Continuum modeling of van der Waals interactions between. carbon nanotube walls

Size: px
Start display at page:

Download "Continuum modeling of van der Waals interactions between. carbon nanotube walls"

Transcription

1 Contuum modelg of van der Waals teractions between carbon nanotube walls W.B. Lu 1, B. Liu 1a), J. Wu 1, J. Xiao, K.C. Hwang 1, S. Y. Fu 3,4 a), Y. Huang 1 FML, Department of Engeerg Mechanics, Tsghua University, Beijg 184, People's Republic of Cha, Department of Mechanical Engeerg, Northwestern University, Evanston, Illois 6181, USA, 3 Technical Inst. of Physics & Chemistry, Chese Academy of Sciences, Beijg 119, People's Republic of Cha, 4 Department of Civil & Environmental Eng., Northwestern University, Evanston, Illois 6181, USA, ABSTRACT Prior contuum models of van der Waals force between carbon nanotube walls assume that the pressures be either the same on the walls, or versely proportional to wall radius. A new contuum model is obtaed analytically from the Lennard-Jones potential for van der Waals force, with the above assumptions. Bucklg of a double-wall carbon nanotube under external pressure is studied, and the critical bucklg pressure is much smaller than those models volvg the above assumptions. a) Authors to whom correspondence should be addressed. Electrical addresses: y-huang@northwestern.edu and liub@tsghua.edu.cn 1

2 In order to overcome limitations of atomistic simulations, contuum models have been developed for carbon nanotubes (CNT), such as the lear elastic shell theory 1,, fite-deformation membrane theory 3 and shell theory 4 based on teratomic potentials. For multi-wall CNTs, the teraction between walls is governed by the van der Waals force, which is characterized by the Lennard-Jones 6-1 potential, V ( d) = 4ε ( σ d) ( σ d) the distance between a pair of atoms, and derivative gives the force between two atoms, F V ( d) 1 6, where d is σ =.3415nm and ε =.39ev for carbon 5. Its = (positive for attractive force). There are two types of contuum models to represent the van der Waals force between CNT walls. One assumes the pressure to be the same, p = p, between two adjacent CNT walls 6, where p and p are pressures on the ner and er walls. The other assumes the pressure to be versely proportional to the wall radius 7,8, i.e., pr = pr, where R and R are the ner and er wall radii (Fig. 1). The purpose of this letter is to avoid the above assumptions and obta the pressures on ner and er walls analytically from the Lennard-Jones 6-1 potential. Such analytical expressions will be useful the contuum modelg of multi-wall CNTs and their composite materials. Analytical expressions are also obtaed for the effective pressures on the ner and er walls of electrically charged double-wall CNTs. Cyldrical coordates ( R, θ, z ) are used for the double-wall CNT with the ner and er radii R and R shown Fig. 1. With losg generality, the distance between an atom on the ner wall ( R,,) and an atom on the er wall ( R, θ, z ) is

3 d = R + R R R cosθ + z. The forces between two atoms are equal and opposite, and are obtaed from the Lennard-Jones potential as F V ( d) the normal direction give the normal forces as ( cosθ ) ( cosθ ) R = (Fig. 1). Their projections along F = F R R d and R F = F R R d, which are not equal anymore (Fig. 1). Figure 1. A schematic diagram of double-wall carbon nanotube The carbon atoms on each wall are represented by their area density ρ c = 4 ( 3 3l ) such that the number of carbon atoms is ρ da over the area da, where l c is the equilibrium bond length (of graphene). This accurately represents the average behavior of van der Waals teractions between atoms from adjacent CNT walls 9. For an fitesimal area da on the ner wall, the net force the normal direction is ( cos ) π 1 c R c c = A c, which gives the pressure on the ρ da F ρ da ρ da dz F R θ R d R dθ ner wall as = π ( cos ) (positive for compression). p ρ R dz F R θ R d dθ 1 c Similarly, the pressure on the er wall is = π ( cos ). p ρ R dz F R R θ d dθ 1 c For the Lennard-Jones 6-1 potential, the above pressures are obtaed analytically as 3

4 p 11 σ R R 31 E 13 E 11 3πεσρcR R + R R + R = 5, (1) 3R σ R R 16 E 7 E 5 R + R R + R and p π where m = ( 1 s θ ) 11 σ R R 31 E 13 + E 11 3πεσρcR R + R R + R = 5, () 3R σ R R 16 E 7 + E 5 R + R R + R m θ, and k 4R ( ) R R R E k d relation ( )( 1 ) ( 3)( ) ( 4) 1 m k E = m k E m E, and π ( ) ( 1 s θ ) 1 E = K k = k dθ m m m 4 and 1 ( ) elliptic tegrals of 1 st and nd kd, respectively. = + ; E m satisfies the recurrg E = E k = π 1 k s d θ θ are the complete Figure. The normalized pressure, and pressure multiplied by the wall radius R, on the ner and er walls of a double-wall CNT versus the normalized sum of ner and er wall radii. Results of Ref. 8 are also shown for comparison. Figure shows the normalized pressure, ( 8 c ) p πεσρ, versus normalized radius, ( ) R + R σ, for the ter-wall spacg R R = σ, which is the equilibrium spacg due to 4

5 van der Waals force between graphenes 9. It is observed that p and p have different signs, and therefore p p. The result of He et al. 8, π ρc p dz F R dθ =, also shown Fig., is ( absolute value) much larger than Eq. (1) because the force F was not projected to the normal direction, and therefore misses the factor ( cos ) R θ R d side the tegration. For small ter-wall spacg R R = σ (not shown Fig. ), all pressures are positive (i.e., repulsive force), while they become negative (i.e., attractive force) for large ter-wall spacg R R = σ. Figure also shows the normalized product of pressure and radius, ( 8 c ) pr πεσ ρ, which has different signs for the ner and er walls, and therefore pr pr. There exist other potentials that are more accurate than the Lennard-Jones 6-1 potential to represent the C-C repulsive term, such as a registry dependent potential to describe the corrugation terlayer teractions graphene nanostructures (Kolmogorov et al. 1 ), or a modified Morse potential based on the ab itio LDA calculations (Wang et al. 11 ) that has been verified for graphite subject to high pressure 1. We use the Morse-type potential 11 to calculate the pressures p and p of a double-wall CNT with an ner wall radius.35nm and the ter-wall spacg.3nm. The resultg pressures are p =35. and p =6.7GPa, which give p p and p R p R. These conclusions also hold, general, for other potentials. Equations (1) and () are used to study bucklg of a double-wall CNT subjected to external pressure p ext. The deformation is uniform prior to bucklg, but its rate becomes 5

6 non-uniform at the onset of bucklg. The analysis is similar to that for a sgle-wall CNT 13 except that (i) the er wall is subjected to a net external pressure p ext -p ; (ii) the ner wall is subjected to an external pressure p ; and (iii) p and p are related to the ner and er wall radii R and R via Eqs. (1) and (). Figure 3 shows the critical external pressure at the onset of bucklg, (p ext ) cr, versus L/R for a (8,8)@(13,13) double-wall CNT, where L and R are the length and er radius; (p ext ) cr is much larger than that for the er wall [(13,13) sgle-wall CNT] 13, almost 4 times for long CNTs. This reflects the resistance of vdw force between walls agast bucklg. Results based on prior assumptions overestimate the critical external pressure for bucklg; the assumption p = p overestimates by 75% for long CNTs, and pr = pr overestimates by 6%. Figure 3. The critical external pressure at the onset of bucklg, (p ext ) cr, versus the length to er radius ratio, L/R, for a (8,8)@(13,13) double-wall CNT. Results for the (13,13) sgle-wall CNT, and those based on prior assumptions are also shown. Equations (1) and () can be expressed the Taylor series of the small parameter ( R R ) ( R R ) ξ = + as 6

7 p 5 11 σ 1 σ 7 1+ ξ 1+ ξ R R 8 R R, (3) 3 σ 6 σ 3 ± ξ + O( ξ ) 4 R R 5 R R = 8πεσρc 5 11 where + terms are for p and terms for p. Similarly, p R and p R are given by pr 4 1 σ 1 5 σ 1 11 ξ ξ R R ξ 16 R R ξ 4, (4) 1 σ 1 σ ± + + O( ξ ) 8 R R R R = 8πεσ ρc 4 1 where + terms are for pr and terms for p R. For the ter-wall spacg R R = σ as Fig., p, p.6πεσρc ( ξ 3ξ ),.3 c = ± + (and therefore p p ), and ( ) p R p R = πεσ ρ ± + ξ (and therefore p R p R ). Figure 3 also shows the critical external pressure at the onset of bucklg, (p ext ) cr, based on the Taylor series expansion (3) and (4), which agrees very well with the exact solution based on Eqs. (1) and (). The last example to illustrate p p and p R p R is for two concentric tubes 1 with electrical charges, which are characterized by the electrostatic potential V ( d) ~ d and F = V d ~ d, where force ( ) d = R + R R R cosθ + z is the distance between electrical charges. The electrical charges on the ner and er tubes are represented by their area densities (number of charges per unit area) ρ and ρ. The pressures on the ner and π er walls are then given by = ( cos ) and ρ ρ θ θ 1 p R dz F R R d d ( cos ) π 1 p = R dz F R R d d. For F V ( d) ~ d ρ ρ θ θ =, it can be shown 7

8 analytically that the pressure on the ner wall is identically zero, p, while the pressure on the er wall is not, p, such that p p and p R p R. In summary, contuum models for van der Waals force or electrostatic force between CNT walls are obtaed analytically. They bypass assumptions prior studies, and have been applied to determe the critical external pressure for bucklg of double-wall CNTs. Y.H. acknowledges the supports from the NSF (Grant No. CMMI 8417) and ONR Composites for Mare Structures Program (Grant No. N , Program Manager Dr. Y. D. S. Rajapakse). B. Liu acknowledges the supports from the NSFC (Grant Nos. 1734, 1735, 98166). K.C. Hwang also acknowledges the support from NSFC (Grant No ) and National Basic Research Program of Cha (973 Program, Grant No. 7CB93683). S.Y. Fu acknowledges the support from CAS (Grant Nos. 5--1) and NSFC (Grant Nos ). 8

9 1 B. I. Yakobson, C. J. Brabec, and J. Bernholc, Phys. Rev. Lett. 76 (14), (1996). Y. Huang, J. Wu, and K. C. Hwang, Phys. Rev. B 74 (4), (6). 3 P. Zhang, Y. Huang, H. Gao, and K.C. Hwang, ASME J. Appl. Mech. 69 (4), (). 4 J. Wu, K. C. Hwang, and Y. Huang, J. Mech. Phys. Solids 56 (1), 79-9 (8). 5 L. A. Girifalco, M. Hodak, and R. S. Lee, Phys. Rev. B 6 (19), (). 6 A. Pantano, D. M. Parks, and M. C. Boyce, J. Mech. Phys. Solids 5 (4), (4). 7 C. Q. Ru, J. Mech. Phys. Solids 49 (6), (1). 8 X. Q. He, S. Kitipornchai, and K. M. Liew, J. Mech. Phys. Solids 53 (), (5). 9 W. B. Lu, J. Wu, L. Y. Jiang, Y. Huang, K.C. Hwang and B. Liu, Philo. Mag. 87 (14-15), 1-3 (7). 1 A. K. Kolmogorov and V.H. Crespi, Phys. Rev. B 71, (5). 11 Y. Wang, D. Tomanek and G. F. Bertsch, Phys. Rev. B 44, (1991). 1 D. Qian, W. K. Liu and R. S. Ruoff, J. Phys. Chem. B 15, (1). 13 J. Wu, K. C. Hwang, J. Song, and Y. Huang, ASME J. Appl. Mech. 75 (6), 616 (8). 9

Critical Strain of Carbon Nanotubes: An Atomic-Scale Finite Element Study

Critical Strain of Carbon Nanotubes: An Atomic-Scale Finite Element Study X. Guo A. Y. T. Leung 1 e-mail: bcaleung@cityu.edu.hk Department of Building and Construction, City University of Hong Kong, Hong Kong, China H. Jiang Department of Mechanical and Aerospace Engineering,

More information

VIBRATION CHARACTERISTICS OF EMBEDDED DOUBLE WALLED CARBON NANOTUBES SUBJECTED TO AN AXIAL PRESSURE

VIBRATION CHARACTERISTICS OF EMBEDDED DOUBLE WALLED CARBON NANOTUBES SUBJECTED TO AN AXIAL PRESSURE 18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS VIBRATION CHARACTERISTICS OF EMBEDDED DOUBLE WALLED CARBON NANOTUBES SUBJECTED TO AN AXIAL PRESSURE X. W. Lei 1, T. Natsuki 2, J. X. Shi 1, Q. Q. Ni

More information

σ) 6] (1) ( r i Mechanics of C 60 in Nanotubes Dong Qian, Wing Kam Liu, and Rodney S. Ruoff*

σ) 6] (1) ( r i Mechanics of C 60 in Nanotubes Dong Qian, Wing Kam Liu, and Rodney S. Ruoff* J. Phys. Chem. B 2001, 105, 10753-10758 10753 Mechanics of C 60 in Nanotubes Dong Qian, Wing Kam Liu, and Rodney S. Ruoff* Northwestern UniVersity, Department of Mechanical Engineering, EVanston, Illinois

More information

Free Vibrations of Carbon Nanotubes with Defects

Free Vibrations of Carbon Nanotubes with Defects Mechanics and Mechanical Engineering Vol. 17, No. 2 (2013) 157 166 c Lodz University of Technology Free Vibrations of Carbon Nanotubes with Defects Aleksander Muc Aleksander Banaś Ma lgorzata Chwa l Institute

More information

Torsional Buckling of Double-Walled Carbon Nanotubes

Torsional Buckling of Double-Walled Carbon Nanotubes Torsional Buckling of Double-Walled Carbon Nanotubes S. H. Soong Engineering Science Programme, National University of Singapore Kent Ridge, Singapore 119260 ABSTRACT This paper is concerned with the torsional

More information

Effects of Defects on the Strength of Nanotubes: Experimental- Computational Comparisons

Effects of Defects on the Strength of Nanotubes: Experimental- Computational Comparisons Effects of Defects on the Strength of Nanotubes: Experimental- Computational Comparisons T. Belytschko, S. P. Xiao and R. Ruoff Department of Mechanical Engineering Northwestern University, 2145 Sheridan

More information

Local buckling of carbon nanotubes under bending

Local buckling of carbon nanotubes under bending APPLIED PHYSICS LETTERS 91, 093128 2007 Local buckling of carbon nanotubes under bending Q. Wang a Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba R3T

More information

Molecular Dynamics Simulation of Fracture of Graphene

Molecular Dynamics Simulation of Fracture of Graphene Molecular Dynamics Simulation of Fracture of Graphene Dewapriya M. A. N. 1, Rajapakse R. K. N. D. 1,*, Srikantha Phani A. 2 1 School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada

More information

Buckling of double-walled carbon nanotubes modeled by solid shell elements

Buckling of double-walled carbon nanotubes modeled by solid shell elements Buckling of double-walled carbon nanotubes modeled by solid shell elements C. M. Wang and Y. Q. MaY. Y. ZhangK. K. Ang Citation: Journal of Applied Physics 99, 11317 (2006); doi: 10.1063/1.2202108 View

More information

Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes

Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes B. Liu, H. Jiang, Y. Huang, S. Qu, and M.-F. Yu Department of Mechanical and Industrial Engineering, University

More information

175-IJN Article No SPIN IN CARBON NANOTUBE-BASED OSCILLATORS

175-IJN Article No SPIN IN CARBON NANOTUBE-BASED OSCILLATORS 175-IJN Article No. 49 FA International Journal of Nanoscience Vol. 5, No. 1 (26) 47 55 World Scientific Publishing Company SPIN IN CARBON NANOTUBE-BASED OSCILLATORS SHAOPING XIAO Department of Mechanical

More information

Pressure-induced hard-to-soft transition of a single carbon nanotube

Pressure-induced hard-to-soft transition of a single carbon nanotube PHYSICAL REVIEW B 70, 165417 (2004) Pressure-induced hard-to-soft transition of a single carbon nanotube D. Y. Sun, 1 D. J. Shu, 1 M. Ji, 2 Feng Liu, 3 M. Wang, 4 and X. G. Gong 2,1, * 1 Institute of Solid

More information

Mathematical modelling for a C60 carbon nanotube oscillator

Mathematical modelling for a C60 carbon nanotube oscillator University o Wollongong Research Online Faculty o Inormatics - Papers (Archive) Faculty o Engineering and Inormation Sciences 006 Mathematical modelling or a C60 caron nanotue oscillator Barry J. Cox University

More information

Bending instability characteristics of double-walled carbon nanotubes

Bending instability characteristics of double-walled carbon nanotubes PHYSICAL REVIEW B 71, 045403 (005) Bending instability characteristics of double-walled carbon nanotubes Quan Wang, 1 Ting Hu, Guanhua Chen, 3 and Qing Jiang, * 1 Department of Mechanical, Materials and

More information

A New Extension of Cauchy Born Rule for Monolayer Crystal Films

A New Extension of Cauchy Born Rule for Monolayer Crystal Films Nanoscale Res Lett (2010) 5:863 867 DOI 10.1007/s11671-010-9576-3 NANO EXPRESS A New Extension of Cauchy Born Rule for Monolayer Crystal Films Sheng Lu Chongdu Cho Received: 23 February 2010 / Accepted:

More information

Radial Breathing Mode Frequency of Multi-Walled Carbon Nanotube Via Multiple-Elastic Thin Shell Theory

Radial Breathing Mode Frequency of Multi-Walled Carbon Nanotube Via Multiple-Elastic Thin Shell Theory Int. J. anosci. anotechnol. Vol. 7 o. 3 Sep. 011 pp. 137-14 adial Breathing Mode Frequency of Multi-Walled Carbon anotube Via Multiple-Elastic Thin Shell Theory S. Basir Jafari 1. Malekfar 1* and S. E.

More information

Science and Technology, Dalian University of Technology, Dalian , P. R. China b

Science and Technology, Dalian University of Technology, Dalian , P. R. China b Electronic Supplementary Information for Fabrication of Superior-Performance SnO 2 @C Composites for Lithium-Ion Anodes Using Tubular Mesoporous Carbons with Thin Carbon Wall and High Pore Volume Fei Han,

More information

Computer Simulations of Carbon Nanostructures under Pressure

Computer Simulations of Carbon Nanostructures under Pressure Fullerenes, Nanotubes, and Carbon Nanostructures, 13: 13 20, 2005 Copyright # Taylor & Francis, Inc. ISSN 1536-383X print/1536-4046 online DOI: 10.1081/FST-200039164 Computer Simulations of Carbon Nanostructures

More information

MOLECULAR SIMULATION FOR PREDICTING MECHANICAL STRENGTH OF 3-D JUNCTIONED CARBON NANOSTRUCTURES

MOLECULAR SIMULATION FOR PREDICTING MECHANICAL STRENGTH OF 3-D JUNCTIONED CARBON NANOSTRUCTURES ECCM16-16 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Spain, 22-26 June 214 MOLECULAR SIMULATION FOR PREDICTING MECHANICAL STRENGTH OF 3-D JUNCTIONED CARBON NANOSTRUCTURES S. Sihn a,b*, V.

More information

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core Commun. Theor. Phys. 56 774 778 Vol. 56, No. 4, October 5, A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core JIANG

More information

The stress transfer efficiency of a single-walled carbon nanotube in epoxy matrix

The stress transfer efficiency of a single-walled carbon nanotube in epoxy matrix JOURNAL OF MATERIALS SCIENCE 39 (2 004)4481 4486 The stress transfer efficiency of a single-walled carbon nanotube in epoxy matrix K. Q. XIAO, L. C. ZHANG School of Aerospace, Mechanical and Mechatronic

More information

Nonlocal material properties of single walled carbon nanotubes

Nonlocal material properties of single walled carbon nanotubes Nonlocal material properties of single walled carbon nanotubes J. V. Araújo dos Santos * and C. M. Mota Soares IDMEC, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal Av. Rovisco Pais,

More information

Bending buckling of single-walled carbon nanotubes by atomic-scale finite element

Bending buckling of single-walled carbon nanotubes by atomic-scale finite element Available online at www.sciencedirect.com Composites: Part B 39 (2008) 202 208 www.elsevier.com/locate/compositesb Bending buckling of single-walled carbon nanotubes by atomic-scale finite element X. Guo

More information

Ideal torsional strengths and stiffnesses of carbon nanotubes

Ideal torsional strengths and stiffnesses of carbon nanotubes PHYSICAL REVIEW B 72, 045425 2005 Ideal torsional strengths and stiffnesses of carbon nanotubes Elif Ertekin and D. C. Chrzan* Department of Materials Science and Engineering, University of California,

More information

Nanoscale Mechanics: A Quantum-Continuum Approach

Nanoscale Mechanics: A Quantum-Continuum Approach Nanoscale Mechanics: A Quantum-Continuum Approach V.Venkatasubramanian a and S.Bharath b a Department of Mechanical Engineering, IIT Madras b Department of Chemical Engineering, IIT Madras 1. Introduction

More information

Buckling of Double-walled Carbon Nanotubes

Buckling of Double-walled Carbon Nanotubes Buckling o Double-walled Carbon anotubes Y. H. Teo Engineering Science Programme ational University o Singapore Kent idge Singapore 960 Abstract This paper is concerned with the buckling o double-walled

More information

RSC Advances.

RSC Advances. This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after

More information

Ranges of Applicability for the Continuum-beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams?

Ranges of Applicability for the Continuum-beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams? NASA/CR-2001-211013 ICASE Report No. 2001-16 Ranges of Applicability for the Continuum-beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams? Vasyl Michael Harik ICASE, Hampton,

More information

Nonlinear Mechanics of Monolayer Graphene Rui Huang

Nonlinear Mechanics of Monolayer Graphene Rui Huang Nonlinear Mechanics of Monolayer Graphene Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin

More information

Simple model of van der Waals interactions between two radially deformed single-wall carbon nanotubes

Simple model of van der Waals interactions between two radially deformed single-wall carbon nanotubes Simple model of van der Waals interactions between two radially deformed single-wall carbon nanotubes A. Popescu and L. M. Woods Department of Physics, University of South Florida, Tampa, Florida 33620,

More information

Carbon nanotube oscillators: Effect of small bending strain

Carbon nanotube oscillators: Effect of small bending strain Proceedings of ICTACEM 2014 International Conference on Theoretical, Applied, Computational and Experimental Mechanics December 29-31, 2014, IIT Kharagpur, India ICTACEM-2014/405 Carbon nanotube oscillators:

More information

Theoretical comparative study on hydrogen storage of BC 3 and carbon nanotubes

Theoretical comparative study on hydrogen storage of BC 3 and carbon nanotubes J. At. Mol. Sci. doi: 10.4208/jams.121011.011412a Vol. 3, No. 4, pp. 367-374 November 2012 Theoretical comparative study on hydrogen storage of BC 3 and carbon nanotubes Xiu-Ying Liu a,, Li-Ying Zhang

More information

Influence of imperfections on carbon nanotube properties

Influence of imperfections on carbon nanotube properties 1 8 nd International Conference on Physical and Numerical Simulation of Materials Processing, ICPNS 16 Seattle Marriott Waterfront, Seattle, Washington, USA, October 14-17, 2016 Influence of imperfections

More information

Studies of fullerenes and carbon nanotubes by an extended bond order potential

Studies of fullerenes and carbon nanotubes by an extended bond order potential Nanotechnology 10 (1999) 263 268. Printed in the UK PII: S0957-4484(99)01334-3 Studies of fullerenes and carbon nanotubes by an extended bond order potential Jianwei Che, Tahir Çağın and William A Goddard

More information

Large scale growth and characterization of atomic hexagonal boron. nitride layers

Large scale growth and characterization of atomic hexagonal boron. nitride layers Supporting on-line material Large scale growth and characterization of atomic hexagonal boron nitride layers Li Song, Lijie Ci, Hao Lu, Pavel B. Sorokin, Chuanhong Jin, Jie Ni, Alexander G. Kvashnin, Dmitry

More information

Water-methanol separation with carbon nanotubes and electric fields

Water-methanol separation with carbon nanotubes and electric fields Electronic Supplementary Material (ESI) for Nanoscale. This journal is The Royal Society of Chemistry 215 Supplementary Information: Water-methanol separation with carbon nanotubes and electric fields

More information

Supporting Information

Supporting Information Electronic Supplementary Material (ESI) for Nanoscale. This journal is The Royal Society of Chemistry 207 Supporting Information Carbon Nanoscroll- Silk Crystallite Hybrid Structure with Controllable Hydration

More information

Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity

Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity Renfu Li Post-Doctoral Fellow George A. Kardomateas Professor of Aerospace Engineering Fellow ASME Georgia Institute of Technology, Atlanta, Georgia 3033-050 Thermal Buckling of Multi-Walled Carbon Nanotubes

More information

Tinselenidene: a Two-dimensional Auxetic Material with Ultralow Lattice Thermal Conductivity and Ultrahigh Hole Mobility

Tinselenidene: a Two-dimensional Auxetic Material with Ultralow Lattice Thermal Conductivity and Ultrahigh Hole Mobility Tinselenidene: a Two-dimensional Auxetic Material with Ultralow Lattice Thermal Conductivity and Ultrahigh Hole Mobility Li-Chuan Zhang, Guangzhao Qin, Wu-Zhang Fang, Hui-Juan Cui, Qing-Rong Zheng, Qing-Bo

More information

MOLECULAR DYNAMICS SIMULATIONS OF HEAT TRANSFER ISSUES IN CARBON NANOTUBES

MOLECULAR DYNAMICS SIMULATIONS OF HEAT TRANSFER ISSUES IN CARBON NANOTUBES The st International Symposium on Micro & Nano Technology, 4-7 March, 4, Honolulu, Hawaii, USA MOLECULAR DYNAMICS SIMULATIONS OF HEAT TRANSFER ISSUES IN CARBON NANOTUBES S. Maruyama, Y. Igarashi, Y. Taniguchi

More information

Nanotube AFM Probe Resolution

Nanotube AFM Probe Resolution Influence of Elastic Deformation on Single-Wall Carbon Nanotube AFM Probe Resolution Ian R. Shapiro, Santiago D. Solares, Maria J. Esplandiu, Lawrence A. Wade, William A. Goddard,* and C. Patrick Collier*

More information

Terahertz Wave Propagation in a Nanotube Conveying Fluid Taking into Account Surface Effect

Terahertz Wave Propagation in a Nanotube Conveying Fluid Taking into Account Surface Effect Materials 13, 6, 393-399; doi:1.339/ma66393 Article OPEN ACCE materials IN 1996-1944 www.mdpi.com/journal/materials Terahertz Wave Propagation in a Nanotube Conveying Fluid Taking into Account urface Effect

More information

Mechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model

Mechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model Mechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model Mechanical Properties of Polymer Rubber Materials Based on a New Constitutive Model J.B. Sang*, L.F. Sun, S.F. Xing,

More information

Fracture of vacancy-defected carbon nanotubes and their embedded nanocomposites

Fracture of vacancy-defected carbon nanotubes and their embedded nanocomposites PHYSICAL REVIEW B 73, 115406 2006 Fracture of vacancy-defected carbon nanotubes and their embedded nanocomposites Shaoping Xiao and Wenyi Hou Department of Mechanical and Industrial Engineering, and Center

More information

Structural Bioinformatics (C3210) Molecular Mechanics

Structural Bioinformatics (C3210) Molecular Mechanics Structural Bioinformatics (C3210) Molecular Mechanics How to Calculate Energies Calculation of molecular energies is of key importance in protein folding, molecular modelling etc. There are two main computational

More information

Strength and Stability Analysis of a Single Walled Black Phosphorus Tube under Axial Compression

Strength and Stability Analysis of a Single Walled Black Phosphorus Tube under Axial Compression Strength and Stability Analysis of a Single Walled Black Phosphorus Tube under Axial Compression Kun Cai 1, 2, Jing Wan 1, Ning Wei 1, Qinghua Qin 2* 1 College of Water Resources and Architectural Engineering,

More information

arxiv: v1 [cond-mat.stat-mech] 6 Jan 2014

arxiv: v1 [cond-mat.stat-mech] 6 Jan 2014 arxiv:1401.1181v1 [cond-mat.stat-mech] 6 Jan 2014 Determination of Forces from a Potential in Molecular Dynamics (note) Bernard Monasse Mines-ParisTech, Cemef bernard.monasse@mines-paristech.fr January

More information

Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet

Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet Copyright 05 Tech Science Press CMC, vol.8, no., pp.03-7, 05 Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet G. Q. Xie, J. P. Wang, Q. L. Zhang Abstract: Small-scale effect on the

More information

Imperfect Gases. NC State University

Imperfect Gases. NC State University Chemistry 431 Lecture 3 Imperfect Gases NC State University The Compression Factor One way to represent the relationship between ideal and real gases is to plot the deviation from ideality as the gas is

More information

Response of Carbon Nanotube (CNT) Ply Subjected to a Pulsed Magnetic Field

Response of Carbon Nanotube (CNT) Ply Subjected to a Pulsed Magnetic Field Response of Carbon Nanotube (CNT) Ply Subjected to a Pulsed Magnetic Field Ali Nassiri 1,2,*, Brad Kinsey 3 1. Department of Materials Science and Engineering, The Ohio State University, 2041 College Road

More information

Basic 8 Micro-Nano Materials Science. and engineering

Basic 8 Micro-Nano Materials Science. and engineering Basic 8 Micro-Nano Materials Science and Analysis Atomistic simulations in materials science and engineering Assistant Prof. Y. Kinoshita and Prof. N. Ohno Dept. of Comp. Sci. Eng. and Dept. of Mech. Sci.

More information

MD simulation of methane in nanochannels

MD simulation of methane in nanochannels MD simulation of methane in nanochannels COCIM, Arica, Chile M. Horsch, M. Heitzig, and J. Vrabec University of Stuttgart November 6, 2008 Scope and structure Molecular model for graphite and the fluid-wall

More information

Supplementary Figure 1(a) The trajectory of the levitated pyrolytic graphite test sample (blue curve) and

Supplementary Figure 1(a) The trajectory of the levitated pyrolytic graphite test sample (blue curve) and Supplementary Figure 1(a) The trajectory of the levitated pyrolytic graphite test sample (blue curve) and the envelope from free vibration theory (red curve). (b) The FFT of the displacement-time curve

More information

A finite deformation membrane based on inter-atomic potentials for single atomic layer films Application to the mechanics of carbon nanotubes

A finite deformation membrane based on inter-atomic potentials for single atomic layer films Application to the mechanics of carbon nanotubes A finite deformation membrane based on inter-atomic potentials for single atomic layer films Application to the mechanics of carbon nanotubes Marino Arroyo and Ted Belytschko Department of Mechanical Engineering

More information

Nanopumping Molecules via a Carbon Nanotube

Nanopumping Molecules via a Carbon Nanotube DOI 10.1007/s12274-009-9096-6 Research Article 00938 Nanopumping Molecules via a Carbon Nanotube Min Chen 1,2,3, Ji Zang 3, Dingquan Xiao 1, C. Zhang 4, and Feng Liu 3 1 Department of Materials Science

More information

The atomic-scale finite element method

The atomic-scale finite element method Comput. Methods Appl. Mech. Engrg. 193 (2004) 1849 1864 www.elsevier.com/locate/cma The atomic-scale finite element method B. Liu, Y. Huang a, *, H. Jiang a,s.qu a, K.C. Hwang b a Department of Mechanical

More information

Supporting Information

Supporting Information Supporting Information Novel Electrically-Conductive Porous PDMS/Carbon Nanofibre Composites for Deformable Strain-Sensors and Conductors Shuying Wu,, Jin Zhang, Raj B. Ladani, Anil R. Ravindran, Adrian

More information

Multiwalled nanotube faceting unravelled

Multiwalled nanotube faceting unravelled Multiwalled nanotube faceting unravelled Itai Leven, Roberto Guerra, Andrea Vanossi, Erio Tosatti, and Oded Hod NATURE NANOTECHNOLOGY www.nature.com/naturenanotechnology 1 1. Achiral DWCNTs optimized using

More information

Carbon Nanocone: A Promising Thermal Rectifier

Carbon Nanocone: A Promising Thermal Rectifier Carbon Nanocone: A Promising Thermal Rectifier Nuo Yang 1, Gang Zhang 2, a) 3,1, b) and Baowen Li 1 Department of Physics and Centre for Computational Science and Engineering, National University of Singapore,

More information

Induced Local Buckling of Carbon Nanotubes. by a Point Loading

Induced Local Buckling of Carbon Nanotubes. by a Point Loading Adv. Studies Theor. Phys., Vol., 008, no. 1, 3-35 Induced Local Buckling of Carbon Nanotubes by a Point Loading Quan Wang Department of Mechanical and Manufacturing Engineering, University of Manitoba,

More information

From Atoms to Materials: Predictive Theory and Simulations

From Atoms to Materials: Predictive Theory and Simulations From Atoms to Materials: Predictive Theory and Simulations Week 3 Lecture 4 Potentials for metals and semiconductors Ale Strachan strachan@purdue.edu School of Materials Engineering & Birck anotechnology

More information

The calculation of energy gaps in small single-walled carbon nanotubes within a symmetry-adapted tight-binding model

The calculation of energy gaps in small single-walled carbon nanotubes within a symmetry-adapted tight-binding model The calculation of energy gaps in small single-walled carbon nanotubes within a symmetry-adapted tight-binding model Yang Jie( ) a), Dong Quan-Li( ) a), Jiang Zhao-Tan( ) b), and Zhang Jie( ) a) a) Beijing

More information

MOLECULAR DYNAMICS SIMULATION OF HYDROGEN STORAGE IN SINGLE-WALLED CARBON NANOTUBES

MOLECULAR DYNAMICS SIMULATION OF HYDROGEN STORAGE IN SINGLE-WALLED CARBON NANOTUBES MOLECULAR DYNAMICS SIMULATION OF HYDROGEN STORAGE IN SINGLE-WALLED CARBON NANOTUBES Shigeo MARUYAMA Engineering Research Institute The University of Tokyo 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan

More information

Torsional vibration of carbon nanotubes under initial compression stress

Torsional vibration of carbon nanotubes under initial compression stress Brazilian Journal of Physics, vol. 40, no. 3, September 83 Torsional vibration of carbon nanotubes under initial compression stress M.M. Selim Department of Natural and Applied Sciences, AL-Aflaj community

More information

Temperature phase transition model for the DNA-CNTs-based nanotweezers

Temperature phase transition model for the DNA-CNTs-based nanotweezers J Math Chem (2013) 51:278 288 DOI 10.1007/s10910-012-0082-y ORIGINAL PAPER Temperature phase transition model for the DNA-CNTs-based nanotweezers Anh D. Phan Lilia M. Woods N. A. Viet Received: 12 June

More information

Defense Technical Information Center Compilation Part Notice

Defense Technical Information Center Compilation Part Notice UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADP012151 TITLE: Chemical Bonding of Polymer on Carbon Nanotube DISTRIBUTION: Approved for public release, distribution unlimited

More information

Deformation Mechanisms of Very Long Single-Wall Carbon Nanotubes Subject to Compressive Loading

Deformation Mechanisms of Very Long Single-Wall Carbon Nanotubes Subject to Compressive Loading Markus J. Buehler Yong Kong Huajian Gao e-mail: hjgao@mf.mpg.de Max Planck Institute for Metals Research, Heisenbergstr. 3, 70569 Stuttgart, Germany Deformation Mechanisms of Very Long Single-Wall Carbon

More information

An on-site test method for optical efficiency of large-size parabolic trough collectors

An on-site test method for optical efficiency of large-size parabolic trough collectors Available onle at www.sciencedirect.com ScienceDirect Energy Procedia 105 (2017 ) 486 491 The 8 th International Conference on Applied Energy ICAE2016 An on-site test method for optical efficiency of large-size

More information

ON THE NANO TORSIONAL PENDULUM

ON THE NANO TORSIONAL PENDULUM THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 0, Number /009, pp.000-000. ON THE NANO TORSIONAL PENDULUM Pier Paolo DELSANTO, Ligia MUNTEANU, Veturia

More information

Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack

Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack Chin. Phys. B Vol. 19, No. 1 010 01610 Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack Fang Qi-Hong 方棋洪, Song Hao-Peng 宋豪鹏, and Liu You-Wen 刘又文

More information

Physica E 44 (2011) Contents lists available at ScienceDirect. Physica E. journal homepage:

Physica E 44 (2011) Contents lists available at ScienceDirect. Physica E. journal homepage: Physica E 44 (2011) 12 16 Contents lists available at ScienceDirect Physica E journal homepage: www.elsevier.com/locate/physe Elastic instability of bilayer graphene using atomistic finite element Y. Chandra

More information

Interaction-induced depolarized light scattering spectra of exohedral complexes of Ne and Ar with fullerenes and nanotubes

Interaction-induced depolarized light scattering spectra of exohedral complexes of Ne and Ar with fullerenes and nanotubes Materials Science-Poland, Vol. 3, No., 005 Interaction-induced depolarized light scattering spectra of exohedral complexes of Ne and Ar with fullerenes and nanotubes Z. DENDZIK *, M. KOŚMIDER, A. DAWID,

More information

Mathematical Modelling in Nanotechnology

Mathematical Modelling in Nanotechnology NMG Mathematical Modelling in Nanotechnology Dr Ngamta (Natalie) Thamwattana Nanomechanics Group, University of Wollongong Nanomechanics Group Supported by the Discovery Project scheme of the Australian

More information

Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat

Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat J. Jamari e-mail: j.jamari@ctw.utwente.nl D. J. Schipper University of Twente, Surface Technology and Tribology, Faculty of Engineering Technology, Drienerloolaan 5, Postbus 17, 7500 AE, Enschede, The

More information

Static and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method

Static and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method 8(2011) 463 472 Static and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method Abstract Static and free vibration analysis of carbon nano wires

More information

NSF/ITR: LARGE-SCALE QUANTUM- MECHANICAL MOLECULAR DYNAMICS SIMULATIONS

NSF/ITR: LARGE-SCALE QUANTUM- MECHANICAL MOLECULAR DYNAMICS SIMULATIONS NSF/ITR: LARGE-SCALE QUANTUM- MECHANICAL MOLECULAR DYNAMICS SIMULATIONS C. S. Jayanthi and S.Y. Wu (Principal Investigators) Lei Liu (Post-doc) Ming Yu (Post-doc) Chris Leahy (Graduate Student) Alex Tchernatinsky

More information

The Periodic Table and Chemical Reactivity

The Periodic Table and Chemical Reactivity The and Chemical Reactivity Noble gases Less electronegative elements More electronegative elements Then what is electronegativity? The tendency of an atom to attract an electron (or electron density)

More information

lectures accompanying the book: Solid State Physics: An Introduction, by Philip ofmann (2nd edition 2015, ISBN-10: 3527412824, ISBN-13: 978-3527412822, Wiley-VC Berlin. www.philiphofmann.net 1 Bonds between

More information

MODELLING OF SINGLE-WALL CARBON NANOTUBES MECHANICAL BEHAVIOUR

MODELLING OF SINGLE-WALL CARBON NANOTUBES MECHANICAL BEHAVIOUR 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver

More information

Electrical conductance of carbon nanotori in contact with single-wall carbon nanotubes

Electrical conductance of carbon nanotori in contact with single-wall carbon nanotubes JOURNAL OF APPLIED PHYSICS VOLUME 96, NUMBER 4 15 AUGUST 2004 Electrical conductance of carbon nanotori in contact with single-wall carbon nanotubes Y. Y. Chou and G.-Y. Guo Department of Physics, National

More information

Supporting Online Material for

Supporting Online Material for www.sciencemag.org/cgi/content/full/310/5753/1480/dc1 Supporting Online Material for Electrowetting in Carbon Nanotubes J. Y. Chen, A. Kutana, C. P. Collier,* K. P. Giapis* *To whom correspondence should

More information

Stability of Thick Spherical Shells

Stability of Thick Spherical Shells Continuum Mech. Thermodyn. (1995) 7: 249-258 Stability of Thick Spherical Shells I-Shih Liu 1 Instituto de Matemática, Universidade Federal do Rio de Janeiro Caixa Postal 68530, Rio de Janeiro 21945-970,

More information

Supporting Infromation

Supporting Infromation Supporting Infromation Transparent and Flexible Self-Charging Power Film and Its Application in Sliding-Unlock System in Touchpad Technology Jianjun Luo 1,#, Wei Tang 1,#, Feng Ru Fan 1, Chaofeng Liu 1,

More information

Module17: Intermolecular Force between Surfaces and Particles. Lecture 23: Intermolecular Force between Surfaces and Particles

Module17: Intermolecular Force between Surfaces and Particles. Lecture 23: Intermolecular Force between Surfaces and Particles Module17: Intermolecular Force between Surfaces and Particles Lecture 23: Intermolecular Force between Surfaces and Particles 1 We now try to understand the nature of spontaneous instability in a confined

More information

Supporting Information

Supporting Information Supporting Information Fe 3 O 4 @Carbon Nanosheets for All-Solid-State Supercapacitor Electrodes Huailin Fan, Ruiting Niu, & Jiaqi Duan, Wei Liu and Wenzhong Shen * State Key Laboratory of Coal Conversion,

More information

Vibration Characteristics of Multiwalled Carbon Nanotubes Embedded in Elastic Media by a Nonlocal Elastic Shell Model

Vibration Characteristics of Multiwalled Carbon Nanotubes Embedded in Elastic Media by a Nonlocal Elastic Shell Model Renfu Li Post-Doctoral Fellow George A. Kardomateas Professor of Aerospace Engineering Fellow ASME Georgia Institute of Technology, Atlanta, GA 3033-0150 Vibration Characteristics of Multiwalled Carbon

More information

Band structure engineering of graphene by strain: First-principles calculations

Band structure engineering of graphene by strain: First-principles calculations Band structure engineering of graphene by strain: First-principles calculations Gui Gui, Jin Li, and Jianxin Zhong* Laboratory for Quantum Engineering and Micro-Nano Energy Technology, Xiangtan University,

More information

Material Properties & Characterization - Surfaces

Material Properties & Characterization - Surfaces 1) XPS Spectrum analysis: The figure below shows an XPS spectrum measured on the surface of a clean insoluble homo-polyether. Using the formulas and tables in this document, answer the following questions:

More information

FE modelling of multi-walled carbon nanotubes

FE modelling of multi-walled carbon nanotubes Estonian Journal of Engineering, 2009, 15, 2, 77 86 doi: 10.3176/eng.2009.2.01 FE modelling of multi-walled carbon nanotubes Marino Brcic, Marko Canadija, Josip Brnic, Domagoj Lanc, Sanjin Krscanski and

More information

This article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author s institution, sharing

More information

Thermodynamic study of liquid with solver ζ & suitable η max as a pole in basic two parameter Khasare s equation of state

Thermodynamic study of liquid with solver ζ & suitable η max as a pole in basic two parameter Khasare s equation of state Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research,, 3 (5):353-359 ISSN: 976-86 CODEN (USA): AASRFC Thermodynamic study of liquid with solver ζ & suitable η max as

More information

Nonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory

Nonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory Nonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory Tai-Ping Chang 1 and Quey-Jen Yeh 1 Department of Construction Engineering, National Kaohsiung First

More information

Transversal electric field effect in multilayer graphene nanoribbon

Transversal electric field effect in multilayer graphene nanoribbon Transversal electric field effect in multilayer graphene nanoribbon S. Bala kumar and Jing Guo a) Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32608, USA

More information

Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part II: parametric study

Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part II: parametric study Acta ech 6, 97 6 () DOI.7/s77--6- Keivan Kiani Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part II: parametric study Received: August 9 / Revised:

More information

STANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius

STANDARD SAMPLE. Reduced section  Diameter. Diameter. 2 Gauge length. Radius MATERIAL PROPERTIES TENSILE MEASUREMENT F l l 0 A 0 F STANDARD SAMPLE Reduced section 2 " 1 4 0.505" Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius TYPICAL APPARATUS Load cell Extensometer Specimen

More information

Experimental Study on the Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids

Experimental Study on the Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids International Journal of Thermophysics, Vol. 27, No. 2, March 2006 ( 2006) DOI: 10.1007/s10765-006-0054-1 Experimental Study on the Effective Thermal Conductivity and Thermal Diffusivity of Nanofluids

More information

COMPUTATIONAL STUDIES ON FORMATION AND PROPERTIES OF CARBON NANOTUBES

COMPUTATIONAL STUDIES ON FORMATION AND PROPERTIES OF CARBON NANOTUBES COMPUTATIONAL STUDIES ON FORMATION AND PROPERTIES OF CARBON NANOTUBES Weiqiao Deng, Jianwei Che, Xin Xu, Tahir Çagin, and William A Goddard, III Materials and Process Simulation Center, Beckman Institute,

More information

5.62 Physical Chemistry II Spring 2008

5.62 Physical Chemistry II Spring 2008 MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.62 Lecture #20: Virial

More information

Mechanical Interactions at the Interfaces of Atomically Thin Materials (Graphene)

Mechanical Interactions at the Interfaces of Atomically Thin Materials (Graphene) Mechanical Interactions at the Interfaces of Atomically Thin Materials (Graphene) Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering

More information

MULTIPACTOR ON A DIELECTRIC SURFACE WITH LONGITUDINAL RF ELECTRIC FIELD ACTION

MULTIPACTOR ON A DIELECTRIC SURFACE WITH LONGITUDINAL RF ELECTRIC FIELD ACTION Progress In Electromagnetics Research Letters, Vol. 24, 177 185, 211 MULTIPACTOR ON A DIELECTRIC SURFACE WITH LONGITUDINAL RF ELECTRIC FIELD ACTION F. Zhu *, Z. Zhang, J. Luo, and S. Dai Key Laboratory

More information