Biomedical Engineering Reference
In-Depth Information
The overall osmotic pressure is then
∏=∏+∏+∏
t
.
(4.10)
r
e
p
In addition to these forces, it has been recognized that, as the diameter of fibers
and number of strands increases, the induced force also increases (dimensional
effect). Also, the temperature of the system will significantly contribute to the
performance of the PAN artificial muscle.
The polymer-polymer affinity arising from the interaction between the polymer
fibers and the solvent is believed to be an important driving force, although it is not
yet clarified to explain the exact mechanism of PAN contraction-elongation behavior.
One possible explanation is based on the carboxylic acid groups having the molecular
geometry of activated PAN. At low pH concentrations, all carboxylic acid groups
on activated PAN are likely to be protonated and contracting the polymer chain
through neutral charge of the acid groups and hydrogen bonding between neighbor-
ing carboxylic acid groups. At high pH concentrations, protons have been removed
from the carboxylic acid groups and give off negative charges. Negative charge
repulsion between neighboring acid groups likely forces the polymer backbone to
elongate. Electrical activation can be made for hydrogen and oxygen evolution. At
the anode, oxygen evolves via 2H
2
O
→
O
2
+ 4H
+
4
e
+
and the counter reaction at
H
2
+ 2OH
-
; the decreased pH causes the PAN fibers
contract by the same effect as chemical activation. Elongation is simply obtained
with reversing the polarity of DC while water diffuses into the PAN polymer network.
We also looked at the Donnan equilibrium carefully. If we assume that polymer
and aqueous solution are composed of three parts—A, B, and C—in turn from the
anode side, the concentration of cation is changed abruptly across the boundary but
uniform in any of A, B, and C, the transport rates of cation,
h
, from A to B and from
B to C are the same, and all ion-ion interactions are neglected, the cation concen-
tration in each part can be expressed by,
the cathode is 2H
2
O + 2
e
-
→
C
A
(
t
) =
C
A
(1 -
ht
)
(4.11)
V
V
A
C
B
(
t
) =
C
B
(1 -
ht
) +
C
A
ht
(1 -
ht
)
(4.12)
B
V
V
V
V
C
C
(
t
) =
C
C
+
C
B
B
ht
+
C
A
A
h
2
t
2
(4.13)
C
C
where
C
i
(
t
) = the cation concentrations in the
i
th species—namely, A, B, and C,
respectively. As the osmotic pressure
π
obeys van't Hoff's law,
∆π
can be given as
∆π
=
π
1
-
π
2
=
RT
[
C
B
(
t
) -
C
A
(
t
)] -
RT
[
C
B
(
t
) -
C
C
(
t
)]
(4.14)
V
V
V
V
B
A
=
RT
[
C
C
(
t
) +
C
B
ht
+
C
A
h
2
t
2
-
C
A
(1 -
ht
)]
C
C
