Biomedical Engineering Reference
In-Depth Information
on a dielectric surface, thermal ionization, and migration (sometimes field
assisted) of point defects. Interfaces such as grain boundaries are active sites
for the creation and retention of space charges. Depending on the nature of
the interface, the space charge could be transient, permanent, temperature
dependent, or field sensitive. The complexity of the interface-space charge
relationship often makes it difficult to quantify its effect on the bulk
electrical property. The space charge can significantly influence the electrical
properties (ionic and electronic conductivity) of nanocomposites.
15.2.3 Electronic conductivity
For an electronic conductor such as a metal, conduction occurs by the
motion of free electrons. The mobility,
μ
, of free electrons is limited by
scattering:
m ¼
e
t=
m
½
15
:
11
where
is the mean free time between scattering events, m is the mass of the
electron (m=9.11
τ
10
31
kg), and e is the elementary electron charge.
6
s
e
¼
ð
n
i
z
i
e
Þ
e
t=
m
½
15
:
12
The electronic conductivity of metals ranges from 10
16
to 10
8
Scm
1
and is
temperature dependent. Generally,
increasing temperature decreases the
electronic conductivity.
15.2.4 Ionic conductivity
In solids, the ionic conduction process is very different from the electronic
conduction mechanism in metals. Ion mobility in solids generally takes place
by a hopping and diffusion mechanism. In semi-solids such as polymers, a
polymer chain motion contributes to the transport of ions. The effectiveness
of the hopping mechanism is related to the diffusivity, D, of solids:
D
0
e
D
G
act
=
RT
D
¼
½
15
:
13
where D
0
is a constant representing the attempt frequency of the hopping
mechanism,
G
act
is the energy barrier, R is the gas constant, and T is the
temperature (K). The mobility of ions in solids is expressed by:
Δ
m
i
¼
ð
z
jj
FD
Þ=
RT
½
15
:
14
where |z
i
| is the valence of ions, and F is the Faraday constant.
Substitution of the expression for ion mobility into equation 15.5 for
