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

660 Polymers, Ferroelectric

extensive attention as new ferroelectric or piezoelectric which responds not only to stress, but also to temperature
materials. Compared to current ceramic-based materials, change. Pyroelectric crystals whose spontaneous polariza-
polymeric materials could offer many unique features, tion can be reversed by an external electric field are called
such as light weight, low cost, great mechanical strength, ferroelectrics.
easy processability into thin and flexible films of various
shapes and sizes, high reliability, large strain, and, most
A. Piezoelectric d Constant
importantly, flexible architecture design via molecular
tailoring. The magnitude of the induced strain x by an external field
It was not until 1969 that Kawai demonstrated the E or the dielectric displacement D by a stress X is repre-
significant increase of piezoelectricity in poly(vinylidene sented in terms of the piezoelectric d constant (an impor-
fluoride); pyroelectricity and ferroelectricity were re- tant parameter for acoustic applications)
ported in 1971. Since then, tremendous growth in the
new field of ferroelectric polymers has occurred. The x = dE (1a)
exploration of the chemistry, physics, and technology of D = dX. (1b)
poly(vinylidene fluoride) led to the search for other classes
of novel ferroelectric polymers, such as its copolymers, The effect in Eq. (1b) is the direct piezoelectric effect,
odd-numbered polyamides, cyanopolymers, polyureas, where the induced charge is proportional to the mechan-
polythioureas, biopolymers (including polypeptides), and ical stress, whereas the effect in Eq. (1a) is the converse
ferroelectric liquid crystal polymers. Significant progress piezoelectric effect. Extending Eqs. (1a) and (1b) with
has been made both in finding new materials and in better the use of the linear elastic (Hooke’s law) and dielectric
understanding structure–property relationships. equations, and writing the results in matrix notation form
In this review, the primary goals are to update current yields
research in ferroelectric polymers and provide a funda- E
x i = s X j + d mi E m , (2a)
mental understanding of ferroelectric physics. Since many ij
extensive reviews of poly(vinylidene fluoride) and its D m = d mi X i + ε mk E k , (2b)
X
copolymers already exist in great detail, only a brief E X
summary is given of their chemical synthesis, structure- where s is the elastic compliance, ε is the dielectric per-
ij
ik
electrical property relationships, and applications. Some mittivity, i, j = 1, 2,..., 6, and m, k, = 1, 2, 3. The su-
emphasis will be on the newly developed VDF/TrFE/ perscripts refer to the conditions under which these quan-
CTFE terpolymers containing vinylidene difluoride tities are measured, that is, compliance is measured under
(VDF), trifluoroethylene (TrFE), and chlorotrifluo- constant electric field, and permittivity is measured under
roethylene (CTFE) units. These processable terpolymers constant stress. ε 0 is the vacuum dielectric permittivity
−12
show high dielectric constants, narrow polarization (=8.85 × 10 F/m).
hysteresis loops, and large electrostrictive responses at
ambient temperature. The last section will cover some
B. Piezoelectric g Constant
other novel ferroelectric polymers, such as polyamides,
polyurethanes, and polyureas. No attempt is made to The induced electric field E is related to an external stress
discuss ferroelectric biopolymers and ferroelectric liquid X through the piezoelectric voltage constant g, which is
crystal polymers, comprehensive reviews of which are an important parameter for sensor applications:
available elsewhere.
E = gX. (3)
Taking into account D = dX, we obtain
I. DEFINITION OF PIEZO-, PYRO-,
AND FERROELECTRICS d
g = . (4)
εε 0
It is well established that electrical properties such as
piezoelectricity and pyroelectricity can only exist in ma-
C. Field-Related and Charge-Related
terials lacking a center of symmetry. In fact, among the 32
Electrostrictive Coefficients
classes of the crystal point symmetry group, only 20 can
exhibit piezoelectric and pyroelectric effects. A piezoelec- Generally, there are two phenomenologies used to de-
tric material is one that develops electric polarization only scribe the electric field-induced strain: the electrostric-
when mechanical stress is applied. Pyroelectric materials tive and piezoelectric effects. The piezoelectric effect is
possess a permanent polarity (spontaneous polarization) a primary electromechanical coupling effect in which the