Biomedical Engineering Reference
In-Depth Information
l
is the C-C bond length 1.54 Å and
C
n
is the Flory characteristic ratio, or rigidity factor
(6.95 for poly(methyl methacrylate) and poly(2-hydroxyethyl methacrylate [48], whereas 8.9
for poly(vinyl alcohol) [45] and 14.4 in case of a methacrylate chain).
Mesh size is
1 3
/
2 1 2
/
ξ
=
Q r
(
)
(5.57)
0
In a highly swollen hydrogel, diffusion coefficient can be calculated from [47]
a
Y
Q
D
≅
1
−
exp
−
(5.58)
ξ
−
1
Y
is a structural parameter, near unity. For most polymers,
Y
= 1 is a good approximation
[47]. In the case where mesh size is unknown, another form of Equation 5.58 was derived
for a highly swollen hydrogel:
Y
Q
−
3 4
/
D aQ
≅
exp
−
(5.59)
1
−
On the other perspective, the diffusion coefficient of solute depends on solvent content as
following [49-51]:
D
2
=
D
2,s
exp(-
β
(1 -
C
1
))
(5.60)
where
D
2,s
is the diffusion coefficient in the fully swollen polymer,
β
is a constant, and
C
1
is
the solute concentration normalized with respect to the equilibrium solvent content in the
membrane. Clearly, cross-linking density affects mesh size, which further influences the
diffusivity of the drug in the membrane.
Temperature Effect
The free volume of the polymer predicts that the diffusivity of the solute in the polymeric
membrane is related to the solute size and the swelling behavior of the membrane; hence,
the release rate of a given drug is controlled by swelling of the polymer. Recall from Fick's
second law, where diffusivity is also a function of temperature, and it serves another factor
that controls the drug release rate.
Simon [52] studied the release flux through a planar membrane with a temperature gra-
dient imposed to a concentration gradient. The steady-state flux was given by
(
E
+
E T
)(
−
T
)
C D
exp
−
s
d
0
s
A
RT T
(5.61)
0
S
J
=
L
where
E
s
and
E
d
are overall energy of salvation and activation energy for diffusion through
the polymer, respectively.
T
0
is the temperature at which diffusivity is
D
and
T
s
is the
temperature at the donor-membrane interface, assuming linear temperature gradient at
steady-state. All other parameters are the same as defined in other equations.
