Page 128 - Optofluidics Fundamentals, Devices, and Applications

108 Cha pte r S i x

6-1 Introduction to Colloidal Crystals

6-1-1 Colloids and Colloidal Photonic Crystals
The term “colloid”—which means “glue” in Greek—was first used
by Thomas Graham in 1861 to describe materials that could not
penetrate through a membrane. Today, the word “colloid” is used to
denote particulates, with sizes between 1 nm and 10 μm, dispersed
in an immiscible continuous phase [1]. Therefore, an unlimited
number of materials—ranging from sand and clay to micelles and
carbon black—can be classified as colloids. The dispersion stabilities
and rheological properties of such materials have been widely
studied during the last two centuries. Recent advances in colloidal
synthesis have accelerated the study of colloids—not only for their
monodispersity, but also because many properties of the colloidal
particles, including density, surface charge, and material affinity,
can be controlled by varying the synthetic scheme. Even the design
of particles with anisotropic shapes, internal structures, or chemical
patterns can be achieved [2]. Based on colloidal particles with
controlled properties, the crystallization into various lattices has
been studied for two main applications, namely, the attainment of
“visible” models for atomic or molecular assemblies and the devel-
opment of photonic bandgap materials. Monodisperse colloidal
particles with high surface charge density dispersed in a polar
medium spontaneously form non-close-packed crystals, a process
that is induced by the repulsive interparticle potential. Depending
on the volume fraction of the colloids and the strength of the
repulsion, the particles appear as either face-centered cubic (fcc) or
body-centered cubic (bcc) structures in the thermodynamic equilib-
rium [3,4]. On the other hand, bidisperse colloidal systems with
oppositely charged colloids enable the preparation of various crystal
lattices, which have many similarities with atomic or molecular
systems, although the valences of atoms are not consistent with
those of colloidal systems [5,6]. In addition to these similarities in
regard to the formation of crystals, bandgap properties are also
observed in both atomic and colloidal crystals. At the atomic scale,
because crystals exhibit a periodic modulation of the potential for
the propagation of electrons, they may affect the conductivity of the
electrons and sometimes even prevent their propagation at certain
energy levels. It is well known that semiconductors have an
electronic bandgap between the valence and conduction bands.
Analogously, if the periodicity of a colloidal crystal lattice is
comparable to the wavelength of light, the lattice will interact with
the electromagnetic waves and induce a photonic bandgap. Photons
with energy in this gap cannot propagate through the crystal. In this
case, the crystal is a “photonic crystal” [7].