192
J. Richardi et al.
8.4 Assemblies of Cobalt Nanoparticles
8.4.1 Key Parameters Involved in the Nanoparticle
Organization
For a long time, experimentalists and theoreticians have sought the optimal conditions
to obtain well-defined self-organization of NPs in 2D and 3D lattices. Here, we will
focus on the self-assembly in solution. Three major parameters have become evident
for this process: the speed of evaporation, the monodispersity of the particle size and
the interaction between the NPs.
Concerning the evaporation speed, it has been observed that it has too be sufficiently small to allow the cluster of nanoparticles to come together to form mesostructures. This is usually empirically reached by a confinement of the beaker used for
the evaporation.
Concerning the monodispersity, experiments have shown that well-ordered superlattices are observed at polydispersities lower than 5%, while polydispersities larger
than 12% suppress ordered assemblies [46]. The theoretical study of solid–fluid transitions in hard-sphere systems using Monte Carlo simulations has given explanation
for this observation [47, 48]. It reveals the existence of a terminal polydispersity
above which, no crystallization can occur. The highest polydispersity is 5.7% for the
solid and about 12% for the fluid. Fractionation enables a fluid of larger polydispersity to crystallize into several solids of smaller polydispersity and different average
size. Therefore, a batch of nanocrystals synthesized with an average polydispersity smaller than 12% may form superlattices by fractionation, while within a large
superlattice, the average polydispersity should be smaller than 6%. Simulations have
shown that kinetic factors are the reason for the existence of the terminal polysdispersity [49]. Usually the free energy barrier to nucleation continuously decreases with
increasing concentration enabling the formation of crystals. The simulations show
that in polydisperse samples, the free energy barrier passes through a minimum, thus
suppressing crystallization. Recent simulations have also shown that the fractionation may be a complex process [50]. We have carried out simulations in the 2D
case using Lennard–Jones potential, which show this transition from an ordered to a
disordered state when the polydispersity is increased. For a polydispersity of 6%, the
left side of Fig. 8.6 shows an ordered assembly characterized by well-defined spots
in the two-dimensional pair distribution function (see insert). This order disappears
for a polydispersity of 15% on the right side of Fig. 8.6.
The third key parameter is the interaction potential between the NPs. To obtain
a self-assembly purely by confinement due to the evaporation of the solvent, this
interaction has to be repulsive even at the end of evaporation. In general, the interaction for two magnetic particles covered with chain-like ligands in a solvent may
be expressed in the following way [51–53]:
u tot (r ) = u vdW (r ) + u elastic (r ) + u mix (r ) + u ionic (r ) + u dipole (r )
(8.1)
J. Richardi et al.
8.4 Assemblies of Cobalt Nanoparticles
8.4.1 Key Parameters Involved in the Nanoparticle
Organization
For a long time, experimentalists and theoreticians have sought the optimal conditions
to obtain well-defined self-organization of NPs in 2D and 3D lattices. Here, we will
focus on the self-assembly in solution. Three major parameters have become evident
for this process: the speed of evaporation, the monodispersity of the particle size and
the interaction between the NPs.
Concerning the evaporation speed, it has been observed that it has too be sufficiently small to allow the cluster of nanoparticles to come together to form mesostructures. This is usually empirically reached by a confinement of the beaker used for
the evaporation.
Concerning the monodispersity, experiments have shown that well-ordered superlattices are observed at polydispersities lower than 5%, while polydispersities larger
than 12% suppress ordered assemblies [46]. The theoretical study of solid–fluid transitions in hard-sphere systems using Monte Carlo simulations has given explanation
for this observation [47, 48]. It reveals the existence of a terminal polydispersity
above which, no crystallization can occur. The highest polydispersity is 5.7% for the
solid and about 12% for the fluid. Fractionation enables a fluid of larger polydispersity to crystallize into several solids of smaller polydispersity and different average
size. Therefore, a batch of nanocrystals synthesized with an average polydispersity smaller than 12% may form superlattices by fractionation, while within a large
superlattice, the average polydispersity should be smaller than 6%. Simulations have
shown that kinetic factors are the reason for the existence of the terminal polysdispersity [49]. Usually the free energy barrier to nucleation continuously decreases with
increasing concentration enabling the formation of crystals. The simulations show
that in polydisperse samples, the free energy barrier passes through a minimum, thus
suppressing crystallization. Recent simulations have also shown that the fractionation may be a complex process [50]. We have carried out simulations in the 2D
case using Lennard–Jones potential, which show this transition from an ordered to a
disordered state when the polydispersity is increased. For a polydispersity of 6%, the
left side of Fig. 8.6 shows an ordered assembly characterized by well-defined spots
in the two-dimensional pair distribution function (see insert). This order disappears
for a polydispersity of 15% on the right side of Fig. 8.6.
The third key parameter is the interaction potential between the NPs. To obtain
a self-assembly purely by confinement due to the evaporation of the solvent, this
interaction has to be repulsive even at the end of evaporation. In general, the interaction for two magnetic particles covered with chain-like ligands in a solvent may
be expressed in the following way [51–53]:
u tot (r ) = u vdW (r ) + u elastic (r ) + u mix (r ) + u ionic (r ) + u dipole (r )
(8.1)