Physical Society Colloquium
Jammed Ellipsoids Beat Jammed Spheres:
Experiments with
Colloids and Candies
Paul Chaikin
Princeton University
Packing problems, how densely objects can fill a volume, are among the most
ancient and persistent problems in mathematics and science. For equal
spheres, it has only recently been proved that the face-centered cubic
lattice has the highest possible packing fraction φ ~ 0.7404. It is also
well-known that the corresponding random (amorphous) jammed packings have φ
~0.64. The density of packings in lattice and amorphous forms is intimately
related to the existence of liquid, liquid crystal and crystal phases and
is responsible for their melting transitions.
For colloidal architecture there is great flexibility if we use
non-spherical particles as building blocks. The first step is to understand
how such systems densely pack. Here we show experimentally and with
simulations that ellipsoids can randomly pack more densely than spheres; up
to φ ~0.68 - 0.71 for spheroids with an aspect ratio close to that of
M&M® Candies. General ellipsoids approach φ ~0.75 exceeding the
crystalline packings of spheres. We suggest that the higher density relates
directly to the higher number of degrees of freedom per particle,
f. We
support this claim by measurements of the number of contacts per particle
Z, obtaining Z ~10 for our M&M® Candies as compared to Z ~ 6 for spheres.
This is consistent with the isostatic conjecture for granular materials,
that Z=2f. We have also found the ellipsoids can be packed in a crystalline
array to a density, φ ~.7707 which exceeds the highest previous packing.
Results on spherical and lithographically prepared disk-like colloids,
their thermodynamics and their control with electric and light fields will
also be presented.
Friday, December 12th 2003, 13:00
Ernest Rutherford Physics Building, Keys Auditorium (room 112)
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