Biomedical Engineering Reference
In-Depth Information
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FIGURE 6.12
A possible charge redistribution configuration in ionic gels.
gel strip in electric field can be described by Flory's theory of osmotic pressure
(1953a, 1953b, 1969). According to Flory's theory, the equilibrium volume
V
g
of an
ionic gel is determined by:
∑
()
+
(
)
=
Π
Network
V T CC
−
0
(6.27)
g
i g
,
i s
,
i
where
Π
Network
(
V
g
) is the osmotic pressure of a neutral gel
R
is the universal gas constant
T
is the absolute temperature
C
i,g
,
C
i,s
determine the ionic concentrations of species
i
in the gel and the outer
solution, respectively
subscript
i
stands for mobile cations M
+
, anions P
-
, hydrogen ion H
+
, and hydroxyl
ion OH
-
Equation (6.27) implies that if the gel has no charge, its equilibrium volume is
determined by the competition between the attractive forces due to polymer-polymer
affinity and the network elasticity.
If the gel also has electrical charges, there will be strong ionic concentration
gradients on the boundaries of the gel and the aqueous solution. These contribute
to the osmotic pressure and thus cause the ionic gel to swell or shrink accordingly.
Let us assume that the osmotic pressure in the gel on the anode side is
Π
1
and
that of the cathode side is denoted by
Π
2
) causes the
strip to bend such that the amount of bending is dependent on the difference between
the stretches
Π
2
. The difference
∆Π
= (
Π
1
-
λ
-
on the anode side and the cathode side, respectively. Then,
based on equation (6.24), the stretches
λ
+
and
λ
+
and
λ
-
are related to the state of uniaxial
stresses
σ
+
=
Π
1
and
σ
-
=
Π
2
, such that one has
(
)
(
)
−
2
Π
1
=
Y
/
3
λλ
−
(6.28)
+
+
+
(
)
(
)
−
2
Π
2
=
Y
/
3
λλ
−
(6.29)
−
−
−
