Biomedical Engineering Reference
In-Depth Information
To identify the crystalline-like particles from the liquid-like particles in 2D
crystal nuclei, a local 2D bond-order parameter is defined as follows [
37
-
41
]:
6
.r
i
/
D
M
1
ˇ
j
e
i6
ij
ˇ
X
(7.40)
where
r
i
is the center of particle
i
,and
ij
is the angle subtended between the vector
from particle
i
to its
j
th nearest neighbor and the arbitrarily chosen
x
axis.
M
is the
number of nearest neighbors of particle
i
. The mean value of
6
(
r
i
) for crystalline
structures obtained from the experiments is 0.8, which is taken as the criterion for a
crystal-like particle.
Figure
7.6
a reveals that at relatively low supersaturations, the structure of
crystalline clusters is a bit fluid-like and more disordered at the beginning and
gradually approaches to the ordered structure in the bulk crystalline phase at a size
close to the critical size of nuclei. The transition from the initial metastable structure
to the final stable structure is a continuous process.
On the other hand, at high supersaturations (decreasing frequency gives rise to the
increase in supersaturation) [
60
], Fig.
7.6
b shows the structural transition occurring
under conditions of
f
D
3,000 Hz and
V
pp
D
2.5 V. Different from the behavior
of
can be as high as 0.8 instantaneously even before it
reaches its transition size ( 30) (in Fig.
7.6
b(i)). This implies that the nucleus can
have a crystalline structure even before it becomes stable in structure. Nevertheless,
the crystalline structure of the precritical nuclei is transient and fluctuated. In
Fig.
7.6
b(ii) and (iv), the structure of the nucleus is ordered. In the subsequent
seconds, as shown in Fig.
7.6
b(iii) and (v), it becomes disordered again. Only when
the size is beyond the critical size 30, the crystalline structure becomes stable. As
the supersaturation is increased further by decreasing frequency,
h
6
i
in Fig.
7.6
(a),
h
6
i
remains more
or less 0.8 in the whole growth process from the beginning, and crystal nuclei are
initially created with a crystalline structure as suggested by CNT [
44
].
The results in Fig.
7.6
indicate that the initial structure of crystal nuclei and
the structural evolution of crystal nuclei are
supersaturation-dependent
.Atlow
supersaturations, a metastable liquid-like structure is likely to occur first. This is
h
6
i
I
Fig. 7.6
is a function of nuclei size
N
. Monodisperse colloidal
particles (polystyrene spheres of diameter 0.99 mm, polydispersity
(continued) a critical size. (
iv
)
h
6
i
5%, Bangs Laboratories)
were dispersed uniformly in deionized water. The colloidal suspension was then sealed between
two parallel horizontal conducting glass plates coated with indium tin oxide (
ITO
).The gap between
the two glass plates is
H
D 120 ˙ 5 mm. The dynamic process is recorded by a digital camera
(
CCD
) for analysis.
AEF
alternating electric field. (
b
) Phase diagram of the system when the
concentration of Na
2
SO
4
is 2 10
-4
M.
V
pp
, peak-to-peak voltage. Due to the nature of 2D crystals,
h
6
i for a perfect 2D crystal is 0.8. (
b
) Transient crystalline structure of nuclei under condition of
V
pp
D 2.5 V,
f
D 3,000 Hz. (
i
) Fluctuation of order parameter during the growth. (
ii
,
iii
) Due to the
structural fluctuation, nuclei can have a transient crystalline structure. (
iv
,
v
) Liquid-like structure
displayed by precritical nuclei. Reprinted with permission from Ref. [
44
] © 2008 Wiley-VCH
Ve r l a g G m b H & C o
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