Deformation of Carbon Nanotubes Colliding with a …...All content following this page was uploaded by Shabeer Ahmad Mian on 05 June 2014. The user has requested enhancement of the

Seediscussionsstatsandauthorprofilesforthispublicationathttpswwwresearchgatenetpublication224822750

DeformationofCarbonNanotubesCollidingwithaSiliconSurfaceandItsDependenceonTemperature

ArticleinJournalofNanoscienceandNanotechnologymiddotJanuary2012

DOI101166jnn20125332middotSourcePubMed

CITATIONS

0

READS

60

5authorsincluding

Someoftheauthorsofthispublicationarealsoworkingontheserelatedprojects

searchingstableelectrodematerialforlithiumionbatterysystemViewproject

ComputationalStudyontheadhesionmechanismofmarinemusselsViewproject

LetonSaha

TohokuUniversity

15PUBLICATIONS114CITATIONS

SEEPROFILE

ShabeerAhmadMian

UniversityofPeshawar


SEEPROFILE

JoyantaKSaha

JagannathUniversity-Bangladesh


SEEPROFILE

JoonkyungJang

PusanNationalUniversity


SEEPROFILE

AllcontentfollowingthispagewasuploadedbyShabeerAhmadMianon05June2014

Theuserhasrequestedenhancementofthedownloadedfile

Delivered by Publishing Technology to Korea Institute of Science amp Technology (KIST)IP 1611223482 On Wed 28 May 2014 021102

Copyright American Scientific Publishers

RESEARCH

ARTIC

LE

Copyright copy 2012 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofNanoscience and Nanotechnology

Vol 12 674ndash679 2012

Deformation of Carbon Nanotubes Colliding with aSilicon Surface and Its Dependence on Temperature

Leton C Saha Shabeer A Mian Hyojeong Kim Joyanta K Saha and Joonkyung Janglowast

Department of Nanomaterials Engineering Pusan National University Miryang 627-706 Republic of Korea

Using molecular dynamics simulation we investigated the carbon nanotubes (CNTs) colliding witha silicon surface at a speed of 600 ms mimicking cold spray experiments of CNTs Dependingon temperature (300ndash900 K) the CNT is deposited on or bounces off the surface after impact onthe surface The CNT was more deformed as its temperature rose The deformation of CNT wasmaximal for the collision geometry where the long axis of CNT lies parallel to the surface planeHowever its vibrational energy was maximal when the CNT collided with its long axis perpendicularto the surface

Keywords Carbon Nanotube Collision Molecular Dynamics Deformation TemperatureDependence

1 INTRODUCTION

Carbon nanotubes (CNTs)1 have been commonly usedin surface coating processes such as cold spray2ndash4 high-velocity oxyfuel (HVOF)5 and plasma spray6 In theseprocesses CNTs are sprayed on the surface at a high speed(typically more than 400 ms) A deformation or fractureof CNT can result from such a high speed collision witha surface It is well known that both temperature and veloc-ity of CNT largely affect the result of such coating In par-ticular we are interested in how the temperature of CNTaffects the cold spray process where the speed of CNT istypically several hundreds of ms In our previous study78

we investigated CNTs colliding with and being depositedon a silicon surface at a speed of 5 kms This speed ismuch higher than that in a typical cold spray process andthe effects of temperature was not consideredThere have been several simulation studies on how tem-

perature affects the structure9ndash11 or conductivity1213 ofa single isolated CNT There have been studies on the col-lisions between CNT and surface without considering theeffects of temperature781415 Herein we investigate howthe temperature of CNT influences its deformation anddeposition in a collision with a surface relevant to coldspray experiment (temperature and speed range form 400to 900 K and from 400 to 1500 ms respectively) We con-sider two representative collision geometries of CNT thefirst is radial collision where the CNT impacts with its longaxis parallel to the surface In the other geometry called

lowastAuthor to whom correspondence should be addressed

axial collision the long axis of CNT lies perpendicular tothe surface during its impact In the radial collision thedeformation mainly involves a compression in the diam-eter of CNT This radial movement is known to be quiteflexible (60 collapse in diameter was found to be fullyreversible in experiment)1617 On the other hand the axialcollision primarily compresses the long axis of CNT whichis quite stiff and hard18 By using molecular dynamics sim-ulation method detailed in Refs [7 and 8] we study themolecular details underlying the deformation and vibra-tional energy of CNT at various temperatures We foundthat the CNT in the radial collision sticks to or bounceoff the surface depending on its temperature CNTs in theaxial collision bound to the surface regardless of temper-ature In general the CNT is more distorted in the radialcollision than in the axial collision On the other hand thevibrational energy of CNT was higher in the axial colli-sion The deformation of CNT increased with the rise intemperature Compared to the radial collision the axialcollision gave rise to a CNT more strongly bound to thesurface

2 SIMULATION DETAILS

We simulated a (6 6) single-walled CNT impacting onthe Si (110) surface The CNT made from 384 C atomswas 38 nm long and 081 nm in diameter Two differ-ent collision geometries axial and radial collisions wereconsidered as shown in Figures 1(a) and 2(a) The CNTcollides with the surface at a projectile speed vp where

674 J Nanosci Nanotechnol 2012 Vol 12 No 1 1533-4880201212674006 doi101166jnn20125332



RESEARCH

ARTIC

LE

Saha et al Deformation of Carbon Nanotubes Colliding with a Silicon Surface and Its Dependence on Temperature

the arrows in Figures 1(a) and 2(a) denotes its movingdirection (speed here refers to the magnitude of projec-tile velocity) We fixed vp to 600 ms which is withinthe range of impact velocities in the cold spray processThe Si (110) surface consisted of a slab of Si crystal witha thickness of 30 nm The atoms in the bottom layer ofthe slab were fixed in simulation The surface has lateraldimensions of 82 nmtimes 88 nm The periodic boundaryconditions19 were imposed and the length of the periodiccell along the Z direction was taken to be 50 nm Thesurface consisted of 10800 Si atoms Before collision weseparately equilibrated the temperature CNT and the sur-face by running constant temperature (NVT) MD19 simu-lations The equilibrated temperature of CNT TCNT wasvaried as 300 600 and 900 K The surface was equili-brated at 300 K After equilibration we added a projectilespeed vp to CNT for its collision with the surface The col-lision of the CNT was simulated using a constant energy(NVE) MD method19

We used the Tersoff potential20 to model the interactionbetween the CNT and surface The interatomic potentialbetween atoms i and j Vij is given by

Vij = fCrij VRrij +bijVArij (1)

where rij represents the interatomic distance The repulsiveand attractive energies VRrij and VArij respectivelyare represented as

VRrij = Aij exp minusrij (2)

VArij =minusBij exp minusrij (3)

In Eq (1) the cutoff function fCrij limits theinteraction as

fC =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

1 rij lt Rij

12+ 1

2cos

[rij minusRij

Sij minusRij

]Rij lt rij lt Sij

0 rij gt Sij

(4)

bij is the bond order of interaction and is given by

bij = ij1+nii

niij

minus12ni (5)

withij =

sumk =ij

fCrik13ikgijk (6)

gijk is given by

gijk= 1+ c2idii

minus c2id2i + himinus cosijk2

(7)

All the symbols not explained above are parame-ters which can be calculated by using the followingcombination rules

ij = i+j2 ij = i+j2 (8)

Aij = AiAj12 Bij = BiBj

12 (9)

Rij = RiRj12 Sij = SiSj

12 (10)

The parameters i i Ai Bi Ri and Si for Si and Care listed in Ref [20] Tersoff potential has been developedand widely accepted for studying covalent bonding of car-bon and silicon The melting of CNT at high temperaturehas been studied previously by using the same potential11

The MD trajectory was propagated using the velocityVerlet algorithm19 with a time step of 02 or 04 fs Thetime of impact was defined as the time at which the CNTapproaches within 0178 nm of the surface (0178 nm isthe CndashSi distance in a silicon carbide nanotube)21 TheMD simulation typically ran for 17 ps after impact Theabove MD methods were implemented using the DLPOLYpackage22

The energy of CNT was analyzed as follows At eachtime of simulation the position and velocity of the centerof mass were calculated The internal position and velocityof the ith C atom ri and vi were obtained by subtractingthese values from the position and velocity of each C atomrespectively The internal kinetic energy Kint is given bythe sum over each atom as

Kint = m2sumi

v2i (11)

The angular momentum L and the moment of the inertiatensor I were also calculated from ris and vis The rota-tional kinetic energy Krot and vibrational kinetic energyKvib were calculated as

Krot = 12(Iminus1 L) middot L (12)

Kvib = Kint minusKrot (13)

The vibrational temperature Tvib is given by

Tvib = 2Kvib3times384minus6kB (14)

where kB is the Boltzmann constantWe quantified the deformation of the CNT by calculat-

ing the root-mean-squared displacement (RMSD) To doso the displacement of each C atom from its initial valuewas calculated The average of the displacement squaredwas taken by summing over all the C atoms We usedthe numerical method Kabsch23 implemented in the VisualMolecular Dynamics package24

3 RESULTS AND DISCUSSION

Let us examine the snapshots of CNT in its collisionwith the Si (110) surface Figure 1(a) shows the axialcollision of CNT at a projectile speed of vp = 600 msFigures 1(bndashd) show the snapshots (17 ps after impact) ofCNTs deposited on the surface at different temperatures ofCNT 300 600 and 900 K respectively Due to the highspeed impact every CNT penetrates into the surface andstands up vertically Since the CNT is mechanically strongagainst external forces in its axial direction its structure

J Nanosci Nanotechnol 12 674ndash679 2012 675



RESEARCH

ARTIC

LE

Deformation of Carbon Nanotubes Colliding with a Silicon Surface and Its Dependence on Temperature Saha et al

Fig 1 (a) Simulation snapshot of a (6 6) CNT colliding with a Si (110) surface at a projectile speed of 600 ms The long axis of CNT liesperpendicular to the surface plane The arrow denotes the moving direction of the CNT (bndashd) Snapshots of CNTs taken at 17 ps after impact with thesurface at their temperatures TCNTs of 300 (b) 600 (c) and 900 K (d) Throughout the paper the surface temperature was fixed to 300 K

has not much changed after collision Its deformation islocalized at its bottom which penetrated into the surfaceThe structures of CNT shown in Figures 1(bndashd) are sim-ilar to each other but there is indeed some quantitativedifference as shown belowFigure 2(a) explains the radial collision of CNT with the

Si surface Figures 2(bndashd) illustrate the collisions of CNTsinitially equilibrated at temperatures of 300 600 and900 K respectively Interestingly the final result of col-lision depended on temperature The CNT bounced backfrom the surface in the case of TCNT = 300 K (Fig 2(b)the arrow represents the moving direction of CNT) Withincreasing TCNT to 600 K (Fig 2(c)) the CNT binds withthe surface but its long axis stood up vertically on the sur-face In this case the CNT lies down on the surface at thetime of impact Then one of the open ends of CNT stuckto the surface while the other end bounced off the surfaceThis gives rise to a gradual standing up of CNT and thevertical erection Further increasing TCNT to 900 K gave aCNT lying down on the surface (Fig 2(d)) as expected foran ordinary radial collisionIn Figure 3 we plotted the binding energy of CNT

EB versus TCNT The binding energy25 is defined as EB =minusEtotalminus ESi+ECNT where Etotal ESi and ECNT are the

potential energies of total system the silicon surface andCNT respectively In the figure filled (open) bars are forthe radial (axial) collision No binding energy is reportedfor the radial collision at TCNT = 300 K because the CNTbounces off in this case EB at TCNT of 600 K are nearlythe same for both the radial and axial collisions This isreasonable because we saw above that the radial collisionin this case gave a CNT standing vertically on the sur-face as in the axial collision Only at the highest TCNT(900 K) we can compare the binding energies of CNTlying down and standing up on the surface The standing-up CNT resulting from the axial collision has a bindingenergy higher (by 418 kcalmol) than that of a lying downCNT from the radial collisionWe now study the dynamics for the deformation and

excitation in vibration energy of CNT The deformationdynamics was studied by plotting the RMSD as a func-tion of time elapsed after impact (Fig 4(a) solid line)After impact the RMSD rapidly increases and reachesa maximum due to the impact This maximum in defor-mation is followed by a relaxation in which the RMSDdecreases and levels off This relaxation was modeledby fitting the RMSD to an exponential function of timea exp minust+ b (drawn as a dotted line) The fitting

676 J Nanosci Nanotechnol 12 674ndash679 2012



RESEARCH

ARTIC

LE


Fig 2 (a) Simulation snapshot of a (6 6) CNT colliding with a Si (110) surface at a projectile speed of 600 ms (bndashd) Snapshots of CNTs taken at17 ps after impact with the surface at TCNTs of 300 (b) 600 (c) and 900 K (d) The arrows in (a) and (b) denotes the moving direction of the CNT

parameter b (0031 nm) is the long-time asymptotic RMSDand quantifies the deformation of CNT78

Figure 4(b) (solid line) shows the time-dependent vibra-tional temperature Tvib for TCNT = 600 K As in the RMSDcurve Tvib rapidly rises after impact and reaches a max-imum (819 K) After reaching maximum Tvib decays intime which could be modeled by fitting to an exponen-tial function a exp minust+ bvib as above Such a fitting

Fig 3 Surface binding energy of CNT EB We plot EB versus TCNT forthe radial (filled bars) and axial (blank bars) collisions

Fig 4 (a) Deformation dynamics of the CNT colliding with a Si (110)surface TCNT = 300 K The RMSD from the initial configuration of CNTwas plotted as a function of the time elapsed after impact The RMSDafter its maximum is fitted to an exponential function of time (dottedline) (b) Dynamics of the vibrational temperature of CNT in collisionwith the same surface as above We plot the vibrational temperature Tvib

versus time and applied the same exponential fitting as in (a) (dottedline) TCNT = 600 K




RESEARCH

ARTIC

LE


(drawn as a dotted line) gave us the long time asymptoticvalue of Tvib bvib (416 K in this case) bvib quantifies theexcitation in the vibrational energy of CNTLet us quantitatively investigate the deformation of CNT

by varying its temperature In Figure 5 the maximalRMSD MSD (see Fig 4(a)) and b are plotted versus TCNTfor the radial (filled circles) and axial (filled squares) col-lisions of CNT Irrespective of temperature MSD is higherfor the radial collision than for the axial collision The rea-son is that the CNT is more flexible in its radial deforma-tion (shrinkage in diameter) than in its axial compressionalong its long axis Consequently the radial collision givesa more deformation of the CNT In the case of axial colli-sion MSD rises with increasing TCNT varying from 0044to 0054 nm MSD remained roughly constant (approxi-mately 007 nm) for the radial collisionThe long-time deformation of CNT was quantified as b

and is plotted versus TCNT in Figure 5(b) For comparisonwe also plot the results for an isolated CNT (open cir-cles) For both the axial and radial collisions b increaseswith raising temperature Notice that the deformation atTCNT = 300 K is virtually identical to that of an isolatedCNT meaning there is no permanent deformation As thetemperature increases the deformation increases b rangesfrom 003 to 005 nm and from 003 to 004 nm for theradial and axial collisions respectively Presumably anincreased temperature makes the CNT more flexible lead-ing to an increased deformation of it At TCNT = 900 Kb for the radial collision is higher than that for the axialcollision because of the flexibility of CNT in its radialcompression At TCNT = 600 K however b for the radialcollision is lower than that for the axial collision becausethe CNT stands up after impacting on the surface

300 600 900

0030

0035

0040

0045

0050

b (n

m)

TCNT (K)

(b)

004

006

008

MS

D (n

m) (a)

Fig 5 Temperature dependence of the deformation of CNT (a) Themaximal deformation MSD in the RMSD curve (Fig 4(a)) is calculatedfor various temperatures and is plotted versus TCNT for the radial (filledcircles) and axial (filled squares) collisions (b) The long-time asymp-totic deformation b is plotted versus TCNT for an isolated CNT (opencircles) and for CNTs in the axial (filled squares) and radial (filled circles)collisions

TCNT (K)300 600 900

300

350

400

450(b)

b vib

(K)

600

900

1200

TM

(K

)

(a)

Fig 6 Temperature dependence of the vibrational energy of CNT(a) We checked the maximal value in Tvib curve as in Figure 4(b) byvarying temperature Such a maximum TM is plotted versus TCNT for theradial (filled circles) and axial (filled squares) collisions (b) The long-time vibrational temperature bvib is plotted as a function of TCNT for theradial (filled circles) and axial (filled squares) collisions

We study the dynamics of vibrational energy by vary-ing temperature Figure 6 shows the results for the radial(filled circle) and axial (filled square) collisions For eachTCNT we checked the maximum in the vibrational temper-ature curve as shown in Figure 4(b) Such maximal TMsare plotted versus TCNT in Figure 6(a) For both of col-lision geometries TM evidently increases with increasingTCNT Unlike MSD TM is higher for the axial collision thanfor the radial collision We can explain this as followsDue to a smaller contact area CNT in the axial collisionthe vibrationally excited CNT has a narrower channel fordissipating its extra energy to the surface In the radialcollision on the other hand the CNT has a larger con-tact area with the surface so that it can dump out its extraenergy more efficiently to the surface TM varies from 487to 1120 K and from 381 to 978 K for the axial and radialcollisions respectivelyFinally the long-time vibrational temperature bvib is

plotted as a function of TCNT in Figure 6(b) bvib for theaxial collision increases with temperature rise (changingfrom 405 to 426 K) bvib for the radial collision shows thesame behavior except the anomaly at 600 K The anomalyagain arises from the fact that the CNT in this case standsup on the surface as in the axial collision Because of thesmall contact area of CNT with the surface it is harder forthe CNT to transfer its vibrational energy to the surfacecompared to the radial collision at 900 K In contrast theCNT at TCNT = 900 K lies down on the surface and easilytransfers its extra energy to the surface having a smallerbvib bvib for the radial collision ranged from 307 to 357 KAs for TM bvib for the axial collision is higher than that forthe radial collision For this we can use the same expla-nation as for TM above




RESEARCH

ARTIC

LE


4 CONCLUSION

Using MD simulations we investigated the collision anddeposition of CNT on a Si (110) surface By choosinga projectile speed of CNT relevant to cold spray exper-iment (600 ms) we systematically varied the tempera-ture of CNT from 300 to 900 K We also considered tworepresentative geometries for the collision the radial andaxial collisions in which the impact on the surface com-presses the diameter and long axis of CNT respectivelyDepending on temperature the CNT binds to the surfaceor bounces off the surface The deformation increased withthe rise in temperature regardless of collision geometriesDue to the flexibility of CNT in its radial motion thedeformation was larger for the radial collisions Howeverbecause of the small contact area of CNT with the surfacethe CNT in the axial collisions ended up with a highervibrational energy than in the radial collision We alsofound the axial collision led to a higher binding energy ofCNT with the surface

Acknowledgments This study was supported by KoreaResearch Foundation Grants funded by the Korean Gov-ernment (MEST) (Nos 20110027445 and 2008-521-C00123)

References and Notes

1 S Iijima Nature 354 56 (1991)2 C-J Li W-Y Li and Y-Y Wang Surf Coat Technol 198 469

(2005)3 S R Bakshi V Singh D G McCartney S Seal and A Agarwal

Scripta Mater 59 499 (2008)4 S R Bakshi V Singh K Balane D G McCartney S Seal and

A Agarwal Surf Coat Technol 202 5162 (2008)

5 T Laha and A Agarwal Mater Sci Eng A 480 323 (2008)6 T Laha A Agarwal T Mckechnie and S Seal Mater Sci Eng A

381 249 (2004)7 L C Saha S A Mian H Kim and J Jang J Phys Chem C

113 16668 (2009)8 L C Saha G C Schatz and J Jang J Phys Chem C 114 12565

(2010)9 M J Lopez I Cabria N H March and J A Alonso Carbon

43 1371 (2005)10 K M Liew C H Wong X Q He and M J Tan Phys Rev B

71 075424 (2005)11 Y Kowaki A Harada F Shimojo and K Hoshino J Phys Con-

dens Matter 19 436224 (2007)12 J Che T Cagin and W A Goddard III Nanotechnology 11 65

(2000)13 K Bi Y Chen J Yang Y Wang and M Chen Phys Lett A 350

150 (2006)14 M Cheng and Y Lu IEEE Transactions on Magnetics 42 891

(2006)15 H Yin and C Luo Modelling Simulation Mater Sci Eng 13 1403

(2005)16 M Minary-Jolandan and M-F Yu J Appl Phys 103 073516

(2008)17 M-F Yu T Kowalewski and R S Ruoff Phys Rev Lett 85 1456

(2000)18 F N Dzegilenko D Srivastava and S Saini Nanotechnology 10

253 (1999)19 M P Allen and D J Tildesley Computer Simulation of Liquids

Clarendon Press Oxford UK (1987)20 J Tersoff Phys Rev B 39 5566 (1989)21 J X Zhao and Y H Ding J Chem Theory Comput 5 1099

(2009)22 W Smith C W Yong and P M Rodger Mol Simul 28 385

(2002)23 W Kabsch Acta Crystallogr Sect A 34 827 (1978)24 W Humphrey A Dalke and K Schulten J Mol Graphics 14 33

(1996)25 Q Zheng Q Xue K Yan L Hao Q Li and X Gao J Phys

Chem C 111 4628 (2007)

Received 30 November 2010 Accepted 26 December 2010


View publication statsView publication stats



RESEARCH

ARTIC

LE

Copyright copy 2012 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofNanoscience and Nanotechnology

Vol 12 674ndash679 2012

Deformation of Carbon Nanotubes Colliding with aSilicon Surface and Its Dependence on Temperature

Leton C Saha Shabeer A Mian Hyojeong Kim Joyanta K Saha and Joonkyung Janglowast

Department of Nanomaterials Engineering Pusan National University Miryang 627-706 Republic of Korea

Using molecular dynamics simulation we investigated the carbon nanotubes (CNTs) colliding witha silicon surface at a speed of 600 ms mimicking cold spray experiments of CNTs Dependingon temperature (300ndash900 K) the CNT is deposited on or bounces off the surface after impact onthe surface The CNT was more deformed as its temperature rose The deformation of CNT wasmaximal for the collision geometry where the long axis of CNT lies parallel to the surface planeHowever its vibrational energy was maximal when the CNT collided with its long axis perpendicularto the surface

Keywords Carbon Nanotube Collision Molecular Dynamics Deformation TemperatureDependence

1 INTRODUCTION

Carbon nanotubes (CNTs)1 have been commonly usedin surface coating processes such as cold spray2ndash4 high-velocity oxyfuel (HVOF)5 and plasma spray6 In theseprocesses CNTs are sprayed on the surface at a high speed(typically more than 400 ms) A deformation or fractureof CNT can result from such a high speed collision witha surface It is well known that both temperature and veloc-ity of CNT largely affect the result of such coating In par-ticular we are interested in how the temperature of CNTaffects the cold spray process where the speed of CNT istypically several hundreds of ms In our previous study78

we investigated CNTs colliding with and being depositedon a silicon surface at a speed of 5 kms This speed ismuch higher than that in a typical cold spray process andthe effects of temperature was not consideredThere have been several simulation studies on how tem-

perature affects the structure9ndash11 or conductivity1213 ofa single isolated CNT There have been studies on the col-lisions between CNT and surface without considering theeffects of temperature781415 Herein we investigate howthe temperature of CNT influences its deformation anddeposition in a collision with a surface relevant to coldspray experiment (temperature and speed range form 400to 900 K and from 400 to 1500 ms respectively) We con-sider two representative collision geometries of CNT thefirst is radial collision where the CNT impacts with its longaxis parallel to the surface In the other geometry called

lowastAuthor to whom correspondence should be addressed

axial collision the long axis of CNT lies perpendicular tothe surface during its impact In the radial collision thedeformation mainly involves a compression in the diam-eter of CNT This radial movement is known to be quiteflexible (60 collapse in diameter was found to be fullyreversible in experiment)1617 On the other hand the axialcollision primarily compresses the long axis of CNT whichis quite stiff and hard18 By using molecular dynamics sim-ulation method detailed in Refs [7 and 8] we study themolecular details underlying the deformation and vibra-tional energy of CNT at various temperatures We foundthat the CNT in the radial collision sticks to or bounceoff the surface depending on its temperature CNTs in theaxial collision bound to the surface regardless of temper-ature In general the CNT is more distorted in the radialcollision than in the axial collision On the other hand thevibrational energy of CNT was higher in the axial colli-sion The deformation of CNT increased with the rise intemperature Compared to the radial collision the axialcollision gave rise to a CNT more strongly bound to thesurface

2 SIMULATION DETAILS

We simulated a (6 6) single-walled CNT impacting onthe Si (110) surface The CNT made from 384 C atomswas 38 nm long and 081 nm in diameter Two differ-ent collision geometries axial and radial collisions wereconsidered as shown in Figures 1(a) and 2(a) The CNTcollides with the surface at a projectile speed vp where

674 J Nanosci Nanotechnol 2012 Vol 12 No 1 1533-4880201212674006 doi101166jnn20125332



RESEARCH

ARTIC

LE









fC =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

1 rij lt Rij

12+ 1

2cos

[rij minusRij

Sij minusRij

]Rij lt rij lt Sij

0 rij gt Sij

(4)


bij = ij1+nii

niij

minus12ni (5)

withij =

sumk =ij

fCrik13ikgijk (6)

gijk is given by

gijk= 1+ c2idii


(7)


ij = i+j2 ij = i+j2 (8)


12 (9)


12 (10)




Kint = m2sumi

v2i (11)













RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE





300 600 900

0030

0035

0040

0045

0050

b (n

m)

TCNT (K)

(b)

004

006

008

MS

D (n

m) (a)


TCNT (K)300 600 900

300

350

400

450(b)

b vib

(K)

600

900

1200

TM

(K

)

(a)







RESEARCH

ARTIC

LE


4 CONCLUSION


























Chem C 111 4628 (2007)






RESEARCH

ARTIC

LE









fC =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

1 rij lt Rij

12+ 1

2cos

[rij minusRij

Sij minusRij

]Rij lt rij lt Sij

0 rij gt Sij

(4)


bij = ij1+nii

niij

minus12ni (5)

withij =

sumk =ij

fCrik13ikgijk (6)

gijk is given by

gijk= 1+ c2idii


(7)


ij = i+j2 ij = i+j2 (8)


12 (9)


12 (10)




Kint = m2sumi

v2i (11)













RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE





300 600 900

0030

0035

0040

0045

0050

b (n

m)

TCNT (K)

(b)

004

006

008

MS

D (n

m) (a)


TCNT (K)300 600 900

300

350

400

450(b)

b vib

(K)

600

900

1200

TM

(K

)

(a)







RESEARCH

ARTIC

LE


4 CONCLUSION


























Chem C 111 4628 (2007)






RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE





300 600 900

0030

0035

0040

0045

0050

b (n

m)

TCNT (K)

(b)

004

006

008

MS

D (n

m) (a)


TCNT (K)300 600 900

300

350

400

450(b)

b vib

(K)

600

900

1200

TM

(K

)

(a)







RESEARCH

ARTIC

LE


4 CONCLUSION


























Chem C 111 4628 (2007)






RESEARCH

ARTIC

LE











RESEARCH

ARTIC

LE





300 600 900

0030

0035

0040

0045

0050

b (n

m)

TCNT (K)

(b)

004

006

008

MS

D (n

m) (a)


TCNT (K)300 600 900

300

350

400

450(b)

b vib

(K)

600

900

1200

TM

(K

)

(a)







RESEARCH

ARTIC

LE


4 CONCLUSION


























Chem C 111 4628 (2007)






RESEARCH

ARTIC

LE





300 600 900

0030

0035

0040

0045

0050

b (n

m)

TCNT (K)

(b)

004

006

008

MS

D (n

m) (a)


TCNT (K)300 600 900

300

350

400

450(b)

b vib

(K)

600

900

1200

TM

(K

)

(a)







RESEARCH

ARTIC

LE


4 CONCLUSION


























Chem C 111 4628 (2007)






RESEARCH

ARTIC

LE


4 CONCLUSION


























Chem C 111 4628 (2007)




Deformation of Carbon Nanotubes Colliding with a …...All content following this page was uploaded by Shabeer Ahmad Mian on 05 June 2014. The user has requested enhancement of the

Documents