Interrelation of Elasticity and Thermal Bath in Nanotube Cantilevers.

We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65) ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.

High-frequency gas effusion through nanopores in suspended graphene.

Porous, atomically thin graphene membranes have interesting properties for filtration and sieving applications. Here, graphene membranes are used to pump gases through nanopores using optothermal forces, enabling the study of gas flow through nanopores at frequencies above 100 kHz. At these frequencies, the motion of graphene is closely linked to the dynamic gas flow through the nanopore and can thus be used to study gas permeation at the nanoscale. By monitoring the time delay between the actuation force and the membrane mechanical motion, the permeation time-constants of various gases through pores with diameters from 10-400 nm are shown to be significantly different. Thus, a method is presented for differentiating gases based on their molecular mass and for studying gas flow mechanisms. The presented microscopic effusion-based gas sensing methodology provides a nanomechanical alternative for large-scale mass-spectrometry and optical spectrometry based gas characterisation methods.

Nonlinear dynamic characterization of two-dimensional materials.

Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's material properties has remained elusive. Here we show a method for determining the Young's modulus of suspended 2D material membranes from their nonlinear dynamic response. To demonstrate the method, we perform measurements on graphene and MoS2 nanodrums electrostatically driven into the nonlinear regime at multiple driving forces. We show that a set of frequency response curves can be fitted using only the cubic spring constant as a fit parameter, which we then relate to the Young's modulus of the material using membrane theory. The presented method is fast, contactless, and provides a platform for high-frequency characterization of the mechanical properties of 2D materials.