Nonlocal mass nanosensors based on vibrating monolayer graphene sheets

Single layer graphene sheets (SLGS) as a nanoscale label-free mass sensor are proposed. A mathematical framework according to nonlocal elasticity is considered. The nonlocal elasticity incorporates the small-scale effects or nonlocality in the analysis. Rectangular graphene resonators are assumed to be in cantilevered configuration. Closed-form nonlocal equations are derived for the frequency shift due to the added mass based on four types of different mass loadings. From the potential and kinetic energy of the mass loaded graphene sheets, generalised nondimensional calibration constants are proposed for an explicit relationship among the added mass, nonlocal parameter and the frequency shift. These equations based on nonlocal elasticity in turn are used for sensing the added mass (e.g. adenosine bio-fragment). Molecular mechanics simulation is used to validate the new nonlocal sensor equations. The optimal values of span of nonlocal parameter are used and compared with the molecular mechanics simulation results. The nonlocal approach generally predicts the frequency shift accurately compared to the local approach in most cases. Numerical results show the importance of considering the distributed nature of the added mass while using the nonlocal theory. The performance of the sensor is governed on the spatial distribution of the attached mass on the graphene sheet. Discussion on the numerical results illustrate that the sensitivity of graphene sensors is in the order of Gigahertz/zeptogram.