Thermal crumpling of perforated two-dimensional sheets

Abstract

Thermalized elastic membranes without distant self-avoidance are believed to undergo a crumpling transition when the microscopic bending stiffness is comparable to $kT$, the scale of thermal fluctuations. Most potential physical realizations of such membranes have a bending stiffness well in excess of experimentally achievable temperatures and are therefore unlikely ever to access the crumpling regime. We propose a mechanism to tune the onset of the crumpling transition by altering the geometry and topology of the sheet itself. We carry out extensive molecular dynamics simulations of perforated sheets with a dense periodic array of holes and observe that the critical temperature is controlled by the total fraction of removed area, independent of the precise arrangement and size of the individual holes. The critical exponents for the perforated membrane are compatible with those of the standard crumpling transition.

arXiv comment10 pages, 12 figures. Version accepted for publication in Nature Communications

References in corpus (24)

• Intrinsic ripples in graphene
• Strong scaling of general-purpose molecular dynamics simulations on GPUs
• Two-Dimensional Matter: Order, Curvature and Defects
• Self-Consistent Theory of Polymerized Membranes
• The Effect of Intrinsic Crumpling on the Mechanics of Free-Standing Graphene
• The Statistical Mechanics of Membranes
• Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene
• Crumpling transition and flat phase of polymerized phantom membranes
• Scaling behavior and strain dependence of in-plane elastic properties of graphene
• Response of thermalized ribbons to pulling and bending
• The Flat Phase of Crystalline Membranes
• The Structure of Physical Crystalline Membranes within the Self-Consistent Screening Approximation
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
• Thermal fluctuations of free standing graphene
• Non-Hookean statistical mechanics of clamped graphene ribbons
• High Precision Fourier Monte Carlo Simulation of Crystalline Membranes
• Nonlocal effective average action approach to crystalline phantom membranes
• The Critical Exponents of Crystalline Random Surfaces
• First-order phase transition of fixed connectivity surfaces
• Polymerized Membranes, a Review
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• M.C.R.G. Study of Fixed-connectivity Surfaces
• Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes
• Stiffening Thermal Membranes by Cutting

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• Wrapping liquids, solids, and gases in thin sheets
• Thermal buckling and symmetry breaking in thin ribbons under compression
• Buckling and metastability in membranes with dilation arrays
• Disorder-induced rippled phases and multicriticality in free-standing graphene
• Spontaneous tilt of single-clamped thermal elastic sheets
• Anomalous thermal expansion in Ising-like puckered sheets
• Deformation of graphene sheet: Interaction of fermions with phonons
• Vibrations and tunneling of strained nanoribbons at finite temperature
• Folding pathways to crumpling in thermalized elastic frames
• Percolation and Dissolution of Borromean Networks
• Lifting map for ordered surfaces
• Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets