Anomalous thermal expansion in Ising-like puckered sheets

Abstract

Motivated by efforts to create thin nanoscale metamaterials and understand atomically thin binary monolayers, we study the finite temperature statistical mechanics of arrays of bistable buckled dilations embedded in free-standing two-dimensional crystalline membranes that are allowed to fluctuate in three dimensions. The buckled nodes behave like discrete, but highly compressible, Ising spins, leading to a phase transition at $T_c$ with singularities in the staggered "magnetization," susceptibility, and specific heat, studied via molecular dynamics simulations. Unlike conventional Ising models, we observe a striking divergence and sign change of the coefficient of thermal expansion near $T_c$ caused by the coupling of flexural phonons to the buckled spin texture. We argue that a phenomenological model coupling Ising degrees of freedom to the flexural phonons in a thin elastic sheet can explain this unusual response.

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Cited by in corpus (5)

• Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells
• Thermal control of nucleation and propagation transition stresses in discrete lattices with non-local interactions and non-convex energy
• Self-Ordering of Buckling, Bending, Bumping Beams
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• Buckling in a rotationally invariant spin-elastic model