Facile "Pick-up" experiments and Monte Carlo simulations for the entanglement of tunable staple-like particles

TL;DR

This paper introduces simple experimental and computational methods to measure and predict the entanglement of staple-like particles, revealing how geometry influences entanglement strength and enabling the design of advanced tunable materials.

Contribution

It presents a novel pick-up test, a geometrical entanglement model, and a Monte Carlo simulation to analyze and optimize entanglement in staple-like particles.

Findings

Entanglement is highly sensitive to backbone thickness.

The model accurately predicts entanglement density.

Designs can be optimized for maximum entanglement.

Abstract

Entangled matter provides intriguing perspectives in terms of deformation mechanisms, mechanical properties, assembly and disassembly. However, collective entanglement mechanisms are complex, occur over multiple length scales, and they are not fully understood to this day. In this report, we propose a simple pick-up test to measure the entanglement in staple-like particles with various leg lengths, crown-leg angles, and backbone thickness. We also present a new "throw-bounce-tangle" model based on a 3D geometrical entanglement criterion between two staples, and a Monte Carlo approach to predict the probabilities of entanglement in a bundle of staples. This relatively simple model is computationally efficient and it predicts an average density of entanglement which is consistent with the entanglement strength measured experimentally. Entanglement is very sensitive to the thickness of the backbone of the staples, even in regimes where that thickness is a small fraction (<0.04) of the other dimensions. We demonstrate an interesting use for this model to optimize staple-like particles for maximum entanglement. New designs of tunable "entangled granular metamaterials" can produce attractive combinations of strength, extensibility, and toughness that may soon outperform lightweight engineering materials such as solid foams and lattices.