MANIPULATING COLLOIDAL CRYSTALLIZATION FOR PHOTONIC
APPLICATIONS: FROM SELF-ORGANIZATION TO DO-IT-YOURSELF
ORGANIZATION
ALFONS VAN BLAADEREN,‘.’ KRASSIMIR P. VELIKOV,’ JACOB P.
HOOGENBOOM,‘** DIRK L. J. VOSSEN,1.2 ANAND YETHIRAJ,‘.2 ROEL
DULLENS,’ TEUN VAN DILLEN, ALBERT POLMAN2
‘Condensed Matter Dept., Debye Inst., Utrecht. University, P. 0. Box 80000,
3508 TA Utrecht, The Netherlands
2FOM Inst. for Atomic and Molecular Physics, P.O. Box 41883, 1009 DB
Amsterdam, The Netherlands
A.vanBlaaderen@phys.ut&
INTRODUCTION
Photonic crystals are regular three-dimensional (3D) structures with which the
propagation and spontaneous emission of photons can be manipulated in new ways if the
feature sizes are roughly half the wavelength and the coupling with the electromagnetic
radiation is sufficiently strong. ‘Early’ speculation on these new possibilities can be found
in the Refs.l-4 A more recent overview can be found in Ref.5 and, of course, the other
chapters in this book. A useful analogy to guide thinking about the properties and the
applications of photonic crystals is the propagation of electrons in a semiconductor in
comparison to the propagation of photons scattered by a regular 3D dielectric material. An
example is the possibility of opening up a region of energy, a photonic band gap, for
which the propagation of photons is forbidden, in analogy to the electronic band gap
present in semiconductors. However, there are also important differences; for instance, the
scattering of photons cannot be described well by scalar wave equations because the
polarization of light cannot be neglected. Most theoretical and experimental work for
visible light applications have until now focused on pure dielectric structures,
interestingly, recent calculations have shown that metallo-dielectric structures should also
be considered as having very interesting photonic properties in the visible, including, if
one neglects absorption, a complete band gap.@ And even with absorption taken into
account, it seems that for relatively thin photonic crystals most of the interesting optical
properties remain.8
Because the feature sizes of photonic crystals need to be about half the wavelength of
the electromagnetic radiation of interest, the actual realization of such structures for near-
infrared and visible light is quite a challenge. In this paper we want to give an overview of
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C.M. Soukoulis (ed.). Phoronic Crysrois and Lighr Loco&&m in rhe 2Ist Cenrury, 239-25 I.
0 200 I Kluwer Academic Publishers. Primed in the Nerherlonds.
240
the methods we are currently investigating to achieve well-defined 3D structures with
submicron feature sizes by the manipulation of the self-organization of colloidal particles.
We will focus here primarily on colloidal crystals for which the inter-particle spacing is
close to the particle’s size, so the structures can be dried. This will allow for a large
dielectric contrast and also for the possibility to use the colloidal crystals as templates to
make so-called ‘inverse’ structures. This last process, recently reviewed in Ref.9, is not
-
part of the present paper, but it requires the same high quality crystals needed for photonic
crystals made directly from (metallo-)dielectric spheres. It is the present understanding
that only inverse structures of the colloidal crystal lattices can be easily made (like face
-
centered cubic, FCC) will have a complete band gap. However, the density-of-states can
also be modulated quite strongly in photonic crystals of high-index-core-shell systems.
Moreover, binary structures or other complex structures like 3D quasicrystals have hardly
been investigated and by removing one of the sphere sizes, by heating or dissolving them,
relatively low filling fractions can be obtained. In the case of metallo-dielectric spheres
the situation is reversed and the ‘reverse’ structures do not have a complete band gap,
while many crystalline symmetries of spherical particles in liquids have a complete band
gap.6-8
Before going into specific examples of the manipulation of colloidal crystallization,
we will first explain what we mean by the two terms:
colloidal
and
self-organization.
An
important aspect in the definition of what should be called a colloid or colloidal particle is
the fact that these particles, which can consist of macromolecules or other subunits,
undergo so-called Brownian motion. This erratic motion is the direct result of the not
completely averaged-out collisional effects of solvent molecules constantly hitting the
particle. Brownian motion ensures that a concentrated colloidal dispersion in which many
particles interact with each other can find a thermodynamically well-defined equilibrium
state. If certain criteria are met, such as the concentration of particles and a high
monodispersity (narrow width in the size distribution), these systems will spontaneously
form regular 3D structures or colloidal crystals completely analogous to molecular
crystals.tO~lt This kind of (mostly first-order) phase transition can be described by
statistical mechanics and we will use the possibility of such calculations as our definition
of ‘pure’ self-organization (SO). A self-organizing system thus organizes itself in a state
of lowest free energy. Therefore, shaking a box with ball bearings, even though the balls
under the right frequency and amplitude might arrange themselves on a lattice, is not
considered self-organization. 12 On the other end of the extreme, one has ‘do-it-yourself-
organization’ (DYO) where control over the kind of structures that can be made is highest,
but where no minimizing principle guides the organization of matter. Most methods used
in making integrated circuits, like lithography, are DYO and in most cases 3D structures
need to be built up in a layer-by-layer fashion. Although DYO methods offer great control,
they are generally slow, costly, and not easy to extend to many unit cells in three
dimensions because errors tend to accumulate. On the other hand, pure SO leads relatively
easily to larger 3D structures, but control over, e.g., crystal symmetry and orientation is
harder to achieve.
After a brief experimental section, we first will describe the kind of colloidal model
particles we are using, with reference to the literature on how these can be made and
characterized. Subsequently, we will give typical examples of how colloidal
crystallization can be manipulated. Manipulation is possible by playing with the boundary .
conditions, like crystallization against a corrugated wall or between two confining walls,
by using strong electric fields both at low frequencies and optical frequencies, by a flow
field and, even further away from equilibrium, by controlled drying. Finally, we will show
how high-energy heavy ion-irradiation can be used to deform inorganic photonic crystals
in a controlled way.
EXPERIMENTAL
As this paper is intended to give an ‘educational’ oversight of the projects being pursued
to manipulate colloidal crystallization, the experimental section is relatively short and
intended to give an idea on how the experiments were performed. For details we will refer
as much as possible to literature.
The seeded growth of fluorescent silica core-shell colloids and the particle
characterization by many different techniques (e.g., scanning and transmission
electronmicroscopy SEM, TEM and light scattering) is described in Refs.t3-l5 Very
monodisperse silica seed particles can be made by performing silica growth in a
microemulsion. Recently, the fluorescent core colloidal model system properties have
been extended by the development of a polymethylmethacrylate (PMMA) shell layer that
can both be density and index matched. 17 Other core-shell systems with nanocrystalline
and metal cores are briefly described in Refs. 15718 and references cited in that paper.
The fluorescently dyed PMMA templates used in the colloidal epitaxy studies were
made by electron beam lithography. 19 We also used particle templates made by optical
tweezers (see below).
The effects of electric fields of low frequencies were also studied using confocal
microscopy on matched fluorescent core-shell colloids. The colloids were imaged through
transparent tinindiumoxide electrodes, more experimental details are given in Ref.2o The
effects of a flow field on the structures generated in these electro-rheological fluids were
studied similarly as described by Amos et al. z1
Multiple time-shared optical tweezers were constructed as described by Visscher22
using opto acoustic modulaters to manipulate a 1064 nm cw laser beam. The set-up
constructed by us can be combined with confocal microscopy (Leica TCS). The positively
charged cover glasses were made as described in Ref.23 using a silane coupling agent (3-
aminopropyltriethoxysilane).
Controlled drying experiments were performed as given in Ref.24 using silica spheres
dispersed in ethanol.
Deformation by ion (Xe4+,
4 MeV) irradiation with fluences about 1014 ions/cm’ is
described in Ref. 25
RESULTS AND DISCUSSION
Core Shell Colloids
The colloidal particles used all have a core-shell geometry, with cores of metal (silver,
gold), a nano-crystal (e.g., ZnS or CdS), or a high index dielectric material (e.g., ZnS).
The shells used are made of silica or polymethylmethacrylate (PMMA) and both can be
covalently labeled with organic dyes. The advantage of using a core-shell approach is the
increase in flexibility in tuning both the optical properties and the interaction potential
between the colloidal particles. For instance, in the case of a high index core and a lower
index shell, like ZnS covered with silica, the high index filling fraction can be optimized
even when the spheres are touching and at the same time the strong Van der Waals forces
that would be present between pure ZnS particles can be reduced significantly.tO Further,
the core-shell approach allows a quite natural way of random doping of the photonic
crystals. An example is shown in Fig. 1 where a fluorescence scanning confocal
microscopy picture is shown of a solid solution of 10% larger fluoresceine labeled silica
spheres on the lattice positions of a crystal of rhodamine labeled spheres (diameter 950
242
nm). Although this particular example is not so interesting for photonic applications, it
does illustrate a general procedure in which photonic crystals can be ‘doped’ in a random
way by using core-shell systems. For instance, in the case of the synthesis of ‘air-sphere’
or ‘inverted’ photonic crystals where a colloidal crystal is used as template and the
particles are removed after deposition of other material by oxidation and heat or by
dissolving them, high dielectric material can be positioned on lattice positions (which
would normally be air) by using high-index core-shell particles. Also, in the reverse
situation where one would like to dope a photonic crystal of (metallo)dielectric spheres
with a ‘hole’ (low dielectric material), one could, for instance, use a latex sphere as dopant
and later bum it away, or one could make use of hollow particles as shown in Fig. 2.15.18
Figure 1.
Confocal
micrograph of a solid
solution of fluoresceine
labeled particles (white) on
a crystalline lattice of
rhodamine
labeled spheres
(bar 2 pm)
Figure
2. TEM picture of
hollow silica spheres (radius
60
nm) created after
dissolution of the ZnS cores.
Figure 3. TEM picture of
silica spheres made by
seeded growth were the
initial seeds were grown in a
microemulsion. Radius: 35
nm, relative width of the size
distribution: 2 %.
Manipulating Colloidal Crystallization: Colloidal Epitaxy
The ability to manipulate the boundaries of the container in which crystallization takes
place is a powerful way to steer the crystallization process. The reason for the increased
possibilities compared to the atomic world is directly related to the size of colloids.
Because colloids are so much larger than atoms, truly ‘atomically’ smooth walls can be
made easily. If the container walls are only several particle diameters away, then this
distance determines the crystal structure that will optimally fit. At high volume fractions
of particles the most important contribution to the free energy is the packing efficiency.
Not only can the orientation of the crystals be induced, but also new structures, like
buckling phases, have been found.26
Furthermore, making corrugations on container walls that are of the size of the
colloidal building blocks is also possible. We made use of such structured walls to
manipulate colloidal crystallization in ways which are very similar to epitaxial crystal
growth. By having the spheres slowly fall down through sedimentation on the template
and by heterogeneous nucleation at the wall, large crystals could be made. We have grown
large, pure face centered cubic (FCC) crystals from particles that interacted with an almost
hard-sphere potential both on non-close-packed (100) and (110) crystal faces. These
crystals could be grown mm’s thick (several thousand layers).‘9
.
Here we show the first results obtained by growing hard-sphere like colloidal crystals
onto a template with the (110) crystal face of a hexagonally-close-packed (HCP) crystal
(Fig. 4). The HCP colloidal crystal structure is meta-stable compared to FCC crystals for
particles with a hard-sphere potential and becomes even more unfavorable in free energy
243
for softer potentials. The free-energy difference between an FCC and HCP stacking for
hard-sphere-like potentials is quite small though (on the order of -lOA U/particle).27
However, as far as we know, a pure HCP crystal has not yet been observed. These results
not only open up the use of HCP colloidal crystals for photonic applications, but will also
allow a systematic study of the effects of stacking errors. Hard-sphere crystals have the
tendency not to crystallize in the thermodynamically most stable FCC form, but instead
with a random stacking sequence of close packed layers (ABC stacking is FCC, while ABA
is HCP). In the same way as this has been done with the HCP templating, it is also
possible to grow any desired stacking sequence!
Electrostatic repulsion on flat walls can also be used to influence colloidal
crystallization. Recently, 2D templates made with regions of opposite surface charge were
shown to direct 2D colloidal crystal formation. 28 Also non-close-packed structures could
be formed additionally using capillary forces in a similar way as described in the section
on controlled drying.
,
A
l3
Figure 4. Confocal micrographs of the first colloidal HCP crystal. a) (Dyed) PMMA template with
holes in the symmetry of the (110) HCP plane. b) 8 th (and vaguely 7th) layer of the HCP crystal
above the template. Sphere diameter 1.4 pm fluorescent core diameter 385 nm.
Manipulating Colloidal Crystallization: Electric Fields, Low Frequencies
Colloidal particles dispersed in a solvent with low conductivity and subjected to a
relatively high electric field (-1 V/pm) are called electro-rheological fluids because the
application of the field can turn the low viscosity dispersion, reversibly, into a solid with a
yield stress. By application of the field,
stron g dipolar interactions (tens of k7J arise
between the particles because of their dielectric mismatch (at zero frequency) with the
solvent and the particles form strings spanning the container size in milliseconds. For
photonic applications, far out-of-equilibrium structures where the interactions are many
times kT are not so interesting. When structures can form that are closer to equilibrium
(interactions only a few times kT), a lot of interesting possibilities for control are opened
up. In this regime of interactions the system can reach the lowest free energy
configuration. We have recently shown experimentally that this is (most likely) a body
centered tetragonal (BCT) crystal. 20 An energy calculation29 had already shown that this
structure has a lower energy than an FCC crystal, and, furthermore, it has been found in
computer simulations.30 However, a full free energy calculation, including entropy, has
not been done. In addition we found an interesting metastable sheet-like configuration that
formed from the strings of particles and that slowly turned into the BCT crystals (see also
the figures in the section on flow).20
In the same work we have also shown that if the initial charge stabilized dispersion is
made concentrated enough that an FCC colloidal crystal is formed, it can be switched
through a martensitic crystal transition from FCC into BCT. Moreover, without a field the