Biomedical Engineering Reference
In-Depth Information
heterogeneous nucleation occurs in the range between 1 and -1, or
f
(
m,R
0
) between
0 and 1, depending on the nature of the substrate surface and the supersaturation.
Note that for homogeneous nucleation, one has
f
00
(
m,R
0
)
D
f
(
m,R
0
)
D
1and
a
(
R
s
)
2
N
o
!
4
1. In this case, (
7.32
)isconvertedto
exp
16
cf
2
3kTŒkT
J
D
B
:
(7.36)
.1
C
/
2
ln
This implies that (
7.29
) is applicable to both homogeneous and heterogeneous
nucleation.
Similar to 3D nucleation, 2D nucleation can also adopt a similar form [
49
]:
8
<
0
1
9
=
1=2
exp
2
step
cf
/
.
h
2D
s
C
1
ln
.1
C
/
h
@
A
.1
C
/
f
2D
.m
2D
;R
0
2D
/
J
2D
D
:
.kT/
2
ln
;
ˇ
kink
ı
m
2D
;R
0
2D
;R
o
s
;N
(7.37)
with
aR
0
2D
f
2D
.m
2D
;R
0
2D
;/
1=2
ı.m
2D
;R
0
2D
;R
s
o
o
;N
/
D
N
(7.38)
where
D
s
denotes the surface diffusivity. In the case of 2D homogeneous nucleation,
one has
ı.m
2D
;R
0
2D
;R
s
o
/
D
f
2D
.m
2D
;R
0
2D
/
;N
,and(
7.37
) can be simplified as
follows:
(
)
1=2
exp
2D
s
n
1
.1
C
/
h
h
2
.kT/
2
ln
ln
ˇ
kink
J
2D
D
(7.39)
.1
C
/
Here
n
1
is the number of single particles (monomers), and
ˇ
kink
is the sticking
possibility.
7.3.2.3
Nonstationary (or Nonsteady) State
From the initiation of nucleation (
t
0) to the stationary/steady state, there must
be a transit state where the size distribution of clusters will change with time.
This state is known as the nonstationary (or nonsteady) state. Similarly, when
nucleation comes to the end, we will also experience this state. When the nucleation
is nonstationary,
dZ
n
/dt
D
0, and flux
J
n
is a function of both
n
and
t
. The nucleation
rate is then time dependent and this nonstationary nucleation rate
¤
J
nonst
.t/
D
J
n
.t/
.
In other word,
J
nonst
(
t
) will change with time.
