Biomedical Engineering Reference
In-Depth Information
(
)
(
)
−
2
σ
=−
E
/
3
λ
−
λ
,
(6.107)
+
+
+
+
(
)
(
)
−
2
σ
=−
E
/
3
λ
−
λ
,
(6.108)
−
−
−
−
where
E
+
and
E
-
are elastic moduli and functions of the pH or local ionic concen-
tration and temperature and
λ
-
refer to the stretches in the most remote fibers
in the gel under bending. From equation (6.106), it is calculated that
λ
+
and
2
π
C
b
(
)
=−
(
)
22
−
σσ
=
CZ
,
16
N Qb
π
/
wt
K
co
s
2
π
Zb
/
],
(6.109)
+
gg
1
−
2
π
C
(
)
=−
(
)
22
−
σσ
=−
CZ
,
16
N Qb
π
/
wt
K
cos
2
π
Zb
/
],
(6.110)
−
gg
1
b
Thus, equations (6.107), (6.108), (6.109), and (6.110) give rise to the following
set of cubic equations for
λ
+
-
λ
-
:
(
)
(
)
3
2
λ
+
3
σ
/
E
λ
−=
1
0
,
(6.111)
+
+
+
+
(
)
(
)
3
2
λ
+
3
σ
/
E
λ
−=
1
0
,
(6.112)
−
−
−
−
The possible curvature with a real value is then calculated as
(
)
(
)
κ
=
λ
−
λ
/
2
C
*,
(6.113)
E
+
−
Now, from equations (6.101) through (6.113), it is clear that the nonhomoge-
neous force field and the curvature in bending of ionic gels can be electrically
controlled by means of an imposed voltage
V
across the gel. In this context, the
difference
λ
+
-
λ
-
is related through equations (6.107) and (6.108) to the stresses
σ
+
-
σ
-
. These stresses are in turn related to the charge
Q
and other physical param-
eters by equations (6.109) and (6.110). The total charge
Q
is then related to the
voltage
V
and other electrical parameters
C
g
and
R
g
by equation (6.26) as described
before. This then allows the designer to control such deformations in ionic gels
robotically by means of a voltage controller.
Thus, it turns out that the effect of a coulombic type of ionic interaction tends
to be the opposite of the cationic electro-osmotic drag. This means that the migration
of hydrated cations towards the cathode tends to swell the cathode side of the IPMNC
strip and increase the osmotic pressure while, at the same time, decreasing the
osmotic pressure on the anode side and thus giving rise to bending towards the anode
side for a cationic IPMNC.
