Page 146 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Colloidal Photonic Crystals 123

If the colloidal particles confined in an emulsion droplet interact
with each other (with a repulsive potential), they can form spherical
non-close-packed crystals, thereby retaining the droplet volume.
Especially, if the emulsion phase is photocurable, the spherical
crystals can be captured by UV irradiation within a second. To achieve
this, silica particles dispersed in a highly polar photocurable resin
with a similar refractive index are used. Due to the diminishing van
der Waals attractions by index matching, the repulsive potential
dominates. This can be induced by either solvation films generated
on the particle surface or electrostatics; thus, the particles adopt a
polycrystalline form in suspension [32,33]. To generate monodisperse
emulsion droplets, microfluidic devices composed of coaxial inner
and outer glass capillaries are prepared. As inner and outer flows,
the silica suspension and a surfactant-loaded aqueous solution are
introduced using syringe pumps. If the outer flow is faster than the
inner one, the monodisperse suspension droplets are generated in
the dripping regime, without jetting. In this regime, the size and
generation frequency of the droplets are determined by the outer
and inner flow rates, respectively. Because the drag force by the
outer flow and the capillary force by the inner tip are balanced at
every moment during droplet generation, the size of the droplet can
be estimated using the following equation:
3πμ(d − d )(v − v ) ~ πd γ (6-3)
drop tip outer inner tip
in which the drag force given by the Stokes equation is modified due
to screening by the inner capillary. Here, μ, d , d , v , v , and γ
drop tip outer inner
are the viscosity of the continuous phase, the droplet diameter, the
inner-tip diameter, the velocities of the outer and inner flows, and the
interfacial tension, respectively [34].
As shown in Fig. 6-5a, the generated droplets are photopoly-
merized downstream by UV irradiation. The solidified emulsion
droplets show Bragg diffraction colors which depend on the particle
diameter and the volume fraction. Because the repulsive potential
induces crystallization, the volume fraction of particles determines
the lattice constant. The wavelength of the reflection color for normal-
incident light on the (111) plane can be estimated by Bragg’s law:

/
/
⎛ π ⎞ 13 12 1//2
λ = ⎜ ⎟ ⎛ ⎞ 8 2 φ + n 2 1 ( − φ) ) (6-4)
⎜ ⎟ ( d n
⎝32 φ⎠ ⎝ ⎠ 3 p m
This equation assumes a constant interparticle distance, with all
the nearest neighbors within a given volume fraction and d, φ, n ,
m
and n being the diameter and volume fraction of the particles, and
p
the refractive indices of the matrix and the particle, respectively.
Figure 6-5b shows an arrangement of silica beads confined in droplets