Vibration of a carbyne nanomechanical mass sensor with surface effect

Abstract

This paper presents a comprehensive model to investigate the influence of surface elasticity and residual surface tension on the natural frequency of flexural vibrations of nanomechanical mass sensor using a carbyne resonator. Carbyne is modeled as an equivalent continuum circular cross-section Timoshenko nanobeam including rotary inertia and shear deformation effects. Surface stress and surface elasticity are presented via the Young–Laplace equation. The analytical solution is presented and verified with molecular dynamics solution. The results show that the carbyne resonator can measure a very small mass with weight below 10−3 zg. The effects of surface elasticity, residual surface tension, carbyne length, and mass position on the fundamental frequencies are illustrated. This study is helpful for characterizing the mechanical behavior of high-precision measurement devices such as chemical and biological sensor.