Environmental Engineering Reference
In-Depth Information
nanocrystal has the same structure of the corresponding bulk [162]. Since the structure and
energy differences between solid and liquid are small in comparison with that between solid
and gas or between liquid and gas, the above expression for the bulk may be extended to
nanometer size with the same form [181],
γ
sv
(
D
)/γ
lv
(
D
) =
w
.
(5.14)
Combining Eqs. (4.12) and (5.14) as well as the expression for the bulk, there is [211],
γ
(
D
)
1
⎛
2
S
1
⎞
⎡
⎤
.
(5.15)
lv
γ
=
1
−
exp
⎜
⎝
−
b
⎟
⎠
⎣
⎦
2
D
/
h
−
1
3
R
2
D
h
−
1
lv
0
In terms of Eq. (5.15), comparisons of γ
lv
(
D
)/γ
lv0
for Na and Al droplets between the
model predictions and the computer simulation results [212] are shown in figures 11 and 12
where the parameters involved in Eq. (5.15) are listed in table 14. It is evident that the model
predictions are in agreement with the computer simulation results for Na and Al. This
agreement in return confirms the validity of the assumption in Eq. (5.14). As a comparison,
the predictions of Eq. (4.9) with δ = δ
∞
=
h
are also shown in these two figures.
1.0
Al
0.8
0.6
0.4
Eq. (5.15): Current model
Eq. (5.13): Tolman model
Simulated [Ref. 212]
0.2
0.0
0
5
10
15
20
D
/
δ
Figure 12.
D
/
δ
(
δ
=
h
) dependence of
γ
lv
(
D
)/
γ
lv0
for Al [212].
Although Eq. (5.15) is deduced in light of the relation between γ
sv0
and the broken bond
number of surface atoms for metals [162], this relation should be also applicable to other
types of materials. Figure 13 shows γ
lv
(
D
) function of water droplets in terms of Eq. (5.15).
The model prediction also corresponds well to the computer simulation results [54]. Note that
the definition for
h
in this case is redefined as O-H bond length [213]. Similarly, the
prediction of similarly with δ =
h
is also shown in figure 13.
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