Nanoscale Mass Sensor Research Articles

Nanoscale mass measurement based on suspended graphene

A highly sensitive nanoscale mass sensor was developed for weight measurement of single microparticles using a suspended graphene structure. The sensor is composed of an array of holes covered with suspended monolayer graphene. Based on the shift of the 2D Raman peak in graphene, originating from the elongation of carbon–carbon bonds under pressure, the mass of microparticles in suspended graphene can be measured. The results show that the sensor can detect microparticles with mass ranging from 0.1 ng to 3 ng. The peak shift ratio is −69.8 cm−1 per 1% strain for the experimental value and −72.3 cm−1 per 1% strain for the calculated value. The demonstrated concept presents a promising path for nano-mass measurement applications.

Thermal Buckling and Postbuckling Behaviors of Couple Stress and Surface Energy-Enriched FG-CNTR Nanobeams

Small-sized structural elements such as beams, plates, and shells are usually used as nanomechanical resonators, nanoscale mass sensors, nanoelectromechanical actuators, and nanoenergy harvesters. At the nanoscale, the structures usually possess a high surface area-to-bulk volume ratio, leading to the free energy related to surface atoms becoming considerable compared to that of the bulk part. Earlier reports indicated several physical reasons for size-dependent phenomena, e.g., nonlocal stress, surface energy, and couple stress. To provide an in-depth insight into the mechanical behavior of small-scale structures, size-dependent continuum models including two or more physical factors have attracted the attention of the academic community. This research analyzes the thermal buckling and postbuckling characteristics of functionally graded carbon nanotube-reinforced (FG-CNTR) nanobeams with a tri-parameter, nonlinear elastic foundation and subjected to a uniform temperature rise. Chen-Yao’s surface energy theory and Yang’s symmetrical couple stress theory are combined to capture two types of size effects in nanobeams. The postbuckling model is formulated based on the Euler–Bernoulli deformation hypothesis and Euler–Lagrange equation. Using a two-step perturbation technique, the related postbuckling equilibrium path is determined. In numerical analysis, the impacts of surface energy, couple stress, elastic foundation, boundary conditions, geometric factor, layout type, and volume fraction of CNTs on the thermal buckling and postbuckling behaviors of nanobeams are revealed. It is indicated that considering couple stress or surface energy can lead to a significant increase in the postbuckling stability of nanobeams compared to the case in which it is not considered. In addition, there is a reverse competition between couple stress or surface energy effects on the thermal buckling responses of nanobeams. As the temperature rise will cause the material elastic moduli softening, the thermal buckling load–deflection curves of nanobeams with the temperature-independent case are much higher than those with the temperature-dependent cases.

Vibration Characteristics of Diamond Nanothreads Controlled by Lattice Defects Aimed at Application to Nanoscale Mass Sensors

Vibration Characteristics of Diamond Nanothreads Controlled by Lattice Defects Aimed at Application to Nanoscale Mass Sensors

Theory and modeling of a novel class of nanoplate-based mass sensors with corner point supports

A novel class of nanoplate-based mass sensor with corner point supports for detecting attached nanoparticles is proposed. Exact solutions for vibrations of three types of nanoscale mass sensors are obtained by a symplectic superposition method combining with nonlocal elasticity theory. A comparison between theoretical prediction and FEM simulation is presented and excellent agreement is reported. Influences of design parameters on the frequency shift are investigated. Numerical results show that increasing magnetic field strength and environment temperature can effectively enhance the sensitivity of the mass sensor, and the nanoplate-based sensor point-supported at only one corner is the optimal design.

Modeling of novel nanoscale mass sensor made of smart FG magneto-electro-elastic nanofilm integrated with graphene layers

This paper is devoted to presenting theoretical modeling for a novel nano-mass sensor system composed of smart core integrated with graphene layers in its top and bottom surfaces. The smart core is made of a functionally graded (FG) magneto-electro-elastic (MEE) nanofilm. On the basis of the nonlocal strain gradient theory and first-order shear deformation plate theory, the size-dependent governing equations for this graphene/FG-MEE/graphene nanofilm based nano-mass sensor system are derived. The frequency shift behavior of this system is investigated with consideration of different distribution configurations, different attaching locations, and different total masses of the attached nanoparticles. Furthermore, the influences of graphene faces, FG index of the MEE core, nonlocal and strain gradient parameters, as well as external electric and magnetic potentials on the frequency shift behavior of the nanoscale mass sensor are examined in detail. Significant enhancement of the frequency shift and frequency shift ratio can be observed for the nano-mass sensor system by covering graphene in the top and bottom surfaces of FG-MEE nanofilm. The theoretical model and conclusion presented in this paper may serve as an inspiration to researchers for exploiting nanoscale mass sensors with high sensitivities.

Nano-scale mass sensor based on the vibration analysis of a magneto-electro-elastic nanoplate resting on a visco-Pasternak substrate

In this paper, a magneto-electro-elastic nanoplate resting on a visco-Pasternak medium with added concentrated nanoparticles is presented as a mass nanosensor according to the vibration analysis. The MEE nanoplate is supposed to be subject to external electric voltage and magnetic potential. In order to take into account the size effect on the sensitivity of the sensor, the nonlocal elasticity theory in conjunction with the Kirchhoff plate theory is applied. Partial differential equations are derived by implementing Hamilton’s variational principle. Equilibrium equations were solved analytically to determine an explicit closed-form statement for both the damped frequency shift and the relative damped frequency shift using Navier’s approach. A genetic algorithm (GA) is employed to achieve the optimal added nanoparticle location to gain the most sensitivity performance of the nanosensor. Numerical studies are performed to illustrate the variation of the sensitivity property corresponding to various values of the number of attached nanoparticles, the mass of each nanoparticle, the nonlocal parameter, external electric voltage and magnetic potential, the aspect ratio, and visco-Pasternak parameters. Some numerical outcomes of this paper show that the minimum value of the damped frequency shift occurs for a certain value of the length-to-thickness ratio. Also, it is shown that the external magnetic and external electric potentials have a different effect on the sensitivity property. It is anticipated that the results reported in this work can be considered as a benchmark in future micro-structures issues.

Application of the generalized Hooke's law for viscoelastic materials (GHVMs) in nanoscale mass sensing applications of viscoelastic nanoplates: A theoretical study

Abstract Reviewing the literature reveals that in all previous research works related to the damped vibration analysis of nanoplates except (Rajabi and Hosseini-Hashemi, 2017a), the material damping of nanoplates has been represented by the Kelvin-Voigt model without any reasonable justification. The Kelvin-Voigt model has no instantaneous elasticity in creep and also shows unrealistic behavior in relaxation. Due to these drawbacks, the Kelvin-Voigt model fails to capture time domain characteristics of viscoelastic solid materials correctly. On the other hand, the Zener model can predict both creep and relaxation functions of a viscoelastic solid material well in the time domain. In the present paper based on the combination of generalized Hooke's law for viscoelastic materials (GHVMs) and the nonlocal elasticity theory, a general 2-D theory of nonlocal viscoelasticity is obtained. A nanoscale mass-sensor is proposed based on the damped vibration analysis of a viscoelastic orthotropic Kirchhoff-Love nanoplate. The material damping of the nanoplate is represented by the Zener model for illustration purposes. For simply supported boundary conditions, analytical expression is obtained for the eigenfrequencies of the sensor.

On the application of viscoelastic orthotropic double-nanoplates systems as nanoscale mass-sensors via the generalized Hooke’s law for viscoelastic materials and Eringen’s nonlocal elasticity theory

Reviewing the literature reveals that in all previous research works related to the damped vibration analysis of nanoplates, the material damping of nanoplates has been represented by Kelvin-Voigt model without any reasonable justification. The Kelvin-Voigt model has no instantaneous elasticity in creep and also shows unrealistic behavior in relaxation. Due to these drawbacks, the Kelvin-Voigt model fails to capture time domain characteristics of viscoelastic solid materials correctly. On the other hand, the Zener model can predict both creep and relaxation functions of a viscoelastic solid material well in the time domain.The generalized Hooke’s law for viscoelastic materials (GHLVMs) bridges the differential form of linear viscoelasticity and the integral form of linear viscoelasticity. In the present study based on the combination of GHLVMs and the nonlocal elasticity theory, a general 2-D theory of nonlocal viscoelasticity is obtained. A nanoscale mass-sensor is proposed based on the damped frequency analysis of a viscoelastic orthotropic double-nanoplates system (VODNS). The material damping of the nanoplates is represented by the Zener model. It has been assumed that the nanoplates obey the Kirchhoff-Love plate hypotheses. Detailed parametric study is presented.

A new nanoscale mass sensor based on a bilayer graphene nanoribbon: The effect of interlayer shear on frequencies shift

In this study a new nanoscale mass sensor has been introduced. Specifically we have investigated a cantilevered bilayer graphene nanoribbon (GNR) as our resonator. It has been assumed that a point mass is rigidly attached to the sensor. Graphene nanoribbons with single or few layers have extremely high sensitivity to environmental changes. Multibeam shear model as proposed by Liu and coworkers in 2011, accounts for the interlayer shear but neglects the intralayer stretch. In the presence of a nanoparticle the shift in resonant frequency of a cantilevered graphene nanoribbon has been investigated. It also has been shown that the interlayer shear can significantly affect the sensitivity of graphene nanoribbons based nanoscale mass sensors.

Nanoscale mass sensing based on vibration of single-layered graphene sheet in thermal environments

Based on vibration analysis, single-layered graphene sheet (SLGS) with multiple attached nanoparticles is developed as nanoscale mass sensor in thermal environments. Graphene sensors are assumed to be in simply-supported configuration. Based on the nonlocal plate theory which incorporates size effects into the classical theory, closed-form expressions for the frequencies and relative frequency shifts of SLGS-based mass sensor are derived using the Galerkin method. The suggested model is justified by a good agreement between the results given by the present model and available data in literature. The effects of temperature difference, nonlocal parameter, the location of the nanoparticle and the number of nanoparticles on the relative frequency shift of the mass sensor are also elucidated. The obtained results show that the sensitivity of the SLGS-based mass sensor increases with increasing temperature difference. Open image in new window

Vibration analysis of nanomechanical mass sensor using double-layered graphene sheets resonators

Graphene sheets (GSs) are two-dimensional material with extremely favorable mass sensor properties. In the study, we examined the potential of nanoscale mass sensor based on simply supported double-layered graphene sheets (DLGSs) attached nanoparticles. Using the continuum elasticity theory, the influences of the attached mass and position of the nanoparticles on the frequency shifts of DLGSs are investigated in detail. The result shows that the frequency shift in DLGSs is much higher than that of the single-layered graphene sheets (SLGSs). The DLGSs based nanomechanical resonator could provide higher sensitivity than SLGSs.

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.

An atomic-resolution nanomechanical mass sensor based on circular monolayer graphene sheet: Theoretical analysis of vibrational properties

Graphene sheet (GS) is a two-dimensional material with extremely favorable mass sensor properties. In this work, the potential of a nanoscale mass sensor based on individual single layer GS is examined. An atomic-resolution nanomechanical mass sensor is modeled by a fixed supported circular monolayer GS with attached nanoparticles, based on a continuum elastic model and Rayleigh's energy method. We analyze the vibrational properties of the GS used as a mass sensor in detail, and the relationship between the attached mass and the vibrational frequency (frequency shift) of the GS is simulated and discussed using the two models. The sensitivity of vibrational frequency (frequency shift) to both aspect ratio and vibration mode is demonstrated, and comparison of the two models proves their accuracy and that of the simulation of the monolayer GS mass sensor.

Zeptogram sensing from gigahertz vibration: Graphene based nanosensor

We develop the mathematical framework for using single layer graphene sheet as nanoscale label-free mass sensors. Graphene resonators are assumed to be in the cantilevered configuration. Four types of mass loadings are considered and closed-form equations are derived for the frequency shift due to the added mass. Using the potential and kinetic energy of the mass loaded graphene sheets, generalised non-dimensional calibration constants are proposed for an explicit relationship between the added mass and the frequency shift. These equations in turn are used for sensing the added mass. Numerical results illustrate that the sensitivity of graphene sensors is in the order of gigahertz/zeptogram. We show that the performance of the sensor depends on the spatial distribution of the attached mass on the graphene sheet.

Tracking atoms on and off a nanoscale mass sensor

Tracking atoms on and off a nanoscale mass sensor

The calibration of carbon nanotube based bionanosensors

We derive the calibration constants necessary for using single-walled carbon nanotubes (CNTs) as nanoscale mass sensors. The CNT resonators are assumed to be either in cantilevered or in bridged configurations. Two cases, namely, when the added mass can be considered as a point mass and when the added mass is distributed over a larger area is considered. Closed-form transcendental equations have been derived for the frequency shift due to the added mass. Using the energy principles, generalized nondimensional calibration constants have been derived for an explicit relationship between the added mass and the frequency shift. A molecular mechanics model based on the universal force field potential is used to validate the new results presented. The results indicate that the distributed nature of the mass to be detected has considerable effect on the performance of the sensor.

An approach to a multi-walled carbon nanotube based mass sensor

We propose an approach to a nanoscale mass sensor based on a gold electrode structure, on which a multi-walled carbon nanotube (MWCNT) bridge can be placed and soldered. The structure is comprised of three electrodes with a width of 2 or 4 μm. Two outer electrodes with a length of 10 or 15 μm serve as source and drain electrodes for the MWCNT bridge, whereas an inner electrode with a length of 8 or 13 μm is for electrostatic excitation of the CNT. Some structures have an extra pair of outer electrodes, which may deflect the inner electrodes and thereby be used for stretching or compressing the bridging nanotube. The free standing MWCNTs were fabricated by chemical vapour deposition of Fe(II) phthalocyanine. A nanomanipulator with an x− y− z translation stage was used for placing the MWCNTs across the source–drain electrodes. The nanotubes were soldered onto the substrate by electron beam induced deposition of an organometallic compound.