Environmental Engineering Reference
In-Depth Information
1.0
0.8
0.6
γ
ss
(
D
)/
γ
ss0
0.4
γ
sl
(
D
)/
γ
sl0
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
D
0
/
D
Figure 1. γ(
D
)/γ as a function of
D
′
0
/
D
in terms of Eq. (2.22) and Eq. (3.4) with
D
′
0
= 3
h
. For γ
ss
(
D
)/γ
ss0
function, the solid line and the segment line are obtained by use of negative and positive
f
, respectively.
The symbols ■ and ▲ are the computer simulation results of γ
sl
(16
h
)/γ
sl0
= 0.58 for unknown fcc metal
[15] and those for Cu [107] where γ
ss0
=594 mJ/m
2
.
Table 4. The comparison of
γ
sl
(
D
)/
γ
sl0
values between the model predictions in terms of
Eq. (2.21) with
D
′
0
= 3
h
and the corresponding experimental results [13] where the
experimental data of
γ
sl
(
D
=4 nm) are obtained by measuring the slope of experimental
data of melting temperature versus 1/
D
with two points of
D =
4 nm and
D
≈
8.6 nm in
terms of Gibbs-Thomson equation
γ
sl
(
D
)/γ
sl0
κ
(Mpa
-1
×10
-5
)
Benzene 0.67 0.66 87
Naphthalene 0.68 0.69 ≈ 87
Chlorobenzene 0.89 0.63 67
Heptane 0.63 0.80 134
Trans-decalin 0.60 0.68
≈ 87
Since κ values of crystals are not found, κ values of the corresponding liquid are used, which leads to minor
error [53]. Note that κ values of naphthalene and
Trans
-decalin have been estimated as that of benzene.
Ref. [13]
Eq. (2.21)
The above agreement between Eq. (2.21) or Eq. (2.22) and experiments denotes that the
energetic and structural differences between crystal and liquid decrease with size, which is
proportional to surface/volume ratio with a 1/
D
relationship [27]. The success of model
prediction for γ
sl
(
D
) values in return confirms again that
H
m
and
S
vib
, not
H
m
itself, determine
the sizes of γ
sl0
values as shown in Eq. (2.13) [32].
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