Biomedical Engineering Reference
In-Depth Information
R
0
for the four different systems: DI water filtered by a 200 nm
filter (
curve 1
), 2.5 mg/mL AFPIII DI water solution filtered by a 20 nm filter (
curve 2
), DI water
filtered by a 20 nm filter (
curve 3
). The curves were obtained based on the data given in Fig.
2.7
b
(
R
0
is obtained based on (
2.1
)and(
2.4
)). The entropy of melting per molecule
S
m
Experimental
f
(
m
,
R
0
)
Fig. 2.9
10
23
3.67
JK
1
; the volume per molecule
10
30
m
3
. Reprinted with permission from ref. [
12
].
Copyright (2004) the American Society for Biochemistry and Molecular Biology
32.53
foreign particles or
R
0
!
0. In the case
f
(
m
,
R
0
)
max
D
1, one has a straight line with
the largest slope (line 2 of curve
A
in Fig.
2.7
b). In this regime, as suggested
by the zero-sized effect, the particles behave as if they had “vanished,” although
they are still physically present in water. According (
2.15
), the occurrence of the
particles does not lower the nucleation barrier with respect to that of genuine
homogeneous nucleation. Notice that the nucleation in Regime III is still not
genuine homogeneous nucleation. In the case of genuine homogeneous nucleation,
one has
f
”(
m
,
R
0
)
D
f
(
m
,
R
0
)
D
1andln(
f
”(
m
,
R
0
)(
f
(
m
,
R
0
))
1/2
BN
o
)
D
constant for the
same system, meaning that only one ln(£
V
)versus1/(
T
T
2
) plot can be identified in
this case for the same system, such as DI water filtrated by a 20 nm filter (Fig.
2.7
b,
curve
A
) and DI water filtrated by a 200 nm filter (Fig.
2.7
b, curve
D
). Nevertheless,
in comparison to segment 2 in curve
A
and segment 2
0
in curve
D
, one has two
parallel straight lines instead of a single straight line. This means that the nucleation
occurring at the “zero-sized” regime (Regime III) is still not genuine homogeneous
nucleation, although the height of the nucleation barrier is equivalent to that of
homogeneous nucleation. This result is attributed to the fact that the probability
of nucleation around the foreign particles may still be higher than elsewhere within
the water droplet because of the particle-induced molecular preordering. Based on
the fact that this homogeneous-like nucleation occurs at low supercoolings rather
than at high supercoolings as expected previously [
53
], this type of nucleation is
then referred to as inverse homogeneous-like nucleation.
Figure
2.7
b was converted into
f
(
m
,
R
0
)
R
0
as given in Fig.
2.9
. According
to (
2.26
), the slope of the ln(£
V
)
1/(
T
T
2
)plotis
f
(
m
,
R
0
). If the inverse
