Temperature-dependent critical buckling strains and elastic constants in thermalized nanoribbons

Studies of buckling and instabilities of thin plates date back more than two centuries. However, stability predictions, such as for the critical buckling load, can be dramatically altered for nanomembranes (e.g., graphene) when thermal fluctuations become important. We study, using theory and simulations, thin ribbons under longitudinal compressions and an out-of-plane perturbing field at a wide variety of temperatures. We find that the buckling behavior, obtained via molecular dynamics, can be described by a mean-field theory with renormalized elastic constants when the ribbon length is shorter than the persistence length. The ribbon mechanics become temperature dependent with Young’s modulus Y ∝ T^-η_u/2, bending rigidity κ ∝ T ^η/2, and critical strain ε_c ∝ T ^(η+η_u)/2 where η = 0.67(18) and η_u = 0.41(10). These buckling exponents are close to theoretical predictions and numerical simulations normally obtained via Fourier analysis of height fluctuations of a stress-free membrane.