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Contributions to the Foundations of Nanoscale Mechanics
Nanodesigns
Consulting
Vasyl Michael Harik Василь Харик
Principal Scientist, Nanodesigns Consulting, Newark, DE f. Staff Scientist, ICASE, NASA Langley Research Center
Consulting Clients: NIA/NASA Langley Princeton University based URETI
NASA NAIC (Atlanta) Shevchenko Scientific Society, New York Math-Phys-Tech Section, May 19, 2012
Nanoscale Mechanics & Nanomechanics: Historical Background
Nanodesigns
Consulting
1991 – Iijima (NEC Lab) discovered multiwall carbon nanotubes 1993 – Iijima & NEC Lab discovered single wall carbon nanotubes
1993 – IBM Research Center: molecular dynamics (MD) simulation of CNT crystal showing radial deformation of CNTs 1996 – Iijima (NEC Lab) and Smalley (Rice) won Nobel prize 1996 – Yakobson, et al., showed shell-like buckling of a CNT 1996 – Treacy, et al., studied beam-like vibration of a CNT 1999 – Avoris, et al. (IBM): MD data on radial deformation of CNTs 2000 – Ruoff, et al.: AFM tensile tests of breaking a MWNT 2001 – Harik (NASA Langley): classification of CNTs: four classes 2001 – Harik: CNT scaling laws, limitations of beam & shell models 2001 – 1st ASME Short Course “Mechanics of Carbon Nanotubes”
Shevchenko Scientific Society, New York
Discriptive Characterization of Carbon Nanotubes
Nanodesigns
Consulting
Shevchenko Scientific Society, New York Math-Phys-Tech Section, May 19, 2012
Dresselhaus, Dresselhaus,
Saito, 1995, Physics of
carbon nanotubes, Carbon
v. 33/7, p. 883; MIT team.
Classification of Carbon Nanotubes
Nanodesigns
Consulting
V. M. Harik, Solid State Communications, v. 120, p. 331, 2001; ICASE, NASA LaRC.
Class Ia:
Thin NT shells
Class Ib: Thick NT shells
Class II: Long NT shells
Class III:
NT beams
Radial Deformation of Carbon Nanotubes
Nanodesigns
Consulting
Ruoff, Tersoff, Lorents, Subramoney, Chan, Nature, v. 364, p. 514, 1993, IBM Res. Cntr.
Approximation of van der Waals Forces by Lennard-Jones Potential
Nanodesigns
Consulting
Interlayer distance (Å)
En
erg
y (eV
/ato
m)
0
- 0.05
0.15
3.4 Å 2.5
3.4 Å
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
Deformation of Carbon Nanotubes by van der Waals forces
Nanodesigns
Consulting
Avouris, Hertel, Martel, Schmidt, Shea, Walkup,
Appl. Surface Sci., v. 141, p. 201, 1999; IBM.
(b)
(a) (c)
Deformation of Carbon Nanotubes by van der Waals forces
Nanodesigns
Consulting
Avouris, Hertel, Martel, Schmidt, Shea, Walkup,
Appl. Surface Sci., v. 141, p. 201, 1999; IBM.
Experimental Nanoscale Tests With Vibrating Carbon Nanotubes
Nanodesigns
Consulting
Treacy, Ebbesen, Gibson,
1996, Nature, v. 381, p. 680.
Experimental Nanoscale Tensile Tests of MWNT Strength by the AFM
Nanodesigns
Consulting
Yu, Lourie, Dyer, Moloni, Kelly, Ruoff, Science
v. 287, 637, 2000. Washington University Team.
(a) (b)
Atomic Force Microscopy with Carbon Nanotube Probes
Nanodesigns
Consulting
V: M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
(b)
F
(a)
F F
F
(c)
F
(d)
Deformation of Carbon Nanotubes: Stretching, Bending and Buckling
Nanodesigns
Consulting
V: M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
d NT
L NT
lc-c
K
M
G
K’
Length Scales in the Structure of Carbon Nanotubes
Nanodesigns
Consulting
V. M. Harik, NASA/ICASE Tech. Report, May 2001, Ranges of Applicability of ... Models.
Nanoscale Homogenization Criterion (2001):
LNT > 10a
(b)
F F F
Buckling of Carbon Nanotubes: High Aspect Ratio Effects
Nanodesigns
Consulting
Bu
cklin
g strain
Aspect ratio
d = 0.4 nm
d = 1 nm d = 2 nm
(14,0) CNT
(9,6) CNT
(8,8) CNT
V. M. Harik, 2002, Computational Materials Science, v. 24/3, p. 328; ICASE/NASA Langley
Model Applicability Map: Radius vs. Aspect Ratio
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
1st: V. M. Harik, Solid State Comm., v. 120, p. 331, 2001.
Carbon Nanotube Crystals: Low Ratios of Radius to Carbon Ring
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
Stojkovic, Zhang, Crespi, Phys. Rev. Lett., 2001.
NT(2,2) C NT(3,0) C
Deformation of Carbon Nanotubes: Bending, Buckling and Twisting
Nanodesigns
Consulting
Yakobson, Brabec, Bernholc, 1996. Phys. Review
Letters, v. 76, p. 2511; Rice University Team.
(c)
(d)
Buckling of Carbon Nanotube Shells: Limitations of FEA Shell Models
Nanodesigns
Consulting
Yakobson, et al., Phys. Rev. Lett., 1996; Harik, 2002, NASA LaRC MFMS Program
h = 0.72 Å NT
h = 0.66 Å NT
h = 0.28 Å NT
h = 3.4 Å NT
Radius of carbon nanotube (nm)
Buckling strain
Buckling of Carbon Nanotubes: Effects of Radius and Shell Thickness
Nanodesigns
Consulting
V. M. Harik, et al., 2002, NASA/ICASE Tech. Report, NASA Langley Research Center, VA.
Estimates of Values for the Carbon Nanotube Shell Thickness
Nanodesigns
Consulting
*V: M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
Applicability Map for Shell Models: Radius vs. Aspect Ratio
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
1st: V. M. Harik, et al., NASA- ICASE Tech. Report, 2002.
Buckling of Carbon Nanotube Shells: Limitations of Shell Models
Nanodesigns
Consulting
Arroyo and Belytschko,
Phys. Rev. Lett. (2003).
Ru, 2000, University of Alberta;
Wang, Ru, Mioduchowski, 2002
Atomic Potentials and the Cauchy-Born Rule
Micromechanics and nano-
scale van der Waals model
Interlayer distance (Å)
En
erg
y (eV
/ato
m)
0
- 0.05
0.15
3.4 Å 2.5
Van der Waals Forces in MWNTs
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
Molecular Structural Mechanics of Carbon Nanotube Shells
Nanodesigns
Consulting
Odegard and Gates (2002), NASA LaRC
C-C Beam FEA model of SWNTs & vdW
Li and Chou (2003)
Int J Solids Struct
Li and Chou (2003)
Classification of Carbon Nanotubes
Nanodesigns
Consulting
V. M. Harik, 2002, Computational Materials Science, v. 24/3, p. 328; ICASE/NASA Langley
Class Ia:
Thin NT shells
Class Ib: Thick NT shells
Class II: Long NT shells
Class III:
NT beams
Stacking of Graphene Sheets
Nanodesigns
Consulting
AAA
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
(b) (a) (c)
Sliding of Graphene Sheets; Registry of Carbon Rings
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
Nanoscale Analog of Newton’s Friction Law for Interfacial Sliding of CNT Shells
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
Frankland and Harik, MRS 2002; Surface Sci. Lett., 2003, NASA LaRC
VdW
z
effh
V
0
zeffpullVff
0F0 = 0.1 nN
eff=1.5x10-11 Pa m s
Bingham model (Harik, 1997)
Nanodesigns
Consulting
ASME Short Course: Mechanics of Carbon Nanotubes
V.M. Harik, ASME Annual Congress, 2001 and 2004.
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Translation of Mechanics of Carbon Nanotubes into Ukrainian
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