Biomedical Engineering Reference
In-Depth Information
v V
v
v
v
2
1
2
(
/
)[ln(
1
−
)
+
+
χ
]
1
2
,
s
2
,
s
2
,
s
=
−
M M
1 3
/
c
n
v
v
1
2
v
v
2
,
s
2
,
s
v
−
2
,
r
2
,
r
2
,
r
1
=
ρ
x
vM
c
m
/
ρ
(5.53)
p
p
v
=
2
,
r
(
m
−
m
)
/
ρ
h
membrane-air
membrane-hep
m
/
ρ
p
p
v
=
2
,
s
(
m
−
m
)
/
ρ
membrane-air
membrane-hep
h
M
M
N
=
2
c
r
olume of the polymer could be obtained by considering buoyancy. Conventionally, hep-
tane and air were chosen as the weighting medium because heptane does not induce swell-
ing. After synthesis, sample was weighed in air
m
membrane-air
and in heptane
m
membrane-hep
; after
swelling, sample was weighed in air
m
membrane-air
and heptanes
m
membrane-hep
again. Finally,
sample was d
r
ied to a constant weight
m
p
.
ρ
p
and
ρ
h
are the densit
y
of polymer and heptane,
respectively.
v
is the specific volume of the membrane (cm
3
/g),
V
1
is the m
ola
r volume of
water (volume per water molecule is 30 Å
3
[44]; therefore,
V
1
The volume of the polymer could be obtained by considering buoyancy. Conventionally, hep-
3
num-
ber average molecular weight of the uncross-linked polymer [45], and
M
r
is the molecular
weight of the repeating unit.
N
is the number of repeating units between two cross-links.
χ
is Flory thermodynamic interaction parameter, which varies between 0.49 and 0.51 for
polyvinyl alcohol (PVA) [45]. For HEMA [48]:
1
=
cm /g
),
M
n
is the num-
the num-
χ
= 0.022 + 0.904
v
2,s
(5.54)
The empirical relationship between glass transition temperature and
M
c
is also available
[46].
3 9 10
4
.
×
−
M
=
(5.55)
c
T
T
g
g
0
T
g
is the glass transition temperature of the cross-linked polymer, and
T
g0
is the glass tran-
sition temperature of the uncross-linked polymer with the same chemical composition.
Instead of the number average molecular weight between cross-links, it is more physi-
number average molecular weight between cross-links, it is more physi-
cally sound to use a length scale in describing the structure of the polymer for diffusion,
which is defined as the radius of gyration of a chain between cross-links or the mesh
size of the polymer [47]. Mesh size is proportional to the end-to-end distance of polymer
chain:
the number average molecular weight between cross-links, it is more physi-
=
n
r
2
Nl C
(5.56)
0
