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.

Vasy

l Mic

hael

Har

ik

Mec

hani

cs o

f Car

bon

Nan

otub

es

Nan

odes

igns

Pre

ss, 2

011

Translation of Mechanics of Carbon Nanotubes into Ukrainian

Багато- функціональні

Матеріали

Атомні решітки і

утворення

Наноскопічні Фізика і Хімія

Наномеханіка і Мікромеханіка Обчислювальна

Механіка

Aтоми

Волокно

Композиційний

матеріал

Розмір, (м) 10-10 10-8 10-6 10-3 100

Наноструктури

і кристали

Атомні решітки і скупчення

Групи атомів

Макрo Maкрo

C

C

C

CO

CO

CO

CO2

CO2

CO

Квантова мeханіка

Moлекулярна мeханіка Мікромеханіка

Механіка матеріалів

Наномеханіка

Наноструктурований прошарок

MEMС