In monodisperse hard-sphere
systems, as volume fraction is increased, crystalline phases are
found, and at higher volume fraction still, glass-like behavior
is observed. When two different radii of particles are mixed together
similar behavior is observed, but the phase diagram is much richer,
and includes several different crystal structures. For these
crystalline phases, the most complete
phase diagram and structural work has been done by
Andrew Schofield at University of Edinburgh.
The focus of our work on these systems has been to observe how crystallization occurs. With entropy the only determining factor, and several very complex crystal structures formed, the question is: how does the system find its equilibrium state? We have focused our attention on two particular crystal structures:
AB6 BCC is a body centered cubic structure of large particles with small
particles arranged into squares on each face. This is the fastest growing
binary crystal structure, which at its fastest, crystallizes nearly completely
overnight. The ideal size ratio for this structure is 0.4, and it is a
remarkably stable structure, despite the fact that the sodium cloride AB
structure has a higher packing fraction at this size ratio. The bulk of our crystallization studies have been on this structure.
AB13 is a simple cubic structure of
large particles with an icosahedra of small particles at the center.
Icosahedra in neighboring unit cells align their faces perpendicularly
to each other, forming a superlattice unit of eight simple cubic units.
Much of the work so far on the kinetics of crystallization for these two structures has been done on the International Space Station as part of the Physics of Colloids in Space program. That work has revealed a need for local measurements of the microscopic properties.
To this end, we have developed binary crystal samples for use in the confocal microscopy. In order to study the crystallization kinetics without interference from gravity, it is important that the samples be accurately density matched. This, combined with the use of fluorescent dyes necessary to image particles in the confocal microscope, makes it difficult to retain truly 'hard-sphere' properties. However, we have managed to create dyed samples which crystallize AB6 BCC on a time scale much shorter than the time necessary to settle under gravity.
We analyze the data by finding the particle centers from the intensity profiles in a stack of images. Crystalline particles are then identified from their nearest neighbor configurations using either a spherical- harmonic based algorithm, or voronoi analysis. The development of crystallites can then be tracked as a function of time after a sample has been mixed.
There are two distinct general behaviors that we see in the nucleation
and growth of the crystals. In some samples, which take a longer time
to crystallize and may be at higher volume fraction, a low nucleation
density is observed and crystallites seem to grow independently of one
another (left). In other samples, which crystallize more rapidly, a
higher nucleation density is observed, and crystallites are observed
to interact at very early times while nucleation is still occurring (right).
When the nucleation density is low, the development of individual clusters
can be tracked independently, yielding information about the critical
nucleation size and the growth law of the crystals. However, since there
are few crystallites in a field of view, statistics for these quantities
can be very poor!
When the nucleation density is high, and cluster-cluster interactions
are frequent, cluster tracking is difficult,
and has to correlate with local crystal lattice ordering. I am working
on writing cluster tracking algorithms which will allow consistent tracking,
keeping track of the local crystal lattice.
Johan Mattsson and I have been working on making ellipsoidal particles so
we can watch their ordering behavior and use them as tracer particles for
rotational motion. We are doing this by embedding polystyrene particles in
a film of polyvinyl alcohol and then stretching the films at high temperatures.
These are some pictures of our initial attempts. On the left is at a film aspect
ratio of around 1.25 (picture includes many spherical particles which were not
stretched, it's like a where's Waldo...see if you can spot the ellipsoids!), the picture on the right had an aspect ratio closer to 2.
Manouk, Dan, and I have been working on studying nucleation of colloidal crystals off of a cylindrical surface. It has long been known that layering induced nucleation occurs in colloidal suspensions near a flat interface, and recently, Daan Frenkel (Nature 428, p.404, March 25, 2004) has shown nucleation and detachment events from spherical surfaces with radius of curvature greater than 10 times the particle radius. So, we have been working with the intermediate case: glass micro-pipettes coated with PMMA and PHSA with a taper from one to many hundreds of times the particle radius. Stay tuned for the results of this one!