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A review on nanomechanical resonators and their applications in sensors and molecular transportation

Behrouz Arash, Jin-Wu Jiang, and Timon Rabczuk

Citation: Applied Physics Reviews 2, 021301 (2015); doi: 10.1063/1.4916728

View online: https://www.sodocs.net/doc/0118457404.html,/10.1063/1.4916728

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APPLIED PHYSICS REVIEWS

A review on nanomechanical resonators and their applications in sensors and molecular transportation

Behrouz Arash,1Jin-Wu Jiang,2and Timon Rabczuk 1,a)

Institute of Structural Mechanics,Bauhaus Universit €a t Weimar,Marienstr 15,D-99423Weimar,Germany 2Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai University,Shanghai 200072,People’s Republic of China

(Received 19December 2014;accepted 11March 2015;published online 6April 2015)

Nanotechnology has opened a new area in science and engineering,leading to the development of novel nano-electromechanical systems such as nanoresonators with ultra-high resonant frequencies.The ultra-high-frequency resonators facilitate wide-ranging applications such as ultra-high sensitive sensing,molecular transportation,molecular separation,high-frequency signal processing,and biological imaging.This paper reviews recent studies on dynamic characteristics of nanoresonators.A variety of theoretical approaches,i.e.,continuum modeling,molecular simulations,and multiscale methods,in modeling of nanoresonators are reviewed.The potential application of nanoresonators in design of sensor devices and molecular transportation systems is introduced.The essence of nanoresonator sensors for detection of atoms and molecules with vibration and wave propagation analyses is outlined.The sensitivity of the resonator sensors and their feasibility in detecting different atoms and molecules are particularly discussed.Furthermore,the applicability of molecular transportation using the propagation of mechanical waves in nanoresonators is presented.An extended application of the transportation methods for building nano?ltering systems with ultra-high selectivity is surveyed.The article aims to provide an up-to-date review on the mechanical properties and applications of nanoresonators,and inspire additional

potential of the resonators.V

C 2015AIP Publishing LLC .[https://www.sodocs.net/doc/0118457404.html,/10.1063/1.4916728]TABLE OF CONTENTS

I.INTRODUCTION 1II.

MODELING OF NANORESONATORS ........

2A.Continuum modeling ....................21.Elastic beam model...................32.Elastic shell model ...................43.Elastic plate model ...................54.Surface effects .......................5B.Molecular simulations....................7C.Multiscale methods......................8III.DYNAMIC CHARACTERIZATION OF

NANORESONATORS.......................8A.Resonant frequencies ....................9B.Wave dispersion relations ................10C.Energy dissipation mechanism in

nanoresonators..........................

12IV.APPLICATION OF NANORESONATOR IN

SENSORS .................................13A.Detection with vibration analysis..........14B.Detection with wave propagation analysis ..

V.APPLICATION OF NANORESONATOR

IN MOLECULAR TRANSPORTATION........16A.Transportation with torsional waves .......16B.Transportation with impulse waves ........18VI.CONCLUSION AND FUTURE CHALLENGES

I.INTRODUCTION

Nanomechanical resonators made of carbon nanotubes (CNTs),1graphene sheets (GSs),2and nanowires 3have recently attracted much attention owing to their remarkable mechanical and electrical properties that enable them to reach ultra-high resonant frequency up to the order of giga-hertz.4,5Reaching this frequency range makes nanoresona-tors ideal candidates for applications in nano-sensors for detection of atoms/molecules,6,7nanopumping devices for molecular transportation,8and membranes for separating atoms and molecules without any phase changes.9

In recent years,extensive efforts have been dedicated to design new classes of sensors with high sensitivity,fast response,and high consistency.In order to ful?ll these requirements,the reduction in sizes of sensors is of great signi?cance since it enhances the sensitivity performance,improves the robustness of sensors,and allows integration of more functions in a small lab-on-a-chip device.The demand for miniaturized sensors has motivated scientists to develop

Author to whom correspondence should be addressed.Electronic mail:timon.rabczuk@uni-weimar.de.

1931-9401/2015/2(2)/021301/21/$30.00V

C 2015AIP Publishing LLC 2,021301-1

APPLIED PHYSICS REVIEWS 2,021301(2015)

sensors with higher ef?ciencies in nanoscale size,the so-called nano-sensors.10,11Nano-sensors are promising in a wide variety of applications such as early disease detection, DNA sequencing,detection of gene mutations,and gas detection.12–14

Regarding parameters that are detected by nano-sensors, the sensors are categorized into six main groups:15mechani-cal electrical,optical,magnetic,chemical,and thermal.For example,mechanical nano-sensors detect mechanical varia-bles such as frequency,wave velocity,pressure,and strain. Among different types of nano-sensors,nanomechanical resonator sensors have shown an exceptional ability in design of mass spectrometers with ultra-high mass sensitiv-ity,which enables to detect atoms or molecules at very low concentrations,16–20where existing sensors may not ful?ll an accurate detection.For example,present biosensing devices cannot accurately detect marker proteins,which are relevant to speci?c cancers,in the concentration of$1ng/ml in a blood sample.21Conversely,nanoresonator sensors easily overcome the limitation due to their exceptional detection sensitivity even at single-molecule resolution,7,22,23which enables them to be utilized in lab-on-a-chip sensors. Different techniques proposed in the literature for designing nanoresonator sensors can be generally categorized into two major groups:vibration-based,14,17,24and wave propagation-based methods.24–26The principle of the resonator sensors is to recognize shifts in resonant frequencies or wave velocities,induced in the sensors by surrounding atoms or molecules on their surfaces.

Further to the application of nanoresonators in sensors, the morphology of the nano-materials provides an excellent opportunity to build a new generation of nanodevices for molecular transportation and separating atoms and mole-cules,27–29which signi?cantly reduces the energy consump-tion compared to traditional methods.The molecular separation has great potential in many areas such as clean energy and chemical industries,including hydrogen recov-ery,nitrogen generation,and water puri?cation.30,31 So far,different methods for transportation of atoms and molecules by CNTs as nanochannels have been suggested in the literature by imposing chemical potential,thermal gradients,and electrical?elds.32–34The relatively low ef?-ciency of the proposed methods motivated to use mechanical loads to induce atomic/molecular?ows in CNTs.27,35The essence of molecular transportation using mechanical load-ing is anchored in the propagation of the mechanical waves along a CNT conveying atoms/molecules.The waves gener-ate the required driving forces for moving atoms inside the nanotube through the van der Waals(vdW)interactions between the nanotube wall and molecules encapsulated in the CNT.8,27The methods for the molecular transportation using CNT resonators can be classi?ed into two groups: transportation by torsional waves8,9,27,28,36and transportation by impulse waves.29,35The propagation of mechanical waves in CNTs was then used to propose new nano?ltering devices for separating atoms/molecules by designing precise nano-meter pores in CNT-based membranes,and controlling their sizes for a successful separation.9,28,29

As stated earlier,the performance of nanoresonators for sensing and transportation applications strongly depends on their dynamic characteristics such as quality(Q)-factor.37–39 The Q-factor re?ects the energy dissipated for each vibra-tional cycle of the resonators,which can be affected by the external attachment energy loss,40,41intrinsic nonlinear scat-tering mechanisms,42the effective strain mechanism,43edge effects,44,45grain-boundary-mediated scattering losses,46and temperature scaling phenomenon.47Moreover,the structure of nanoresonators has a large surface-to-volume ratio,which causes a difference in the nature of chemical bonds on the surface.48,49Surface atoms have fewer bonds compared to bulk atoms.Therefore,their equilibrium requirements are different from atoms in the bulk.The difference induces surface stresses,50,51which in turn affects the material prop-erties of the resonators.It is thus indispensable to character-ize the dynamic behavior of nanoresonators for novel designs of resonator-based devices.

This article aims to provide a review on studies invested on mechanical properties of nanoresonators and their appli-cations in sensors and molecular transportation to(1)sum-marize the most recent achievements,(2)review different methods for detection of distinct atoms/molecules and mo-lecular transportation,(3)specify major challenges and restrictions in the modeling of nanoresonators,and(4)clarify key issues of future research studies.To this end,Sec.II focuses on modeling of CNTs,GSs,and nanowires.Section III introduces dynamic characteristics of nanoresonators. The potential application of nanoresonators in designing ultra-high sensitive sensors is reviewed in Sec.IV.Section V surveys the potential of CNT-based nanopumping devices in transportation of atoms and molecules.Section VI summa-rizes the?ndings on the research and outlines some chal-lenges for further studies.

II.MODELING OF NANORESONATORS

Besides experiments52,53which are formidable and expensive at the nanoscale,there are three main approaches for modeling of nanostructures:(a)continuum mechan-ics,54–56(b)molecular dynamics(MD)simulations,57–60and (c)hybrid atomistic–continuum models.61–63Continuum mechanics models are considered as low computational cost methods with relatively simple formulations compared to the two other approaches.However,continuum models are unable to provide detailed information about molecular inter-actions,which hinder the achievement of in-depth insights into the underlying mechanisms of phenomena at the atomic level.MD simulations,in contrast,enable to study character-istics of nanoresonators including detailed molecular interac-tions.Multiscale models can involve continuum and atomistic descriptions of a material at each scale.

In Sec.II A,the theoretical approaches in modeling of nanoresonators are introduced and some benchmark studies are reviewed in more details.

A.Continuum modeling

Methods based on continuum mechanics theory are less computationally intensive compared to the two other

approaches.Moreover,their formulations are not as compli-cated as those of multiscale methods.These advantages make continuum modeling convenient to study some phenomena in nanostructures such as buckling,64,65wave propagation,66,67and free vibration.68–71In local continuum mechanics,nano-materials are considered as continuous macrostructures where the lattice spacing between atoms is ignored and stress at a point is de?ned as a function of strain at that point.Although some research studies have been con-ducted using classical or local continuum mechanics,their applicability at nanoscales is questionable.The limited applicability is rooted in the fact that at nanometer sizes the lattice spacing between atoms becomes gradually important and the discrete structure of the material may not be homog-enized into a continuum.In other words,the material proper-ties at the nanoscale are size dependent,and thus length scale effects should be considered for the prediction of mechanical characteristics of nano-materials.72–75In view of the limitation of local continuum models,nonlocal contin-uum mechanics models were developed,allowing for the consideration of the size effects in analysis of nano-materials.

The essence of the nonlocal elasticity theory developed by Eringen76,77and Aifantis78–80indicates that the stress state at a given reference point is a function of the strain?eld at every point in the body.Hence,the theory could account for the long range forces between atoms and scale effects. Peddieson et al.81demonstrated that the nonlocal continuum mechanics can be used to model nano-materials.Wang67 indicated that the nonlocal continuum theory is needed for a precise estimation of wave dispersion relations in CNTs,and ?rst measured the range of the scale parameter used in the theory.Many researchers have then explored the application of nonlocal continuum mechanics in the modeling of nano-structures.73,82–93Note that the small-scale effect depends on the lattice structure and the physics of phenomenon under investigation.Thus,the validation of nonlocal continuum models with molecular simulations is indispensable to mea-sure the value of the small-scale parameter.In Sec.II A1,a general introduction of the elastic beam,shell,and plate models for analysis of CNTs,GSs,and nanowire resonators based on the nonlocal continuum mechanics is provided.

Based on the nonlocal theory by Eringen,76,77the stress at a reference point x in an elastic continuum depends on strains at every point of the body.The constitutive relation is then obtained as

e1àee0aT2r2Tr?C:e;(1) where e0a is the nonlocal or small-scale parameter;r2is the Laplacian operator;r and e are,respectively,the stress and strain tensors;and C is the fourth-order elasticity tensor.It is simply seen that the local constitutive relation is recovered when the small-scale parameter,e0a,is set to be zero.A con-servative estimation of the small-scale parameter is e0a< 2:0nm for the wave dissipation relation in CNTs.67It is strongly recommended to calibrate the parameter through a veri?cation process with molecular simulations for justifying the applicability of nonlocal models.1.Elastic beam model

The nonlocal Euler-Bernoulli beam model for the free vibration of nanobeams is obtained as94,95

@4w

tq A

wàe0a

eT2

@2w

?0;(2)

where E is the Young’s modulus of the material;wex;tTis the?exural de?ection of the beam;q is the mass density of the material,and A is the cross sectional area of the beam.I is the second moment of area of the beam’s cross-section.For a beam along the x direction and a?exural de?ection in the z-direction,the relevant second moment of area is obtained by I?

z2dydz.The local Euler–Bernoulli beam model is recovered when the small-scale parameter,e0a,is equal to zero in Eq.(2).It was shown by Ref.93that the resonant fre-quency for mode n,x n,of a nanobeam with a length of L and simply supported boundary conditions is obtained as

x n?

???

??????????????????????????????????????????????

n p

q A1àe0a

eT2

n p

v u

u u

:(3)

The Euler beam model is adequate for the dynamic anal-ysis of CNTs and nanowires with high aspect ratios,greater than20(Ref.93)since the model neglects the transverse shear deformation.In this view,the nonlocal Timoshenko beam model was developed to include the effects of trans-verse shear deformation and rotary inertia.82,94,95The dynamic equilibrium equations of the nonlocal Timoshenko beam model in terms of the?exural displacement,w,and rotation,/,is given as82,94,95

K s AG

te0a

eT2q A

@4w

@x2@t2

àq A

@2w

@t2

?0;

@2/

@x2

àK s AG/t

àq I

@2/

@t2

te0a

eT2q I

@4/

@x2@t2

?0;

(4) where K s is the shear correction factor and G is the shear mod-ulus.Note that the beam models presented in Eqs.(2)and(4) are based on the assumption of small amplitude vibrational motion,where relations between strain and deformations are assumed to be linear.For large amplitude vibrational motion, the nonlinear vibration should be considered where relations between strain and deformations are nonlinear.

For the nonlinear vibration of a CNT or nanowire mod-eled by the nonlocal Timoshenko beam theory,the von K a rm a n type nonlinear strain–displacement relations are given by96–98

e xx?

;c xz?

t/;(5)

where u is the axial displacement.The nonlinear equations of motion based on the nonlocal continuum theory can be then derived as96

EA @2u @x t@w @x @2w @x ?q A @2@t u àe 0a eT2@2

;K s GA @2w @x 2t@/@x

tR 1àe 0a eT2R 2?q A @2@t 2w àe 0a eT2@2w @x 2 àq A e 0a eT2@2@t 2@2u @x 2àe 0

a eT2@4u @x 4

;EI @2/@x 2àK s GA @w @x t/ ?q I @2@t 2/àe 0a eT2@2

/@x

2 ;

(6)

where

R 1?EA

@2u @x 2@w @x t32@w @x 2

@2w @x 2t@u @x @2w

@x 2

(7)

and

R 2?EA

@4u @x 4@w @x t3@3u @x 3@2w @x 2t3@2u @x 2@3w @x 3t@u @x @4w

@x 4 tEA 3@2w @x 3t9@w @x @2w @x @3

w @x t32@w @x 2@4w

@x "#:

(8)

Note also that there is no study in the literature reporting

that higher order beam models are necessary to analysis the dynamic behavior of CNTs and nanowires.

2.Elastic shell model

CNTs with low length-to-diameter aspect ratios have

been modeled with elastic shell theories.Two shell theories have been widely considered in the literature for dynamic analysis of nanotubes:the classical shell theory 85,93,94and ?rst order shear deformation theory (FSDT).84,94

In the classical shell theory,the three-dimensional dis-placement components u x ;u y ,and u z in the x ;h ,and z direc-tions,respectively,are assumed to be 84,94

u x x ;h ;z ;t eT?u x ;h ;t eTàz

@x x ;h ;t eT;u y x ;h ;z ;t eT?v x ;h ;t eTàz @w

x ;h ;t eT;u z x ;h ;z ;t eT?w x ;h ;t eT;(9)

where u ;v ;w are the reference surface displacements as illustrated in Figure 1.For a CNT with a radius R ,length L ,and thickness h ,the governing equations of free vibration are given as 93,94

@N xx @x t1R @N h x @h ?q h @2u

@t ;1R @N hh @h t@N x h @x t1R 2@M hh @h t1R @M hh @x ?q h @2v

@t 2;@2M xx @x 2t1R 2@2M hh @h 2t

2R @2M x h @x @h àN hh R ?q h @2w

2;(10)

where N xx ;N hh ;N x h ;M xx ;M hh ;M x h are the components of internal force and the internal moments into which the small-scale effect has been incorporated,93,94x and h denote the longitudinal and circumferential coordinates,respectively.

In the FSDT,the three-dimensional displacement com-ponents u x ;u y ,and u z in the x ;h ,and z directions,respec-tively,are assumed to be 84,94

u x ex ;h ;z ;t T?u ex ;h ;t Tàz w x ex ;h ;t T;u y ex ;h ;z ;t T?v ex ;h ;t Tàz w h ex ;h ;t T;

u z ex ;h ;z ;t T?w ex ;h ;z ;t T;

(11)

where u ;v ;and w are the reference surface displacements,and w x and w h are the rotations of transverse normal about the x àand y àaxis,respectively.The governing equations for free vibration of a nanotube based on the Donnell shell theory are given as 84,94

@N xx @x t1R @N x h

?I 0€u tI 1€w x ;@N x h @x t1R @N hh @h

tQ hh

R ?I 0€v tI 1€w h ;@Q xx @x t1R @Q hh @h àN hh

R ?I 0€w ;@M xx @x t1R @M x h

@h àQ xx ?I 1€u tI 2€w x ;@M x h @x t1R @M hh

àQ hh ?I 1€v tI 2€w h

;(12)

where N xx ;N hh ;N x h ;Q xx ;Q hh ;M xx ;M hh ;M x h are the compo-nents of internal force and the internal moments into which the small-scale effect has been incorporated.84,94I i ?Dh

àh 2

q z i dz ei ?0;1;2Tis the mass moment of inertia.Simulation results presented in the literature reveal that res-onant frequencies of nanotubes obtained from the nonlocal shell models based on classical shell theory and FSDT are in

good

FIG.1.Schematic of a CNT treated as a cylindrical shell.

agreement with those of MD simulations;84,93hence,higher order models are not necessary for the analysis of nanotubes.

3.Elastic plate model

The classical plate theory (CLPT)94,99,100and FSDT (or Mindlin plate theory)89,94,101have been employed in model-ing GSs.

In CLPT,the nonlocal plate model of a single-layered nano-sheet in terms of the ?exural displacements,w ,is given as 94,99,100

D r 4w ?1àe 0a eT2r 2 àI 0@2w @t tI 2@4w @x @t t

@y @t !"#

;(13)

where D is the bending rigidity of the plate.An explicit

formula for resonant frequencies of a rectangular nano-plate with a size of a ?b and simply supported boundary condi-tions can be obtained as 102

x ?????????????????????????????????????????????????D k I 0tI 2k eT1te 0a eT2k v u u t ;k ?m p a 2tn p b 2;

m ;n ?1;2;…eT:

e14T

In FSDT,the governing Mindlin-type equations are 91,94

@N xx @x t@N xy

@y ?I 0€u tI 1€w x

;@N xy @x t@N yy

@y ?I 0€v tI 1€w y

;@Q xx @x t@Q yy

@y tp ?I 0€w

;@M xx @x t@M xy

@y àQ x ?I 1€u tI 2€w x

;@M xy @x t@M yy

àQ y ?I 1€v tI 2€w y

;(15)

where N xx ;N yy ;N xy ;Q xx ;Q yy ;M xx ;M yy ;M xy ;I 0;I 1;I 2are

the components of internal forces,the internal moments in which the small-scale effect are incorporated and mass moments of inertia.91,94u ;v ;w are the reference surface dis-placements;and w x ;w h are the rotations of transverse normal about the x àand y àaxis,respectively.

It has been shown that resonant frequencies of GSs pre-dicted by the nonlocal plate models are in good agreement with those of MD simulations.91,92

4.Surface effects

Atomistic simulation results have shown that material properties of nano-materials are surface dependent.103,104Zhou and Huang 103demonstrated that a solid surface can be either softer or stiffer than its bulk counterpart.Shim et al.104showed that the elasticity of nanoplates intensely depends on surface reconstruction,alignment of bond chains,and oxidation.In addition to atomistic simulations,hierarchi-cal atomistic/continuum simulation approaches were also developed to study surface effects on material properties of

nano-materials.105–108Sun and Zhang 105presented a semi-continuum model for plate-like nanostructures.They indi-cated that the values of the Young’s modulus and Poisson’s ratio are functions of the number of atomic layers in the direction of thickness,and approach the bulk magnitude by increasing the number of atomic layers.Park 108presented a multiscale ?nite element method (FEM)that accounts for at-omistic surface effects in nano-materials.

The simulation observations can be interpreted as the na-ture of the chemical bonding of atoms on the surface is differ-ent from that in the interior (bulk).Atoms at or near a free surface have different equilibrium requirements compared to the atoms in the bulk of the material because of the different environmental conditions.The difference induces surface effects,including the surface energy,surface tension,surface relaxation,and surface reconstruction.109–114The surface effects are critical in understanding the mechanical behavior of nano-materials since they have extremely large surface area to volume ratio,resulting in more surface dependent ma-terial properties.The effects become more prominent in determining physical properties of nano-materials when func-tional materials adhere to their surface.115

The tremendous computational sources needed for the atomistic studies motivated the development of continuum models according to coupled surface-bulk elasticity.The continuum models are based on the continuum model of sur-face elasticity formulated by Gurtin and Murdoch,116,117where the surface of solids is viewed as an elastic membrane with different material properties adhering to the bulk mate-rial without slipping.It was shown that the Gurtin–Murdoch model has the capability of predicting elastic properties of nano-materials.109,118–124Wang and Feng 118examined surface effects on the transverse vibration of nanowires using a re?ned Timoshenko beam model.They demonstrated that the vibration behavior of nanowires is size dependent,especially when their cross-sectional sizes reduce to nano-metres.Park and Klein 109employed a developed surface Cauchy–Born model 108to study the effect of boundary con-ditions and surface stresses on resonant properties of gold nanowires.For the ?rst time,they quanti?ed the variation of resonant frequencies in nanowires due to surface stresses within a ?nite deformation framework.They also investi-gated how the residual and surface elastic parts of the surface stress affect resonant frequencies of metal nanowires.Ansari and Sahmani 123incorporated the Gurtin–Murdoch model into CLPT and FSDT plate theories to study free vibration of nanoplates according for surface stress effects.

In this section,the modi?ed continuum elasticity based on Gurtin–Murdoch theory for free vibration of nanobeams and nano-plates is reviewed.The surface stresses for the Euler-Bernoulli beam model can be obtained as 121

r s xx

?àz 2l s

tk s

eT@2w

2ts s ;

r s xz

?s s @w @x

;(16)

where l s and k s are the surface Lame constants and s s is the residual surface stress under unstrained conditions.The superscript s denotes surface quantities.

In the classical beam theories,since the stress compo-nent r zz is small compared to r xz,and it is assumed that r zz?0.However,the assumption does not satisfy the sur-face conditions in the Gurtin–Murdoch model.Therefore,it is assumed that the stress component r zz linearly varies through the thickness as125,126

r zz?1

@r s

àq s

@2w

at top

@r s

àq s

@2w

at bottom "#à

@r s

àq s

@2w

@t2

at top

@r s

àq s

@2w

@t2

at bottom "#

(17)

The non-zero components of stress for the bulk of the beam can be expressed as121,126

r xx?E e xxt r zz?àzE @2w

2 z s s

@2w

:(18)

According to the stress?eld given by Eq.(18),the Euler-Bernoulli beam model including surface stress effects for free vibration can be obtained as121

2 I s s h àEIà

2l stk s

@4w

@x4

t2b s s @2w

tq A

@2w

?0;(19)

where b is the width of the beam.

Similar to the Euler-Bernoulli beam model,the non-zero components of stress for the bulk of the Timoshenko beam model including surface effects can be written as121

r xx?E e xxt r zz?zE

2 z s s

@2w

;

r xz?K s G c xz?K s G/t

:(20)

By applying the stress?eld given by Eq.(20),the governing equations of the Timoshenko beam considering surface effects is yielded as121

2b s stK s GA

@2w

@x2

tK s GA

àq A

@2w

@t2

?0;

2 I s s

@2w

àK s GA

tEIt

2l stk s

@2/

@x2

àK s GA/àq I

@2/

@t2

?0:(21) Further to the beam models developed for the predic-tion of dynamic behavior of CNTs and nanowires,the modi?ed continuum elasticity based on Gurtin–Murdoch theory has been also introduced in the literature for free vibration response of the nano-plates.Consider a uniform square nano-plate with the side length L and thickness h. The stress r zz linearly varies in the thickness direction of the plate as123

r zz?1@r s xz

@r s

yzàq s@2w

at top

@r s

xzt

@r s

yzàq s@2w

at bottom

@r s

àq s

@2w

at top

@r s

àq s

@2w

at bottom

z:(22)

The non-zero components of stress for the bulk of the nano-plate based on classical plate theory can be obtained as follows:123

r xx?

1à

e xxt e xx

eTt

1à

r zz?à

1à

@2w

2 z

h1à

s s

@2w

ts s

@2w

àq s

@2w

;

r yy?

1à 2

e yyt e xx

eTt

1à

r zz?à

1à 2

@2w

@y2

@2w

@x2

2 z

h1à

s s

@2w

@x2

ts s

@2w

@y2

àq s

@2w

@t2

;

r xy?

1à

c xy?à

2zE

@2w

@x@y

:(23)

Then,the governing equations of classical plate model taking into account surface effects can be derived as123

Eh3

121à 2

@4w

@x4

@4w

@x2@y2

@4w

@y4

h2s s

61à

@4w

@x4

@4w

@x2@y2

@4w

@y4

Lh2

2l stk s

@4w

t2L s s

@2w

Eh3

61t

@4w

@x@y

?q ht2L q s

@2w

h2q s

61à

@4w

@x@t

@4w

@y@t

:(24)

Studies published in the literature reveal that further research works are required to develop continuum shell mod-els taking into account surface effects for the analysis of the dynamic behavior of nanoresonators.26,121,123Since both the small-scale and surface effects dominate the mechanical properties of materials in nanoscale,future studies are sug-gested on deriving continuum models with consideration of both effects.Furthermore,according to insuf?cient results obtained from molecular simulations,more studies are needed to fully verify the continuum models concerning surface effects and to calibrate the quantities corresponding to the surface,i.e.,l s,k s,and s s.

B.Molecular simulations

While the continuum mechanics approaches enable the understanding of the dynamic behavior of nanoresonators, they are unable to provide detailed mechanisms of molecular interactions between the resonators and adsorbed molecules, which induce resonant frequency shifts.Furthermore,the continuum models may not reveal fundamental insights into the underlying mechanisms of some phenomena at the atomic level such as energy dissipation mechanisms in nano-resonators.These limitations impact the ability of continuum mechanics to predict the dynamic behavior of nanoresona-tors.Molecular simulations,in contrast,provide a pathway to study the characteristics of nanoresonators,including detailed molecular interactions.

MD simulation127,128is a powerful tool to simulate atomistic systems governed by interatomic interactions by solving Newtonian equations of motion.A molecular simula-tion contains(1)a model that describes interactions between atoms called force?elds,(2)a numerical time integrator algorithm that determine trajectories of atoms during the time,and(3)extracting data from atomic trajectory information.

For interatomic interactions between carbon atoms in CNTs and GSs,the second-generation reactive empirical bond order(REBO)potential energy developed by Brenner et al.129is often used as an underlying force?eld for hydro-carbons.In the second-generation REBO force?eld,the total potential energy of a system is given by

i X

j?it1

?E Rer ijTà b ij E Aer ijT ;(25)

where E R and E A are,respectively,repulsive and attractive interactions;r ij is the distance between the pairs of adjacent atoms i and j;and b ij is a many-bond empirical bond-order term.The Buckingham-type potential130has been also used to describe the interatomic interactions of nanowires

X N

i?j Aeàr ij qà

r ij

tV long r ij

eT;(26)

where N is the total number of ions.The short-range parame-ters A;C and q were developed by Catlow131and Catlow and Lewis.132V longer ijT?q i q j=r ij is the long-ranged Coulombic interaction,where q i and q j are the atomic charges.

Further to force?elds,auxiliary algorithms are also needed to impose initial boundary conditions and to control system states,such as temperature and pressure,during simu-lations.Among varied methods proposed in literature, Nos e–Hoover,133,134Andersen,135and Berendsen,136ther-mostats has been commonly used as the most accurate and ef?cient methods to re-scale velocities of atoms in MD simu-lations for constant-temperature simulations.Molecular sim-ulations have been widely employed to study the dynamics of nano-materials.However,the review is only restricted to classical MD simulations of CNT,GS,and nanowire resonators.14,16,17,24–26,29,43,45,47,91,92,137–144

Duan et al.143investigated the free vibration of single-walled CNTs(SWCNTs)using MD simulations and the non-local Timoshenko beam model.They investigated the effect of boundary conditions and the length-to-diameter aspect ratio of nanotubes on their resonant https://www.sodocs.net/doc/0118457404.html,ing the molecular simulations,they also calibrated the small-scale parameter.In the simulations,143the condensed-phase opti-mized molecular potentials for atomistic simulation studies (COMPASS)force?eld is used to describe the interatomic interactions.The parameters of COMPASS145–147force?eld have been?tted using ab initio and empirical data.The force ?eld has been proven to be applicable for describing the dynamic response of nano-materials.

Ansari et al.91used MD simulations to investigate the free vibration of square single-layered GSs(SLGSs)with different sizes and boundary conditions.The simulation results were then compared to those obtained from the nonlo-cal plate model to calibrate the appropriate values of the small-scale parameter.The molecular simulations are con-ducted using adaptive intermolecular reactive empirical bond order(AIREBO)potential148that is developed to model hydrocarbon molecules.In the simulations,91one atomic layer at all edges of graphenes is set to be?xed to imitate simply supported boundary conditions.In order to initiate a vibrational motion,a GS is?rst deformed to a vibrational mode shape.The graphene is then allowed to freely vibrate.The histories of the geometric center of free atoms are recorded for a certain duration depending on the size and the boundary conditions of the GS,and then the vibration frequencies are computed using the fast Fourier transform method.91,92Molecular simulations are also employed to study dynamic behavior of nanowires.

Jiang et al.138performed MD simulations to explore the effect of polar surfaces on the Q-factor of zinc oxide(ZnO) nanowire-based nanoresonators.In their simulations,the interatomic interactions are described by the Buckingham-type force?eld.131,132The Nos0e–Hoover thermostat133,134is used to equilibrate the system at a constant temperature.The transverse vibrational motion is then induced by adding a velocity distribution to a ZnO nanowire,which follows the morphology of the?rst bending mode of the wire.The system is allowed to vibrate freely within the NVE(i.e.,the particles number N,the volume V,and the energy E of the system are constant)ensemble.The decay of the oscilla-tion amplitude of the kinetic or potential energy is then used

to measure the Q-factor.Different methods have been used in the literature to calculate the Q-factor.138,144,149–151The maximum potential energy(E)is reduced to EàD E at the end of each oscillation cycle due to energy loss or damping, where D E represents the energy loss in each oscillation cycle.The Q-factor is thus de?ned as Q?2p E=D E.At the end of n cycles,the maximum potential energy E n is related to the initial maximum potential energy(E)by E n?Ee1à2p=QTn.149Jiang et al.138proposed a method to measure the Q-factor by?tting the kinetic energy of a reso-nator to a function EetT?atbe1à2p=QTt cosex tT,where x is the frequency,a and b are two?tting parameters,and Q is the resulting Q-factor.

Note that the choice of the correct potential is one of the most important factors in MD simulations.This choice depends on the various conditions such as the nature of simu-

lations,the material being simulated,and the trade-off between accuracy and computational ef?ciency.

C.Multiscale methods

Generally,a multiscale model can involve continuum and atomistic descriptions of a material at each scale. Multiscale methods are generally classi?ed into hierarchical, semi-concurrent,and concurrent methods.152–155In hierarch-ical or non-concurrent multiscale approaches,information of the?ne-scale is passed to the coarse-scale.A macroscopic constitutive model is assumed and parameters of the model are computed from the microstructure.In semi-concurrent multiscale methods,there is an interaction between the?ne-scale and the coarse-scale during simulations.In concurrent methods,the?ne scale domain is included in the geometry. Studies,which are available in the literature on modeling of nanoresonators using multiscale simulations,usually fall in the?rst category,i.e.,hierarchical methods.

Shi et al.156have numerically studied the free vibration of SWCNTs and multi-walled CNTs(MWCNTs)using atomic?nite element method(AFEM).AFEM is an improved multiscale computation method developed to study static and dynamic behaviors of nanostructures.157,158In AFEM,FEM is applied to both discrete atoms and contin-uum solids.An important advantage of AFEM compared to other multiscale methods is that the atomistic and continuum domains are monolithically linked to each other since they are within the same framework of FEM.The key idea of AFEM is to reduce the number of degrees of freedom by the introduction of a mesh(unit cell),which includes a set of atoms as illustrated in Figure2.It is assumed that the set of atoms in a mesh undergoes a homogeneous deformation.

Li and Chou61,62,159,160have developed the molecular structural mechanics method to characterize the mechanical behavior of CNTs.The concept of this method originated from the observation of geometric similarities between nano-structures and macroscopic space frame structures,where nanotubes are viewed as space frames with beams connect-ing carbon atoms.Following the theory of structural mechan-ics,only three stiffness parameters are required to model the structures:the tensile resistance(EA),the?exural rigidity (EI),and the torsional stiffness(GJ).They are obtained by equality between the potential energy of the atomistic model and the strain energies in structural mechanics.The strain energy for a beam element is given by61,159

U At

U Mt

U T;(27) where U A;U M;and U T are the strain energies for axial ten-sion,bending,and torsion.The energy equivalence between Eq.(27)and the total potential energy of molecular mechan-ics yields explicit relations between the structural mechanics parameters and the molecular mechanics force?eld con-stants as159

?k r;

?k h;

?k s:(28)

Li and Chou62,159,160examined the capability and ef?-ciency of the method in the modeling of free vibration of CNTs and mass detection using nanotube resonators.

Zhao et al.161developed a coarse-grained(CG)model for SWCNTs to study their static and dynamic behaviors. The explicit expressions for stretching,bending,and torsion force?elds of the CG model were derived.Non-bonded CG force?eld between non-connected beads is obtained from analytical results based on the cohesive energy between two nanotubes.Their results show that the CG non-bonded can accurately describe vdW interactions between SWCNTs compared to full MD simulations.Further studies are needed to develop CG models for nanowires and to derive potential functions for them.The evaluation of CG models in predict-ing resonant frequencies and the dispersion relation of nano-resonators is also recommended in the future.

III.DYNAMIC CHARACTERIZATION OF NANORESONATORS

Now,we turn our attention to the dynamic behavior of CNTs,GSs,and nanowires.Intense interests in gigahertz physics of nano-scale materials53,162,163have drawn more attention to vibrational characteristics and phonon dispersion relation of the nano-materials.The study of vibration and wave propagation in CNTs,GSs,and nanowires has there-fore technological importance in gaining a thorough under-standing of their dynamic behavior.The factors

in?uence the dynamic behavior of CNTs,GSs,and nano-wires such as geometrical parameters,surrounding medium, temperature,and boundary conditions are reviewed in Sec.III A.

A.Resonant frequencies

Zhang et al.164developed a nonlocal beam model for the free vibration of double-walled CNTs(DWCNTs)and studied the small-scale effect on the vibrational behavior of CNTs.The free vibration of SWCNTs and DWCNTs based on nonlocal beam theories was investigated by Wang and Varadan.73They derived the small-scale effects on resonant frequencies of CNTs and demonstrated that the small-scale effects decrease with an increase in the length of a CNT.Lee and Chang165developed a nonlocal Euler–Bernoulli beam model for vibration of nanotubes?lled with?uids.They reported that the small-scale effect on the fundamental reso-nant frequency increases with a decrease in the velocity of ?uids.In addition,the viscosity effect on the resonant fre-quency becomes noteworthy when the velocity of increases. Wang166obtained resonant frequencies and critical?ow

velocities for?uid-?lled nanobeams using the nonlocal beam model.Results indicate that scale effects are noticeable in nanoscale lengths.The dynamic response of nanotubes sub-jected to the excitation of a moving nanoparticle was studied using nonlocal continuum theory.167,168Based on the nonlo-cal continuum theory,elastic beam models were developed for the analysis of dynamical behavior of?uid conveying SWCNTs embedded in an elastic medium.169Mahdavi et al.170studied the nonlinear vibration of SWCNTs embed-ded in polymer matrices.The vdW forces between a CNT and matrix are modeled by a nonlinear function of the de?ec-tion of nanotube.They derived the relation between de?ec-tion amplitudes and resonant frequencies of the nanotubes, which is found to be sensitive to boundary conditions and length-to-diameter aspect rations of the tubes.Ke et al.97 developed a Timoshenko beam model based on the nonlocal elasticity theory and von K a rm a n geometric nonlinearity to study nonlinear free vibration of embedded DWCNTs.They explored the effects of the small-scale parameter,length-to-diameter aspect ratios of nanotubes,and boundary conditions on the nonlinear free vibration characteristics of DWCNTs. They concluded that an increase in the small-scale parameter leads to smaller linear(x l)and nonlinear(x nl)resonant fre-quencies but a higher frequency ratio(x nl=x l).Figure3 shows the effect of the small-scale parameter on the frequency ratio of DWCNTs.From the?gure,nanotubes exhibit a hard-spring behavior,i.e.,the nonlinear frequency ratio increases with an increase in the vibration amplitude. Both linear frequency and nonlinear frequency ratio become lower as the aspect ratios of CNTs increases.96Eichler et al.171investigated the damping mechanism in CNT and graphene resonators.They observed that the damping strongly depends on the amplitude of oscillation,and hence should be described by a nonlinear damping force.They reported that the nonlinear damping enables to improve the Q-factor of the resonators.

Although the published studies have obviously shown the small-scale effect on dynamic responses of CNTs,it is again suggested that the veri?cation of results obtained by nonlocal continuum models and calibration of the small-scale parameter are indispensable for applicability and justi-?cation of the models.

In this view,Arash and Ansari84derived a nonlocal shell model based on FSDT to study the vibration behavior of SWCNTs with clamped(CC),simply supported(SS),and clamped-free(CF)boundary conditions under an initial https://www.sodocs.net/doc/0118457404.html,ing results obtained from molecular simulations, they calibrated the small-scale parameter for each boundary condition for a broad range of length-to-diameter aspect ratios.Based on the simulation results,the small-scale parameter depends on end conditions,and varies from1.7to 2nm for CC and CF(5,5)SWCNTs,84respectively.Ansari et al.137investigated the free vibration of SWCNTs and DWCNTs with different boundary conditions with MD sim-ulations at room temperature.137Their simulation results indicate that the fundamental resonant frequency of a CC(5, 5)SWCNT decreases with an increase in the aspect ratio of the tube.From their simulation results,it is observed that the resonant frequency of CNTs strongly depends on their end conditions.The fundamental resonant frequency versus length response of(5,5)SWCNTs with CC,SS,and CF boundary conditions are presented in Figure4.This?gure demonstrates that the fundamental resonant frequency of a CNT with the stiffest boundary conditions,i.e.,CC,is the highest.For example,the fundamental resonant frequency of a CC(5,5)SWCNT with a length of2.45nm is1.9763THz. While the resonant frequencies of the nanotubes with the same size and SS and CF boundary conditions are1.2285 THz and0.4337THz,respectively.It indicates a percentage decrease of37.8%and78.05%.The percentage differences reduce to9.66%and46.21%in a length of9.85nm,which reveal that the effect of boundary conditions is less signi?-cant at high aspect

ratios.

FIG.3.The effect of the small-scale parameter on frequency ratio versus amplitude curves of DWCNTs with an aspect ratio of20and simply sup-ported boundary conditions.Reprinted with permission from Ke et al., Comput.Mater.Sci.47,409(2009).Copyright2009Elsevier.

Pradhan and Phadikar 102reformulated the CLPT and the FSDT using the nonlocal constitutive relations of Eringen to study free vibrations of GSs.The difference in the frequen-cies predicted by CLPT and FSDT is signi?cantly smaller for double layered plate than that of single layered plate.172A nonlocal plate model based on FSDT was derived to inves-tigate vibrational characteristics of multi-layered GSs (MLGSs).87,89,173A nonlocal plate model for the nonlinear vibration of SLGSs in thermal environments was pre-sented,90and the small-scale parameter was calibrated by matching the resonant frequencies of SLGSs obtained from MD simulation results with those of the nonlocal plate model.90Ansari et al.91studied the free vibration of square SLGSs with clamped and simply supported boundary condi-tions using MD simulations.Their simulation results show that the fundamental resonant frequency of a square SLGS with simply supported edges decreases from 0.059to 0.003THz with an increase in the side length of the sheet from 10to 50nm.The resonant frequency of a clamped graphene also varies from 0.115to 0.006THz with an increase in the size of the sheet from 10to 50nm.91Ansari et al.91devel-oped a nonlocal plate model for the free vibration of SLGSs,and calibrated the small-scale parameter for different bound-ary conditions using results of molecular simulations.Their simulation results show that the magnitudes of the small-scale parameter are 1.41nm and 0.87nm for simply sup-ported and clamped graphenes,respectively.Arash and Wang 92investigated free vibrations of SLGSs and double-layered GSs (DLGSs)with different boundary conditions using the nonlocal plate model and MD simulations.They showed that the local plate model overestimates the resonant frequencies of the sheets with a percentage difference up to 62%at sizes of 2.47nm.92Their results showed that the dif-ference between local and nonlocal plate models remains signi?cant in all aspect ratios as presented in Figure 5,and the overestimation is around 50%at aspect ratio of a =b ?4.Therefore,the nonlocal plate model is strictly necessary for the rectangular GSs with a short side.

Besides CNT and GS resonators,nanowire resonators are rapidly emerging as one of the basic building blocks for

current and future nanoelectromechanical systems.151,174Olsson et al.175studied the effect of shearing and rotary iner-tia on resonant properties of unstressed and prestressed gold nanowires.They modeled nanowires using MD simulations and Euler-Bernoulli and Timoshenko beam theories.They showed that Euler-Bernoulli theory overestimates resonant frequencies of nanowires in high resonant modes due to the increasing importance of shearing and rotary inertia in high resonant modes.In contrast,resonant frequencies predicted by Timoshenko beam theory,which account for shearing and rotary inertia,are in good agreement with those obtained from molecular simulations.175The elastic properties of the nano-materials are strongly size-dependent.176–178This size-dependent nanowire behavior is because of surface stresses,which are rooted in the large surface area to volume ratio.It implies that the modeling of the resonators must capture their size-dependent material properties.Park 179studied variations in resonant frequencies of metal nanowires sub-jected to tensile and compressive strain using the surface Cauchy–Born model,which captures surface stress effects.The resonant frequencies of nanowires are more sensitive to compressive than tensile strain.179The resonant frequencies of nanowires was shown to be size dependent,180especially when its cross-sectional sizes decreases to nanoscales.Figure 6shows the fundamental resonant frequency ratio (p 1=p 01)of a nanowire with respect to its diameter (D),where p 1and p 01are the fundamental resonant frequency calculated with and without including the surface effect,respectively.From Figure 6,both the surface effects and the shear defor-mation become prominent in the resonant frequency of small-diameter nanowires.

Future studies are recommended on verifying continuum models,considering the surface effect,and calibrating the surface effect parameters with molecular simulations.

B.Wave dispersion relations

Wang 67?rst investigated the wave propagation in CNTs with nonlocal elastic Euler-Bernoulli and Timoshenko

beam

Elsevier.

FIG.5.Fundamental resonant frequencies of rectangular SLGSs with CCCC boundary conditions (b ?2:46nm).Reprinted with permission from B.Arash and Q.Wang,J.Nanotechnol.Eng.Med.2,011012(2011).Copyright 2011ASME Publications.

models.The work showed the importance of scale effects,and revealed the limitation of models based on local contin-uum mechanics in the analysis of nanotubes.It was also found that the experimental results are qualitatively in agree-ment with the simulations derived from nonlocal continuum models.Further,it was suggested that a conservative esti-mate for the small-scale parameter can be obtained as e 0a <2:1nm for wave propagation of a SWCNT.Wang and Hu 181studied the ?exural wave propagation in armchair (5,5)and (10,10)SWCNTs for a wide range of wave numbers using the nonlocal beam models and MD simulations.Their results show that the nonlocal Timoshenko beam model provides a better estimation for wave dispersion relations in SWCNTs than the nonlocal Euler beam as shown in Figure 7.They

proposed the scale coef?cient e 0?0:288for a wide range of wave lengths from $0.2nm to $70nm for the ?exural wave propagation in a SWCNT by comparing the results of the nonlocal Timoshenko beam model with MD simulation results.Such a speculation of a unique coef?cient may not be practical as pointed out later.15,94

The nonlocal Euler–Bernoulli and Timoshenko beam models were developed by Wang et al.182to investigate the small-scale effect on the wave propagation in DWCNTs.Wang and Varadan 85reported that the nonlocal shell theory is necessary in estimating CNT phonon dispersion relations.Hu et al.183modeled CNTs with the nonlocal shell model,and indicated that the wave dispersion relations obtained by the nonlocal shell model are in good agreement with those of MD simulations.They also reported that the nonlocal shell model is indispensable when the wavelength is less than 2.36nm for transverse wave propagation.Also,nonlocal shell models are required for wavelengths smaller than 0.95nm for torsional waves.183There is a certain band gap region in both ?exural and shear wave modes in which no wave propagation occurs.86The frequency at which this phenomenon occurs is called the escape frequency,which is proportional to the small-scale parameter.Nonlocal beam models based on the Euler-Bernoulli and Timoshenko beam theories were derived to study the wave propagation in CNTs with different boundary conditions.184Waves propa-gating in CNTs subjected to initial axial stress and ?uid-con-veying was studied in Refs.88and 185.Further studies are suggested to study the effect of surface stresses on the dis-persion relation in CNTs,especially CNT resonator interact-ing with active component.The energy dissipation during the wave propagation in CNTs is another topic of interest for an in-depth understanding of dynamic behaviors of nanotube resonators.Arash et al.25developed a ?nite element

model

FIG.6.The natural frequency of a nanowire with a length-to-diameter ratio (l =D )of 5versus its diameter D .The surface effect parameters are set to be s s ?0:89Nm à1and E s ?1:22Nm à1.Reprinted with permission from G.-F.Wang and X.-Q.Feng,J.Phys.D:Appl.Phys.42,155411(2009).Copyright 2009IOP

Publishing.

FIG.7.The dispersion relation of the armchair (5,5)carbon nanotube (local Euler-Bernoulli beam model (E),non-local Euler-Bernoulli beam model (NE),local Timoshenko beam model (T),nonlocal Timoshenko beam model (NT),and MD simulation (MD)).(a)The phase velocity of ?exural wave versus wave number.(b)The zoom of (a).(c)The phase velocity of ?exural wave versus wave length.(d)The zoom of (c).Reprinted with permission from L.Wang and H.Hu,Phys.Rev.B 71,195412(2005).Copyright 2005American Physical Society.

from the weak-form of the elastic plate model.The applic-ability of the?nite element model is veri?ed by MD simula-tions.They showed the small-scale effect is signi?cant at wavelengths less than1nm,where the nonlocal plate model is indispensable in predicting graphene phonon dispersion relations.Their simulation results show that the wave veloc-ity decreases to an asymptotic value when the width of sheets increases to an adequately large size as presented in Figure 8.Further studies are suggested to explore the energy dissi-pation mechanism and the in?uence of the surface effect on the dispersion relation in graphene.A high-order continuum model concerning the surface effect was developed to study the wave propagation in nanowires.186Future studies should verify this continuum model with molecular simulations and calibrate the surface effect parameters.

C.Energy dissipation mechanism in nanoresonators

Nanoresonators are promising in detection of masses, forces,and pressure due to their extremely low mass. However,the key issue limiting the sensitivity of the resona-tors in practical applications is the Q-factor.171,187,188The Q-factor is de?ned as the ratio of the energy stored to the energy dissipated by losses in an oscillator.The parameters affecting the Q-factor can be categorized as intrinsic and ex-trinsic.Extrinsic damping is owing to the interactions of a nanoresonator with its surrounding environment such as for-eign atoms/molecules.Intrinsic damping is because of inher-ent?aws or defects in the structure of a resonator such as dislocations,grain boundaries,and crystalline impurities. There are essentially four major loss mechanisms for nanore-sonators:(1)surface losses,189–191(2)clamping or support losses,192–194(3)gas damping losses,188,195and(4)thermo-elastic damping losses.196,197Surface and thermoelastic damping losses are intrinsic damping parameters,while clamping and gas damping losses are extrinsic damping factors.

Poncharal et al.198introduced methods for investigating the dynamic behavior of CNTs in a transmission electron microscope.Nanotubes with lengths ranging from5to 20l m and diameters varying from8to40nm were reso-nantly excited at the fundamental frequency.The Q-factors of the nanoresonators were measured to be on the order of 500.198Jensen et al.199built a tunable nanoresonator com-prised of a specially prepared MWCNT suspended between a metal electrode and a mobile,piezo-controlled contact. The tunable nanoscale resonator operates at frequencies up to300MHz and is tunable over a range of100MHz with a Q-factor up to1000.The relatively high Q-factor indicates that sliding friction between telescoping sections of the reso-nator is an insigni?cant source of dissipation.199 Experimental studies187reported Q-factors around1000for cantilevered MWCNTs with diameter of20nm at room tem-perature and in a vacuum.Jiang et al.149studied the intrinsic energy dissipation of cantilever SWCNTs and DWCNTs using MD simulations.They investigated the dynamic response of a(5,5)cantilever SWCNT with a length of $3nm,and reported that the Q-factor of the CNT oscillators varies with the temperature(T)following the1=T0:36de-pendence.Their simulation results show that the Q-factor of the(5,5)CNT drops from2?105at0.05K to1:5?103at 293K as shown in Figure9.They indicate that the interlayer interaction introduces a new energy dissipation so that the energy dissipation in DWCNT resonators is much faster than that in SWCNTs.Further studies are recommended on the energy dissipation of nanotube resonators in gaseous and liquid environments.The effect of chirality of CNTs on the Q-factor is another topic of interest.

The resonance frequencies of graphenes are tunable with both electrostatic gate voltage and temperature,and their Q-factors signi?cantly increases up to9000at10K.200 The Q-factor of graphene resonators further increases to104 at5K.201Eichler et al.171studied the damping mechanism in CNT and GS mechanical resonators subjected to tensile stress at low temperature and in high vacuum.They found that the damping strongly depends on the amplitude of motion.They could achieve a Q-factor of105for a GS reso-nator with a size of2l m?800nm at90mK.The Q-factor of a20nm thick MLGSs were found to range from100

to FIG.8.Variation of the phase velocity versus the width of a GS with a

length of15.03nm subjected to a harmonic de?ection of period T?500fs.

Reprinted with permission from Arash et al.,Comput.Methods Appl.Mech.

Elsevier.

FIG.9.(a)The internal energy of a(5,5)SWCNT at the peak of its oscilla-

tion at an initial temperature of8K.(b)The Q-factor versus temperature de-

pendence for the(5,5)SWCNT.Reprinted with permission from Jiang

Physical Society.

1800as the temperature decreased from 300to 50K.163Kim and Park 44utilized MD simulations to investigate the intrin-sic loss mechanisms of GS nanoresonators.They observed that edge modes of vibration are the governing intrinsic loss mechanism that reduces the Q-factor.Molecular simulations were performed to study graphene-based torsional mechani-cal resonators.142The simulation results reveal the radius de-pendence of the Q-factor as Q ?2628=e22R à1t0:004R 2T.The effects of intrinsic grain boundaries on the Q-factor of monolayer CVD-grown graphene nanoresonators were stud-ied using MD simulations.46It was found that the Q-factors of a graphene with grain boundaries are 1–2orders of magni-tude smaller than its pristine graphene counterpart.It was also demonstrated that the Q-factors can be signi?cantly ele-vated by application of modest (1%)tensile strain.46Jiang and Wang 45performed MD simulations to explore edge effects on the Q-factor of graphene nanoresonators with dif-ferent edge con?gurations and various sizes.Q-factor of 3?105is obtained for all kinds of graphene resonators when periodic boundary conditions (PBC)are applied.However,for free boundary conditions (FBC),the Q-factors are greatly reduced by two effects resulting from free edges:(1)the imaginary edge vibration effect and (2)the arti?cial effect.Imaginary edge vibrations exist at free zigzag edges,which imply the instability of free zigzag edges.Imaginary edge vibrations will ?ip between a pair of doubly degenerate warping states during the vibration of a nanoresonator.The ?ipping process breaks the coherence of the vibrational motion,which is the main reason for extremely low Q-factors.The arti?cial effect occurs when a graphene reso-nators is actuated according to an arti?cial vibration mode different with the resonant vibration of the system.Figure 10shows that the Q-factor of a graphene resonator with a size of 1:97?12:78nm and FBC is about three orders smaller than the nanoresonator with PBC in the whole temperature range.Molecular simulations have revealed that the intrinsic energy dissipation in single-layered MoS 2nanoresonators is signi?cantly lower than SLGSs,and thus their Q-factor is higher 139as presented in Figure 11.Furthermore,the higher Q-factors provide MoS 2nanoresonators with higher ?gure of

merits (frequency times Q-factor)compared to graphenes with the same size (see Figure 11).The simulations reveal the potential of MoS 2for high frequency sensing and actua-tion applications.

Further studies are suggested to evaluate the energy dis-sipation mechanism in nano-sheet resonators in gaseous and liquid environments,which would develop novel design of the nanoresonators for speci?c applications such as sensing and detection.

Jiang et al.138investigated the vibration response of zinc oxide (ZnO)nanowires with two different surface condi-tions:reduced surface charges to stabilize the polar surfaces,and free polar surfaces.They found that the Q-factors of ZnO resonators with free polar surfaces are about one order of magnitude higher than nanoresonators with reduced charges on the polar surfaces.The intrinsic energy dissipa-tion in nickel and copper nano-wires under axial and trans-verse vibrational modes was studied by Kunal and Aluru.144The Q-factor was found to be lower for the axial motion compared to the transverse mode.It is also observed that the difference in Q-factor between the two modes increases with a decrease in cross-sectional area of nanowires.

IV.APPLICATION OF NANORESONATOR IN SENSORS

In Sec.IV A ,the potential applications of nanoresona-tors for detecting atoms/molecules with a vibration and wave propagation analysis are introduced and some important studies on differentiation of distinct gases and DNA mole-cules are reviewed in

detail.

FIG.10.Q-factor versus temperature for a graphene resonator with a size of 1.97?12.78nm,and PBC and FBC.Reprinted with permission from J.-W.Jiang and J.-S.Wang,J.Appl.Phys.111,054314(2012).Copyright 2012AIP Publishing

LLC.

FIG.11.Temperature dependence of the (a)Q-factor and (b)?gure of merit (f ?Q )for graphene and MoS 2nanoresonators.Reprinted with permission from Jiang et al .,Nanoscale 6,3618(2014).Copyright 2014RSC Publishing.

A.Detection with vibration analysis

Poncharal et al.198?rst proposed the idea of using CNTs as nanoresonator sensors.Masses sensitivity resolution in the range of pictogram(10à12g)to femtogram(fg)(10à15g) was measured using the dynamic response of cantilever MWCNTs in a transmission electron microscope.202A CNT resonator sensor with a diameter of3.5nm and a length of 300nm was experimentally designed and examined by which a sensitivity resolution of attogram(10à18g)was reached at room temperature.203A mass sensitivity resolution of25 zeptogram(25?10à21g)204was experimentally realized by a SWCNT resonator sensor with a diameter of1nm and a length of900nm at room temperature.The sensitivity resolu-tion was further improved to 1.4zeptogram at5K.An improved sensitivity resolution of0.066zeptogram(Ref.53) was achieved using a SWCNT resonator sensor with150nm length and$1nm diameter.Mass sensitivity resolution of 1.7yoctograms(1.7?10à24g),19which corresponds to the mass of one proton,was reported using a$150nm long CNT with1.7nm diameter as a nanoresonator sensor.

The experimental investigations guaranteed ultra-sensitive nanoresonator sensors for detection of atoms and molecules.In spite of the high sensitivity resolution reported in experiments,experimental studies are limited to detect only one species.The application of nanoresonator sensors in distinction of various types of compounds with close den-sities is still a challenge.Furthermore,the performance of sensors in experiments strongly depends on surrounding con-ditions such as temperature and environmental noises.19 These drawbacks hinder realizations of additional potentials of the sensors.

In view of the developments and limitations of experi-ments,molecular simulations were developed,which enabled the investigation of dynamics characteristics of nanoresonator sensors in detail.Arash et al.17employed MD simulations to study the application of SWCNT resonator sensors in detection of noble gases.They investigated the vibrational responses of the CNTs surrounded with gas atoms to explore their sensitivity resolution.A sensitivity index representing frequency shifts of the nanotube resonator sensors is de?ned as100ef0àf atomsT=f0,in which f atoms and f0are resonant frequencies of a CNT with and without sur-rounding atoms,respectively.A nanotube resonator sensor is then employed to differentiate three types of noble gases,i.e.,Helium(He),Neon(Ne),and Krypton(Kr),that sur-round the CNT.The non-bonded interactions between gas atoms and the nanotube are simulated by6–12Lennard-Jones potential.They reported that the sensitivity resolution of a$5nm long(8,8)CNT can reach an order of10à6fg.It is also observed that when densities of the noble gases around the CNT are8–10Natoms/nm2,the sensitivity index varies from5%to11%for He,27%to32%for Ne,and42% to47%for Kr atoms.These?ndings initiate an ef?cient detection method of distinct atoms,and endorse the applic-ability of the sensors in detecting noble gases.The proposed method based on the vibration analysis was then extended to detect DNA macromolecules whose structures include a number of nucleobases,i.e.,adenine(A),cytosine(C),gua-nine(G),and thymine(T).14An introduction of the simula-tion study14is brie?y introduced in the following.A15nm long(5,5)CNT based nanoresonator sensor is wrapped with a single stranded DNA(ssDNA),while the interaction between the strand and the nanotube is driven by vdW forces.205,206To examine the sensitivity of the sensor,the fundamental resonant frequency of the nanotube is?rst compared to that wrapped by a10-base ssDNA (AAGAAAAAAT).The atomic mass of the ssDNA strand is around1348Da.In simulations,the transverse vibration is induced by applying an initial velocity of0.5nm/ps in the transverse direction to all atoms except the?xed ones at two ends of the tube(see Figure12).The resonant frequencies of the pristine nanotube and the nanotube wrapped by the ssDNA are calculated by the fast Fourier transform(FFT) presented in Figure13.From the?gure,the resonant fre-quencies are0.116THz and0.074THz,respectively.The sensitivity is hence found to be36.31%showing the potential of CNT resonator sensors in detecting macromolecules such as DNA.The simulations also disclose that the method is an ef?cient way to recognize distinct DNA strands even with the same number of bases.14The research provides a rapid method for detection of macromolecules such as DNA.

It should be noted that the proposed nanotube resonator sensors are unable to recognize a particular type of com-pounds in a combination of several species.Therefore,more studies should focus on enhancing the ability of nanoresona-tor sensors in selective detection of a speci?c type of atoms and molecules among different species in a sample.In addi-tion,more studies are needed to enhance the Q-factor of the nanoresonators,which could enable the sensors to detect

in FIG.12.Snapshots of a(5,5)CNT with a length of15nm wrapped by a 10-base ssDNA(AAGAAAAAAT)of the?rst ten bases SPR-2A gene. Reprinted with permission from Arash et al.,J.Nanotechnol.Eng.Med.3, 020902(2012).Copyright2012ASME Publications.

aqueous environments.Currently,the large energy dissipa-tion of nanoresonator sensors hinder their successful applica-tion in detecting atoms/molecules in aqueous environments such as Ca2t,Cr2t,and Cs tin water.15

Further to the application of CNTs in nanoresonator sensors,recent studies on nanoresonators made of nano-sheets 38,39,163have opened a new area that promises ultra-sensitive sensors.By studying nano-electromechanical systems made of SLGSs and MLGSs,Bunch et al.163reported that the high Young’s modulus,the extremely low mass,and the large surface area of the sheets,make these nanoresonators ideal candidates for mass sensors.Inspired by the experimen-tal studies,the potential of GS resonator sensors in detecting noble gases was investigated by Arash et al.16using MD sim-ulations.The sensitivity resolution of graphene mass sensors can reach an order of 10à6fg.These ?ndings endorse the capability of the sensors in the detection of distinct gases.

Further experiments are still needed to explore the potential of graphenes in detecting atoms/molecules and dif-ferentiating distinct types of atoms/molecules.Owing to the unique properties of graphenes,future studies on nanoreso-nator sensors made of graphenes can encompass the detec-tion of macromolecules such as DNA.The future studies should be also conducted on selective detection of distinct compounds among different species with the sensors.In addition,investigations on the improvement of the Q-factor can be another research area,which may extend applications of graphene resonators as sensors in aqueous environments.

B.Detection with wave propagation analysis

In recent years,interests have been generated in the area of gigahertz physics of nanodevices,207,208which have opened a new research area on nano-materials wave charac-teristics.The formation of ripples in graphenes stroked by C60molecules was recently investigated 208and it was dis-cussed that the propagation of the ripples in GSs can be used to detect defects in the sheets.The wave propagation in CNTs and GSs was later investigated to examine the

applicability of designing nanoresonator sensors based on a wave propagation analysis.24–26The essence of the detection is that atoms or molecules on a CNT or graphene sensor would induce a shift in the wave velocity (or phase velocity).In this section,the potential of CNTs and GSs as nano-resonator sensors based on a wave propagation analysis is explored.

In sensors operating based on the vibration analysis,measuring a vibrational motion with a frequency in the range of gigahertz in a relatively long period of time is indispensa-ble.Although the sensors may ful?ll a successful detection of compounds,surrounding noise signals may affect recod-ing trajectories of atoms in a long time.The restriction of accurately measuring ultra-high frequencies may hinder additional applications of the vibration-based sensors.With respect to this restriction,Arash and Wang 26proposed a CNT-based resonator sensor by studying the propagation of impulse waves in nanotubes,which enables to succeed a pre-cise detection in a shorter time compared to the vibration-based sensors.Recording trajectories of atoms in a shorter time enable to remove the negative effects of environmental noises.Moreover,the high bending rigidity of CNTs com-pared to GSs 209avoids the occurrence of ripples in the nano-tube sensors,which ensure a reliable measurement process.To study the applicability of the wave propagation-based sensors,the impulse wave propagation in a $100nm long (22,22)CNT was studied using MD simulations.26In simu-lations,two ends of the tube illustrated by E1and E2in Figure 14(a)are ?xed.An impact load is then applied at the impacted portion of the CNT as illustrated in red in Figure 14(a).The impact is induced by applying an initial velocity to carbon atoms at the impacted portion.The impact loading then generates an impulse wave along the nanotube that propagates as shown in Figure 14(b),and reaches the acquir-ing location as illustrated in Figure 14(c).The wave velocity in the CNT is calculated to be c 0?3500:95m =s.Following the similar procedure,the wave velocity in the nanotube surrounded by Ar atoms at room temperature and pressure with a mass density of 1.6g/cc is obtained to be c g ?3482:41m =s.The sensitivity of the nanotube sur-rounded by Ar atoms with the mass density of 1.6g/cc is therefore calculated to be 0.53%by de?ning a sensitivity index as 100ec 0àc g T=c 0.The wave velocities in the sensor surrounded by Kr and Xe gases are,respectively,3464.11m/s and 3445.97m/at the environmental conditions,revealing sensitivities of 1.05%and 1.57%for Kr and Xe gases,respectively.The ?ndings rationalize the feasibility of the wave propagation-based sensors in detecting different gases at the same environmental conditions of temperature and pressure.

The ?ndings on the sensors operating based on the wave propagation analysis should be realized in future studies.Additional studies on detecting macromolecules with the res-onator sensors are also recommended.The energy dissipa-tion of the nanoresonator sensors in aqueous environments is also suggested to be investigated in the future studies,which could be useful in extending the application of the sensors in aqueous

environments.

FIG.13.Resonant frequency response of a 15nm long (5,5)CNT versus resonant frequency of the nanotube wrapped by a 10-base ssDNA (AAGAAAAAAT).Reprinted with permission from Arash et al .,J.Nanotechnol.Eng.Med.3,020902(2012).Copyright 2012ASME Publications.

Wave propagation-based sensors made of graphenes were also proposed in the literature.25A nonlocal plate model that accounts for the small-scale effect was developed for the analysis of wave propagation in graphenes using FEM.25The FEM model was validated with molecular simu-lations,and the small-scale parameter was determined using results of molecular simulations.The wave velocity in pris-tine graphene is calculated to be 2:42?103m =s.25Similarly,the wave velocity is measured in a graphene with the same size attached by 30Xe,48Kr,100Ar,and 200Ne atoms with a mass of around 6:7?10à6fg for each type of atoms.The sensitivity is obtained to be around 20%,16%,12%,and 8%for Xe,Kr,Ar,and Ne atoms,respectively.The results indicate that the GS resonator sensor operating based on the wave propagation analysis can differentiate dis-tinct gases with the same mass.In previous studies on nano-resonator sensors,surrounding atoms or molecules are assumed to be initially attached on the surface of the sensors,where their density can be locally higher than their density in standard conditions.16,25Regarding the unrealistic assumption,Arash and Wang 24proposed more practical res-onator sensors based on the wave propagation analysis,where detection of gases ?owing from an aperture toward the surface of a GS with a mass ?ow rate was investigated.Meanwhile,a mechanical wave is propagating in the longitu-dinal direction of the graphene.The principle of the detec-tion is based on the measurement of wave velocity shifts in the graphene resonator sensor induced by the gaseous ?ow.The simulation results show that the sensitivity is increased with an increase in the mass ?ow rate of gases,and the sensi-tivity resolution can achieve an order of 10à7fg =ps.In order to explore the applicability of the sensor in differentiating distinct gases,the sensitivity of the GS sensor exposed to Ne,Ar,Kr,and Xe gases with the same mass ?ow rate were also investigated.The results endorse the potential applic-ability of the sensor in detecting distinct type of gases with the same mass ?ow rate.

Although the graphene sensors design based on the wave propagation analysis has been shown to be promising in detecting distinct gases,experimental realization of their applicability is required.The feasibility of the wave propagation-based graphene sensors in detection of macro-molecules should be investigated in the future as well.

V.APPLICATION OF NANORESONATOR IN MOLECULAR TRANSPORTATION

The application of CNTs in ?ltering processes has drawn attentions on achieving more practical designs of sep-aration membrane systems.The cylindrical hollow structure and smooth walls of CNTs provide an excellent opportunity of building nanopumping and nano?ltering devices for water desalination,petroleum ?ltration,and even kidney dialy-sis.210,211Different methods for transportation of atoms and molecules by CNTs have been introduced by imposing chemical potential and thermal gradients,electrical ?elds.32,33,161Since the relatively low ef?ciency of the pro-posed transportation methods,nanopumping effects on the activation of atomic/molecular ?ows in CNTs by applying mechanical loads were investigated using the propagation of torsional and impulse waves.8,27

A.Transportation with torsional waves

Recently,a novel molecular transportation method with CNTs subjected to torsion was proposed and developed in Ref.8.In this method,a CNT conveying atoms/molecules is ?rst subjected to a torsional load.The torsional load induces a buckling instability in the nanotube,which in turn forms torsional kinks.Finally,the propagation of the kinks along the CNT becomes a driving force for moving atoms inside the CNT.8Wang 8examined the method for transporting helium atoms encapsulated in a 2.35nm long (8,0)CNT using MD simulations,and investigated the dependence of the loading rate on the effectiveness and ef?ciency

FIG.14.Propagation of an impulse wave in a $100nm long (22,22)CNT.Two ends of the nanotube are restrained and the impacted portion shown in yellow is subjected to an impact load as illustrated in (a).The impact induces an impulse wave in the tube propagating along the nanotube as shown in (b).The impulse wave reaches the acquiring location as shown in (c).Reprinted with permis-sion from B.Arash and Q.Wang,Sci.Rep.3,1782(2013).Copyright 2013Nature Publishing Group.

transportation of the encapsulated atoms.The simulation study is brie?y introduced in Sec.V A .

Fig.15shows the transportation process of 10helium atoms in the CNT subjected to torsional loading at 1500K.The equilibrium state of the nanotube ?lled by helium atoms is shown in Figure 15(a).The slippery surface of nanotube allows an ultra-fast ?ow through the CNT.The nanotube undergoes a torsional instability at a torsional angle of 2.40rad as illustrated Figure 15(b),which induces a strong reduction of the cross sectional area,leading to the suf?-ciently strong vdW forces for ejecting the helium atoms from the tube.The initiation of torsional kinks and their propagation along the CNT accelerate the motion of the atoms and push them to move rightward as illustrated in Figs.15(c)and 15(d).As a result,all helium atoms are pushed out of the CNT owing to strong vdW forces.The simulations show that applying torsion to CNTs provides an alternative approach for atomic transportation.It is also con-cluded that a complete atomic transportation is possible when torsional loading with a high rate is applied to a CNT as torsional kinks expand along the nanotube to induce more vdW driving force.

The atomic transportation method using the propagation of torsional waves in CNTs was then developed to study an energy pump by pre-twisting a small portion of a long CNT

for ef?cient water transportation.27The effect of the pump length on the ef?ciency of the transportation has been partic-ularly investigated.The pump is made of a portion of the CNT with several atomic layers of carbon atoms illustrated in yellow in Figure 16(a).Two ends of the pump portion shown as E1and E2in Figure 16(a)are restrained.A pre-twisted angle is ?rst applied to E1,which induces a torsion buckling instability in the nanotube as shown in Figure 16(a).Then,the restraint on E2is removed to allow the prop-agation of the local torsion buckling along the CNT as shown in Figure 16(b).The resultant driving forces owing to the vdW forces between the nanotube wall and the encapsulated molecule initiate a molecular transportation.Finally,the water molecule leaves the CNT channel as illustrated in Figure 16(c).The study demonstrates that molecules can be successfully accelerated in a CNT channel with the pump concept.A faster and more ef?cient transportation of the water molecules is also observed for a shorter pump as more energy is stored in the shorter pump compared to its longer counterpart.

The transportation method with CNTs in torsion 8,27was then extended for separating encapsulated helium and carbon atoms.9,28It was shown that the torsional rate and angle can be adjusted to enable effective separations of different spe-cies of atoms using CNTs.9,28The principle of the molecular separation is to design nanopore systems with semi-capped CNTs so that large molecules pumped out with torsional kinks cannot permeate the pores due to the size restriction.However,the pores are permeable to small molecules.Therefore,a selective permeability can be achieved by designing precise nanometer pores.Khosrozadeh et al.28studied molecular separation of gases using a pre-twisted CNT with semi-capped end with molecular simulations.A small portion at one end of the CNT is initially twisted,which induce a torsion buckling instability in the tube.By releasing the twisted portion,torsional kinks propagate in the longitudinal direction of the nanotube.The vdW forces between the encapsulated atoms and the nanotube initiate a motion in the atoms and a consequent separation of the atoms.A successful separation of

atoms/molecules

FIG.15.Molecular dynamics simulations of 10helium atoms encapsulated in a (8,0)CNT in torsion:(a)the initial equilibrium state;(b)the end of the loading process,t ?0:5ps with all atoms in the tube;(c)t ?10ps with half of the atoms push out of the CNT;and (d)t ?25ps with all atoms ejected from the tube.Reprinted with permission from Q.Wang,Nano Lett.9,245(2008).Copyright 2008ACS

Publications.

FIG.16.Transportation of one water molecule in a (8,0)CNT.E1(blue)and E2(blue)are ?xed,and a pre-twisted angle is applied to E1,which results in a torsion buckling of the pump (yellow)as shown in (a).Once the restraint on E2is removed,the potential energy stored in the pump will push the water molecule traveling along the nanotube channel (green).The water molecule moves along the CNT channel as shown in (b).The water mole-cule leaves the CNT channel at 10ps as shown in (c).Reprinted with per-mission from W.H.Duan and Q.Wang,ACS Nano 4,2338(2010).Copyright 2010ACS Publications.

encapsulated in the nanotube is owing to the difference in their inertia and the energy barrier effect of the semi-capped.

According to the mechanism of separation behaviors using the CNT-based nanopores,the control of pore sizes is indispensable for an ef?cient permeability.However,con-trolling an accurate size of pores as well as decorating pores still remains a challenge.The experimental realization of the application of nanoresonators in the molecular transportation and the separation between different molecules is required.Furthermore,other studies are recommended to investigate the feasibility of molecular separation with CNTs in torsion in the separation between macro molecules.

B.Transportation with impulse waves

Although CNTs in torsion has been shown to be applica-ble in separating atoms/molecules,a successful separation is very sensitive to the value of torsional angle.Motivated by the limitation,a more feasible method for an effective molecular separation was proposed by Arash and Wang.29Based on the method,impulse waves propagating along a CNT induce the change of vdW potential between the nano-tube wall and encapsulated molecules in the nanotube.The variation of vdW potential then generates the required driv-ing force for moving atoms/molecules inside the nanotube.

Figure 17shows the separation of the 1600water mole-cules and a lead nanoparticle encapsulated inside a 20nm long CNT with a diameter of 3nm.The nanotube is ?rst sub-jected to an impact load at an impacted portion illustrated in green in Figure 17(a).The impact is induced by an initial

velocity of 15nm/ps in the radial direction to carbon atoms at the impacted portion.The impact load subsequently gener-ates impulse waves in the axial direction of the CNT as seen in Figure 17(b).The propagation of the impulse waves causes a reduction in the cross-sectional area of the nano-tube,leading to driving vdW forces required for a possible ejection of encapsulated molecules.However,the driving forces generated by the ?rst impact load are not strong enough to pump all water molecules out of the tube.The CNT is therefore subjected to a series of impact loads.Figures 17(c)and 17(d)show the molecular separation pro-cess at 60ps and 160ps,respectively.It can be seen that all water molecules are ejected from the nanotube at t ?160ps,while the passage of the lead nanoparticle is blocked as illus-trated in Figure 17(d).Indeed,the two graphenes at two ends of the CNT play the role of a barrier system for separating water molecules and lead nanoparticles.The impulse waves suf?ciently accelerate water molecules to pass the energy barrier for leaving the CNT.However,the pore is too small to allow the passage of the lead nanoparticle.The simulation results show that the CNT-based nanopore system enables to ful?ll a high selectivity separation of mixed molecules.In addition,contrary to the previous separation method with nanotube in torsion,9,28the CNT-based nanopore system enables to ?lter molecules without controlling the amount and rate of loads applied to nanotube.

Although the propagation of impulse waves in CNT-based nanopore systems is promising in molecular sep-aration,further studies are needed to fully evaluate the ef?-ciency of the method.Furthermore,the feasibility of the method can be explored in selective detection of a speci?c species among different species in a sample.

VI.CONCLUSION AND FUTURE CHALLENGES

Nanoresonators hold many potential applications in the ever-growing nanotechnology industry owing to their excel-lent features.A very good understanding of mechanical behaviors of the resonators is then crucial.Among different approaches for modeling nanostructures,MD simulations enable to study characteristics of nanoresonators,including detailed molecular interactions.The nonlocal continuum mechanics theory also provides an alternative method to model nanoresonators,which allows the consideration of the small-scale effects in analysis of the nano-materials.These advantages make the nonlocal continuum modeling as a con-venient way in simulating nano-materials.The nonlocal beam and shell models have been widely employed in analy-sis of dynamic problems of nanoresonators.

A successful application of nonlocal continuum models is strongly depends on the calibration of the small-scale parameter trough a veri?cation process with molecular simu-lation results or experimental tests.The magnitude of the small-scale parameter is a function of many parameters such as boundary conditions,sizes of nanostructures,number of walls,and the nature of motions.

Nanoresonator sensors made of CNTs and graphenes are promising in detecting atoms/molecules at very low concen-trations.Experimental studies on the dynamic behavior

FIG.17.Snapshots of the (22,22)CNT subjected to a periodic impact ve-locity of 15nm/ps with a period of 20ps in the radial direction to the impacted portion of the nanotube:(a)the ?rst impact load at t ?0:5ps,(b)the fourth impact load at t ?60ps,(c)the seventh impact load at t ?120ps,and (d)the end of the separation process at t ?160ps.The length of impacted portion is 1.5nm.Reprinted with permission from B.Arash and Q.Wang,Comput.Mater.Sci.90,50(2014).Copyright 2014Elsevier.

the sensors indicate that their sensitivity resolution can reach the mass of one proton(1:7?10à24g).Molecular studies on nanoresonator sensors indicate the sensors can successfully differentiate distinct atoms/molecules.Moreover,higher sen-sitivity can be achieved by smaller resonators.The sensors are effective devices to detect different DNA strands even with the same number of nucleobases.In future endeavors, the resonator sensors should be able to selectively detect a speci?c species among different species in a sample.The future studies should also focus on improving the Q-factor of nanoresonators for extending their applications as sensors in aqueous environments.

Studies on the wave propagation in CNTs and GSs reveal the applicability of design sensors based on the wave propagation analysis.In simulations of GS sensors attached with gas atoms randomly placed on the sensor,it was shown that distinct noble gases can be successfully differentiated by detecting a recognizable sensitivity.The potential of the wave propagation-based sensors subjected to an impact of different noble gases was explored with MD simulations. The sensitivity of the nanoresonator sensors can reach an order of10à7fg=ps and the resonator sensors can success-fully differentiate distinct gases.The sensitivity increases with an increase in the mass?ow rate of gases.The design of sensors based on the analysis of impulse wave propagation in CNTs showed that the resonator sensors can be employed to detect distinct noble gases at the same environmental conditions of temperature and pressure.

Molecular simulation studies demonstrated that the propagation of mechanical waves in CNTs by applying impact and torsional loading provides ef?cient methods for molecular transportation of atoms and molecules encapsu-lated in the nanotube.The proposed methods can be taken advantage in medicine applications such as drug delivery. The transportation methods have been further developed to realize ultra-high selective separation of various atoms and molecules encapsulated inside nanotubes.Simulation studios show that torsional and impulse waves propagating along a nanotube induce suf?cient vdW driving forces for a separa-tion process.While small molecules are ejected from a CNT-based nanopore system,the passage of large particles is blocked.

The current nanoresonator sensors are unable to detect a particular species of molecules among several species of molecules,which makes them unsuitable for lab-on-chip devices.In future efforts,the sensors should selectively detect a speci?c species among different species in a sample. Another limitation of the present nanoresonator sensors is that they cannot ful?ll a successful detection in aqueous environments because of large energy dissipation of viscos-ity and hydrodynamic loading effects of aqueous environ-ments.Future studies should be conducted to improve the Q-factor of the nanoresonators sensors for their potential applications as sensors in aqueous environments.

The propagation of mechanical waves in CNTs provides an alternative method for molecular transportation and high selective separation of various molecules encapsulated in the nanotubes.The experimental efforts are still required to explore the feasibility of applications of nanoresonators in the molecular transportation and the separation between dif-ferent molecules.

ACKNOWLEDGMENTS

The authors thank the support of the European Research Council-Consolidator Grant(ERC-CoG)under grant “Computational Modeling and Design of Lithium-ion Batteries(COMBAT)”.J.W.J.was supported by the Recruitment Program of Global Youth Experts of China and the start-up funding from Shanghai University.

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六年级上册语文造句、四字词语、成语填空练习(答案)

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物业管理公司合同评审工作程序-制度大全物业管理公司合同评审工作程序之相关制度和职责，质量管理程序文件--物业管理公司合同评审程序1.0目的通过对标书、合同(草案)或订单进行评审,确保其内容明确,并能准确理解用户或发展商的要求,使合同得以顺利履行。2.0适用范围... 质量管理程序文件 --物业管理公司合同评审程序 1.0 目的通过对标书、合同(草案)或订单进行评审,确保其内容明确,并能准确理解用户或发展商的要求,使合同得以顺利履行。 2.0 适用范围适用于本公司各类租赁和提供物业管理服务的标书、合同的草案及正常服务范围以外的维修或安装订单及口头订单等的评审。 3.0 定义订单:指对要求进行说明的文件或记录。 4.0 职责 4.1 总经理主持并组织有关部门或人员对物业委托管理合同或标书等重大项目合同的评审。 4.2 房屋、电话租赁合同及其他一般性服务合同由合同涉及的部门负责人组织评审,公司主管负责人负责审批。 4.3 正常服务范围以外的维修或安装订单由机电班长或订单接收人进行评审。 4.4 合同评审记录由办公室负责保存。 5.0 工作程序 5.1重大项目合同(如物业管理项目标书、物业委托管理合同等)的评审。 5.1.1 总经理负责组织有关部门或人员通过与顾客了解接触、沟通联络以及对市场的调查和分析来了解顾客的真实需要。 5.1.2 在投标或合同签订之前,总经理主持召集专题会议,有关部门或人员对标书或合同草案内容以及服务质量标准等进行评审,确认本公司有能力达到用户或发展商要求。 5.1.3 对合同的评审确保 a)在签订合同之前,各项条款内容明确、合理; b)公司具有满足合同能力,与投标不一致的地方已得到解决; c)当合同变更时,应重新评审,评审后更改的内容及时准确传达到有关部门o 5.1.4各相关部门负责对合同涉及到本部门的内容进行评审,并在《合同评审记录》上填写评审记录,经总经理签字确认。 5.1.5 《合同评审记录》由公司办公室负责保存o 5.2一般性服务合同(如业主公约或物业管理契约,房屋、摊位租赁及电话出租合同等)的评审。 5.2.1 在合同签定之前,由合同签订部门负责人组织有关人员对合同的草案内容进行评审。如合同有标准合同文本(通用范本),只需对标准合同文本进行评审,报公司主管负责人审批。 5.2.2《合同评审记录》由合同签订部门负责保存。

合同评审管理制度

合同评审管理制度一、总则（一）目的为了加强和完善评审程序，防范合同风险，确保公司各项经营工作正常有序地进行，特制定本制度。（二）适用范围 1、一般合同由合同承办部门拟定合同草本及相关文件，再按流程送审。 2、特殊/重大合同（订立价款在五万元以上的合同，投资、股权收购、并购的合同，涉外合同，合同承办部门认为需可行性审查的其他合同）均必须提请公司合同评审小组评审。（三）职责 1、公司成立合同评审小组。合同评审小组由总经理、分管副总、总工（总监）、财务负责人、法务部负责人、采购物流负责人、品质管理部负责人、市场开发部负责人、项目工程部负责人及承办部门（当事部门）负责人组成，合同评审小组的组长为总经理。 2、合同承办部门会同有关部门拟定合同草本，提交相关资信资料，并对合同执行情况进行全程督办。 3、品质管理部负责对产品质量要求和单元产品的生产

能力、交货周期以及技术协议的可行性的审查，并参与单元产品成本的测算。 4、市场开发部负责评审新产品/项目的开发能力及市场前景的评估。 5、工程部负责评审工程项目的生产能力、安装进度以及技术协议的可行性，并参与工程项目成本的测算。 6、物流采购部负责审核采购能力和采购周期，并参与材料成本的测算。 7、财务部负责评审付款与结算方式的合理性和可行性，以及确认成本及利润指标等。 8、法务部负责合同签订及履行过程中所签订的一切书面文件的合法合规性审查，并对可能产生的法律风险提出防范意见。 9、投融资部负责评审与投融资业务有关项目的可行性、技术协议、操作流程等事项。 10、集团公司分管领导、总经理和董事长负责公司所有合同的审批。二、评审原则（一）承办部门应对合同另一方当事人的主体资格和资信进行了解和审查；其他相关业务部门对合同进行专业性审查。（二）法务部对所有合同的立项、签订、履行、审核进行全程参与。（三）紧急采购、特殊原因的物资采购，或其他原因特

合同评审流程

合同评审流程 1、合同评审的目的为了维护公司利益，规避法律及资金风险，保证合同的质量和签订效率，根据《中华人民共和国合同法》及公司实际情况，制定本流程。 2、合同评审的范围公司与其他法人或自然人订立的合作协议、合同金额在人民币1000元（含）以上的各种经济合同均需通过评审方能对外签订。包括：特约商户合作协议、销售合同、采购合同、租赁合同、服务合同等。 3、合同的签订与保管发起部门经办人必须凭走完评审流程的合同评审表至合同专用章保管人处加盖合同专用章。加盖合同专用章时，合同专用章保管人必须严格审核合同评审表的有效性。公司所有经济合同原件及对应的合同评审表均在财务部保管，财务部应定期检查合同的执行情况，督促有关部门认真履行合同条款。 4、合同发起部门的职责 4.1 合同的起草及修订发起部门经办人员负责合同具体条款的拟定及根据合同评审意见对合同进行修改。合同中必须对合同的主体、形式、内容、标的、数量、质量、价款或报酬（含定金、质保金、付款次数及比例、税金、发票等）、履行期限、履行地点和方式、合同担保、合同解释、保密责任、重大经济合同联系制度、违约责任、争议解决方式、合同的变更和解除等予以明确。 4.2 合同的履行当合同开始履行以后，合同发起部门应跟踪合同的履行过程，保证合同的完整履行。

框架合同特别是年度销售及采购的框架合同履行过程中，发起部门的经办人员应定期对帐，确认双方债权债务。在履行合同过程中，发起部门的经办人员若发现并有确切证据证明对方当事人有下列情况之一的，应立即中止履行，并及时书面上报部门负责人。 4.2.1 经营状况严重恶化； 4.2.2转移财产，抽逃资金，以逃避债务； 4.2.3丧失商业信誉； 4.2.4有丧失或者可能丧失履行债务能力的其他情形。 5、合同评审责任人及主要职责 5.1 发起部门负责人发起部门负责人对下属起草的合同条款进行全面审核，并对合同的跟踪及执行情况承担全部责任。 5.2 分管高管对合同内容、标的物的质量、价格、数量、交付期限及方式、价款及信用期限、验收标准等重要合同条款进行审核、批准。 5.3 财务负责人对合同标的物价格、付款方式、信用期限、发票交付、定金条款、违约金条款等涉及公司财务政策的条款进行审核、批准。 5.4 总裁对超过分管高管审批权限的重大合同进行审核、批准。 6、合同评审流程 6.1各类合同评审的流程、评审的具体内容见表一，评审表格式见表二。（若需评审合同表二中未列出，则发起部门参照表二的格式自己设计合同评审表） 6.2 如果需要更多的人参与合同评审，分管高管需在评审表中单独列出。若没有单独增列需要参加评审的人员，则经办人只需走完表一中的评审流程。 7、附件 7.1合同评审流程表

合同评审管理办法

合同评审管理办法第一章总则第一条为确保公司经济（商务）合同的合法性、有效性、可行性，规范合同评审活动,特制定本管理办法。第二条合同评审的目的是依法防范风险,加强对费用和成本进行控制，保证生产经营进度和服务质量，保证及时回款等。第三条经济合同评审的依据为《中华人民共和国合同法》及其他有关制度。第四条凡涉及公司各类物资（设备)的采购、物流运输、建设工程、商务等项目均必须按照规定签订经济或商务合同。第二章组织管理及其职责第五条公司成立合同评审小组。合同评审小组组长戴汉承,副组长郭平、张爱民、张华清,组员刘巍、付沛力、王建武、高章跃、程庆峰。第六条公司合同评审小组的主要职责 (一)审查合同条款是否符合国家法律法规；是否符合公司合同签订基本原则与要求; （二)审查合同当事人的资质、生产能力、质量保证以及风险评估、信誉度等; (三)评审收款与结算方式的合理性和可行性; (四)评审合同的招标程序、合同价格确定的依据、客户资信程度及信用政策；（五)对评审过程认真做好记录,并存档备查。第三章评审范围及内容第七条本办法经济(商务）合同范围内的合同评审,主要包括:建设工程(土建)合同、买卖合同、外包合同、运输合同、商务合同等。第八条凡建设工程(土建）、买卖、运输、外包、商务等项目的合同,均必须提请公司合同评审小组评审。

第九条紧急采购、特殊原因的物资采购，可经公司总经理批准,依照特事特办的原则处理。第十条评审内容（一)建设工程（土建)合同１.审核施工单位的资质、业绩及信誉度； 2．审核费用是否合理。主要测算直接材料费用、直接人工费用、其他费用、间接费用及取费标准、定额选用、交（竣)工日期等； 3．审核质量与技术条款； 4.审核服务与承诺条款； 5.审核合同价款、付款方式是否明确且符合公司规定; ６．审核违约责任、质量索赔条款； 7.审核质量保证及质量保障体系是否满足要求。（二）买卖合同 1.审核供应商的选择情况; 2.审核比价核价、优质优价（性价比）情况；３.审核备品配件、随机配件的供应条款; 4．审核交付周期、质保期、售后服务与承诺条款; ５.审核合同价款、结算方式等是否明确且符合公司要求和规定； 6.审核违约责任、质量索赔条款; 7．审核质量保证及质量保障体系是否满足要求； (三）运输合同 1.审核托运方单位的业绩及信誉度； 2.评审运输费用标准(性价比)是否合理; 3．审核合同价款、结算方式是否合理; 4．评审对方承诺条款; 5.评审运输过程中货物毁损应承担损害赔偿责任条款; 6．审查有无违约责任的条款，是否符合《合同法》的有关规定。

合同签定审核管理制度

合同签定审核管理制度为规范公司经济合同的管理，防范与控制合同风险，有效维护公司的合法权益，特制定本制度。一．规章制度 1．本制度适用于公司对外签订、履行的各类合同、协议等，包括买卖合同、借款合同、租赁合同、加工承揽合同、运输合同、资产转让合同、仓储合同、服务合同等。 2．公司对外合同（协议）需经物流部、业务部、财务部评审通过，并报公司总经理同意后方可对外签定。 3．公司财务类合同，如借（贷）款合同由公司总经理或总经理指定财务负责人对外签定。公司业务类合同由物流部负责对外签定。总经理以外的人员签定合同时，需持对应的法人授权书。 3．1物流部物流经理负责对外签定一级业务类合同。 3．2二级业务类合同，可由业务员负责签定。 4．对外签定合同前的资质审查： 4．1合同的主体订立合同的主体必须是公司及所属各公司中具有法人资格，能独立承担民事责任的组织。订立合同前，应当对对方当事人的主体资格、资信能力、履约能力进行调查，要求对方提供相关资质证件的原件，审核无误后将证件复印，作为合同附件共同保存。不得与不能独立承担民事责任的组织签订合同，也不得与法人单位签订与该单位履约能力明显不相符的经济合同。

公司一般不与自然人签订经济合同，确有必要签订经济合同，应经公司总经理同意。 5．签定合同的形式：订立合同，除即时交割（银货两讫）的简单小额经济事务外，应当采用正式的合同书形式。紧急条件或条件限制时报总经理同意后可采用电报或传真形式。 6．合同的内容 6．1当事人的名称、住所：合同抬头、落款、公章以及对方当事人提供的资信情况载明的当事人的名称、住所应保持一致。合同签字必须规范、可辨。公司与自然人签定的合同，需请自然人签字后，用右手食指在签字上加印手印（顺序不得颠倒）。 6．2合同标的：合同标的应具有唯一性、准确性，买卖合同应详细约定规格、型号、商标、产地、等级等内容；服务合同应约定详细的服务内容及要求；对合同标的无法以文字描述的应将图纸或其他说明性资料作为合同的附件。 6．3数量：合同应采用国家标准的计量单位，一般应约定标的物数量，常年经销合同无法约定确切数量的应约定数量的确定方式（如电报、传真、送货单、发票等）。6．4价款或报酬：价款或者报酬应在合同中明确，采用折扣形式的应约定合同的实际价款；价款的支付方式待应予以明确；价款或报酬的支付期限应约定确切日期或约定在一定条件成就后多少日内支付。 6．5履行期限、地点和方式履行期限应具体明确定，合同履行地点应力争作对本方有利的约定，如买卖合同一般约定交货地点为本公司仓库或本公司的住所地；约定具体地名的应明确至市辖区或县一级；买卖或承运合同在合同中一般应约定交付的手续，即合同履行的标志，如托运单、仓库保管员签单等。 6．6合同的担保

合同评审控制程序

1. 目的使公司与客户之间合作更融洽，为业务部提供更好的服务，为了对顾客满意度进行测量，并以此测量结果作出适当监控和改进，满足顾客的要求，提高顾客满意程度，特制定本程序. 2. 范围适用于对顾客要求的识别、对产品要求的评审及与顾客的沟通。 3. 责任 3.1业务部负责识别顾客的需求与期望，组织有关部门对产品需求进行评审，并负责与顾客沟通。 3.2品质部负责评审对新产品质量要求的检测能力。 3.3 PMC负责评审产品的生产交付能力。 4. 定义无。 5. 内容 5.1客户来源 5.1.1公司广告； 5.1.2展览会； 5.1.3其它人介绍； 5.1.4亲自到公司。 5.2客户查询 5.2.1客户会通过 a.电话； b.FAX； c.书面； d.到公司来查询。 5.2.1公司在跟进时,根据客户要求,用书面或口头答复,如有书面回复,此书面记录入文件。 5.2.2客户如要求目录, 在书面回复上作记录。 5.2.3如客户要报价单, 报价单或公司标准价单寄客户, 报价单入档。 5.2.3上述数据入客户查询或客户档案。 5.3 客户名单

5.3.1业务部负责人负责做好每一份客户清单或客户数据表。 5.3.2客户清单或客户数据表定期更新。 5.3.3客户清单或客户数据表列客户名称/所订购货品类别数据。 5.3.4清单或数据表由营业负责人签名及填上清单最近一次更改日期。 5.4 顾客需求的识别 5.4.1业务部负责识别顾客对产品的需求与期望，根据顾客规定的订货要求，如合同草案、技术协议草案及口头订单等填写在《合同评审表》,应包括： a）顾客明示的产品要求，包括产品质量要求及涉及可用性、交付、支持服务（如运输等）、价格等方面的要求； b）顾客没有明确要求，但预期或规定的用途所要的产品要求。这是一类习惯上隐含的潜在要求，公司为满足顾客要求应作出承诺； c）顾客没有规定，介于国家强制性及法律法规规定的要求。 5.5对产品要求的评审 5.5.1 在投标、接受合同或定单之前，策划中心应已识别了顾客的要求、本公司确定的附加要求及组织相关部门对标书、合同的产品要求已实施评审。 5.5.2 合同评审 5.5.2.1 产品要求的评审应在投标、合同签定之前进行，应确保： a）产品要求（包括顾客的要求和公司自行确定的附加要求）得到规定； b）顾客没有以文件形式提供要求时（如口头定单），顾客的要求应在接受订单前得到确认； c）与以前表述下一致的合同或定单要求（如投标或报价单）已予解决； d）公司有能力满足规定的要求。 5.5.2.2 合同的分类 6常规合同：对公司定型产品所定的合同。 7特殊合同：常规合同以外的所有销售合同，指新产品开发或有定型产品改进要求的合同。 5.5.2.3 业务部负责提供《合同评审表》组织相关部门进行评审。

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