Biomedical Engineering Reference
In-Depth Information
Although the TSC can be captured by Ostwald's rule
,
[
17
], the detailed under-
standing has not been acquired till recently. In this regard, the controlled colloidal
assembly can be applied to examine the mechanism. MSC has attracted much
attention in the past decade due to its importance in both scientific and technological
points of view. However, the understanding of TSC remains to be insufficient. A key
challenge is that the kinetics creating the initial crystalline nuclei from the dense
droplets is unclear and thus it is no way to predict the overall nucleation rate
J
c
of crystals. In the following, we will recap the multistep crystallization (MSC) in
the colloidal model system. The kinetics of MSC is discussed and a mathematical
method is developed to address the local nucleation rate
j
c
of crystal in the droplets.
A typical process of MSC, observed under conditions of
V
pp
D
2.0 V and
f
800 Hz, is presented in Fig.
7.10
. Colloidal particles in the initial mother
solution are uniformly distributed in the solution (i.e., Fig.
7.10
a).
When an AEF is applied to the system, colloidal particles are transported onto
the glass surface where they first form dense droplets (Fig.
7.10
b). Subsequently,
a few subcrystal nuclei are created from the droplets as illustrated in Fig.
7.10
c.
These subnuclei are not stable and will dissolve soon after they are created.
Experimentally, it is found that the crystalline nuclei in the droplets have to acquire
a critical size
D
N
cry
before they can grow stably in the droplets as shown in Fig.
7.7
d.
In the experiments, every droplet can produce only one stable crystal. Moreover,
to form a stable crystal beyond
N
cry
, the droplets have to first acquire a critical
N
. It is found that although, at an early stage, many small dense droplets are
created, only 3 or 4 out of 20 droplets can reach the critical size
size
N
and develop
successfully into a stable crystal. This is consistent with previous observations in
protein crystallization [
75
,
76
]. However, it is contradicting with the assumption by
Kashchiev et al. [
77
]. A detailed analysis on the overall nucleation rate
J
c
of MSC,
determined by the local rate
j
c
in the individual dense droplets, is given in Ref. [
52
].
In general, the MSC in a colloidal model system indicates that amorphous
dense droplets first nucleate from the mother phase. Subsequently, a few unstable
subcrystalline nuclei can be created simultaneously by fluctuation from the tiny
dense droplets, which is different from previous theoretical predictions. Notice that
it is necessary for these crystalline nuclei to reach a critical size
N
cry
to become
stable. However, in contrast to subcrystalline nuclei, a stable mature crystalline
nucleus is not created by fluctuation but by coalescence of subcrystalline nuclei,
which is unexpected. To accommodate a mature crystalline nucleus larger than the
critical size
N
cry
, the dense droplets have to first acquire a critical size
N*
.This
implies that only a fraction of amorphous dense droplets can serve as a precursor
of crystal nucleation. As an outcome, the overall nucleation rate of the crystalline
phase is, to a large extent, determined by the nucleation rate of crystals in the
dense droplets, which is much lower than the previous theoretical expectation. The
calculations indicate that the MSC is indeed kinetically more favorable than one-
step crystallization under the given conditions [
41
].
