Statistical mechanics and entropic repulsion of nanoscale origami

Origami is a kind of scale invariant paradigm for morphing robotics, deployable structures, and metamaterials with tunable thermal, mechanical, or electromagnetic properties. There has been recent interest in using origami principles, along with DNA or graphene (among other materials), to design a wide array of nanoscale devices. However, to properly understand the behavior of these origami-based nanodevices, one must consider the interplay of the geometric mechanics of origami with thermal fluctuations, steric repulsion, van der Waals attraction, and other molecular-scale phenomena. Here we develop a model for the statistical mechanics of folded molecular sheets by drawing inspiration from past work on entropic pressure between biological membranes. We use the model to investigate 1) the thermodynamic multistability of molecular origami structures (i.e. multiple local minima of free energy) and 2) the rate at which thermal fluctuations drive its unfolding–that is, its temporal stability. We find that 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 temperature, and its interfacial energy (between folded layers). We conclude with a brief discussion of how, given a material of interest, the fold pattern may be designed towards transforming nanostructures or molecular origami nanocomposites.