Biomedical Engineering Reference
In-Depth Information
3
Piezoelectric Polymers: PVDF
Fundamentals
In this section, equations are discussed that govern crystals in general, and polyvinylidene
fluoride (PVDF) in particular, since it is this medium that is primarily used in sensing
applications throught this topic.
3.1 Constitutive Equations of Crystals
The constitutive equations for a crystal encompass its mechanical, electrical, and thermal
properties and the relationships between these three are illustrated in Figures 3.1 and
3.2 [1]. In the three outer corners, stress, electric field, and temperature are normally
chosen as independent variables and all can be thought of as 'forces' applied to the
crystal. Alternatively, in the three corresponding inner corners, apparent entropy per unit
volume
S
, electric displacement, and strain, which are the direct results of the 'forces,'
can be considered as dependent variables.
The relationships between these pairs of corners (shown by thick lines) are sometimes
called principal effects.
The symbols corresponding to each variable and properties are illustrated in Figure
3.2 [1].
1. An increase of temperature produces a change of entropy; thus considering a unit
volume:
d
S
=
(C/T )
d
T
(3.1)
where
C
(a scalar) is the heat capacity per unit volume, and
T
is the absolute temper-
ature.
2. A small change in electric field produces a change in electric displacement according
to the equation:
d
D
i
=
k
ij
d
E
j
(3.2)
where
k
ij
is the permittivity tensor.
