Page 153 - Academic Press Encyclopedia of Physical Science and Technology 3rd Polymer

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Encyclopedia of Physical Science and Technology en012f-594 July 26, 2001 11:9

Polymers, Ferroelectric 661

2
E
X
strain is proportional to the electric field, whereas the elec- K 33 = d 2 33 ε ε 0 s . (10)
33
33
trostrictive effect is a secondary effect in which the strain
is proportional to the square of the electric field (this effect
exists in any polymer). Electrostriction can be expressed E. Acoustic Impedance Z
as
The acoustic impedance Z is a parameter used for evalu-
2
x = ME , (5) ating the acoustic energy transfer between two materials.
2
It is defined as Z = pressure/volume · velocity. In solid
2
x = QP . (6) material,
√
where P = εε 0 E in the paraelectric phase and P = P s Z = ρ · c (11)
+ εε 0 E in the ferroelectric phase. The electric field-
related electrostrictive coefficient M and charge-related where ρ is the density and c is the elastic stiffness of the
electrostrictive coefficient Q are related to each other material.
2 2
through M = Qε ε . Piezoelectric ferroelectrics fall into four classes: opti-
0
For an isotropic polymer, cal active polymers, poled polar polymers, ferroelectric
polymers, and ceramic/polymer composites. The poling
2
2
x 33 = Q 33 P , x 31 = Q 31 P , (7) procedure involves the application of an external field
to a ferroelectric to induce a cooperative alignment of
where the two numerals in the subscripts refer to the elec- constituent dipoles. Most polymers in the first group are
tric field directionand the measuredpolarizationdirection, biological materials, such as derivatives of cellulose,
respectively. Therefore, x 33 and x 31 are strains parallel proteins, and synthetic polypeptides. The origin of piezo-
to and perpendicular to the polarization direction, known electricity in these polymers is attributed to the internal
as longitudinal and transverse strains, respectively. For rotation of the dipoles of asymmetric carbon atoms, which
isotropic polymers, both experimental and theoretical data gives rise to optical activity. The second class of piezo-
show that Q 11 < 0, Q 13 > 0, M 33 < 0, and M 13 > 0, hence electric polymers includes polyvinyl chloride (PVC),
the polymer will contract along the polarization direction polyvinyl fluoride (PVF), polyacrylonitriles (PAN), odd-
as the polarization increases. In other words, the polymer numbered nylons, and copolymers of vinylidene cyanide.
will contract along the thickness direction and will expand The piezoelectricity in these polymers is caused by the
along the film direction when an electric field is applied trifluoroethylene (TrFE) or tetrafluoroethylene (TFE).
across the thickness. Recently, other polymers were found to show ferroelectric
It should be noted that most polymers exhibit nonlinear behavior, such as copolymers of vinylidene cyanide,
dielectric behavior and deviate from Eq. (5) in a high field, odd-numbered nylons, and polyureas, in which piezo-
where the field-induced strain will be saturated. electricity arises from the functional polar groups in the
polymer molecules. In the fourth class (polymer/ceramic
composites), the piezoelectric activity comes from the
D. Electromechanical Coupling Factor K intrinsic piezoelectricity of ceramics. Physical properties
of these composites can be controlled by the choice of
The electromechanical coupling factor K is related to the
the ferroelectric ceramics and the polymer matrix. They
conversion rate between electrical energy and mechanical
2
energy; K istheratioofstoredmechanicalenergytoinput have a combination of high piezoelectric activity from the
ferroelectric ceramics and flexibility from the polymer
electrical energy, or the ratio of stored electrical energy to
matrix.
input mechanical energy.
Table I compares the piezoelectric properties of the
When an electric field E is applied to a piezoelectric
2
material, K can be calculated as ferroelectric ceramics and polymers. The piezoelectric
strain constant d 31 of polymers is relatively low com-
2
2
K = d /εε 0 s. (9) pared to that of ceramics. However, the piezoelectric volt-
age constant g 31 is larger. In addition, polymers have a
There are many electromechanical coupling factors corre- high electromechanical coupling factor and low acoustic
sponding to the direction of the applied electric field and impedance, which permit their use in ultrasonic transducer
to the mechanical strain (or stress) direction. For instance, applications and medical instrumentation. The combina-
in cases where a polymer actuator is made with the elec- tion of these properties with their flexibility, light weight,
tric field along the 3-direction, the mechanical coupling toughness, and availability in large-area sheets has led
factor is longitudinal to the electromechanical coupling to tremendous growth in research on novel ferroelectric
factor K 33 , which can be related to the Eq. (9) as polymers.