Page 136 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Colloidal Photonic Crystals 115

prepared inside capillary tubes of different diameters. Because the
crystals exhibit a curved (111) plane of the fcc structure through the
cylindrical surface, their photonic bandgap properties are independent
of the crystal rotation along the axis of the cylinder. From Fig. 6-2e,
we can find the invariability of the reflectance spectra taken from
cylindrical colloidal crystals with rotation.
The aforementioned study on evaporation-induced crystalliza-
tion in a capillary is very meaningful because today’s microfluidic
devices are based largely on soft lithography. In addition, this method
offers several advantages, such as high-quality crystallinity and ease
of shaping. However, evaporation-induced crystallization also has
some intrinsic shortcomings. The principal problem is the long pro-
cessing time. Since evaporation occurs only at the small exit of the
capillary, several hours are required for crystallization to take place
over the whole capillary length. Also, it is impossible to fabricate col-
loidal crystals only at a desired location. This is because the colloids
begin to crystallize from the open end of the capillary. Moreover,
highly concentrated colloidal suspensions are required because the
volume shrinkage of the process is very large.

Centrifugal-Force-Induced Crystallization
Researchers have tried to solve the problems mentioned earlier
related to crystallization in capillaries. Lee et al. first succeeded in
accelerating the colloidal crystallization in microchannels using a
centrifugal force [20]. To do this, they designed a centrifugal micro-
fluidic device containing multiplex microfluidic chips in a disc. While
the conventional evaporation process requires several hours for crys-
tallization to occur, it is possible to crystallize the colloids within sev-
eral minutes using the centrifugal system. The quality and properties
of the centrifugally crystallized colloidal crystals are similar to those
of the crystals obtained using the evaporation process. Figure 6-3a
shows colloidal-crystal patterns incorporated into a microfluidic chip
under a centrifugal force field.
When a centrifugal chip rotates, a force balance can be achieved
between the centrifugal and capillary forces in the microfluidic chan-
nels. The centrifugal force pushes the suspension radially outward
whereas the capillary force holds the solvent inside the channels. Col-
loidal particles dispersed in the stationary suspension precipitate in
the radial direction. The capillary force depends on the surface ten-
sion, γ, and the hydraulic diameter, D , which is usually 4 times the
H
cross-sectional area divided by the wetted perimeter of the channel.
The centrifugal and capillary forces are in balance up to a certain
radial frequency:

Δ=
ρωrr a ⎛ 4 γ ⎞ ⎟ + b (6-1)
⎜
D ⎠
⎝
H