Optimal Number of Faces for Fast Self-Folding Kirigami

TL;DR

This paper investigates how the number of faces affects the speed of spontaneous self-folding in microscopic kirigami structures, revealing an optimal face count for fastest folding due to competing stochastic processes.

Contribution

It combines simulations and analytical models to explain the non-monotonic relationship between face number and folding time, highlighting the roles of 2D and 1D first-passage processes.

Findings

Folding time is minimized at five faces.

First edge closure follows a 2D first-passage process.

Subsequent closures follow 1D first-passage processes, growing logarithmically.

Abstract

We study the spontaneous folding of a 2D template of microscopic panels into a 3D pyramid, driven by thermal fluctuations. Combining numerical simulations and analytical calculations, we find that the total folding time is a non-monotonic function of the number of faces, with a minimum for five faces. The motion of each face is consistent with a Brownian process and folding occurs through a sequence of irreversible binding events that close edges between pairs of faces. The first edge closing is well-described by a first-passage process in 2D, with a characteristic time that decays with the number of faces. By contrast, the subsequent edge closings are all first-passage processes in 1D and so the time of the last one grows logarithmically with the number of faces. It is the interplay between these two different sets of events that explains the non-monotonic behavior. Implications in the self-folding of more complex structures are discussed.