Biomedical Engineering Reference
In-Depth Information
Tabl e 2. 2
The measured transition temperature (
T
)
mid
and the radius
of the local curvature of foreign particles for different systems
(
T
)
mid
(K)
R
s
)(nm)
(
r
c
)
mid
(
D
DI water (20 nm filter)
39.1
2.28
DI water (200 nm filter)
33.9
2.54
AFP III 2.5 mg/mL (20 nm filter)
40.3
1.42
homogeneous-like nucleation takes place (Regime III,
f
(
m
,
R
0
)
D
1), one then
has
f
(
m
,
R
0
)
D
. It follows that the experimental
f
(
m
,
R
0
)
T
curve can be
obtained from the ratio between the slope of the ln(£
V
)
1/
T
(
T
)
2
plot and the
corresponding at different
T.
Because
r
c
can be obtained from (
2.1
)and(
2.13
)
and , one of the most challenging and important steps in obtaining
f
(
m
,
R
0
)
R
0
is
to estimate the average local radius
R
s
of the rough surface of the foreign particles
(compare (
2.14
) and Fig.
2.7
b). As illustrated by Fig.
2.5
a(e.g.,
m
D
0.8), one
has approximately
R
0
1or(
r
c
)
mid
R
s
at the midpoint of the ln(
f
(
m
,
R
0
))
ln(
R
0
)
curve (
ln(
f
(
m
))/2), enabling one to estimate, according to (
2.14
),
R
s
from (
r
c
)
mid
,
which can be obtained from (
T
)
mid
(compare (
2.13
)and(
2.1
); (
T
)
mid
is the
supercooling of the midpoint (
ln(
f
(
m
))/2) of the ln(
f
(
m
,
R
0
))
ln(
T
) plot). The
values of
R
s
for various systems are listed in Table
2.2
.
Interfacial Correlation between Foreign Particles and Nucleating Phase
As shown by Fig.
2.5
a, in the case of
R
0
1, the substrate can be regarded as
being essentially flat, and
f
(
m
,
R
0
) is then solely dependent on
m
.Thisimpliesthat
f
(
m
,
R
0
)
D
f
(
m
) is independent of the supersaturation. According to (
2.26
), the plot
of ln(£
V
)
1/(
T
T
2
) should give rise to a straight line whose slope is determined by
and
f
(
m
). Obviously, for a given system (,
B
0
D
const.), the slope of the straight
line will change according to
f
(
m
)
.
In this sense, the slope of the ln(£
V
)
1/(
T
T
2
)
plot gives the relative
f
(
m
) for the given system. One can analyze the change of the
correlation between the substrate and the crystalline phase in terms of the variation
of the slope.
As given by (
2.7
),
m
is directly associated with
cs
, which is determined by the
interaction and/or structural match between the crystalline phase and the substrate.
For a given crystalline phase and a substrate, an optimal structural match is the
crystallographic orientation
f
hkl
g
, corresponding to the strongest average interaction
or the lowest interfacial energy difference between the crystalline phase and the
substrate between the two phases. This orientation corresponds to the (minimal)
cusp at the ”-plot (Fig.
2.10
a).
As the structural match varies from a perfect to a poor match,
m
decreases from 1
to 0,
1. The extreme case will be
m
!
1, corresponding to the situation where no
crystal-substrate correlation exits. This is the case when substrates exert almost no
influence on nucleation, and nucleation is controlled by homogeneous nucleation
kinetics. The nuclei emerging in this case are completely disordered, bearing no
correlation to the substrate. One has then
f
(
m
,
R
0
)
D
1.
