Colloidal Superparticles From Artificial Atoms - Molecular Self-Assembly: Advances and Applications - page 420

Accordingly, the number of nuclei in this synthesis increases
with time, while the nucleation rate decreases owing to the growth
of nuclei. As a consequence, the nuclei number approaches a value
(N

 u
V

) at a time (t) when t is substantially large, and N is

Final Final

presented as follows:

N

GV
u

P

= 

N (13.10)

Final

This fundamental expression shows that the nuclei number is
directly proportional to the active-monomer formation rate (G) and
inversely proportional to the nuclei growth rate (

 u

). This nucleation
equation should apply not only to superparticle synthesis but also to
nanocrystal synthesis, unless the colloidal particle formation is under
kinetic control (note that this equation should not apply to template-
controlled synthesis).

39

On the basis of this kinetic equation, one can
vary experimental parameters to control the number of superparticle
nuclei in a synthesis, and thus the size of the final product of this
synthesis. With a given amount of precursor, a larger number of
nuclei results in smaller final particles, and vice versa. Importantly,
this relationship bridges the control of the particle size with the
control of the active-monomer formation rate and nuclei growth rate
in the synthesis. Generally speaking, both active-monomer formation
rate and nuclei growth rate are reaction rates, and thus they can be
tuned according to our extensive knowledge regarding the kinetics
of the chemical reactions. In the next section, we will further discuss
this size-control relationship in the successful examples of colloidal
superparticle syntheses.

13.3 Superparticles with a Short-Range Order

To date, several approaches have led to the synthesis of spherical
colloidal superparticles, in which nanocrystal building blocks exhibit
a short-range order.

19,23,24,28,37,40 − 42

In these approaches, hydrogen
bonding, solvophobic interaction, and dipole

−

dipole interactions
are used to trigger the formation of superparticles. Here we discuss
these synthetic approaches and the properties of the resulting
colloidal superparticles.