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| Think about a pile of sand. When you shake the sand, the sand moves, right? However, if you increase the shaking frequency, at some point the sand freezes: the particles are stuck in place and do not move in response to the shaking. This is one example of a granular (athermal, repulsive) jammed system. Other examples of jammed states include: a traffic jam; flow jams (such as grains stuck in a pipe). Jamming is well-studied in granular materials. Experiments showed that the forces are propagated through a jammed granular system in linear chains, called force chains. |
We study a colloidal model system with volume fractions greater
than 0.49 (the hard-sphere glass transition occurs at a volume
fraction of roughly 0.58).
We want to try to study "slow" structures inside dense glasses,
both with and without depletion. How do we define "slow"? What sorts
of structures do slow particles form? The current definition that
we're studying is topological and dynamic (and inspired by a paper by
Doliwa and Heuer, e-print cond-mat/0210121 (2002)). We identify (using a Voronoi algorithm)
the nearest neighbors of each particle at each time. We then
calculate the change in number and identity of nearest neighbors as a
function of lag time. We define a particle as slow over a time
lag when the number and identify of its nearest neighbors do not
change over that timelag.
| This is a two-dimensional snapshot of my sample, from the confocal microscope. Each small colloidal particle is roughly two microns in diameter. Using the confocal, we can take many of these two-dimensional pictures at different heights through the sample, and then locate and track the particles using the IDL routines developed by David Grier, John Crocker, and Eric Weeks, to track our particles. After processing we have a list of particle positions, times, and ID numbers. |
| The first sample is a colloid-only sample at volume fraction 0.52; this is in the liquid-crystal coexistence regime of the phase diagram. The lag time is 1026 seconds. The highlighted particles are those with no nearest neighbor changes in this time; the different colors correspond to different nearest-neighbor clusters. (More active particles are small and green.) Note that for this sample there is a percolating cluster of slow particles. |
| One timestep (18 seconds) later, the largest cluster of slow particles no longer spans the system. The time for breakup of the largest slow cluster in the liquid sample is roughly 1000 seconds. |
| The second sample is a supercooled fluid at volume fraction 0.56. The highlighted particles are particles which are slow by the above definition over a timestep of 3600 seconds. At this timestep, the largest slow cluster percolates. |
| One timestep (18 seconds) later, the percolating supercooled fluid sample has broken up. |
| The third sample is a glass at volume fraction 0.56. The highlighted particles are particles which are slow by the above definition over an entire experiment, a timestep of 39,000 seconds. At this timestep, the largest slow cluster percolates. Over the experimentally accessible timescales, this percolating cluster never breaks up! |
| In the top plot, we plot the average Voronoi volume for particles in non-rearranging clusters versus the lag time. Solid symbols: average Voronoi volume of non-rearranging particles; open symbols: average Voronoi volume of other particles. For all volume fractions studied, the particles that we identify as non-rearranging have smaller local volumes than the other particles in the suspension. In the bottom plot, we plot the average number of particles in a system-spanning cluster of non-rearranging particles, versus the lag time. This gives us a measure of the characteristic time for spanning cluster breakup. Below the glass transition, this timescale increases as the volume fraction increases; above the glass transition we do not observe spanning cluster breakup. |
How can we further characterize the structure of these slow, percolating networks? Are these clusters fractal? Can we measure a correlation length for these networks? Can we think of these slow networks in terms of the jamming picture of Liu and Nagel?
We've started some basic experiments to look at gravitationally-stressed colloids. (Link forthcoming.)