Page 145 - Optofluidics Fundamentals, Devices, and Applications

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droplets are used as the confining geometry for crystallization, the
(111) plane will be formed over the spherical interface [26–28]. This is
because heterogeneous nucleation on the smooth wall of the confining
geometry induces crystallization. If these crystals are generated, they
will exhibit isotropic optical properties, that is, the rotation of the
crystal will not influence the reflection wavelength. However, the
(111) plane, which is characterized by a hexagonal arrangement of the
colloids, cannot form a defect-free spherical surface because—as one
may imagine—a perfect hexagonal arrangement of spheres can only
fill the planes with zero Gaussian curvature. To inspect the generation
of defects at the spherical interface, emulsion droplets containing
anchored PS particles with a repulsive interparticle potential were
used as a model system by Blausch et al. [29] As we can notice from
the classical Euler formula (V − E + F = 2; where V, E, and F are the
numbers of vertices, edges, and faces, respectively), closed systems
will always have +12 defect charges if we count the charges as: … , +2,
+1, 0, −1, −2, … for … , four, five, six, seven, eight, … -fold particles,
respectively. Emulsion model systems have shown that defect
generation is related to the size of the system. If R/l < 5 (where R is the
radius of the emulsion drop and l is the interparticle distance), only
twelve fivefold particles will be observed. However, larger systems
show excess dislocations, which appear as repetitive five- and
sevenfold defects keeping the constraint of total charge of +12. The
number of excess dislocations increases with the size of the system.
On the other hand, particles in extremely large systems cannot feel
the curvature of the emulsion droplet. Therefore, when particles are
confined in a very larger droplet, they assemble spontaneously into
fcc structures from the interface—similar to what happens in the case
of crystallization in a rectangular confined geometry. Thus, a layered
structure of concentric shells composed of hexagonal arrangements
of colloids is formed.
In the following two sections, we will discuss the optofluidic
synthesis of spherical colloidal crystals (called photonic balls) in the
solid and liquid states using photocurable single- and double-emulsion
droplets, respectively. The optofluidic scheme represents a simple and
high-throughput technique for generating photonic balls.

6-3-1 Direct Synthesis of Photonic Balls in the Solid State
Emulsion droplets are useful templates for producing spherical materials.
Especially, if they contain monodisperse colloidal particles, spherical
colloidal crystals can be produced by diffusion-induced consolidation of
the emulsion phase. However, the volume shrinkage of the emulsion
takes a long time and requires complicated conditions. Kim et al. reported
an in situ method for producing photonic balls, without the need of a
diffusion process, using optofluidic devices composed of a monodisperse
emulsion generator and a UV exposure unit [30,31].