Vibration analysis of double wall carbon nanotube based resonators for zeptogram level mass recognition

A study of vibrational characteristics of double walled carbon nanotube modeled using spring elements and lumped masses has been performed. The inner and outer walls of carbon nanotube are modeled as two individual elastic beams interacting each other by van der Waals forces. To simulate the interlayer interactions and describe the van der Waals potentials between carbon atoms on different layers appropriate spring elements are utilized. This paper also investigates the mass recognition characteristics of double walled carbon nanotubes using analytical and finite element procedure. The effect of changes in outer length of the nanotube has been investigated by simulations keeping the inner wall length as constant. The shift in the resonant frequencies corresponding to the attached mass and different boundary conditions has been analyzed. Comparison with other theoretical studies reveals very good correlations in terms of the fundamental frequencies. This investigation is helpful in the applications involving high frequency oscillators and sensors based on nano-electromechanical devices requiring controlled length of inner and outer tubes of double walled carbon nanotube.