Electromechanical vibration of carbon nanocoils Chenghao Deng, Lujun Pan * , He Ma, Ruixue Cui School of Physics and Optoelectronic Technology, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, PR China ARTICLE INFO Article history: Received 27 June 2014 Accepted 9 October 2014 Available online 14 October 2014 ABSTRACT A straightforward method for measuring Young’s modulus of single carbon nanocoils (CNC) is proposed. Acting as a 1D nano-oscillator, a CNC cantilever was stimulated to vibrate under an alternating electric field. Using a classical continuum model, a formula that accounts for the frequency response of vibration was deduced, and this formula was used to accurately determine the resonance frequency of the CNC. Young’s modulus was calcu- lated from the resonance frequency using a theory based on material mechanics. It was found that Young’s modulus increased in the longitudinal direction of the coils both in the vibrating and tensile measurements, which resulted from the decline of graphitization during the growth of the CNCs. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Due to their high resonance frequencies, high quality factors and tiny size, nanomaterials are widely used in nanoelectro- mechanical systems (NEMS), such as in mass sensing [1,2], force measurements [3], resonator infrared sensors [4], and cantilever based ultrahigh-frequency applications [5,6]. As an outstanding member of the nanomaterial family, carbon nanotubes (CNT), which are extremely high in stiff- ness and small in size [7–9], have been used in NEMS [2,10,11]. Young’s modulus of CNTs has been measured and calculated to be as high as 1 TPa [12–15]. However, similar to most 1D nano-oscillators, the inextensible geometry of CNTs limits their behavior, which has led to the development of 3D helical nanostructure-based NEMS [16–18]. Carbon nanocoils (CNCs) are coiled CNTs with more or less incomplete crystal- line structures [19–22]; they are essentially nanoscale springs. In addition to the high Young’s modulus of CNTs, CNCs dis- play unique tensile properties due to their peculiar helical morphology [23]. Moreover, their flexible properties may result in large dynamic ranges in sensing devices [24]. Experimental and theoretical methods [25,26] have been used to investigate the mechanical properties of CNCs. Volodin et al. [27] visualized the helical structure and probed the local elasticity of a coiled CNT along the length direction of the coil using atomic force microscopy (AFM). By laterally compressing the coiled CNT with the AFM probe to obtain the local spring constant, Young’s modulus of the coiled CNT was measured to be 0.7 TPa, which is comparable to that of hexagonal graphene sheets. The model proposed did not refer to the helical structure. With AFM probes in a scanning electron microscope (SEM), Chen et al. [28] suc- ceeded in drawing a single CNC longitudinally and obtained the spring constant of the nanospring, which was 0.12 N/m in the low strain region. An analytical model of the spring constant accounting for geometric nonlinearity explained the deformation of the nanocoil perfectly and revealed Young’s modulus of the CNC to be 2.5GPa. The relative elon- gation of 42% predicted its potential application as a super nanospring. Aiming at NEMS applications, vibration tests have been conducted on CNCs, revealing the resonance frequencies http://dx.doi.org/10.1016/j.carbon.2014.10.019 0008-6223/Ó 2014 Elsevier Ltd. All rights reserved. * Corresponding author: Fax: +86 411 84709304. E-mail address: lpan@dlut.edu.cn (L. Pan). CARBON 81 (2015) 758 – 766 Available at www.sciencedirect.com ScienceDirect journal homepage: www.elsevier.com/locate/carbon