208
J. Richardi et al.
may disappear when ligands with longer alkyl chains such as dodecanoic acid are
used. In this case, the van der Waals attraction is reduced due to the larger contact
distance between the particles and cannot participate in the mesostructure formation.
Mesostructure formation as observed for MNPs has been widely modeled as
confined Stockmeyer fluid in gas–liquid coexistence. The Stockmeyer potential is
made of the two terms essential for the mesostructure formation as discussed above:
a Lennard–Jones term describing the van der Waals attraction and a magnetic dipole
potential. This fluid is confined between two walls describing the film, which is
formed during the evaporation. The mesostructure formation is interpreted as a coexistence of a gas and a condensed phase made of the colloidal particles. The condensed
phase forms the mesostructures observed in the experiments.
The confined Stockmeyer potential is completely described by five parameters:
the dipole strength μ, the density ρ, the temperature T, the film thickness L and the
field strength H. These parameters are usually expressed in reduced units. To observe
mesostructures, a large number of particles up to 12,000 have to be used. The longrange dipole interaction must be correctly handled using Ewald sums. Several Monte
Carlo simulation studies have been carried out for this system and we will summarize
the principal results [7, 81–84].
In the literature [85–98], usually particles with high dipole moments are studied by
simulations studied have. Thus, the cluster distribution and spacing has been studied
for low-density systems made of dipolar hard spheres in a slit geometry [93, 94].
Also the orientational order of dipolar soft spheres has been investigated showing an
enhancement of ferroelectric order due to confinement [95, 96].
Concerning mesostructure formation, we will first discuss the simulation results
for Stockmeyer fluids when a field parallel to the film is applied. Figure 8.17a shows
the formation of an array of regularly spaced columns of similar diameter at a height
of L = 10 [83]. For higher dipoles, the same number of columns is observed, but
the particles form an ordered assembly of body-centered tetragonal type. When the
height is larger than 10, the diameter of the columns stay close to the value observed
for L = 10, which leads to the formation of several layers of columns (Fig. 8.17b).
When the height is smaller than 10, the columns appear flattened (Fig. 8.17c). When
diluted NP solutions are used, the formation of one layer of columns is observed
as in Fig. 8.17a. For concentrated solutions corresponding to the case in Fig. 8.17b,
several layers of columns are obtained.
The self-organization of magnetic NPs has also widely been studied in the case
of a field perpendicular to the film [7, 82]. This case is fundamentally different from
the parallel one previously discussed. This is explained in the following. The dipoles
of the MNPs follow the field direction, which leads to a layer of dipoles pointing in
the same direction at the surface of the evaporation film. The aligned dipoles repel
each other, which would lead to a separation of the NPs. On the other hand, the
NPs are attracted for example by short-range van der Waals attractions as mentioned
above. This interplay of short-range attraction and long-range dipolar repulsion leads
to the formation of pattern such as hexagonal arrays of columns or labyrinths. This
phenomenon can be described by a free energy approach taking into account the
repulsion between the aligned dipoles and the energy corresponding to the surface
J. Richardi et al.
may disappear when ligands with longer alkyl chains such as dodecanoic acid are
used. In this case, the van der Waals attraction is reduced due to the larger contact
distance between the particles and cannot participate in the mesostructure formation.
Mesostructure formation as observed for MNPs has been widely modeled as
confined Stockmeyer fluid in gas–liquid coexistence. The Stockmeyer potential is
made of the two terms essential for the mesostructure formation as discussed above:
a Lennard–Jones term describing the van der Waals attraction and a magnetic dipole
potential. This fluid is confined between two walls describing the film, which is
formed during the evaporation. The mesostructure formation is interpreted as a coexistence of a gas and a condensed phase made of the colloidal particles. The condensed
phase forms the mesostructures observed in the experiments.
The confined Stockmeyer potential is completely described by five parameters:
the dipole strength μ, the density ρ, the temperature T, the film thickness L and the
field strength H. These parameters are usually expressed in reduced units. To observe
mesostructures, a large number of particles up to 12,000 have to be used. The longrange dipole interaction must be correctly handled using Ewald sums. Several Monte
Carlo simulation studies have been carried out for this system and we will summarize
the principal results [7, 81–84].
In the literature [85–98], usually particles with high dipole moments are studied by
simulations studied have. Thus, the cluster distribution and spacing has been studied
for low-density systems made of dipolar hard spheres in a slit geometry [93, 94].
Also the orientational order of dipolar soft spheres has been investigated showing an
enhancement of ferroelectric order due to confinement [95, 96].
Concerning mesostructure formation, we will first discuss the simulation results
for Stockmeyer fluids when a field parallel to the film is applied. Figure 8.17a shows
the formation of an array of regularly spaced columns of similar diameter at a height
of L = 10 [83]. For higher dipoles, the same number of columns is observed, but
the particles form an ordered assembly of body-centered tetragonal type. When the
height is larger than 10, the diameter of the columns stay close to the value observed
for L = 10, which leads to the formation of several layers of columns (Fig. 8.17b).
When the height is smaller than 10, the columns appear flattened (Fig. 8.17c). When
diluted NP solutions are used, the formation of one layer of columns is observed
as in Fig. 8.17a. For concentrated solutions corresponding to the case in Fig. 8.17b,
several layers of columns are obtained.
The self-organization of magnetic NPs has also widely been studied in the case
of a field perpendicular to the film [7, 82]. This case is fundamentally different from
the parallel one previously discussed. This is explained in the following. The dipoles
of the MNPs follow the field direction, which leads to a layer of dipoles pointing in
the same direction at the surface of the evaporation film. The aligned dipoles repel
each other, which would lead to a separation of the NPs. On the other hand, the
NPs are attracted for example by short-range van der Waals attractions as mentioned
above. This interplay of short-range attraction and long-range dipolar repulsion leads
to the formation of pattern such as hexagonal arrays of columns or labyrinths. This
phenomenon can be described by a free energy approach taking into account the
repulsion between the aligned dipoles and the energy corresponding to the surface