Page 153 - Organic Electronics in Sensors and Biotechnology

130 Cha pte r F o u r

a semicrystalline polymer such as PVDF. The important property com-
mon to both materials is that this polarization can be switched between
at least two metastable states by applying an external electric field. For
the presence of the pyroelectric effect it is sufficient that the overall
spontaneous polarization change with the temperature.
This is always the case, when a spontaneous polarization P exists,
since the volume V changes with the temperature, and the total spon-
taneous polarization is defined by the sum of the molecular dipoles p
i
in the unit cell of a crystal, or alternatively (as is in our case) in the
repeat unit of a polymer, divided by its volume. 20

P = 1 ∑ p (4.22)
V i
i
2
The polarization has the units of coulombs per square meter (C/m )
since the dipole moment has the units of coulomb-meters (C ⋅ m). The
ferroelectric materials can thus be regarded as a subgroup of the
pyroelectric materials. Even if this chapter deals only with the pyro-
electric effect, the term ferroelectric will often be present. This is due to
the fact that most effects are termed with respect to the more popular
ferroelectric effect. For example, the phase where a spontaneous
polarization is present is called the ferroelectric phase, even if the term
pyroelectric would be more general.

Pyroelectricity
In general the term pyroelectricity describes the ability of a material to
change its spontaneous polarization vs. temperature. The magnitude
of this change is described by the pyroelectric coefficient. The pyro-
21
electric coefficient is defined as

⎛ dP⎞
p = ⎜ ⎟ (4.23)
pyro ⎝ dT ⎠
,
ME
Here dP is the change in the spontaneous polarization in response
to the change in the temperature dT, normally measured under the
condition of no or constant external electrical field E and mechanical
stress M. The bulk polarization P is represented classically as a mac-
roscopic manifestation of mean field effects due to residual electric-
dipole moments. 22, 23 Discontinuities at the sample boundaries create
a surface charge density σ = nP, where nP is the component of the
polarization normal to the boundary surface.
In the case of a parallel plate capacitor, the magnitude of the pyro-
electric coefficient can be defined with respect to the charge gener-
ated at its electrodes in response to a temperature change:
1 ⎛ dQ⎞
p = ⎜ ⎟ (4.24)
⎝
pyro A dT ⎠
,
ME