Page 132 - Optofluidics Fundamentals, Devices, and Applications

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evaporation front will increase due to the convective transport of
colloids from the bulk. Hard spheres, which do not interact with the
neighboring particles until they touch each other, begin to crystallize
from the suspension at a particle volume fraction of 0.494—this order-
ing is driven purely by entropy. Because the particles tend to occupy
the largest free volume possible, they arrange into fcc or hexagonal
close-packed (hcp) lattices, which have an identical maximum
packing fraction of 0.7404, the highest among all the possible sphere
arrangements. (In fact, the fcc structure is the equilibrium state, due
to slight differences in energy, but both the fcc and hcp structures can
be generated experimentally.) On the other hand, soft spheres show
much more complex crystallization behavior, which is influenced by
interparticle interactions, such as van der Waals forces, electrostatic
potentials, and steric hindrance. Practically, most of the colloidal par-
ticles in polar solvents are soft spheres submitted to van der Waals
attractions and electrostatic repulsions. Especially, the largeelectrostatic
repulsion—overcoming the attractive forces—gives a high stability to
the colloidal suspensions. Both inorganic and polymeric colloidal
particles may have surface charges that originate from the functional
groups on their surface, and thus can be dispersed in a polar medium
without forming aggregates. Surface charges change depending on
the pH conditions. The hydroxyl, sulfonic, and carboxylic groups are
typical examples of functional groups that give negative charges
under basic conditions. Oppositely, the amine group gives positive
charges under acidic conditions. When decreasing or increasing the
pH value of a solvent by titration, the surface charge will become zero
at a certain point (called the isoelectric point). Uniform silica particles
can be prepared by a sol–gel procedure, with the Stöber–Fink–Bohn
method being the most famous technique [12]. During the sol–gel
process, hydroxyl groups are intrinsically formed at the surface of the
silica spheres. These hydroxyl groups can be substituted by different
functional groups using silane coupling agents [13]. On the other
hand, monodisperse polystyrene (PS) particles can be synthesized by
emulsion polymerization—with or without surfactant—in polar
media [14]. In this case, either a surfactant or linear copolymers with
functional end groups form micelles and stabilize the colloids by
anchoring on their surface. Functional groups are generated during
the synthesis process by surfactants, comonomers, or initiators, which
are mostly located at the surface.
Soft spheres with repulsive potentials can be crystallized at much
lower concentrations, because their effective size is larger than that of
hard spheres with the same particle size. Experimentally, the crystal-
lization of soft spheres can proceed at extremely low concentrations
as particle volume fraction of 1%, although the threshold concentration
depends on the strength of the potential. Generally, colloids crystal-
lize into the fcc structure at relatively high concentrations for a wide
range of repulsive strengths. On the other hand, particles exhibiting