Biomedical Engineering Reference
In-Depth Information
By assuming immobile, impenetrable polymer chains suspended in a mobile solvent
continuum, diffusion of solute may only proceed through the solvent phase permeating
the whole membrane. The polymer molecules of the solvated membrane are forming a
network immersed in the solvent and exhibiting a wide spectrum of holes. The solute
can diffuse through the membrane if it finds a hole larger than the solute molecules.
Average free volume in the membrane is contributed by solvent molecules and polymer
chains:
v
f
= (1 -
→
p
)
V
f,water
+
→
p
V
f,polymer
(5.48)
By assumption, the free volume contributed by polymer chains is not permeable to solutes;
therefore,
v
f
→
(1 -
→
p
)
V
f,water
(5.49)
where
→
p
is the polymer volumetric fraction (distinguish it from solute volumetric ratio
→
).
Volume degree of swelling is
1
φ
p
Q
=
(5.50)
Instead of volume, Yasuda et al. [39-41] considered the cross-sectional area of the free
volume as the permeating criteria. The normalized diffusion coefficient (
D
/
D
0
) as a func-
tion of the probability of finding a hole larger than solute
P
(
π
a
2
):
2
D
D
a
φ
π
p
2
=
P a
(
)exp
−
B
(5.51)
π
V
1
−
φ
0
f water
,
p
where
B
is a constant of water and
V
f,water
is the free volume of water.
For cross-linked systems, Peppas et al. [42] considered volume as a permeating param-
Peppas et al. [42] considered volume as a permeating param-
eter and expressed the normalized diffusion coefficient as a function of polymer volume
ratio and solute size:
-linked systems, Peppas et al. [42] considered volume as a permeating param-
linked systems, Peppas et al. [42] considered volume as a permeating param-
D
D
−
v
=
f M
(
)exp
solute
c
1
(5.52)
0
V
−
1
solvent
φ
M
c
is the number average molecular weight between cross-links,
f M
(
c
is the probability
function of finding a void big enough to allow diffusion,
v
solute
is t
he s
olute volume, and
v
solvent
is the free volume of solvent. Molar weight between cross-links
M
c
and cross-linking den-
sity
ρ
x
is determined using [43]
