Entanglement transition in rod packings

Kavli Affiliate: L. Mahadevan

| First 5 Authors: Yeonsu Jung, Thomas Plumb-Reyes, Hao-Yu Greg Lin, L. Mahadevan,

| Summary:

Random packings of stiff rods are self-supporting mechanical structures
stabilized by their geometrical and topological complexity. To understand why,
we deploy X-ray computerized tomography to unveil the structure of the packing.
This allows us to define and directly visualize the spatial variations in
"entanglement," a mesoscopic field that characterizes the local average
crossing number, a measure of the topological complexity of the packing. We
show that the entanglement field has information that is distinct from the
density, orientational order, and contact distribution of the packing. We find
that increasing the aspect ratio of the constituent rods in a packing leads to
an abrupt change in the entanglement, correlated with a sharp transition in the
mechanical response of the packing. This leads to an entanglement phase diagram
for the mechanical response of dense rod packings that is likely relevant for a
broad range of problems that goes beyond our specific study.

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