In Situ Scanning Electron Microscope ARTICLE Peeling To ... Situ... · on peeling behavior are described in the General Discussion section. Raman spectroscopy was also per-formed

ROENBECK ET AL . VOL. 8 ’ NO. 1 ’ 124–138 ’ 2014

www.acsnano.org

124

December 16, 2013

C 2013 American Chemical Society

In Situ Scanning Electron MicroscopePeeling To Quantify Surface Energybetween Multiwalled CarbonNanotubes and GrapheneMichael R. Roenbeck,† Xiaoding Wei,§,† Allison M. Beese,§,^,† Mohammad Naraghi,†,z Al’ona Furmanchuk,‡

Jeffrey T. Paci,‡,# George C. Schatz,‡ and Horacio D. Espinosa†,*

†Department of Mechanical Engineering, and ‡Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3111,United States. §These authors contributed equally to this work. ^Present address: Department of Materials Science and Engineering, Pennsylvania StateUniversity, University Park, Pennsylvania 16802. zPresent address: Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station,Texas 77843-3141. #Concurrent Address: Department of Chemistry, University of Victoria, British Columbia, V8W 3V6, Canada.

Over the past several years, research-ers have attempted to scale upthe high strength-to-weight ratio

of carbonnanotubes (CNTs) by incorporatingCNTs in macroscopic yarns and compositematerials. Researchers have developed anumber of techniques to make macroscopicyarns, for instance, (i) dry spinning of CNTyarns by drawing and twisting from CNTarrays, aerogels, or mats1�8 and (ii) wetspinning of CNT yarns by drawing and twist-ing fromCNT sources embedded in chemicalsolutions.9,10 Even though the proceduresare different in technical details, all the yarnsshare CNTs as the smallest building blockswithin the yarns. At the nanoscale, the load iscarriedby the tube�tube interactions throughvan der Waals forces between carbon atoms,noncovalent bonds between functional che-mistries on the surfaces of CNTs, or covalentbonds through cross-linking between tubes.

One major challenge researchers are facingis that although individual CNTs are strongand stable due to sp2 bonding betweencarbon atoms, tube�tube interactions arerelatively weak. This has resulted in therelatively inferior mechanical propertiesof CNT yarns compared to those of theirconstituents.7,11�14 Therefore, researchersare investigating various approaches to in-crease the tube�tube interactions.11 Severalmeans of enhancing CNT�CNT interactionshave been proposed, including inducingcovalent cross-linking between individualCNTs and bundles of CNTs via high-energyradiation15,16 and chemically derived surfacefunctionalizations.17�22 However, thesetreatments, aimed at increasing interactionbetween adjacent tubes, come at the ex-pense of introducing structural defects inthe CNTs themselves. Very few publicationsto-date report on experimental studies of

* Address correspondence [email protected].

Received for review May 16, 2013and accepted December 16, 2013.

Published online10.1021/nn402485n

ABSTRACT Understanding atomic interactions between constituents is critical to

the design of high-performance nanocomposites. Here, we report an experimental�computational approach to investigate the adhesion energy between as-produced arc

discharge multiwalled carbon nanotubes (MWCNTs) and graphene. An in situ scanning

electron microscope (SEM) experiment is used to peel MWCNTs from graphene grown

on copper foils. The force during peeling is obtained by monitoring the deflection of a

cantilever. Finite element and molecular mechanics simulations are performed to

assist the data analysis and interpretation of the results. A finite element analysis of the experimental configuration is employed to confirm the

applicability of Kendall's peeling model to obtain the adhesion energy. Molecular mechanics simulations are used to estimate the effective contact width at

the MWCNT�graphene interface. The measured surface energy is γ = 0.20 ( 0.09 J 3m�2 or γ = 0.36 ( 0.16 J 3m

�2, depending on the assumed

conformation of the tube cross section during peeling. The scatter in the data is believed to result from an amorphous carbon coating on the MWCNTs,

observed using transmission electron microscopy (TEM), and the surface roughness of graphene as characterized by atomic force microscopy (AFM).

KEYWORDS: carbon nanotubes . graphene . in situ SEM testing . adhesion energy . molecularmechanics . chemical functionalization

ARTIC

LE


www.acsnano.org

125

the mechanical properties of pristine or functionalizedsurfaces at the tube level.23�25 Consequently, there isa demand for developing an experimental techniquethat can characterize the tube interface propertiesat the tube�tube level. Here we propose an in situ

experimental approach that can be used to investigatethe effects of various chemical modifications on thematerial properties of tube surfaces.Rather than having perfectly aligned CNTs, yarns

consist of complex CNT networks, due to randomnessand entanglement in the CNT sources. Some alignmentis typically achieved during the spinning process. Inthe context of this study, yarns produced by twistingand stretching ribbons of freestanding mats of CNTsare of particular interest.7,26 The smallest constituentsin macroscopic yarns spun from such mats are CNTs,which are arranged into bundles typically exhibitingsome degree of orientation. These bundles form anetwork leading to filament structures.7,26,27 This com-plex structure results in various deformation and failuremechanisms acting at each length scale: from failureof the CNTs themselves, to peeling or shearing of theCNTs within bundles, to peeling or shearing fromadjacent CNT bundles, where the network of bundlesis subjected to macroscopic axial elongation. At thetube level, the interface failure between adjacent CNTsin a macroscopic yarn can be classified as eitherpeeling, shearing, or mixed modes. Peeling resemblesMode I fracture, while shearing corresponds to Mode IIfracture. If CNTs were perfectly aligned with oneanother along the axis of the fiber, shearing wouldbe expected to be the predominant mode of failure.However, as perfect alignment of all of the CNTs withina yarn cannot be achieved, it is important to alsocharacterize peeling. Developing an understanding ofshear and peeling behavior between individual CNTscan provide mechanistic understanding of variousfunctionalizations for improved CNT�CNT interac-tions, leading to higher-performance CNT-based yarns.Shearing in situ scanning electron microscopy (SEM)of CNTs was recently addressed by Espinosa andco-workers.28 In this manuscript, we extend the workto peeling.The peeling of CNTs from a substrate has been

investigated through both simulations and experi-ments. Sasaki et al. conducted molecular mechanicssimulations of single-walled carbonnanotubes (SWCNTs)peeling from graphitic surfaces, showing that sufficientlylong SWCNTs adhered to graphite would transition froma line contact regime to a point contact regime beforeseparating completely duringpeeling.29,30 Strus et al. usedatomic forcemicroscopy (AFM) to peel CNTs from varioussubstrates and compared their force-vs-displacementrelations with results from an elastica model.31,32

They reported interfacial energy as the integral underexperimentally obtained force-vs-displacement curvesand verified the conformational states predicted

numerically by Sasaki et al. Buchoux et al. also usedAFM, in this case to peel CVD-grown SWCNTs fromgraphite and mica substrates.33 They calculated adhe-sion energy normalized per unit length of the CNTsthrough a force balance by assuming that changes inthe profiles of small-diameter tubes were negligiblesuch that cantilever deflection and debonding lengthcould be considered equal. Ishikawa et al. performedin situ SEM nanoscale peeling tests of a multiwalledcarbon nanotube (MWCNT) from graphite using anovel device they developed with force and displace-ment resolutions similar to those of AFM.34,35 Theyreported adhesive energy as the integral under theexperimentallymeasured force-vs-displacement curve,and verified that this energywas larger than the energyrequired for pushing and rolling MWCNTs on graphite,as reported previously in the literature.36,37 Ke et al.investigated self-peeling of SWCNT bundles throughin situ SEM experiments.38 They applied classical peel-ing analysis to compute the energy release rate at thepeeling point normalized by bundle bending stiffness,withoutmeasuring force. These studies did not providea direct measurement of the surface energy in terms ofenergy per unit area, so it is difficult to compare theperformance of each system in terms of normalizedmaterial properties.To fill in this gap, we present an approach combining

in situ SEM peeling experiments and theoretical com-putations. This study focuses on evaluating the surfaceenergy of individual MWCNTs peeled from a graphenesubstrate. The direct visualization of the peeling pro-cess through in situ SEM testing, combined with forcemeasurements, provides fundamental insights intothe nanoscale interactions between these materials.When combined with an analytical model, finiteelement simulations, and atomistic calculations, theapproach also enables the estimation of energy con-tributions within the framework of fracture mechanics.The method presented here is envisioned as a tech-nique that can be used to evaluate the effect onnanoscale interactions between CNTs caused by che-mical functionalizations, with the results presentedhere serving as baseline values for interactions be-tween nonfunctionalized CNTs.

Experimental Methodology. In the peeling tests, as-produced MWCNTs were attached to, and sub-sequently peeled from, a substrate of graphene oncopper (Figure 1) in order to experimentally evaluatethe surface energy between the CNT and graphene.Within an SEM chamber, a tube was attached to the tipof an AFM cantilever of known stiffness that extendedfrom a nanomanipulator. The tube was manipulatedsuch that it lay on a graphene substratemounted on anSEM stage. After a line contact was formed betweenthe tube and the graphene, the stage was pulledaway from the fixed cantilever to peel the tube fromthe graphene substrate. Images of the peeling process

ARTIC

LE


www.acsnano.org

126

were recorded to track both the profile of the tubeand the deflection of the AFM cantilever. The verticalpeeling forces were calculated by visually trackingthe cantilever deflection and accounting for the offsetangle,R (see Figure 1). After each test, the profile of thefully separated CNT was compared with its originalshape to ensure the tube remained straight and did notchange in length. For data analysis after the test, thepeeling angle and cantilever deflection immediatelypreceding a peel were evaluated and used to calculatethe surface energy of the CNT�graphene interface.

In theory, peeling two layers of graphene as op-posed to peeling a MWCNT from graphene will benefitthe surface energy calculation by simplifying thecontact width determination. However, we chosethe MWCNT�graphene system for experimental rea-sons. On the basis of our experience, manipulatinggraphene, a 2-D material, is much more difficultthan manipulating a carbon nanotube, which is a 1-Dmaterial. In addition, there are several problems thatcould result from using a graphene layer instead of acarbon nanotube. For example, graphene tends toform tapered sections with uneven cross-sectionalwidths, as highlighted by Sen et al.39 Variable contactwidth along the length of the graphene layer couldnot be assessed in SEM due to resolution limitations.An additional challenge could arise pertaining to ma-nipulation: one would need to ensure that the two-dimensional graphene sheet adheres well to theAFM cantilever. Typical methods of adhesion, such asamorphous carbon deposition, may not work properlyfor welding homogeneously along the contact line fora 2-D material to provide a well-defined boundarycondition. Furthermore, since this study is envisionedas a test bed for assessing the changes in surfaceenergy associated with chemical functionalization,treatment of a monolayer of graphene may reduce

the structural integrity of the layer. Such effects shouldnot be as drastic for MWCNTs, where the inner shellsshould remain intact despite outer surface chemicalfunctionalization. Therefore, MWCNTs are chosen inthe current study.

The structures of 78 representative MWCNTs wereexamined using high-resolution transmission electronmicroscopy (HR-TEM) (Figure 2a and Figure 2b). Thenumber of walls in each tube used in the experimentswas estimated from the HR-TEM characterization of20 tubes (among the 78 tubes investigated) with outerdiameters similar to those measured in the in situ SEMexperiments. From the TEM images, the outer diameterand number of walls in each tube were measured fromline scans transverse to themain axis of the CNT. Linearinterpolation of the number of walls as a functionof tube outer diameter provided a statistical basisfor estimating the number of walls within tubes testedin the SEM.While TEM images of this representative setshowed that some tubes (Figure 2a)were relatively freeof amorphous carbon coating, others (Figure 2b) wereheavily coated. The potential effects of this coatingon peeling behavior are described in the GeneralDiscussion section. Raman spectroscopy was also per-formed on the tubes to assess the defect density. Theratio of the D to G peaks (Figure 2c) was approximately0.1, indicating that the defect density of the tubes waslow. The diameters of individual tubes used in thein situ SEM tests were measured by calculating the fullwidth at half-maximum (fwhm) of line scans perpendi-cular to the main axis of the CNT in the SEM images ofeach tube.

Graphene was chosen as the peeling substratebecause it mimics the interaction surface from whichCNTs would peel within dry-spun CNT yarns. A repre-sentative SEM image of a graphene surface (Figure 3a)shows copper grain boundaries (thick dark lines) as

Figure 1. In situ SEM peeling setup. (a) Testing schematic. A MWCNT is adhered to a graphene surface at an angle θ with anoffset R, both of which can be characterized directly from SEM images. The stage is then slowly pulled away, causing theMWCNT topeel from the graphene substrate. (b) SEM imageof aMWCNT carbonwelded to a cantilever tip and in contactwitha graphene surface. Arrows denote the path of the CNT, including the line contact beneath the three top arrows.

ARTIC

LE


www.acsnano.org

127

well as the presence of small ripples (thin white lines).Copper grain boundaries were avoided during testing,as they were visible in the SEM. SEM images of the foilshowed that copper grain boundaries were greaterthan 20 μm in any linear dimension, far exceedingthe typical line contact region between the tube andthe substrate (∼3 μm). The topography of the gra-phene surface was characterized by atomic force

microscopy (AFM) in noncontact mode, as shown inFigure 3c. Both atomically smooth and rippled regionswere identified. The rippled regions had roughnessvalues of approximately 4 nm in height with ∼200 nmspacing between ripples. The effect of graphene rough-nesson thesurfaceenergymeasurementwill bedescribedin the General Discussion section. Raman analysis of thegraphene-on-copper foil exhibited the characteristic D, G,

Figure 2. MWCNT sample characterization. (a, b) Sample HR-TEM images of as-produced arc-discharge MWCNTs. The tubesobserved in the TEM were well-ordered and straight with variable amorphous carbon present on their outer surfaces.(c) Raman spectrum forMWCNTs. The ratio of theD peak to theG peak suggests that the defect density of theMWCNTs is low.

Figure 3. Graphene substrate characterization. (a) Representative SEM image of a graphene-on-copper surface showingthree copper grains forming a junction.Wrinkles in variousorientations are also apparent in the image. (b) Raman spectrumofgraphene-on-copper surface. The presence of a G peak and a 2D peak are indicative of the presence of graphene on thesurface. (c) Representative AFM image of a graphene-on-copper surface used to characterize wrinkles. Line scan over 5 μmindicates ripples are about 4 nm high and spaced ∼200 nm apart.

ARTIC

LE


www.acsnano.org

128

and 2D peaks for graphene (Figure 3b). The ratioof the D to G peaks of 0.2 is indicative of a low defectdensity. Additionally, the ratio of the 2D toGpeaks of∼2.4confirmed that monolayer graphene was indeed presenton the copper foil, where a ratio of ca. 2�4 is characteristicof monolayer graphene.40�42

As a means of validating the results of peeling fromthe graphene-on-copper foil, MWCNT peeling testswere also performed on freshly cleaved highly orderedpyrolytic graphite (HOPG) surfaces. HOPG has beenused as a peeling substrate in previous CNT peelingstudies, in part because topographical AFM scans haveshown that the material is atomically flat.31�35 Whilemonolayer graphene-on-copper was the primary sub-strate used in the present study, results from peelingtests with HOPG further demonstrate the ability of theexperimental method to acquire surface energies ofunfunctionalized graphitic interfaces.

Kendall Analysis. MWCNT peeling studies were ana-lyzed using the classical peeling formula developedby Kendall,43 which assumes that an elastic film peelsfrom a rigid substrate under a constant axial load,incrementally progressing the peel front without chang-ing the shape of the film. The corresponding energybalance yields

F(1 � cos(θ)) ¼ 2γw � F2

2Eπdt(1)

where F is the applied force, θ is the angle ofthe applied force with respect to the substrate (seeFigure 1), γ is the interface surface energy, w is thecontact width between the two surfaces, E is the elasticmodulus of the CNT (E = 1 TPa12,13,44), d is the outerdiameter of the CNT, and t is the single wall thickness(t = 0.34 nm, as we assume only the outer wall carriesthe tensile load). The term on the left-hand side ofthe equation corresponds to the external work of thecantilever acting on the CNT, while the first and secondterms on the right-hand side of the equation denotechanges in adhesion energy and changes in strainenergy, respectively. In order to derive γ, w needs tobe determined. Additional details describing the cal-culation of these parameters as well as the applicabilityof Kendall's formula to the peeling tests are included insubsequent sections.

Atomistic Methodology. Molecular mechanics simula-tions were used to determine the contact widths,w, byrelaxing MWCNTs onto a single sheet of grapheneusing atomistic modeling techniques. Our model be-gins by considering a large defect-free graphene sheetthat represents graphene on the surface of a polycrys-talline copper foil. Recently published STM imagesof CVD grown graphene on polycrystalline copper foilsindicate the presence of an intact graphene lattice.45

It was also shown that the interaction of copperwith graphene stimulates the partial dislocation ofatoms in the surface layer of the copper substrate only.

Therefore, we assume, similarly to the aforementionedexperiments, that the carbon�carbon bonds in thegraphene used here are not broken during peeling.Copper atoms are omitted in the present theoreticalmodel since they are beyond the scope of this study.Instead, the copper�graphene interactions are mod-eled indirectly by assuming that the carbon atoms ofthe graphene layer are fixed in space after the structureis relaxed. As the analysis in the Atomistic Prediction ofContact Width section suggests, the presence of thecopper instead of free space below the graphene isexpected to change the surface energy by ∼6%.

The large sizes of the experimental samples wereaddressed in the modeling by wrapping correspond-ing bonds and interactions in zigzag MWCNT-gra-phene structures across the longitudinal axial periodof the sheet. Hydrogen atomswere added to graphenecarbon atoms along the two other edges in order toeliminate edge effects in the nonperiodic directions.The length ofMWCNTs in all simulations is 8 units (or 16circumferential rings of carbon atoms). The procedurefor choosing an appropriate axial length of the bound-ary box is described in the Methods section. In order tosatisfy a minimum image criterion, the nonbondedcutoff was set to 12 Å.

All simulations were performed using the MM3potential as implemented in the molecular mechanicspackage Tinker 6.0.46 According to earlier studies,47�49

the MM3 potential has been found satisfactory fordescribing CNT properties where C�C bond breakingdoes not occur. In particular, dispersion interactions areincluded so that nonbonded interactions commonbetween proteins and CNTs are included. The carbonatoms were modeled as alkene (type 2) atoms. Thepotential energy of the structures in all simulations wasminimized to an rms gradient of 0.0001 kcal/mol/Å.Zigzag CNTs with various numbers of walls wereallowed to fully relax on the fixed graphene surface.Two protocols were used in relaxation calculations,designed to explore both collapsed and noncollapsedstructures. In the first, the cylindrical shape of the CNTwas deformed by applying displacements to selectedatoms, in such a way as to try to induce collapse. Ateach step, the configuration of the tube was optimizedsubject to the displacement constraints. After the innerinterwall distance reached 3.4 Å, all the constraintswere released, and a full relaxation of the structure onthe graphene surface was performed. In the second,full relaxations from the initially cylindrical startingstructures were performed.

RESULTS AND DISCUSSION

Experimental Peeling Process. Forces exerted on theCNTs were obtained by digital image correlation ofSEM images which tracked the deflection of the AFMcantilever throughout each peel test. The precise peelfront propagation lengthwas not required for Kendall's

ARTIC

LE


www.acsnano.org

129

analysis, but an estimate of this helped determinewhether or not the observed peel suffered from com-plications with the in situ experiment. In particular,peels with large displacements (∼1 μm) and largefluctuations in force were not considered in the anal-ysis, as theymay have arisen fromvarious experimentalfactors that could have led to excessively high forcesand significant deviations from the Kendall analysis.Additional explanation of these factors is provided inthe General Discussion section.

Finite Element Simulation Verification. While Kendall'sformula is used in this study to calculate surfaceenergy, the assumption of shape constancy duringpeeling does not apply in the employed experimentalprotocol, as the cantilever restricts the motion ofthe CNT. Hence, during a small but finite advancementof the peeling front, the shape of the tube changesslightly. The effect of this discrepancy between theexperimental and analytical boundary conditions onadhesion energy is investigated using finite elementanalysis (FEA). In the FEA calculations, the tube wasmodeled as a 1-D beamwith a cylindrical cross-sectionmatching that estimated from experiments. Three-node quadratic beam elements were used to accountfor the tensile and bending deformations. As inFigure 4a, in the initial state (1), the CNT is straightand slack: no external loading is applied, and thus thereis no strain energy in the system. At the left end ofthe tube, displacement and rotation were constrained,and at the right end, a spring element with a springconstant equivalent to that of the AFM cantilever usedin the peeling experiments was connected to the tube.Note that during peeling, the AFM cantilever does notmove horizontally but can move in the vertical direc-tion. Hence, to obtain an initial shape consistent withthe experiment, the spring element was progressivelydisplaced until the position of the right end of the tubecoincided with the position of the tube, just before

peeling in an experiment (see Figure 4b). The FEA simu-lation predicted a tube profile that closely matchedthe experimental observation (see Figure 4c). At thisconfiguration, the force applied at the right end of thetube, F, as well as the strain energy stored in the tube,Einitial, were obtained. To compute the energy releaserate numerically, a virtual motion of the peeling front(10 nm in length) was assumed. After the systemequilibrated, the strain energy of the tube after peel-ing, Efinal, was obtained. Also, integrating the cantileverforce vs cantilever displacement yielded the externalwork, Wext, performed on the tube. Thus, according toGriffith's analysis,50 the energy release rate, G, duringpeeling can be obtained numerically; namely,

G ¼ Wext � (Efinal � Einitial) (2)

To compare, Kendall's formula can also be appliedto calculate the energy release rate. By inputting thecantilever force, F, and the peeling angle, θ, extractedfrom the simulation result right before peeling, theenergy release rate given by Kendall's model is

G ¼ F(1 � cos(θ))þ F2

2Eπdt(3)

We performed FEM calculations on multiple peelingexperiments (varying tube length and peeling angle)and consistently found only a 5% overestimationof the energy release rate by Kendall's model com-pared to Griffith's analysis. Thus, Kendall's analysisis used to compute the energy release rate from whichγ is obtained.

Atomistic Prediction of Contact Width. Earlierstudies49,51,52 demonstrated that van der Waals interac-tions between CNTs and substrates can lead to defor-mation and even collapse of the tube, especiallyfor nanotubes with large diameters. In addition, otherobservations suggest53,54 that tube twisting may beused as a marker for detection of nanotube collapse.

Figure 4. FEA simulations. (a) Schematic of the FEA simulation setup. An initially flat CNTwith lengthmatching thatmeasuredin the experiment is bent from configuration (1) to (2) to (3), with the left end held fixed. The right end in configuration (3)corresponds to the experimental measurement. A roller is added to the right end after configuration (3) to prevent the tubefrom translating horizontally during peeling. (b) Schematic of the FEA peelingmodel. The springwith constant k correspondsto the cantilever stiffness. The solid line represents the CNT configuration right before peeling, and the dashed line representsthe CNT configuration after peeling 10 nm. (c) Comparison of the CNT shapes right before peeling obtained from the FEAsimulation and experimental observation.

ARTIC

LE


www.acsnano.org

130

Since only straight CNTs were observed in the currentexperiments, we assume that the MWCNTs are notcollapsed before being put on the surface. However,depending on the diameter and number of walls,we expect some deformation on the graphene sur-face. Since it is difficult experimentally to determinethe actual contact surface between the CNT and sub-strate, we have used atomisticmodeling to describe theshapes of MWCNTs in these experiments. Such studiesare well-known for SWCNTs andDWCNTs49,55,56 of smalldiameters but not for MWCNTs.

The adhesion energy and, therefore, contact sur-face can be treated as a function of radial deformationof the MWCNT. To determine this contact surface,we need to define the operational range of van derWaals (vdWs) forces associated with contact betweenthe nanotube and surface. A complete treatment of thevdWs forces should include Casimir effects in describ-ing nanotube interactions.57 However, we begin withconsiderations of the less-general Lennard-Jones po-tential given by

V ¼ εrmr

� �12

� 2rmr

� �6" #

(4)

where ε is the well depth, and rm is the separationdistance at which the well has a minimum. For graphi-tic materials, it is known that rm ≈ 3.4 Å. At r = rm,V = �ε. At r = 2rm, V = �0.03 ε. Thus, tube atoms at∼6.8 Å from the graphene sheet each contribute∼3%of the energy of an atom at the vdWs minimum. Notevery atom within 6.8 Å of the graphene sheet con-tributes equally. Instead, those at theminimum separa-tion make a full ε contribution and those at largerseparations make a contribution scaled appropriatelywith distance. The energy differences between differ-ent locations in the vdWs registry are small (∼50%)compared to the vdWs energy at the minimum.58 Also,upon geometry optimization, atoms will take on geo-metries that tend to minimize their vdWs energies.

In the experiments, an atom in the MWCNT isinteracting with all of the atoms in the graphene-on-copper. This implies that summing of the asso-ciated pairwise interactions is required. Steele hasdone such a summation for the (100) face of a simplecubic lattice, a result that depends on the positionof the atom relative to the lattice.59 It is also possibleto replace the discrete set of atoms of the surface witha continuous distribution and to replace the sum withintegration over the surface. The result is a 4,10potentialthat describes the interaction between an atom and thesurface as a function of separation.59 It is given by

Vs(z) ¼ 2πε ∑¥

k¼ 1

25

1z�þ k

� �10

� 1z�þ k

� �4( )

(5)

where k is an integer that indexes the planes, z* = z/(2�1/6rm), and z is the shortest distance between the

atomand the surface. Steele showed that this provides agood approximation to the full-summation result, forseparations between ∼r = rm and r = 2rm and beyond,for atoms that are the same size as those that comprisethe surface (see Figure 2.3 of ref 59, solid dots). Theexpression goes as 1/r3 asymptotically (see also ref 60).The remaining sum is over planes, with the secondplane contributing ∼6% of the first. Similarly, replacingthis final sum with an integral results in a 3,9 potentialthat does a poor job at approximating the full summa-tion result for r less than approximately 4rm, but thenprovides the same result as the full sum out to asymp-totically large distances, where it has 1/r3 behavior.59

Thus, one option is to use eq 5 to help in describingthe interactions of the tube atoms within∼rm to 2rm ofthe surface; the experimental estimate of the energy ofan atomat the vdWsminimum (0.26 J 3m

�2� 0.043 eV/atom) can be scaled using eq 5 for larger separationsup to 2rm.

61�63 The curve predicted by eq 5 has a welldepth that is approximately 2/3 of that predicted byperforming the full sum for an ideal-registry-typeposition (see Figure 2.3, curve “S”, of ref 59). Includingsuch a factor to scale down the well depth should bedone to account for the inability of atoms to enter intoideal vdWs registry.

The geometry of the MWCNT�surface interactionin our molecular mechanics simulations is such thatthere were relatively few atoms that have rm < r < 6.8 Åfrom the graphene surface (see Figure 5b), comparedto the number of atomswith separations close to r= rm=3.4 Å. The rm < r < 6.8 Å atoms are those present in theouter wall of the tube, near the edges of the flattenedregions of the tube. The use of a cutoff distance largerthan 6.8 Å would lead to a logical inconsistencybecause we are using a per atom energy based ongraphite; thus, atoms in the second-to-outer wall of theCNT are part of the bulk-like graphite that make thisenergy approximation possible. To first approximation,the vdWs interaction “sees” into materials to a depthapproximately equal to the separation (∼3.4 Å in ourcase), suggesting our per atom approximation isreasonable.64 There is evidence that as few as two tothree layers of graphene or walls on a CNT are enoughfor the associated vdWs interactions to be close tothose of bulk graphite.65,66 A Lennard-Jones-basedargument would suggest the same. TEM studies pre-sented here suggest that the tubes used in experi-ments have greater than 10 walls, which is more thanenough to justify this bulk approximation.

On the basis of the above discussion, the energycontribution of an atom in the outer wall of the tubecan be estimated as

Eat ¼ 23

Vs(rm þ dz)Vs(rm)

� �0:043 eV (6)

where dz = z � rm, for atoms with z ∼ rm to z = 2rm.These atoms were those located near where restrictions

ARTIC

LE


www.acsnano.org

131

due to the curvature of the tube confine them tothis z range. Only k = 0 was used in the calculations ofVs, an approximation that should result in errors muchless than the∼6%referencedabove, due to cancellationof errors.

To show the effect of defining the contact widthusing a separation of e6.8 Å, we have performed twotypes of calculations using theMM3MWCNT/graphenemodel. In the first, after relaxing the tubes on thegraphene surface, the atoms located in the outer wallin a plane perpendicular to the longitudinal direc-tion of the tube were identified for each segmentof the tube. Then their positions were fitted to apolynomial function. The function values at e6.8 Åtube�graphene separation were used to determinethe contact width. The values were averaged over allsegments along the tube. In the second, we explicitlyaccounted for the fact that carbon atoms from the flatand curved segments of a CNT contribute differently tothe adhesion energy. Initially, the van der Waals inter-action energy per atom was calculated as a function of

interlayer distance between two graphene sheets(see Figure 5a). Then, the integral of the binding energyover all atoms of a CNT was calculated based on eq 6.Comparison of the CNT�over�graphene binding en-ergy with the one for graphene�over�graphenewas then used to define the contact width. Both cal-culations resulted in contact width estimates that areeffectively the same.

The degree of radial deformation of the CNTsis a function of the number of walls and the outerdiameter. In the limit of large wall number and smallouter diameter, no deformation occurs. In that case,the contact width can be calculated using an equationfor a cylinder interacting with a stiff substrate:

wcylinder ¼ D

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � 1 � 6:8

D

� �2s

(7)

where D and wcylinder (black lines in Figure 5c, andSupporting Information, Figure S3, and Figure S7)are the diameter and contact width of a rigid cylinder,

Figure 5. Molecular mechanics simulations of contact width. (a) The vdWs interaction energy per carbon atom based oninteraction of graphene layers. (b) Flattened and fully collapsed structures that MWCNTs form due to interactions withgraphene surfaces. (c) Contactwidth variation as a functionof CNTdiameter andnumber ofwalls. The regionof fully collapsedstructures is highlighted in gray, while the region of flattened structures is highlighted in pink. Each line corresponds to acertain number of walls.

ARTIC

LE


www.acsnano.org

132

respectively. Radial deformations become increasinglylarge with increasing diameter of the outer wall (pinkregion in Figure 5c). At some point the structuresbecome flexible enough to collapse (gray region inFigure 5c). We determined from simulations that thepoint at which fully collapsed tubes are energeticallystable is defined by the diameter of the innerwall. At aninner wall diameter of approximately 31 Å, contactbetween opposing tube sides is no longer sufficientlystabilized by van der Waals forces to prevent the tubefrom returning to a more cylindrical shape, regardlessof how collapsed the initial tube geometry guess is.Therefore, the following equation was developedand used to determine the borderline below whichfull collapse is impossible:

Dout ¼ Dinner þ 2(Inter)(N � 1) (8)

where Dout is the outer diameter of the tube, Dinner =31 Å, Inter = 3.4 Å is the interwall distance, and N is thenumber of walls. The tubes will be nearly cylindricalin cross section for D < Dout, for a given N. The fourpoints adjacent to the solid cylinder line in SupportingInformation, Figure S3 correspond to examples of suchtubes.

ForD>Dout, collapse is possible. For thesediameters,the following equationwas used for the collapsedwidthestimates (see the Methods section for parametrizationdetails):

wcollapsed ¼ 3:699þ 1:556D � 8:175N (9)

where D is in Å. For each collapsed structure, a corre-sponding noncollapsed structure might also exist.Contact widths for such “flattened” structures can beobtained by applying corrections to eq 9 using:

wflattened ¼ wcollapsed

� N �0:00438þ 0:41164N

� �[(1 � H)D

þH(Aþ B exp( �D=C))] (10)

where

H ¼ 1

1þ exp�2(D � 8N)

N

� � (11)

A ¼ 24:85þ 13:26N (12)

B ¼ �29:76 � 13:78N (13)

C ¼ 14:10þ 9:23N (14)

Details of the development of these expressions can befound in the Methods section.

The stability of flattened versus collapsed config-urations is determined by the balance between theforce necessary to bend a graphitic sheet of a particularthickness, and the stabilization from van der Waalsforces in the central collapsed region of the tube. If the

central collapsed region is too small, the van derWaals forces do not provide enough stabilization,and the structure springs back to a flattened shape.Both flattened and collapsed structures may be stable,in which case there is an energy barrier associated withtransforming geometry from one structure to another.At some D for a given N, flattened and collapsedstructures are approximately energetically equal.We derived the following equation to describe the lineseparating the D and N values for which flattenedversus collapsed structures are most stable:

20:196Nþ 215:954 ¼ πDinner (15)

Supporting Information, Figure S4 is a cartoon illustrat-ing the behavior captured by eqs 8 and 15. At evenlarger D values for a given N, only collapsed structuresare stable (see Supporting Information, Figure S4d).

By summing pairwise vdWs interactions, the energyassociated with a pair of planes can be calculated.It is given by60

W ¼ �A

12πDp2 (16)

where A is a Hamaker coefficient andDp is the distancebetween planes. The coefficient A is described by

A ¼ π2CF1F2 (17)

where F1 and F2 are the numbers of atoms per unitvolume, and C is the coefficient in the associatedatom�atom pair potential, Wp = �C/r6. Inclusionof Casimir effects (i.e., the full dielectric responseof the material) does not change the form givenby eq 17, but changes the expression for A.60,64 Thus,the pairwise and full vdWs expressions forW have thesame form.

Formetals (including semimetals) in or near contact(Dp e 20 Å) in vacuum, A ≈ 4 � 10�19 J,60,64 so W =0.092 J 3m

�2. Two surfaces are created, so this givesa surface energy of 0.046 J 3m

�2. However, as explainedin ref 60, it is necessary to use a cutoff distance thatis substantially less than the interatomic distancerequired to use eq 17 to calculate surface energies,as it is necessary to consider the atomic struc-ture of surfaces when they are in contact. Using γ =A/[24π(0.165 nm)2] as suggested in this reference givesγ = 0.2 J 3m

�2, which is within experimental error of theaverage of the experimental values in previous reports(0.26 J 3m

�2).61�63

It is also useful to consider estimating the energycontribution from the rounded areas where the tubeflattening ceases, by using the Derjaguin approxi-mation.64 The approximation involves consideringthe surface of a material as a combination of piece-wiseunits that are parallel to the opposing surface, allowing forthe use of eq 17 for each piece, and then summing.However, for the regions in question, the radius of curva-ture isnot largecompared to theseparationbetweensuch

ARTIC

LE


www.acsnano.org

133

regions and the graphene surface, so the approximationwould not be very good.

Experimental Surface Energy. Experimental results foreight in situ SEM peeling tests are reported in Table 1.The tubes employed in the experiment had diametersin the range of 19�30 nm. Surface energywas calculatedfor each test using eq 1. The results listed for Tube 1 arefrom two subsequent tests with the same tube. SEMimages of Tube 1 before and after the first test showed itmaintains its straight profile before and after peeling. Theresults listed for tubes 2 and 3 are from single testsperformed on each tube. In the case of tube 3, two peelsweremeasured from the same test, but the tubewas notdisconnected between the peels.

To provide a thorough interpretation of the experi-mental results, we measure energy values in multipleforms (Table 1). First, we report adhesion energy perunit length, which makes no assumptions about thecontact width at the interface. The average adhe-sion energy is 6.0 nJ 3m

�1 with a standard devia-tion of 2.6 nJ 3m

�1. However, as noted previously,surface energymay be amorewidely applicablemetricto remove tube size dependency. Therefore, we reporttwo columns of calculated surface energy values,which vary depending on the assumed conforma-tion of the tube during peeling. If the tube is takento be fully collapsed, the average surface energy is0.20 J 3m

�2 with a standard deviation of 0.09 J 3m�2. If,

instead, the tube is taken to be flattened, the averagesurface energy is 0.36 J 3m

�2 with a standard deviationof 0.16 J 3m

�2. The largest scatter is found in the surfaceenergy extracted from tube 3. This could be becausethis tube had the smallest diameter among thosetested. As such, it is possible that tube 3 was affectedmore than the other tubes by factors discussed in themanuscript (contact conditions, surface inhomogene-ities, contact width determination, etc.), resulting inlarger variations in the measurement.

In addition, the results of two peels from an HOPGsubstrate, with applied loads and peeling angles simi-lar to those reported with the graphene-on-coppersubstrate, are included in Table 1. The measurementsfall within the range of values obtained with the

graphene-on-copper substrate. Our simulations sug-gest that the lowest energy tubes in all tests wereflattened; however, we also present surface energiesfor collapsed tubes, as experimental conditions mayfavor this metastable configuration (see Figure 5c). Thevariation among the results could stem from multiplesources, which merit a detailed discussion.

GENERAL DISCUSSION

First, it is worth noting how these experimentalresults compare to other results reported previouslyin the literature for related materials. In addition tostudieswith carbon nanotubes, direct comparisonwiththe surface energy of bulk graphite is also appropriatebased on the analysis described earlier.65,66 There issome variation in the literature regarding acceptedvalues for the experimental and theoretical surfaceenergy of graphite, ranging from 0.035 J 3m

�2 to0.875 J 3m

�2.61�63,67�73 Some experimental studieswith graphite67,74 report values of 0.19 and 0.33 J 3m

�2.The results of the in situ SEM peeling tests reported hereare in good agreement with the recent experimentalsurface energy studies of these carbon materials. Theexperimental scatter falls within the range of otherpreviously reported experimental values for graphite.There are several sources of experimental uncertainty

and variability that may have contributed to the varia-tion in calculated surface energies and deviations fromthe average experimental value of γ = 0.26 J 3m

�2

reported earlier.61�63 For example, whileMWCNTs devel-oped through arc discharge only contain carbonaceousmaterials, amorphous carbon ispresent on theoutermostlayers of the tubes (e.g., see Figure 2), either directly fromfabrication or due to induced amorphous carbon deposi-tion by the electron beam in the SEM chamber. As thisamorphous carbon lacks the well-ordered sp2 bondingstructure of carbon nanotubes and graphene surfaces, itmay introduce additional interactions beyond whatwould be expected for idealized peeling between atom-ically smooth graphitic surfaces.56

Another source of scatter in the measured sur-face energy might be the roughness of the graphenesurface. As shown in Figure 3, because of the different

TABLE 1. Experimental Measurements and Calculated Surface Energy Values For Graphene-on-Copper and HOPG

Substrates

substrate tube no. test no.

peel angle,

θ [deg]

force,

F [nN]

outer

diameter [nm]

number of

walls

adhesion energy,

G (nJ 3m�1)

collapsed

contact width,

w [nm]

flattened

contact width,

w [nm]

collapsed surface

energy, γ [J 3m�2]

flattened surface

energy, γ [J 3m�2]

graphene 1 1 66 14 30 37 8.3 ( 1.9 15.8 8.6 0.26 ( 0.08 0.48 ( 0.19graphene 1 2 58 15 30 37 7.1 ( 1.8 15.8 8.6 0.22 ( 0.07 0.41 ( 0.17graphene 1 2 56 13 30 37 5.6 ( 1.3 15.8 8.6 0.18 ( 0.05 0.33 ( 0.13graphene 2 1 66 9 20 22 5.5 ( 1.1 13.5 7.7 0.20 ( 0.06 0.36 ( 0.14graphene 3 1 68 2 19 21 1.2 ( 0.7 13.3 7.6 0.05 ( 0.03 0.08 ( 0.06graphene 3 1 61 16 19 21 8.0 ( 1.5 13.3 7.6 0.30 ( 0.08 0.53 ( 0.20HOPG 4 1 69 12 21 24 7.6 ( 1.2 13.8 7.7 0.27 ( 0.08 0.49 ( 0.19HOPG 5 1 49 10 21 24 3.5 ( 0.6 13.8 7.7 0.13 ( 0.04 0.23 ( 0.09

ARTIC

LE


www.acsnano.org

134

thermal expansion properties of the copper foil andgraphene membrane, the substrate exhibits somewavy regions after processing.41,75�77 The rippledgraphene will inherently affect the contact area atthe interface. While limitations in SEM resolution pre-vent highly precise in situ characterization of peelingsurfaces, deviations in surface roughnessmay also con-tribute to the measured surface energy.The presence of molecules such as water in the SEM

chamber may also affect the surface energy measuredin this study. While in situ SEM tests were conductedin stable vacuum (∼10�5 Torr), and tests were notperformed until the tubes and graphene were in thevacuum for at least 2 h, molecules such as water mayremain on both the carbon nanotube and graphenesurfaces. When the surfaces come into contact, mol-ecules on each surface may interact with one anotherand introduce additional interaction energy contribu-tions. However, even if it were possible to conductthese tests in higher vacuum, this would present otherchallenges. For example, the time required for cuttingthe tubes during sample preparation would increase,78

resulting in additional exposure of the CNT to theelectron beam. The combinations of voltage and cur-rent conditions used during peeling and tube cuttingin this study (see the Methods section), as well asthe equilibration pressure conditions, reflect attemptsto establish a compromise among the factors thatmustbe considered in in situ SEM experiments.Another experimental aspect to be discussed is

the fact that the first tube was peeled multiple times.It could be argued that structural deformations at theatomic level may have formed after repeated peeling.Limitations in SEM resolution prevent investigations atthis scale. However, the tubemaintaineda straight profilebefore and after testing, and the surface energy of thetube�graphene interface is consistent among the peel-ing tests. These observations suggest that any atomic-scale deformations did not significantly affect the surfaceenergy values in this case. Nevertheless, the ideal studyincorporating this method would only perform one peeltest per tube to avoid this issue in the future.Ultimately, this novel method enables direct visua-

lization of peeling forces and displacements and pro-vides substantial insights into MWCNT peeling behaviorthrough direct integration of experiments and simula-tions. Although the primary substrate of interest in thecurrent study is graphene-on-copper, the results frompeels performed on HOPG are in good agreement withthe former, and the values obtained with bothmethodscompare favorably with the theoretical surface energyof graphite. These results with two distinct substrates

further support the claim that this method is capable ofexperimentally ascertaining adhesion energies and sur-faceenergies. In addition, the consistencybetweeneachset of experimental results and the theoretical graphitesurface energy suggests that bothmonolayer grapheneand HOPG can be used as baseline substrates forevaluating the changes in surface energy associatedwith chemical functionalization.

CONCLUDING REMARKS

Here we report a new method for quantifyingthe surface energy of bare CNT�graphene interfacesthrough in situ SEM peeling experiments, which iscombined with molecular mechanics and FEA simula-tions. Novel features of the method include directvisualization of the peeling and the estimation ofcontact width through detailed atomistic simulation,which allows the calculation of surface energy usingfracture mechanics concepts. Average values of 0.20(0.09 J 3m

�2 and 0.36 ( 0.16 J 3m�2 for the surface

energy of bare CNT�graphene surfaces were mea-sured, depending on the assumptions made for thetube conformation during peeling. Both estimates ofthe surface energy agree with the average experimen-tal value of 0.26 J 3m

�2 within the stated uncertainties.Potential reasons for variation including amorphouscarbon interactions, molecules such as water on thegraphitic surfaces, and substrate surface roughness arediscussed.The combination of experimental and computa-

tional studies in this work provides a foundation forunderstanding the interactions that occur betweenmaterials at the nanometer length scale. By investigat-ing the behavior of these nanoscale building blocks,we aim to provide direction for enhancing surfaceinteractions, for example, tube�tube, within larger-scale carbon-based yarns, and composites.In addition to experimentally measuring the sur-

face energy of bare tubes and graphene, this ap-proach is also envisioned as a means of quantifyingthe changes in surface energy associated with che-mical functionalization. Chemical cross-linking be-tween nanoscale constituents could lead to thedevelopment of strong, lightweight yarns derivedfrom CNTs, graphene, and other carbonmaterials thatwould be appealing for many potential applica-tions, including next-generation textiles and artificialmuscles.1 The method presented here may serve as atest bed for a variety of chemistries in nanoscalepeeling, providing a foundation for improving themechanical performance of carbon-based materialsfrom the bottom up.

METHODS

Materials. As-producedarc-dischargemultiwalled carbonnano-tubes (nTec) are used in this study because of their well-ordered

structure, high-purity carbon content, and excellent mechanicalproperties as compared to tubes grown by chemical vapor depo-sition.12 Geometries of representative MWCNTs are measuredusing high resolution TEM (JEOL 2100F). The primary substrate in

ARTIC

LE


www.acsnano.org

135

the peeling test is a mostly monolayer CVD-grown grapheneon copper foil (Graphene Supermarket) analyzed using AFM(XE-120, Park Systems Corp.) and Raman spectroscopy (HR800,Horiba Jobin Yvon). Freshly cleaved HOPG (SPI) was also used asan additional graphitic substrate for validation.

Experimental Methods. The tests described here are carried outin an FEI NovaNano 600 SEM. Before testing, the SEM chamberis cleaned with oxygen plasma for at least 1 h to minimizesample contamination. MWCNTs are brushed onto a cut copperTEM grid and placed in the chamber together with a verticallyoriented strip of graphene on copper. High-resolution picturesof selected MWCNTs are taken such that their diameters can beestimated by averaging, overmultiple cross-sectional line scans,and calculating the full width at half-maximumof the average ofthe scans. For a given tube, an AFM cantilever (MikroMasch) ofknown stiffness is brought into contact with a danglingMWCNTusing a nanomanipulator (Klocke). When the CNT is pulled taut,as determined from tube straightening, the CNT is cut with theelectron beam at low voltage (5 kV) and high current (1.8 nA)based on established CNT cutting protocols.78 All other manip-ulation of the samples takes place under high voltage (30 kV)and low current (∼0.1 nA) in order to reduce amorphouscarbon deposition and potential damage to the specimens.78

After cutting, the MWCNT is welded to the surface of the AFMcantilever with electron beam-induced deposition of amorphouscarbon at high magnification (∼300 000�) for approximately5 min. The length and orientation of the tube are recorded fromimages after this deposition to serve as a reference for checkingwhether any observable deformation of the tubes occurs aftertesting. The graphene surface is inspected to identify a flatlocation for placement of the CNT such that it will not interactwith any visible imperfections. The graphene surface is rotated(approximately 30 degrees with respect to the cantilever arm) inorder to promote peeling at low angles, reducing the likelihoodof inducing structural changes in CNTs due to sharp bendsand kinks.79 In a given test, the force, F, is measured by digitalimage correlation of cantilever displacement including correc-tion for cantilever drift. The offset angle, R, is measured directlyfrom digital images in the frame before peeling.

Uncertainty Analysis. The analysis is based on uncertainties inthe terms of the classical peeling formula developed by Kendall,eq 1. Experimental results indicated that the second term on theright-hand side of the equation, associated with strain energy,is much smaller than the other two terms in all tests. Conse-quently, uncertainty in strain energy is neglected for thepurposes of this analysis.

The force F applied to the CNT during testing is measured as

F ¼ kδ

cos(R)(18)

where k is the AFM cantilever stiffness, δ is the cantileverdeflection, and R is the offset angle of the tube. The cantileverstiffness is given by

k ¼ Ecwctc3

4Lc3(19)

where Ec,wc, tc, and Lc are the elastic modulus, width, thickness,and length of the cantilever, respectively. Ec is taken to be 169GPa based on the established value for silicon in the Æ110ædirections, in accordance with AFM cantilever manufacturingconditions.80

By rearranging eq 1 for surface energy γ and substitutingeqs 18 and 19, the experimental uncertainty can be estimated bythe square root of the sum of squared errors (see, e.g., ref 81) as

Δγ

γ¼ (

Δw

w

� �2

þ Δδ

δ

� �2

þ Δwc

wc

� �2

þ 3Δtctc

� �2

þ 3ΔLcLc

� �2

þ cotθ

2

� �Δθ

!2

þ(tan(R)ΔR)2)1=2 (20)

Among these components of uncertainty, the largest factor inany test is either uncertainty in contactwidth,w, or displacement,δ. To estimate uncertainty in adhesion energy, G, the sameformula is used excluding the term for contact width.

The uncertainty in contact width arises from two features:the uncertainty in the number of walls of each MWCNT usedfor peeling, and the uncertainty in themeasured outer diameterof eachMWCNT. First, the outer diameters and numbers of wallsof 20 arc discharge MWCNTs were measured using HR-TEM,which provide a statistical measure of the number of walls for agiven tube diameter. Figure S1 (in the Supporting Information)shows the number of walls corresponding to each of the 20tubes as measured from HR-TEM images. A linear best-fit inter-polation is applied to estimate the number of walls correspond-ing to tubes of different diameters. For this sample of datapoints, the standard error of the estimate, s, is calculated to be∼2.7 from the variation between the linear fit and the experi-mental points. The parameter s is then rounded up to an integernumber of walls, s0 =3, to provide a conservative estimate of thisstandard error over all diameters. An envelope (shaded region)is then defined to account for the tubeswithin(1s0 , as shown inSupporting Information, Figure S1.

Second, the outer diameter of each MWCNT used in testingis measured directly from SEM images. The outer diameteris measured by calculating the full width at half-maximum ofbrightness profiles corresponding to line scans across the long-itudinal axis of the tube. Uncertainty in diameter associatedwithusing this procedure is also incorporated into the total uncer-tainty in contact width. An uncertainty of (1.5 nm (1/2 pixel)is assigned to tubes 2 and 3, while an uncertainty of (2.9 nm(1 pixel) is assigned to tube 1 due to lower image quality.

The diameter and number of walls are then incorporateddirectly into the contact width formula derived from molecularmechanics simulations. For uncertainty considerations, twoextremes are evaluated for each tube: the maximum diameterwith the fewest number of walls, corresponding to a maximumcontact width for a given tube, and theminimum diameter withthe largest number of walls, corresponding to the minimumcontact width for a given tube. The largest difference associatedwith these two extremes is taken as Δw.

Variation in displacement, δ, is taken as the differencebetween deflections measured by digital image correlationtracking two separate regions of the cantilever during eachtest, which should provide equivalent displacements. In theevent of an exactmatch between the twomeasured deflections,an error of(1 pixel is assigned to reflect limitations in resolutionof the digital image correlation software. Three independentexperiments were conducted in which an AFM cantilever(extending from a nanomanipulator) and a TEM grid attachedto the SEM stage were placed within the same viewing windowand observed for several minutes (i.e., much longer than anyindividual peeling test). The results of these experiments in-dicated that AFM cantilever drift was linear with respect to time,while drift in stage position over time was negligible. Havingestablished a basis for characterizing the cantilever drift aslinear, the effect of drift on total displacement was determinedand incorporated on a test-by-test basis, not by assuming aglobal rate of drift over all tests. Consequently, cantilever drift isaccounted for by incorporating a linear estimate of drift con-tribution to displacement when reporting δ values in this study.

Variations in cantilever width wc and cantilever thickness tcare taken as the standard deviation of nine measurements ofeach of these values from SEM images. Uncertainty in cantileverlength Lc is taken to be the same as the uncertainty in thicknessassociated with each cantilever. Deviations in θ and R are takento be (2.5 degrees based on standard deviations of anglesmeasured in a representative SEM image of a MWCNT. All vari-ations in angle are assumed to be planar, as changes in out-of-plane orientation cannot bemeasured due to limitations in SEMdepth of focus.

Typical experimental uncertainty values in surface energyassociated with the assumptions presented here and incorpo-rated into eq 20were approximately 30%assuming the collapsedconfiguration and 40% assuming the flattened configuration.For adhesion energy, experimental uncertainty was approxi-mately 20%.

Boundary Box Size Optimization Protocol for Atomistic Simulations.The graphene layer and zigzag (383,0) SWCNT were generatedwith VMD.82 The (383,0) SWCNT was chosen to match the tube

ARTIC

LE


www.acsnano.org

136

diameter to experiments. Hydrogen atoms were added to thetwo graphene edges that are nonperiodic. Each structure wasaligned in such a way that the periodic direction is alwaysaligned with the x-axis of the simulation cell. The box y- andz-dimensions were set equal to 800 Å. The cell length alongthe periodic boundary was varied between 32 Å and 32.6 Å. Foreach such length the MWCNT (or graphene) structure wasallowed to move until the total potential energy reached itsminimum value. Final values were plotted as a function of thecell length (see Supporting Information, Figure S2).

The cell length associated with the energy minimum wasassigned as the optimum longitudinal boundary. We assumedthat the interaction of graphene with the copper foil preventsdramatic structural changes in graphene while it interactswith the CNT. Therefore, the optimum longitudinal cell lengthin this study was chosen equal to that from the graphene curve(32.2991 Å).

Parameterization for Fully Collapsed Structures. To obtain thecollapsed configurations, the tubes were deformed by applyingdisplacements to selected atoms, which tended to inducecollapse. At each step, the configurations of the tubeswere opti-mized for the given displacement constraints. After the innerinterwall distance reached 3.4 Å, all constraints were released,and full relaxations of the structures on the graphene sur-face were performed. For tubes with small diameters or largenumbers of walls, the deformed configurations returned tonearly cylindrical shapes (see example on Supporting Informa-tion, Figure S3). Only fully collapsed final configurations wereused to parametrize the contact width formula (see eq 9).

Parameterization for Flattened Structures. The differences incontact widths between fully collapsed and flattened structuresof the same outer diameter and number ofwalls can be approxi-mated as a function of the heights of the flattened tubes. Asshown in Supporting Information, Figure S5 and the insetof Figure S6, the heights of flattened tubes increase withdiameter and then reach saturation beyond certain diametervalues. The increases are linear. The deviations from linearityand subsequent saturations can be described using exponentialgrowth functions (colored lines on Figure S6). Linear fitting ofdata for tubes with one to eight walls led to eqs 12�14.

We used exponential switch functions (see eq 11) to achievesmooth transitions from the linear to exponential regions.The switch points were located at the points of deviationfrom linearity. The values for deviation points were fit witha linear equation, which suggested the 8N term. Good fitsfor the curviness of the transition were produced using 1/N.This suggested the equation

height ¼ (1 � H(x))DþH(x) Aþ B exp�D

C

� � !(21)

for the saturation height shown in Supporting Information,Figure S6. Fitted lines are shown along with the original datapoints. The heights of the flattened tubes from eq 21were used toproduce equations for contact width differences (Wcorr) betweencorresponding flattened and collapsed tubes. On the basis of thedata, we found that the Wcorr to height ratio was strongly depen-dent on N. This is because N defines the susceptibility of a tubeto radial deformation and, therefore, its height. After correctingfor this, we established a linear relationship by plotting 1/N as afunction of Wcorr/(height � N). The result was eq 10. We esti-mate that the error associated with the model is þ3.769 nm and�0.403nm, basedondeviations of themodel from thedata points.

There are also other sources of uncertainty associated withthe theoretical estimates for the contact widths. MM3 is con-sidered to be among the best force fields for this typeof problem. However, it is not expected to predict exact results.Also, due to computational limitations, the training sets forour fitting (see Supporting Information, Figures S3, S6, and S7)are quite far from the experimental estimates for tube sizes.Thus, although good fits were achieved, such extrapolationsare always associated with uncertainty. Better estimates may beavailable via the next generation of supercomputers.

Conflict of Interest: The authors declare no competingfinancial interest.

Supporting Information Available: HR-TEM data relatingnumber of CNT walls to outer diameter (Figure S1); plots ofcontact width vs diameter for collapsed (Figure S3) and flat-tened (Figure S7) tubes from atomistic simulations; additionalplots (Figures S2 and S6) and illustrations (Figures S4 and S5)pertaining to atomistic simulations. This material is availablefree of charge via the Internet at http://pubs.acs.org.

Acknowledgment. This work was supported by ARO MURIaward W911NF-09-1-0541 and NSF award CMMI-1235480.J.T.P. thanks Raul Esquivel-Sirvent for helpful discussions. Theauthors would like to thank Dr. Shuyou Li of the Electron ProbeInstrumentation Center (EPIC) at Northwestern University forobtaining TEM images and Rodrigo Bernal for helpful dis-cussions and assistance with digital image correlation. Theauthors also thank Dr. Xinqi Chen of the Keck-II Center atNorthwestern University for assistance with acquiring Ramanspectra of graphene-on-copper. This research used resourcesof the QUEST cluster at Northwestern University, WestGridand Compute/Calcul Canada. M.R.R. gratefully acknowledgessupport from the Department of Defense (DoD) through theNational Defense Science & Engineering Graduate Fellowship(NDSEG) Program and the Northwestern University Ryan Fel-lowship & International Institute for Nanotechnology. M.R.R.also thanks Rafael Soler-Crespo for helpful discussions.

REFERENCES AND NOTES1. Zhang, M.; Atkinson, K. R.; Baughman, R. H. Multifunctional

Carbon Nanotube Yarns by Downsizing an Ancient Tech-nology. Science 2004, 306, 1358–1361.

2. Min, J.; Cai, J. Y.; Sridhar, M.; Easton, C. D.; Gengenbach, T. R.;McDonnell, J.; Humphries, W.; Lucas, S. High PerformanceCarbonNanotube Spun Yarns from aCrosslinked Network.Carbon 2012, 52, 520–527.

3. Koziol, K.; Vilatela, J.; Moisala, A.; Motta, M.; Cunniff, P.;Sennett, M.; Windle, A. High-Performance Carbon Nano-tube Fiber. Science 2007, 318, 1892–1895.

4. Zhang, S.; Zhu, L.; Minus, M. L.; Chae, H. G.; Jagannathan, S.;Wong, C. P.; Kowalik, J.; Roberson, L. B.; Kumar, S. Solid-State Spun Fibers and Yarns from 1-mm Long CarbonNanotube Forests Synthesized by Water-Assisted Chemi-cal Vapor Deposition. J. Mater. Sci. 2008, 43, 4356–4362.

5. Tran, C. D.; Humphries, W.; Smith, S. M.; Huynh, C.; Lucas, S.Improving the Tensile Strength of Carbon Nanotube SpunYarns Using aModified Spinning Process. Carbon 2009, 47,2662–2670.

6. Denis-Lutard, V.; Derre, A.; Maugey, M.; Mercader, C.;Moisan, S.; Zakri, C.; Poulin, P. New Wet Spinning Processfor the Continuous Production of Polymer/Carbon Nano-tubes Composite Fibers. Recent Advances in Textile Com-posites: Proceedings of the 10th International Conferenceon Textile Composites; DEStech Publications, Inc: Lancaster,PA, 2010; pp 167�172.

7. Naraghi, M.; Filleter, T.; Moravsky, A.; Locascio, M.; Loutfy,R. O.; Espinosa, H. D. A Multiscale Study of High Perfor-mance Double-Walled Nanotube�Polymer Fibers. ACSNano 2010, 4, 6463–6476.

8. Ryu, S.; Lee, Y.; Hwang, J. W.; Hong, S.; Kim, C.; Park, T. G.;Lee, H.; Hong, S. H. High-Strength Carbon Nanotube FibersFabricated by Infiltration and Curing of Mussel-InspiredCatecholamine Polymer. Adv. Mater. 2011, 23, 1971–1975.

9. Li, Y. L.; Kinloch, I. A.; Windle, A. H. Direct Spinning ofCarbon Nanotube Fibers from Chemical Vapor DepositionSynthesis. Science 2004, 304, 276–278.

10. Zhang, X.; Li, Q.; Tu, Y.; Li, Y.; Coulter, J. Y.; Zheng, L.; Zhao,Y.; Jia, Q.; Peterson, D. E.; Zhu, Y. Strong Carbon-NanotubeFibers Spun from Long Carbon-Nanotube Arrays. Small2007, 3, 244–248.

11. Lu, W.; Zu, M.; Byun, J.-H.; Kim, B.-S.; Chou, T.-W. State ofthe Art of Carbon Nanotube Fibers: Opportunities andChallenges. Adv. Mater. 2012, 24, 1805–1833.

12. Peng, B.; Locascio, M.; Zapol, P.; Li, S.; Mielke, S. L.; Schatz,G. C.; Espinosa, H. D. Measurements of Near-Ultimate

ARTIC

LE


www.acsnano.org

137

Strength for Multiwalled Carbon Nanotubes and Irradiation-Induced Crosslinking Improvements. Nat. Nanotechnol2008, 3, 626–631.

13. Locascio, M.; Peng, B.; Zapol, P.; Zhu, Y.; Li, S.; Belytschko, T.;Espinosa, H. D. Tailoring the Load Carrying Capacity ofMWCNTs through Inter-Shell Atomic Bridging. Exp. Mech.2009, 49, 169–182.

14. Yu, M.-F.; Lourie, O.; Dyer, M. J.; Moloni, K.; Kelly, T. F.; Ruoff,R. S. Strength and Breaking Mechanism of MultiwalledCarbon Nanotubes under Tensile Load. Science 2000, 287,637–640.

15. Kis, A.; Csanyi, G.; Salvetat, J.-P.; Lee, T. N.; Couteau, E.; Kulik,A. J.; Benoit, W.; Brugger, J.; Forro, L. Reinforcement ofSingle-Walled Carbon Nanotube Bundles by IntertubeBridging. Nat. Mater. 2004, 3, 153–157.

16. Filleter, T.; Bernal, R.; Li, S.; Espinosa, H. D. UltrahighStrength and Stiffness in Cross-Linked Hierarchical CarbonNanotube Bundles. Adv. Mater. 2011, 23, 2855–2860.

17. Banerjee, S.; Kahn, M. G. C.; Wong, S. S. Rational ChemicalStrategies for CarbonNanotube Functionalization. Chem.;Eur. J. 2003, 9, 1898–1908.

18. Banerjee, S.; Hemraj-Benny, T.; Wong, S. S. CovalentSurface Chemistry of Single-Walled Carbon Nanotubes.Adv. Mater. 2005, 17, 17–29.

19. Balasubramanian, K.; Burghard, M. Chemically Functiona-lized Carbon Nanotubes. Small 2004, 1, 180–192.

20. Peng, X.; Wong, S. S. Functional Covalent Chemistry ofCarbonNanotube Surfaces. Adv. Mater. 2009, 21, 625–642.

21. Tasis, D.; Tagmatarchis, N.; Bianco, A.; Prato, M. Chemistryof Carbon Nanotubes. Chem. Rev. 2006, 106, 1105–1136.

22. Gao, C.; Guo, Z.; Liu, J. H.; Huang, X. J. The New Age ofCarbon Nanotubes: An Updated Review of FunctionalizedCarbon Nanotubes in Electrochemical Sensors. Nanoscale2012, 4, 1948–1963.

23. Barber, A. H.; Cohen, S. R.; Eitan, A.; Schadler, L. S.; Wagner,H. D. Fracture Transitions at a Carbon-Nanotube/PolymerInterface. Adv. Mater. 2006, 18, 83–87.

24. Tsuda, T.; Ogasawara, T.; Deng, F.; Takeda, N. DirectMeasurements of Interfacial Shear Strength ofMultiwalledCarbon Nanotube/PEEK Composite Using a Nano-PulloutMethod. Compos. Sci. Technol. 2011, 71, 1295–1300.

25. Ganesan, Y.; Peng, C.; Lu, Y.; Loya, P. E.; Moloney, P.; Barrera,E.; Yakobson, B. I.; Tour, J. M.; Ballarini, R.; Lou, J. InterfaceToughness of Carbon Nanotube Reinforced Epoxy Com-posites. ACS Appl. Mater. Interfaces 2011, 3, 129–134.

26. Beese, A. M.; Sarkar, S.; Nair, A.; Naraghi, M.; An, Z.;Moravsky, A.; Loutfy, R. O.; Buehler, M. J.; Nguyen, S. T.;Espinosa, H. D. Bio-Inspired Carbon Nanotube�PolymerComposite Yarns with Hydrogen Bond-Mediated LateralInteractions. ACS Nano 2013, 7, 3434–3446.

27. Naraghi, M.; Bratzel, G. H.; Filleter, T.; An, Z.; Wei, X.; Nguyen,S. T.; Buehler, M. J.; Espinosa, H. D. Atomistic Investigationof Load Transfer between DWNT Bundles “Crosslinked” byPMMAOligomers. Adv. Funct. Mater. 2013, 23, 1883–1892.

28. Wei, X.; Naraghi, M.; Espinosa, H. D. Optimal Length ScalesEmerging from Shear Load Transfer in Natural Materials:Application to Carbon-Based Nanocomposite Design. ACSNano 2012, 6, 2333–2344.

29. Sasaki, N.; Toyoda, A.; Saitoh, H.; Itamura, N.; Ohyama, M.;Miura, K. Theoretical Simulation of Atomic-Scale Peelingof Single-Walled Carbon Nanotube from Graphite Surface.e-J. Surf. Sci. Nanotechnol. 2006, 4, 133–137.

30. Sasaki, N.; Toyoda, A.; Itamura, N.; Miura, K. Simulation ofNanoscale Peeling and Adhesion of Single-Walled CarbonNanotube on Graphite Surface. e-J. Surf. Sci. Nanotechnol.2008, 6, 72–78.

31. Strus, M.; Zalamea, L.; Raman, A.; Pipes, R. B.; Nguyen, C. V;Stach, E. A. Peeling Force Spectroscopy: Exposing theAdhesive Nanomechanics of One-Dimensional Nano-structures. Nano Lett 2008, 8, 544–550.

32. Strus, M. C.; Cano, C. I.; Pipes, R. B.; Nguyen, C. V.; Raman, A.Interfacial Energy between Carbon Nanotubes andPolymers Measured from Nanoscale Peel Tests in theAtomic Force Microscope. Compos. Sci. Technol. 2009,69, 1580–1586.

33. Buchoux, J.; Bellon, L.; Marsaudon, S.; Aimé, J. P. CarbonNanotubes Adhesion and Nanomechanical Behavior fromPeeling Force Spectroscopy. Eur. Phys. J. B 2011, 69–77.

34. Ishikawa, M.; Harada, R.; Sasaki, N.; Miura, K. Visualization ofNanoscale Peeling of Carbon Nanotube on Graphite. Appl.Phys. Lett. 2008, 93, 083122.

35. Ishikawa, M.; Harada, R.; Sasaki, N.; Miura, K. Adhesion andPeeling Forces of Carbon Nanotubes on a Substrate. Phys.Rev. B 2009, 80, 193406.

36. Miura, K.; Ishikawa,M.; Kitanishi, R.; Yoshimura, M.; Ueda, K.;Tatsumi, Y.; Minami, N. Bundle Structure and Sliding ofSingle-Walled Carbon Nanotubes Observed by Frictional-Force Microscopy. Appl. Phys. Lett. 2001, 78, 832–834.

37. Miura, K.; Takagi, T.; Kamiya, S.; Sahashi, T.; Yamauchi, M.Natural Rolling of Zigzag Multiwalled Carbon Nanotubeson Graphite. Nano Lett. 2001, 1, 161–163.

38. Ke, C.; Zheng, M.; Zhou, G.; Cui, W.; Pugno, N.; Miles,R. N. Mechanical Peeling of Free-Standing Single-WalledCarbon-Nanotube Bundles. Small 2010, 6, 438–445.

39. Sen, D.; Novoselov, K. S.; Reis, P. M.; Buehler, M. J. TearingGraphene Sheets from Adhesive Substrates ProducesTapered Nanoribbons. Small 2010, 6, 1108–1116.

40. Ismach, A.; Druzgalski, C.; Penwell, S.; Schwartzberg, A.;Zheng, M.; Javey, A.; Bokor, J.; Zhang, Y. Direct ChemicalVapor Deposition of Graphene on Dielectric Surfaces.Nano Lett 2010, 10, 1542–1548.

41. Li, X.; Cai, W.; Colombo, L.; Ruoff, R. S. Evolution ofGraphene Growth on Ni and Cu by Carbon Isotope Label-ing. Nano Lett 2009, 9, 4268–4272.

42. Ferrari, A.; Meyer, J.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.;Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.;Geim, A. K. Raman Spectrum of Graphene and GrapheneLayers. Phys. Rev. Lett. 2006, 97, 187401.

43. Kendall, K. Thin-Film Peeling-the Elastic Term. J. Phys. D:Appl. Phys. 1975, 8, 1449–1452.

44. Haskins, R. W.; Maier, R. S.; Ebeling, R. M.; Marsh, C. P.;Majure, D. L.; Bednar, A. J.; Welch, C. R.; Barker, B. C.; Wu,D. T. Tight-Binding Molecular Dynamics Study of the Roleof Defects on Carbon Nanotube Moduli and Failure.J. Chem. Phys. 2007, 127, 074708.

45. Tian, J.; Cao, H.; Wu, W.; Yu, Q.; Guisinger, N. P.; Chen, Y. P.Graphene Induced Surface Reconstruction of Cu. NanoLett. 2012, 12, 3893–3899.

46. Ponder, J. W. http://dasher.wustl.edu/tinker (accessedOctober 2011).

47. Sears, A.; Batra, R. C. Macroscopic Properties of CarbonNanotubes from Molecular-Mechanics Simulations. Phys.Rev. B 2004, 69, 235406.

48. Filleter, T.; Yockel, S.; Naraghi, M.; Paci, J. T.; Compton, O. C.;Mayes, M. L.; Nguyen, S. T.; Schatz, G. C.; Espinosa, H. D.Experimental-Computational Study of Shear Interactionswithin Double-Walled Carbon Nanotube Bundles. NanoLett. 2012, 12, 732–742.

49. Hertel, T.; Walkup, R. E.; Avouris, P. Deformation of CarbonNanotubes by Surface van der Waals Forces. Phys. Rev. B1998, 58, 13870–13873.

50. Griffith, A. A. The Phenomena of Rupture and Flow inSolids. Philos. Trans. R. Soc., A 1921, 221, 163–198.

51. Ruoff, R. S.; Tersoff, J.; Lorents, D. C.; Subramoney, S.; Chan,B. Radial Deformation of Carbon Nanotubes by van derWaals Forces. Nature 1993, 364, 514–516.

52. Park, M. H.; Jang, J. W.; Lee, C. E.; Lee, C. J. Interwall Supportin Double-Walled Carbon Nanotubes Studied by ScanningTunneling Microscopy. Appl. Phys. Lett. 2005, 86,023110.

53. Chopra, N. G.; Benedict, L. X.; Crespi, V. H.; Cohen, M. L.;Louie, S. G.; Zettl, A. Fully Collapsed Carbon Nanotubes.Nature 1995, 377, 135–138.

54. Yu, M.-F.; Dyer, M. J.; Chen, J.; Qian, D.; Liu, W. K.; Ruoff, R. S.Locked Twist in Multiwalled Carbon-Nanotube Ribbons.Phys. Rev. B 2001, 64, 241403.

55. Zhang, S.; Khare, R.; Belytschko, T.; Hsia, K. J.; Mielke, S. L.;Schatz, G. C. Transition States and Minimum Energy Path-ways for the Collapse of Carbon Nanotubes. Phys. Rev. B2006, 73, 075423.

ARTIC

LE


www.acsnano.org

138

56. Ma, X.; Wang, H.; Yang, W. Tribological Behavior of AlignedSingle-Walled Carbon Nanotubes. J. Eng. Mater. Technol.2004, 126, 258–264.

57. Rodriguez, A. W.; Capasso, F.; Johnson, S. G. The CasimirEffect inMicrostructured Geometries.Nat. Photonics 2011,5, 211–221.

58. Kolmogorov, A. N.; Crespi, V. H. Registry-Dependent Inter-layer Potential for Graphitic Systems. Phys. Rev. B 2005, 71,235415.

59. Steele, W. A. The Interaction of Gases with Solid Surfaces;Pergamon Press: Oxford, UK, 1974.

60. Israelachvili, J. N. Intermolecular and Surface Forces;Academic Press: San Diego CA, 1992.

61. Benedict, L. X.; Chopra, N. G.; Cohen, M. L.; Zettl, A.;Louie, S. G.; Crespi, V. H. Microscopic Determination ofthe Interlayer Binding Energy in Graphite. Chem. Phys. Lett.1998, 286, 490–496.

62. Zacharia, R.; Ulbricht, H.; Hertel, T. Interlayer CohesiveEnergy of Graphite from Thermal Desorption of Polyaro-matic Hydrocarbons. Phys. Rev. B 2004, 69, 155406.

63. Girifalco, L.; Lad, R. Energy of Cohesion, Compressibility,and the Potential Energy Functions of the Graphite Sys-tem. J. Chem. Phys. 1956, 25, 693–697.

64. Parsegian, V. A. Van Der Waals Forces: A Handbook forBiologists, Chemists, Engineers, and Physicists; CambridgeUniversity Press: UK, 2006.

65. Blagov, E.; Klimchitskaya, G.; Mostepanenko, V. van derWaals Interaction between a Microparticle and a Single-Walled Carbon Nanotube. Phys. Rev. B 2007, 75, 235413.

66. Koenig, S. P.; Boddeti, N. G.; Dunn, M. L.; Bunch, J. S.Ultrastrong Adhesion of Graphene Membranes. Nat. Na-notechnol. 2011, 6, 543–546.

67. Schrader, M. E.; Loeb, G. I. Modern Approaches to Wett-ability: Theory and Applications; Plenum Press: New York,1992.

68. Schrader, M. E. Ultrahigh Vacuum Techniques in theMeasurement of Contact Angles. IV. Water on Graphite(0001). J. Phys. Chem. 1975, 79, 2508–2515.

69. Schrader, M. E. Ultrahigh-Vacuum Techniques in the Mea-surement of Contact Angles. 5. LEED Study of the Effect ofStructure on the Wettability of Graphite. J. Phys. Chem.1980, 84, 2774–2779.

70. Bryant, P.; Gutshall, P.; Taylor, L. A Study of Mechanisms ofGraphite Friction and Wear. Wear 1964, 7, 118–126.

71. Brennan, R. O. The Interlayer Binding in Graphite. J. Chem.Phys. 1952, 20, 40–48.

72. Crowell, A. D. Potential Energy Functions for Graphite.J. Chem. Phys. 1958, 29, 446–447.

73. Putnam, F. A.; Fort, T., Jr. Physical Adsorption of PatchwiseHeterogeneous Surfaces. I. Heterogeneity, Two-Dimen-sional Phase Transitions, and Spreading Pressure of theKrypton-Graphitized Carbon Black Systemnear 100 deg. K.J. Phys. Chem. 1975, 79, 459–467.

74. Liu, Z.; Liu, J. Z.; Cheng, Y.; Li, Z.; Wang, L.; Zheng, Q.Interlayer Binding Energy of Graphite: A MesoscopicDetermination from Deformation. Phys. Rev. B 2012, 85,205418.

75. Mattevi, C.; Eda, G.; Agnoli, S.; Miller, S.; Mkhoyan, K. A.;Celik, O.; Mastrogiovanni, D.; Granozzi, G.; Garfunkel, E.;Chhowalla, M. Evolution of Electrical, Chemical, andStructural Properties of Transparent and Conducting Che-mically Derived Graphene Thin Films. Adv. Funct. Mater.2009, 19, 2577–2583.

76. Cai, W.; Piner, R. D.; Stadermann, F. J.; Park, S.; Shaibat, M. A.;Ishii, Y.; Yang, D.; Velamakanni, A.; An, S. J.; Stoller, M.; An, J.;Chen, D.; Ruoff, R. S. Synthesis and Solid-State NMRStructural Characterization of 13c-Labeled GraphiteOxide. Science 2008, 321, 1815–1817.

77. Obraztsov, A. N.; Obraztsova, E. A.; Tyurnina, A. V.; Zolotukhin,A. A. Chemical Vapor Deposition of Thin Graphite Films ofNanometer Thickness. Carbon 2007, 45, 2017–2021.

78. Yuzvinsky, T. D.; Fennimore, A. M.; Mickelson, W.; Esquivias,C.; Zettl, A. Precision Cutting of Nanotubes with aLow-Energy Electron Beam. Appl. Phys. Lett. 2005, 86,053109.

79. Li, X.; Yang, W.; Liu, B. Bending Induced Rippling andTwisting of Multiwalled Carbon Nanotubes. Phys. Rev. Lett.2007, 98, 205502.

80. Hopcroft, M. A.; Nix, W. D.; Kenny, T. W. What Is the Young'sModulus of Silicon?. J. Microelectromech. Syst. 2010, 19,229–238.

81. Ku, H. H. Notes on the Use of Propagation of ErrorFormulas. Precision Measurement and Calibration, NBS SP300 1969, 1, 331–341.

82. Humphrey,W.;Dalke, A.; Schulten, K. VMD;VisualMolecularDynamics. J. Mol. Graph. 1996, 14, 33–38.

ARTIC

LE

Documents

In Situ Scanning Electron Microscope ARTICLE Peeling To ... Situ... · on peeling behavior are described in the General Discussion section. Raman spectroscopy was also per-formed