The spontaneous emergence of ordered phases in crumpled sheets

TL;DR

This study uses X-ray tomography to analyze crumpled aluminum sheets, revealing spontaneous ordered domains near the surface and core, with properties evolving as the sheet becomes more compact.

Contribution

It introduces an algorithm to trace labyrinthine paths in 3D crumpled sheets and uncovers spontaneous ordering phenomena during crumpling.

Findings

Ordered domains grow with compaction

Domain orientation varies with position

Spontaneous symmetry breaking observed

Abstract

X-ray tomography is performed to acquire 3D images of crumpled aluminum foils. We develop an algorithm to trace out the labyrinthian paths in the three perpendicular cross sections of the data matrices. The tangent-tangent correlation function along each path is found to decay exponentially with an effective persistence length that shortens as the crumpled ball becomes more compact. In the mean time, we observed ordered domains near the crust, similar to the lamellae phase mixed by the amorphous portion in lyotropic liquid crystals. The size and density of these domains grow with further compaction, and their orientation favors either perpendicular or parallel to the radial direction. Ordering is also identified near the core with an arbitrary orientation, exemplary of the spontaneous symmetry breaking.