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decrease particle collision frequency because it is determined
by Brownian motion and/or convection, while the successful
particle binding rate can be substantially decreased by utilizing the
short-range interparticle attractive interactions, or using a slow
surface
−
19,23,24
−
functionalization
reaction.
Indeed,
dipole
dipole
36
37
23
have
been successfully used to synthesize colloidal superparticles. In
addition, solvophobic interactions are important interactions to
tailor the superparticle growth through kinetic control or micelle-
template confinement.
interactions,
π−π
interactions,
and hydrogen bonds
1,20,21,25,38
In the following section, we
discuss the separation of nucleation and growth in the formation of
superparticles, and the superparticle nucleation rate.
13.2
Superparticle Nucleation Rate
Owing to the nature of superparticles, their precursors, and building
blocks, classical nucleation theory is not valid to describe their
formation. Here we propose to use a kinetic nucleation model to
describe the superparticle formation. In this model, nucleation is
governed by the reactions of an active species that is created from
the reactions of precursors, while the reactions of these active
species also results in the growth of superparticles. In other words,
nucleation and growth are two competitive kinetic processes in the
consumption of active species. In a synthesis with a slow particle-
aggregation rate, the active-monomer formation rate (G) and the
superparticle growth rate (
u
) are often much larger than the
nucleation rate (dN/dt), and thus one can roughly assume that G
and
u
remain constant during the nucleation stage. Accordingly, the
kinetic expression of superparticle formation can be described as
follows:
d
d
N
t
-
=
GV
V
uN
(13.8)
P
N
is the volume of a
nucleus, and N is the number density of nuclei. The solution of this
derivative equation is as follows:
where V
is the volume of an active monomer, V
P
N
È
˘
Ê
Ë
Á
ˆ
¯
˜
GV
u
u
V
P
=
- -
Nt
()
Í
Í
1
exp
t
˙
˙
(13.9)
Î
˚
N
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