Page 196 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 3 CHARACTERISTICS AND BEHAVIOR OF NANOPARTICLES AND ITS DISPERSION SYSTEMS
order formation of electrostatically stabilized col- earlier, can only give those for particles larger than a
loidal particles with radius of 50 nm onto a planar few microns. The molecular simulation cells, on the
surface with counter charge, as shown in (a), are other hand, cannot accommodate micron or submi-
examined, and the adsorbed particles show ordered cron particles, but it becomes possible if the particle
or disordered arrays, as shown in (b) and (c), size is extremely small.
depending strongly on the operating conditions such Shinto et al. [5, 6] succeeded in obtaining interaction
as the concentration in the bulk phase, electrolyte forces between nanoparticles with a few nanometers in
concentration, and surface charge densities. The diameter immersed in simple fluids by large-scale MD
simulation results in various systems are to be com- simulations, and discussed the effect of solvophobicity
pared, quantitatively, with experimental findings to or solvophilicity onto the interparticle interaction.
brush up the BD method applicable to various engi- Another study showed interaction forces between
neering problems. nanoparticles and a substrate exposed to vapor with
various pressures lower than the saturated one by the
b. Langevin dynamics grand canonical MC simulations, discussing the rela-
The BD needs interparticle interactions as a bridging tion between the condition of capillary bridge and the
property from a lower layer of the multi-scale simu- interaction forces [7]. Note here that the particle diam-
lation structure. The molecular simulations, as stated eter has its UPPER limit around several nanometers.
earlier, suffer from the huge difference in the scale to The simulation methods explained in the following
provide it, and further they are not appropriate to pre- are summarized in Fig. 3.8.3. The smallest one, MD,
dict the effects of surfactants, polymers, and additives has its typical scale of a few nanometers as described
that often drastically change the nature of the interac- above. The basic idea and features of other methods
tion. On the other hand, one may employ a direct are to be contrasted with this smallest size.
measurement by AFM, using a “colloid probe” which
has a particle glued on the top of the cantilever apex, (ii) Langevin dynamics
but the lower limit for the measurement is a few For a larger size of particles, say, above 10 nm, the
microns in general. Thus we need a lower layer just MD or MC cannot be used. Also difficult to be
beneath the BD to obtain the surface forces, which applied are the effect of surfactants or polymers
should be the Langevin dynamics (LD). onto surface forces because of their large-scale and
The essence of the method is the elimination of the slow behavior for relaxation and/or structure change.
solvent molecules, which is in principle same as the The LD should fill this portion in the multi-scale
BD. Because both the BD and LD share their basic simulations.
equation as the Langevin equation, they sometimes Solvent molecules are not explicitly included in this
classify the two methods into the same category, call- simulation, and the solute molecules such as surfac-
ing either Brownian or stochastic dynamics. The LD, tants, polymers, and additives are the elements in the
similar to the BD, has rather a long history in the simulation that explicitly appear in a cell. Instead, the
physics field, but has only limited studies for engi- basic equation should include a random force to
neering aspects. Utilization of the LD would benefit express thermal motion by solvent molecules, and a
the multi-scale simulation structure by capability of friction term that mimics viscosity attenuation pro-
providing, e.g., interaction forces between surfaces portional to the solute’s velocity, resulting in the
adsorbed by surfactants, to the BD or SD. The LD, on so-called Langevin equation.
the other hand, needs the molecular-level information Another important point in this method is to use,
called the potential of mean force between (coarse- not the direct interaction forces as employed in MD,
grained) elements as shown in Fig. 3.8.1, which will but the one including the effect of solvent molecules.
be explained in the next section. For example, ions and sites in a surfactant molecule
The above is the possible multi-scale simulation with hydrophilic and hydrophobic parts exchange far
structure, and the next section describes the basic different forces from those of direct interactions in
concept and the feature of each simulation unit, vacua, because of the effect of water molecules exist-
reversely from molecular scale to meso/macroscale. ing between them. This kind of interaction forces or
potential energies can be determined by conducting a
MD simulation at a fixed distance between the ele-
3.8.2 Simulation methods in nano/mesoscale ments surrounded by water molecules that explicitly
appear in the simulation. Conducting it with various
(i) Evaluation of interaction forces between nanoparticles
distances and integrating against the distance, one can
by large-scale molecular simulations obtain the interaction potential for the LD, or the
The interparticle forces directly affect the behavior of potential of mean force (PMF, also called as solvent
the particulate system, which is especially of crucial averaged force). Setting this potential in LD without
importance for nanoparticles because they prevail solvents, the elements (ions, sites in complex mole-
more for smaller particles over other forces like grav- cules, etc.) would feel a force as if the solvent mole-
ity or inertia. The colloidal-probe AFM, as described cules exist and surround them. This PMF is the one

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