Biomedical Engineering Reference
In-Depth Information
Now, from equations (6.26), (6.39), (6.40), (6.41), (6.44), (6.45), (6.62), and
(6.63), it is clear that the nonhomogeneous force field and the curvature in bending
of ionic gels can be electrically controlled by means of an imposed voltage
V
across
the gel. Note that in case of complete symmetry in bending of a strip of length
l
g
,
width
w
g
, and thickness
t
g
, and only one kind of cation and fixed anions,
Y
+
=
Y
-
=
Y
,
(
)
κ
E
=
12
/
YC
* (
ΠΠ
−
)
(6.64)
2
1
or
∑
(
)
( )
−
()
+
κ
E
=
12
/
YC
* {
RT
[
C
t
C
t
]
2
Π
},
j
=
M
P
(6.65)
C j
,
A j
,
hw
j
where
C
c,j
(
t
) and
C
A,j
(
t
) are the average molal charge concentrations in gram-moles
per cubic meters on the cathode side and the anode side of the gel strip, respectively.
Note that, due to migration of cations towards the cathode side, the difference
between the average total charges on the cathode side and the anode side is simply
the accumulated charge
Q
given by equation (6.26) and is also given by
1
2
∑
()
−
()
Qn
=
*(
eAl wt
)
[
Ct
Ct
],
j
=
MP
,
(6.66)
ν
ggg
Cj
,
Aj
,
j
or
∑
()
−
()
2
Qn Al wt
/( *
(
))
=
[
C t
C t
],
j
=
M
,
P
(6.67)
ν
ggg
Cj
,
Aj
,
j
where
n
* is the valence of the cations,
e
= 1.602192E-19 C is the charge of an
electron, and
A
v
= 6.022E23 is the Avogadro's number. Thus, from equations (6.26),
(6.65), and (6.67), a simple expression for the voltage-induced local curvature in
gels (also in IPMNCs) can be found
(
)
κ
=
12
/
YC
* {
RT
[
2
Q
/ (
n
*(
eA
l w t
))]
+
2
Π
}
(6.68)
E
ν
g
g g
hw
Π
hw
is the pressure generated due to the migration of hydrated water
with the cations and can be obtained by noting that
Note that
2
λλ
−
Π
hw
=
(/ (
Y
3
−
)
(6.68a)
hw
hw
λ
hw
is the contribution to the stretch on the cathode side by the migrated
hydrated water. Furthermore, it is related to the displaced volume
V
hw
of the migrated
hydrated water such that
where
