Thermal fluctuations (eventually) unfold nanoscale origami

Abstract

Origami is a scale invariant paradigm for morphing robotics, deployable structures (e.g. satellites, disaster relief shelters, medical stents), and metamaterials with tunable thermal, mechanical, or electromagnetic properties. There has been a resurgence of interest in using origami principles – along with 2D materials or DNA – to design a wide array of nanoscale devices. In this work, we take cognizance of the fact that small-scale devices are vulnerable to entropic thermal fluctuations and thus a foundational question underlying small-scale origami pertains to its stability, i.e. the origami structure’s propensity to “unfold” due to thermal fluctuations and the rate at which the unfolding will ensue. To properly understand the behavior of these origami-based nanodevices, we must simultaneously consider the geometric mechanics of origami along with the interplay between thermal fluctuations, entropic repulsive forces, van der Waals attraction, and other molecular-scale phenomena. In this work, to elucidate the rich behavior underpinning the evolution of an origami device at the nanoscale, we develop a minimal statistical mechanics model of folded nanoscale sheets. We use the model to investigate (1) the thermodynamic multistability of nanoscale origami structures and (2) the rate at which thermal fluctuations drive its unfolding—that is, its temporal stability. We identify, for the first time, an entropic torque that is a critical driving force for the unfolding process. Both the thermodynamic multistability and temporal stability have a nontrivial dependence on the origami’s bending stiffness, the radii of curvature of its creases, the ambient temperature, its thickness, and its interfacial energy (between folded layers). Specifically, for graphene, we show that there is a critical side length below which it can no longer be folded with stability; similarly, there exists a critical crease diameter, membrane thickness (e.g. for multilayer graphene), and temperature above which a crease cannot be stably folded. To investigate the rate of thermally driven unfolding, we extend Kramers’ escape rate theory to cases where the minima of the energy well occurs at a boundary. Rates of unfolding are found to span from effectively zero to instantaneous, and there is a clear interplay between temperature, geometry, and mechanical properties on the unfolding rate.