Thermal stiffening of clamped elastic ribbons

Abstract

We use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic membrane clamped at both ends. We directly extract the eigenmodes from resonant peaks in the frequency domain of the time-dependent height and measure the dependence of the corresponding eigenfrequencies on the microscopic bending rigidity of the membrane, taking care also of the subtle role of thermal contraction in generating a tension when the projected area is fixed. At finite temperatures we show that the effective (macroscopic) bending rigidity tends to a constant as the bare bending rigidity vanishes, consistent with theoretical arguments that the large-scale bending rigidity of the membrane arises from a strong thermal renormalization of the microscopic bending rigidity. Experimental realizations include covalently-bonded two-dimensional atomically thin membranes such as graphene and molybdenum disulfide or soft matter systems such as the spectrin skeleton of red blood cells or diblock copolymers.

7 pages, 5 figures

References in corpus (12)

• Strong scaling of general-purpose molecular dynamics simulations on GPUs
• Virus shapes and buckling transitions in spherical shells
• Graphene as an electronic membrane
• Crumpling transition and flat phase of polymerized phantom membranes
• Suppression of anharmonicities in crystalline membranes by external strain
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
• Thermal fluctuations of free standing graphene
• Fluctuating shells under pressure
• Buckling transition in icosahedral shells subjected to volume conservation constraint and pressure: relations to virus maturation
• Non-Hookean statistical mechanics of clamped graphene ribbons
• Fourier Monte Carlo Renormalization Group Approach to Crystalline Membranes
• Effects of scars on crystalline shell stability under external pressure

Cited by in corpus (11)

• Buckling of thermalized elastic sheets
• Thermalized buckling of isotropically compressed thin sheets
• Thermal buckling transition of crystalline membranes in a field
• Hydrodynamic charge and heat transport on inhomogeneous curved spaces
• Spontaneous tilt of single-clamped thermal elastic sheets
• Anomalous thermal expansion in Ising-like puckered sheets
• Vibrations and tunneling of strained nanoribbons at finite temperature
• Semi-implicit methods for the dynamics of elastic sheets
• Curvature as an external field in mechanical antiferromagnets
• Emergent dynamic stress regulators via coordinated thermal fluctuations and stress in harmonic crystalline lattices
• A molecular dynamics simulation of thermalization of crystalline lattice with harmonic interaction