Biomedical Engineering Reference
In-Depth Information
cm
3
Table 11.2.
Density of the water/polymer mixture in
g
/
for different average degree of poly-
merization,
x
, (colums) and % of water content,
φ
w
(rows)
φ
w
0 %
20 %
40 %
60 %
80 %
100 %
600
1.1703
1.1424
1.0836
1.0566
1.0177
0.9871
300
1.1763
1.1415
1.0984
1.0623
1.0161
0.9871
150
1.1634
1.1419
1.0976
1.0582
1.0168
0.9871
x
i
75
1.1677
1.1482
1.1033
1.0536
1.0170
0.9871
30
1.1815
1.1422
1.0953
1.0570
1.0175
0.9871
1
1.0497
1.0196
1.0071
0.9953
0.9866
0.9871
Table 11.3.
Diffusion coefficient of water (10
−
6
cm
2
/
s
) with respect to monomers per chain
(colums) and % of water content
φ
w
(rows)
φ
w
2 %
20 %
40 %
60 %
80 %
100 %
600
0.41
3.39
13.5
24.2
36.8
42.0
300
0.42
4.97
13.2
24.5
33.9
42.0
150
0.40
4.56
13.8
22.2
35.6
42.0
x
i
75
0.47
2.79
12.0
23.9
34.7
42.0
30
0.39
3.56
12.3
24.2
35.8
42.0
1
0.51
4.38
16.4
25.9
36.8
42.0
almost linearly with the degree of swelling, while it is little or no affected by the
degree of polymerization. It is important to observe that the Einstein relation holds
only if the regime of normal diffusion is reached. Reminding that normal diffusion
is reached when log
with
unit slope, we observe that the normal diffusion of water is reliably reached during
the data production runs of 7 ns, since the aforementioned slope ranges from 0
(
MSD
(
t
))
is an affine linear function with respect to log
(
t
)
.
87
to 1
00. Consequently, the diffusivity coefficients obtained for water transport in the
polymer matrix can be assumed to be reliable.
As similar procedure may be applied to calculate
D
i
(
φ
w
,
.
x
)
, resorting to a table
similar to Table 11.3 for any
i
N
. Although all aforementioned simplifica-
tions, this task requires a large number of microscale simulations. To fulfill this task
with a moderate computational cost, we have initially performed the simpler inves-
tigation of calculating the matrix of values
D
i
(
φ
w
,
=
1
,...,
. This corresponds to estimate
the diffusivity of a polymer chain of length
x
i
into a mixture of the same average
degree of polymerization.
The results (see Table 11.4) show that the polymer diffuses much less than wa-
ter due to its larger molecular weight. The exceptions are the systems with single
PLA monomers (highly degraded matrices) for which a much higher PLA diffu-
sion constant is obtained. This is likely due to the low molecular weight of PLA
monomers. The analysis of the results for PLA diffusivity shows that the polymer
diffusion coefficient depends on the swelling, while it is not affected by the poly-
x
i
)
