Biomedical Engineering Reference
In-Depth Information
7.3.2.4
Experimental Verification of Nucleation Kinetics Based
on Colloidal Crystallization
Although theoretical analysis on the above states of nucleation has been published
for long time, experimental verification, in particular, the direct measurement for
the distribution of subcritical nuclei had never been achieved till recently when the
electrically controlled 2D colloidal nucleation was carried out [
13
]. By measuring
the size distribution of subcritical nuclei on the surface of flat electrode, we
observed the evolution among the different kinetics: nonstationary, stationary, and
equilibrium states [
49
] in the process of pre-nucleation. Figure
7.5
apresenteda
typical distribution at different time. Once the driving force is applied, the small
nuclei are formed. Subsequently, the cluster size exceeded the critical size of nuclei,
and the nuclei were growing to the crystallites gradually. Figure
7.5
a reflected this
image of nucleation kinetics. Here we defined a transient point
n
*
(
t
), where the
size distribution approached to a steady number of clusters in the nucleation (see
Fig.
7.5
a, inset).
It follows from Fig.
7.5
that, first, the system starts from a nonstationary state
(
t
D
3.2 s) at the beginning and gradually approaches toward the stationary state
(
t
20 s) in which the distribution of nucleating clusters
Z
n
is independent of time.
Second, a nucleation event is successful once the distribution of nucleating clusters
Z
n
>
D
1
in any time. Therefore, the cluster size at
Z
n
D
1 can be defined as the
critical size of nucleation
n
*
.
Before reaching the stationary state,
n
*
is time dependent. Only after reaching
the stationary state, the critical size of nucleus
n
*
can acquire a constant value
(Fig.
7.5
b). In other words, it makes sense to discuss the critical size of nucleus
only at the stationary state.
In Fig.
7.5
c, the average nucleation rate in the unit area of surface according to the
fitting slope of curves was measured. Figure
7.5
d presents the nucleation rate density
under different driving forces. The linear fitting of the plot of ln(
J
)
)
indicates that (
7.39
) can be applied to quantify the nucleation kinetics of 2D
nucleation.
1/ln(1
C
7.3.3
Initial Stage of Nucleation: Is Classical Nucleation
Theory Accurate?
Although the basic treatments of classical nucleation theories (CNTs) have been
approved to be correct as shown in Sect.
7.3.2.3
, some aspects of nucleation
remain unclear. In the analysis of nucleation kinetics in Sect.
7.3.2
, the structure
of crystal nuclei is supposed to be identical to the bulk crystals. Is this assumption
correct? If not, what are the consequences? In the following, we will describe
the interfacial structural evolution during nucleation, the impact of the interfacial
structure of nucleating clusters on the nucleation energy barrier, in terms of 2D
colloidal crystallization model system.
