Biomedical Engineering Reference
In-Depth Information
swelled again. If the 50% acetone-water solution were to be replaced by 100% pure
water, then the gel would continuously swell beyond its original size in presence of
an electric field.
The mean field theory formulated by Flory (1941, 1953a, 1953b, 1969) and
Huggins (1941) explains the shrink-swell phenomenon according to:
1
−
∆
F
kT
φ
(
)
+
N
ln
1
−
φ
φ
0
φ
∆
Z
L
0
(1.20)
FkT
=
ν
g
1
2
(
)
0
(
)
2
2
2
+
2
αβ
+
−
3
−
221
f
+
ln
αβ
where the total free energy to be minimized is given by:
FF F
g
=+
(1.21)
e
where
F
g
= free energy due to gel deformation
F
e
= free energy due to work done against electric field
ν
= number of polymers cross-linked in the network
N
0
= number of freely jointed segments of polymer
f
= number of ionized segments out of
N
0
total
L
0
= length of cylindrical polymer sample
D
0
= diameter of cylindrical polymer sample
φ
0
= concentration of polymer (no interaction between segments or
reference states)
∆
Z
0
= elemental disk's thickness before applied electricity
Z
= distance of element from free end of the gel
β
= factor increasing
∆
Z
0
after application of electricity
α
= factor increasing
D
0
after application of electricity
T
= absolute temperature
k
= Boltzmann constant
φ
= volume fraction of polymer network
∆
F
= free energy decrease as a result of contact between two polymer
networks
Free energy needed to expand the gel network against electric potential (work
done against electric potential) is given by:
(
)
(
)
(
)
(
)
FfeEZL
=
ν
β
−
1
∆
ZBkTZL
≡
ν
∆
β
−
1
(1.22)
e
0
0
0
0
where
e
is electron charge and
B
=
feEZ
/
kT
is reduced electric potential. Minimizing
the total free energy equation
F
, we get:
