Mechanical vibrations of carbon nanotube-based mass sensors: an analytical approach

The purpose of this paper is to examine the potential of single-walled carbon nanotubes as mass sensors by developing analytical expressions and then comparing the outcome with structural mechanics corresponding predictions.

The carbon nanotube (CNT) resonators are assumed to be either single or double clamped. Analytical formulas capable of describing the vibrational behavior of such CNT-based nanoresonators with an attached mass at nanotube tip or various intermediate positions are developed by combining the Euler–Bernoulli theory and Krylov–Duncan functions.

The validity and the accuracy of these formulas are examined for a wide range of cases via comparisons with corresponding results arisen by spring- or beam-based structural mechanics predictions. Both structural mechanics approaches utilize three-dimensional nanoscale elements formulated according to the molecular theory. The results indicate that the new sensor equations may be utilized for the estimation of vibration response of CNT-based mass sensors with reasonable accuracy.

Simple analytical formulas are proved to approximate the mass sensing ability of CNTs adequately, the fact that may significantly contribute in the effort of developing new sensor devices.