COURSE TITLE Physical & Optical Properties

COURSE COORDINATOR Mr. Xunlin Qiu

EXPERIMENT NO W5
TOTAL PAGES 12
SUBMISSION DATE 20th August 2012
MEMBERS OF THE LAB GROUP
STUDENT ID STUDENT NAME SIGNATURE
764316 Muhammad Farooq
526085 Muhammad Farhan
PIEZOELECTRICITY

Introduction
A piezoelectric material is one that yields an electric charge when a mechanical stress is applied.
Many crystals generate an electric charge when subjected to a mechanical load; this correlation has
become known as the piezoelectric effect. Piezoelectric measuring technology is the perfect tool for
carrying out measurement tasks with extreme requirements in terms of geometry, temperature range
and dynamics. The piezoelectric effect was discovered in 1880 by the Curie brothers. The prefix piezo
comes from the Greek piezein, to press. The two physicists found that the surfaces of certain crystals
become electrically charged when the crystal is mechanically loaded. This electric charge is exactly
proportional to the force acting on the crystal. It is measured in pico-coulombs (pC). This phenomenon
is known as the direct effect.
Piezoelectricity is a property of many non-centrosymmetric ceramics, polymers and other biological
systems. A subset of piezoelectricity is pyroelectricity, whereby the polarization is a function of
temperature. Some pyroelectric materials are ferroelectric, although not all ferroelectrics are
pyroelectric.
The properties of polymers are so different in comparison to inorganics that they are uniquely qualified
to fill niche areas where single crystals and ceramics are incapable of performing as effectively. The
piezoelectric strain constant for the polymer is lower than that of the ceramic. However, piezoelectric
polymers have much higher piezoelectric stress constants indicating that they are much better sensors
than ceramics. Piezoelectric polymeric sensors and actuators offer the advantage of processing
flexibility because they are lightweight, tough, readily manufactured into large areas, and can be cut and
formed into complex shapes. Polymers also exhibit high strength and high impact resistance. Other
notable features of polymers are low dielectric constant, low elastic stiffness, and low density, which
result in a high voltage sensitivity (excellent sensor characteristic), and low acoustic and mechanical
impedance (crucial for medical and underwater applications). Polymers also typically possess a high
dielectric breakdown and high. Based on these features, piezoelectric polymers possess their own
established area for technical applications and useful device configurations.









Fig 1. Piezoelectric Effect
Piezoelectric
Material
Compression

Production of Foams
The most common method of producing foam is the use of chemical or physical nucleating agents in
molten polymer.
One method is stretching polymers that contain tiny mineral particles under suitable conditions. These
particles serve as a stress concentrator for micro cracks during biaxial stretching of the film.
The polymer foams produced show a lateral youngs modulus of the order of GPa and a thickness
Youngs modulus of the order of MPa. The special mechanical characteristic is one of the most
important origins for the large piezoelectricity of ferroelectrics.





Fig 2. Schematic view of biaxial stretching of filler loaded polymer matrix

Inflation
Voids spontaneously open up during stretching of the polymers that contain tiny mineral particles are
too flat for efficient charging by means of the internal micro plasma discharges because the plasma
electron cannot be accelerated sufficiently to ionize the gas molecules. In addition, flat void lead to
rather stiff films with reduced electromechanical response. By means of a suitable pressure and
temperature treatment, the size of the internal voids can be adjusted.










Fig 3.Schematic view of inflation process


Increase of pressure
Saturation with gas Releasing the external pressure
Gas molecules
Holes
Polymer

There are two reasons why inflation is very useful for the optimization of the electromechanical
properties of ferroelectrets. Firstly, voids with proper size have higher charging efficiency.
Secondly the piezoelectricity activity of ferroelectrets depends upon the materials structure, elastic
modulus and effective polarization.

















Fig 4. Dependence of Piezoelectric activity and elastic stiffness on sample density and cross
section of the corresponding cellular structures
Charging of ferroelectrets
Polymer foams are charged to achieve piezoelectric effect. The voids inside the foam must be internally
charged. This can be done by means of direct charging, corona discharge without a grid at high corona-
point voltage or electron beam charging.
If the electric field in the voids is higher than the threshold value the internal breakdown of the voids
occurs. Charges of opposite polarity are separated and finally deposited on the top and bottom surface
of the voids. These internally charged voids act as macroscopic dipoles. With sufficiently high electric
fields, the direction of macroscopic dipoles can be reversed and the resulting electric displacement
versus electric field curves exhibit hysteresis behavior.

P
i
e
z
o
e
l
e
c
t
r
i
c

A
c
t
i
v
i
t
y


E
l
a
s
t
i
c

S
t
i
f
f
n
e
s
s


Density













Fig 5. Hysteresis behavior of ferroelectrets

Experimental procedure
Charging of samples
A direct contact method was used to charge the samples
The process of charging the samples is as follows:

Turn off the HV power supplier before when touching any part of the setup
Sample was mounted between the two electrodes and high voltage supply
Output voltage was set as desired
switch on the voltage supply and charge the sample for 15 sec
short circuit the samples by folding them in aluminum foil
follow the same procedure for inflated and non-inflated samples

Table 1. Voltages applied to charge the samples
sample Inflated
Non-
inflated
# 1 2 3 4 5 6 7 8
Voltage /
kV
2.5 3.0 3.3 3.7 4.0 5.0 6.0 6.0


P
E
P
P

Fig 6. Schematic view of direct contact charging

Measurement of Dynamic d
33


The piezoelectric d
33
coefficient of the samples is measured by means of a dynamic method after
charging and short circuiting the samples. A bias force of 3 N superimposed with a sinusoidal force with
an amplitude of 1 N and a frequency of 2 Hz, is applied to the sample , and the resulting electrical
response of the sample is amplified with a Bruel & Kjaer model 2635 charge amplifier and recorded by
means of an oscilloscope.


Fig 7. Illustration of the dynamic piezoelectric d
33
coefficient measurement system

Results & Discussion
Model for the piezoelectricity of ferroelectrets
The lateral dimension of the voids is much larger than the vertical dimension; a simplified model is
proposed to depict the piezoelectricity of the ferroelectrets.
The model consist of polymer layers and air layers of thickness S
1 i
& S
2 j,
respectively
Where
i = 1, 2, 3
j = 1
n = total no of solid layers
I we Apply Gauss law on the top and bottom electrode

p
E
11 = - o
0

p
E
12 = o
0

From the above two equations we can obtain the following relation
E
11
= E
12
= E
1

p
E
11
+E
21

=
1

p
E
12
+E
21

=
1

Following relation is deduced from the above equations
E
21
=

1

+E
11

p

After applying Kirchoffs second law for short circuit
v = u
E
11
S
11
+E
12
S
12
+E
21
S
21
= u
Let S be total thickness then
S
11
+S
12
= S
1

S = S
11
+S
12
+S
21
= 2S
1
+S
2

Using above three equations the result obtained is
E
21
=
2E
1
S
1
S
2

E
21
=
2S
1

(2S
1
+
P
S
2
)

E
1
=

1
S
2

(2S
1
+
P
S
2
)

Thickness of the foam changes as a pressure p is applied to the foam, the thickness change is

due to compression in the air layers, the variation of the electrode charge is controlled by
0o

0
5
2

Therefore,

S
2
=

p
E
1
S
2
=

p
_

(2S
1
+
p
S
2
)
1

1
S
2

p
(

(2S
1
+
p
S
2
))
2
_ =
2
p
S
1

1
(2S
1
+
p
S
2
)
2


The stress relation is
S
2
S
=
p
Y

S
2
p
=
s
Y

The piezoelectric coefficient is obtained
u
33
=

p
=

S
2

S
2
p
=
2S
1

S
(2S
1
+
P
S
2
)
2
Y



Solid PP
E
11

p
S
11

Air
E
21
S
21

Solid PP
E
12

p
S
12




Fig 8. Three Layer Simplified Model

Properties & Crucial Factors for piezoelectricity of ferroelectrets

If we compare the different traditional piezoelectric materials with ferroelectrets we will come to know
that among the favorable properties of ferroelectrets are their large piezoelectric d
33
coefficients, as
listed in table 2. Optimized PP ferroelectrets can show d
33
up to 600 pC/N.

Table 2. Comparison of piezoelectric coefficients of several piezoelectric materials





Ferroelectrets can display a large piezoelectric d
33
coefficient and this is an advantage in applications
depend on thickness change. However, they have a small value for d
31
, which relates the voltage
across a sample to the length change in the transverse direction. Usually d
33
is the only coefficient used
to evaluate the piezoelectric properties of ferroelectrets.
Bottom Electrode
-o


o
1

-o
1

o
2

Top Electrode

Actually, piezoelectric activity strongly depends on the cellular structures, elastic stiffness and some
other factors. Research showed that there is an inversely-U-shaped relation between the piezoelectric
activity and the sample density, as shown in figure 4.
Samples with small voids are relatively stiff and therefore have low piezoelectric activity. A controlled
increase of the void height can decrease the elastic stiffness and enhance the piezoelectric activity. Too
large a void height, i.e. more spherical voids, however, causes a large elastic stiffness, and lowers the
piezoelectric activity.

Dependency of d
33
Coefficient as a function of charging voltage

Dynamic measurement system was used to measure the piezoelectric d
33
coefficient of the samples.
First we took the value of the top surface and then the bottom surface. Average was taken of both the
above values. Sinusoidal force of 2 Hz frequency was applied on the samples to get the required
piezoelectric d
33
coefficient value.

The table below gives the values of d
33
coefficient for both the inflated & non inflated samples.

Table 3. Relation between charging voltage and d33 coefficient
Sample Inflated
Non-inflated
Voltage / kV
2.5 3.0 3.5 4 5 7 7
d33 /
[pCN-
1]
Side 1
13.10 15.76 45.25 79.27 122.65 190.14 12.93
Side 2
13.02 22.77 42.86 79.66 139.47 221.94 12.33
Average
13.06 19.265 44.055 79.465 131.06 206.04 12.63

By having a glance we can conclude from the table that as we increase the value of voltage there is an
increase in d
33
coefficient.
From Paschens law, it is known that there is a mediate gap distance at which a minimum is reached in
the curve of breakdown voltage with gap distance. Therefore, for small charging voltages, there is less
charge induced due to micro-plasma discharges. However, beyond this threshold value, the ionization is
more probable, and this leads to a more linear relation between the d
33
coefficient and the charging
voltage.




Figure 9. Graph between charging voltage and d33 coefficient

As it can be seen from the above graph , there is threshold voltage around 3 kV which means that
charging voltage below this value is not enough to produce high piezoelectric property in the material.
By increasing the charging voltage piezoelectric coefficient increases. The higher charging voltage
gives us a higher charge density on the internal void surface and thus in a higher internal electric field
and as a result higher piezoelectric coefficient.
DRS
Least square fit of complex capacitance was done and values for
r
, f
p
, c
33
, d
33
were obtained from
fitted function. After obtaining the above values we calculated the value for k
t
complex
electromechanical coupling factor from the below equation.
k
t
2
=
u
33
2
c
33

r

Effective polarization n
eII
was calculated from the following equations
u
33
=

p
=
s
p
c
33

s
cII
(s
1
+
p
s
2
)
2

For inflated polymer foam
u
33
=

p
c
33

[1 +
s
2
s
1

cII
[1 +
p
s
2
s
1

2

For non-inflated polymer foam
u
33
=

cII
c
33


0
50
100
150
200
250
0 1 2 3 4 5 6 7 8
y = 45.461x - 107.26
R = 0.9867
Threshold Voltage
d
3
3

/

[
p
C
N
-
1
]

Voltage / kV

Table 4. Density of samples

Polypropylene
Film density (kg/m3) (Foam density kg/m3)
900 550


Table 5. Effective polarization n
eII
of samples

Sample
Effective polarization n
eII

non-inflated polymer 5.37 x 10
- 5

inflated polymer foam 2.7 x 10
- 4


Table 6. Parameters of samples
Parameter Inflated Non-inflated
C
0
(=0) / pF 23.193 36.1

r
1.62 1.80
c
33
/ [Nm-2] 1242400.91 4271667.94
d
33
/ [CN-1] 1.399 x 10
-10
2.27 x 10
-11

f
p
/ Hz 403974.14 888120.56
k
t
0.041 0.012

In the table above we can see that inflation decreases relative permittivity and also the capacitance of
polymer since the permittivity of pure polymer is larger than that of air.
As the density decreases by introducing controlled voids, the elastic stiffness is lowered c
33
while the
piezoelectricity activity d
33
is increased, which coincides with the inversely V-shaped behavior of the
two. More charges are separated and trapped on the surfaces of internal voids to yield higher
piezoelectricity.














36.13
36.14
36.15
36.16
36.17
36.18
36.19
1e+06
1e+36
1e+37
C
'
/
p
F
Freq/Hz
Sample Non-inflated 7kV (thickness 50um)
C' (measured, corr.)
C' (measured, raw)
C' (fit)
23.06
23.08
23.1
23.12
23.14
23.16
23.18
23.2
23.22
23.24
23.26
23.28
1e+23
1e+24
C
'
/
p
F
Freq/Hz
Sample inflated 7kV (thickness 70um)
C' (measured, corr.)
C' (measured, raw)
C' (fit)


























REFERENCES
PZT Application Manual

Influence of gas pressure in the voids during charging on the piezoelectricity of ferroelectrets
Xunlin Qiu, Axel Mellinger, and Reimund Gerhard

Spectroscopic study of dielectric barrier discharges in cellular polypropylene ferroelectrets
Xunlin Qiu, Axel Mellinger, Werner Wirges, and Reimund Gerhard

Preparation and Investigation of Polymer-Foam Films and Polymer-Layer Systems for
Ferroelectrets
Peng Fang


Lab Manual