reduce permanent and severe dimensional changes during subsequent steps.

(3) On one side of each sheet (referred to as the electrical high side) a

mask-defined pattern of nine identical aluminum electrodes, as shown in Fig. 7,

is deposited by evaporation in a vacuum chamber. The pattern is defined by an

evaporation mask which is also shown in Fig. 7. Aluminum was selected as the

electrode material because it is easy to evaporate, adheres well to the polymer

substrate, and has good electrical conductivity in thin-film form. Each electrode

consists of a 1-cm-diameter circular area connected to a 0. 2- cm- diameter circular

dot by a strip 10.1-cm long and 0.04-cm wide. The 1-cm-diameter spot defines the

area which ultimately becomes active; the strip serves as an electrical lead, and

the small dot as a pad for later electrical connection to the center conductor of

a low-noise cable. The nine electrodes are deposited side-by-side, so that the

nine strip leads are parallel and 1.6-cm apart, while the 1-cm-diameter spots and

and the 0. 2- cm- diameter pads form respective parallel linear arrays, nominally

10 cm from each other. Approximately 0.2 ym of aluminum is deposited, which

results in a strip lead resistance of less than 100 fl.
"igure 7. a) Mask, b) PVF2 sheet after deposition of positive (high) electrodes, c) PVF2

sheet after deposition of negative (low) ground strip and ready for poling, d)

Bilaminate transducer after wire bonding, e) Bilaminate transducer after positive

electrode is connected to miniature connector, f) Finished transducer and

mating coaxial cable.
- 36 -

(4) On the opposite side of each sheet a strip electrode, 3-cm wide and

approximately O.l-ym thick, is deposited in line with the array of 1- cm- diameter

dots. During poling, this strip serves as a common electrical ground electrode.

Fig. 7 shows how this strip is oriented.

(5) Each sheet, together with two strips of tin foil for electrical contact to the exterior, is then sandwiched between two insulating sheets of 250-ymthick polyethylene terephtalate . One tin-foil strip contacts the common ground

electrode, and the other contacts all nine high-side leads. This assembly is

mounted between the 23 x 23-cm platens of a hydraulic hot press, and a load of

approximately 40 kN (four-tonf gage reading) is applied. The positive output

terminal of a high-voltage d-c power supply is connected to the high electrode,

and the negative terminal is connected to the ground electrode. The steel frame

of the pr(iss and the negative terminal of the power supply are connected to laboratory ground. A poling voltage of 2000 +50 V is applied, corresponding to a field

of about 8 X 10^ V/ cm across the polymer in the region defined by the 1- cm-diameter

areas. The PVF^ is heated to a temperature of 120°C, as measured oy a thermocouple

inserted between the insulating sheets, and cooled immediately thereafter to room

temperature. The heating part of the cycle takes approximately 20 min. and the

cooling p£trt approximately 15 min. This procedure poles the PVF^ selectively in

the regions of the 1-cm areas, and leaves the nine strip-leads effiictively inactive,

Pressure is applied during poling to prevent wrinkling of the polymer sheets under

the combined effects of field and temperature.
-37-

(6) After removal from the press, an aluminum shield electrode, O.l-ym

thick, is deposited on the ground side of each sheet, extending the ground

electrode to cover nominally the entire surface of that side of the sheet. To

avoid depoling the nine activated areas during this evaporation, which heats

the polymer substrate, the part of the ground electrode used during poling consisting of a 1.5-cm-wide strip opposite the set of 1-cm-diameter dots, and

aligned with them, is masked off by a metal strip. Another strip, also 1.5-cm

wide, masks off another area, opposite the set of 0. 2- cm- diameter dots on which

it is centered to provide a clear area for visual alignment of one sheet with

another in a later step.

(7) The high side of each sheet is then coated with a thin layer of contact

cement by wiping the surface with a foam-rubber pad saturated with a solution of

contact cement diluted 5 to 1 with toluene. The contact cement is allowed to dry

at least 15 min. to allow the solvent to evaporate.

(8) Nine pieces of 250-ym-diameter , tinned-copper wire are cut to a length

of 5 cm, and one end is flattened over a length of approximately 0.6 cm, by rolling

the end in a bench- type rolling mill. The flattened portions of the nine wires

are coated with a thin layer of silver-bearing epoxy and are laid on the nine high

leads of one of the sheets, in a manner such that the flattened portion contacts

the 0. 2- cm- diameter dots at the ends of the evaporated leads. A small drop of

contact cement is then applied to each wire immediately behind the flattened portion

to form a fillet for the round wire and to hold the wire in place on the sheet.

Considerable experimentation was conducted with various bonding agents. Contact

cement meeting Federal Specification MMI4-A-130a has been satisfactory.
(9) The two sheets are precisely positioned on separate, mating, vacutmhold-down plates with the high, cement-coated, sides facing out. At the same

time, they are stretched lightly to make them lie as flat as possible. The

plates are then mated so that the cement-coated sides are pressed together to

form a bilaminate assembly. Care must be exercised prior to and during this

step to insure that when the sheets are bonded, the pattern of dots and leads

on one sheet is in satisfactory alignment with the corresponding pattern on the

other sheet, and that trapping of air bubbles is minimized. The assembly is

then placed in the hydraulic press and further pressed under a load of approximately 250 kN (25-tonf gage reading).

(10) The bonded sheets are then cut to yield nine separate bilaminate transducer elements. A 12-ym layer of unpoled PVF2 is then cemented on each side of

the elements, covering all but the small portion of the shield electrode at the

end where electrical contact is to be made. These layers act as a protective

coating to prevent damage to the shield electrode.

(11) The wire lead of each element is trimmed to leave approximately 0.3 cm

protruding outside the polymer sheets. This lead is then soldered to the center

conductor of a female miniature bulkhead coaxial connector. Care is taken not to

damage the connection to the evaporated lead by excessive soldering heat conducted

by the wire.

(12) The exposed parts of the high lead between the connector and the end of

the transducer not covered by the shield electrode are potted in epoxy. After the

epoxy has hardened, electrical contact between the shield side of the transducer is

made by applying a thick coat of liquid, silver-bearing rubber, over the insulating

epoxy and the area surrounding it.
- 39 -

Bibliography

[1] M. G. Broadhurst and G. T. Davis, Piezo- and Pyroelectric Properties

of Electrets, NBSIR 75-787, October 1975.

[2] A. S. DeReggi, Piezoelectric Polymer Transducer for Impact Pressure

Measurement, NBSIR 75-740, July 1975.

[3] D. A. Berlincourt , D. R. Curran, and H. Jaffe in Physical Acoustics , W. P. Mason, Ed. (Academic, New York, 1964) 1, Part A., Chapter 3, p. 188.
NBS-IHA (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 76-1078

2. Gov't Accession

No.

3. Recipient's Accession No.

4, TITLE AND SUBTITLE

Piezoelectric Polymer Transducers for Dynamic Pressure

Measurements

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

A. S. DeReggi, S. Edelman, S.C. Roth

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

National Highway Traffic Safety Administration

Department of Transportation

NASSIF Building

Washington, D.C. 20590

13. Type of Report & Period Covered

Final

14. sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.)

This report describes the construction, testing and calibration of piezoelectric

polymer sensing transducers of two sizes. The piezoelectric material was obtained

by poling 25 ym thick, polyvinylidene fluoride sheet. Sensors with an active area

of 1 cm diameter, intended for dynamic interface-pressure measurements, were calibrated in a fixture generating normal pressure transients by means of piston impact.

Sensors with an active area of 2 mm diameter, intended for measuring dynamic pressures while implanted in the cranium of rhesus monkeys, were calibrated in an oil

cell with a piston-cylinder seal which provided hydraulic pressure transients by means of impact on the piston. The larger sensors had a normal-pressure sensitivity around 3 yV/Pa (20 mV/psi) and the smaller sensors a hydraulic-pressure sensitivity around 0.7 yV/Pa (5 mV/psi).

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Pie zoele ct ri c ; polymer; polyviny lidene fluoride; pressure

sensor; pyroelectric ; transducer

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