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 Tc 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 Tc 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.

Frustrating frustration in snap-induced morphing

“…This difference comes from the fact that the region over which the compression applies scales also with λ s , rather than being determined by external tensions that are independent of B (or λ s ) as in standard buckling problems [34,35,37]. We note that the buckling instability observed here is also different to the, ostensibly similar, problem of dilations in a lattice for which spherical or saddle-like deformations are observed depending on whether the dilation is positive or negative, respectively [19,38].…”