Biomedical Engineering Reference
In-Depth Information
Table 11.1.
Summary of the simulation protocol applied to obtain equilibrated bulk model of PLA
matrices
Simulation
Ensemble
Time
Time step
Temperature
Pressure
#1
NVT
0.2 ps
0.1 fs
300 K
-
#2
NVT
2 ps
1 fs
600 K
-
#3
NVT
100 ps
1 fs
300 K
-
#4
NPT
60 ps
1 fs
300 K
0 GPa
#5
NVT
20 ps
1 fs
750 K
-
#6
NVT
20 ps
1 fs
600 K
-
#7
NVT
20 ps
1 fs
450 K
-
#8
NVT
100 ps
1 fs
300 K
-
#9
NPT
100 ps
1 fs
300 K
0 GPa
1 nm, with a switching function between 0.85 and 0.95 nm for Van der Waals and
Coulomb interactions.
We carefully checked that the potential energy, temperature, pressure and den-
sity reached a stable value after each step of the equilibration procedure. The latest
(#9) simulation has been employed to validate the models by comparing the average
density during the NPT dynamics with the experimental one.
Finally, in order to obtain water and polymer diffusivity by means of an atom-
istic model of the polymer mixture, we select an ensemble of
M
(water or polymer)
molecules in the model and we compute their mean square displacement
MSD
(
t
)
.
Denoting with
M
m
=
1
r
m
(
t
)
1
M
2
2
r
(
t
)
=
the averaging over all the particles, the mean square displacement is defined as
2
MSD
(
t
)=
|
r
(
t
)
−
r
(
0
)
|
.
The diffusion coefficient
D
of water/polymer molecule is then calculated using Ein-
stein's relation
D
=
lim
t
MSD
(
t
)
/
(
6
t
)
.
→
∞
Manipulating Einstein's formula one easily obtain that for sufficiently large times
log
log
MSD
)
. Then, the realm of normal diffusion (also known
(
6
D
)+
log
(
t
)=
(
t
as Fickian diffusion) is reached when log
MSD
)
is a linear function of time with
unit slope. The validity of this fundamental property is equivalent to say that the
application of Fick's law to derive Eqs. (11.1) and (11.2) is correct.
(
t
