contributions to the foundations of nanoscale mechanics ... · contributions to the foundations of...
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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
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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
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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.
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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
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Radial Deformation of Carbon Nanotubes
Nanodesigns
Consulting
Ruoff, Tersoff, Lorents, Subramoney, Chan, Nature, v. 364, p. 514, 1993, IBM Res. Cntr.
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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.
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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.
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(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.
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Experimental Nanoscale Tests With Vibrating Carbon Nanotubes
Nanodesigns
Consulting
Treacy, Ebbesen, Gibson,
1996, Nature, v. 381, p. 680.
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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.
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(a) (b)
Atomic Force Microscopy with Carbon Nanotube Probes
Nanodesigns
Consulting
V: M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
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(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.
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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
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(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
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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.
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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
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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)
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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
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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.
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Estimates of Values for the Carbon Nanotube Shell Thickness
Nanodesigns
Consulting
*V: M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
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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.
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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
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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.
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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)
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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
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Stacking of Graphene Sheets
Nanodesigns
Consulting
AAA
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
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(b) (a) (c)
Sliding of Graphene Sheets; Registry of Carbon Rings
Nanodesigns
Consulting
V. M. Harik, Mechanics of Carbon Nanotubes, Nanodesigns Press, 2011.
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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)
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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
Багато- функціональні
Матеріали
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Механіка матеріалів
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