Advertisement

Journal of Nanoparticle Research

, Volume 13, Issue 3, pp 1075–1091 | Cite as

Indentation analysis of nano-particle using nano-contact mechanics models during nano-manipulation based on atomic force microscopy

  • Khadijeh DaeinabiEmail author
  • Moharam Habibnejad Korayem
Research Paper

Abstract

Atomic force microscopy is applied to measure intermolecular forces and mechanical properties of materials, nano-particle manipulation, surface scanning and imaging with atomic accuracy in the nano-world. During nano-manipulation process, contact forces cause indentation in contact area between nano-particle and tip/substrate which is considerable at nano-scale and affects the nano-manipulation process. Several nano-contact mechanics models such as Hertz, Derjaguin–Muller–Toporov (DMT), Johnson–Kendall–Roberts–Sperling (JKRS), Burnham–Colton–Pollock (BCP), Maugis–Dugdale (MD), Carpick–Ogletree–Salmeron (COS), Pietrement–Troyon (PT), and Sun et al. have been applied as the continuum mechanics approaches at nano-scale. In this article, indentation depth and contact radius between tip and substrate with nano-particle for both spherical and conical tip shape during nano-manipulation process are analyzed and compared by applying theoretical, semiempirical, and empirical nano-contact mechanics models. The effects of adhesion force, as the main contrast point in different nano-contact mechanics models, on nano-manipulation analysis is investigated for different contact radius, and the critical point is discussed for mentioned models.

Keywords

AFM nano-robot Nano-particle manipulation Nano-contact mechanics models Indentation depth Contact area Adhesion force Instrumentation 

List of symbols

a

Spherical contact-radius

a0(α)

Contact-radius at zero applied force

b

Cylindrical contact-radius

E

Young’s moduli

Ep

Nano-particle Young’s moduli

E*

Elastic constant

F

Applied load

Fad

Adhesion force

Fs

Particle–substrate force in contact area

FT

Pushing force

Ft

Tip–particle force in contact area

FY

Lateral tip force

Fy

Bending force of the cantilever

FZ

Normal tip force

Fz

Bending force of the cantilever

G

Shear modulus

H

Probe height

Ip

Moment of inertia

K

Elastic modulus

Ky

Lateral spring constant of the cantilever

Kz

Normal spring constant of the cantilever

Kθ

Torsional spring constant of the cantilever

L

Length of the cantilever

Mθ

Torsional torque of the cantilever

m

The ratio of the width of the annular region c to a

\( \tilde{R} \)

Effective radius of two contacted surfaces

Rp

Nano-particle radius

Rt

Spherical tip radius

t

Thickness of the cantilever

V

Shear force

w

Width of the cantilever

yp

Horizontal deflection of the probe

ys

Horizontal displacement of substrate

yT

Horizontal displacement of tip

zp

Vertical deflection of the probe

zs

Vertical displacement of substrate

zT

Vertical displacement of tip

α

Dimensionless parameter dependent on λ

δ

Indentation depth

δs

Indentation depth between nano-particle and substrate

δt

Indentation depth between tip and nano-particle

\( \phi \)

Angle of tip–particle contact

\( \varphi \)

Half angle of conical tip

γt

Tip surface energy

γp

Nano-particle surface energy

γtp

Tip–particle interface surface energy

λ

Tabor dimensionless parameter

θ

Twist angle of the probe

σ

Molecular diameter

ρ

Density

υ

Poison’s coefficients

ω

Adhesion energy

Ψ

Pushing force angle

∆γ

Work of adhesion force

References

  1. Bhushan B (2005) Nanotribology and nanomechanics, an introduction. Springer, Berlin, pp 419–590CrossRefGoogle Scholar
  2. Binnig G, Quate CF, Gerber C (1986) Atomic force microscope. Phys Rev Lett 56:930–933CrossRefGoogle Scholar
  3. Binning G, Rohrer H (2000) Scanning tunneling microscopy. IBM J Res Develop 44:279–293CrossRefGoogle Scholar
  4. Burnham NA, Kulik AJ (1999) Surface forces and adhesion. In: Bhushan B (ed) Handbook of micro/nanotribology, Chap. 5. CRC Press LLC, Boca RatonGoogle Scholar
  5. Carpick RW, Ogletree DF, Salmeron M (1999) A general equation for fitting contact area and friction vs load measurements. J Colloid Interface Sci 211:395–400CrossRefGoogle Scholar
  6. Fatikow S (2008) Automated nanohandling by microrobots. Springer, Heidelberg, pp 1–8CrossRefGoogle Scholar
  7. Israelachvili J (1992) Intermolecular and surface forces. Academic Press, London, pp 316–327Google Scholar
  8. Johnson KL (1985) Contact mechanics. Cambridge University, London, pp 84–106Google Scholar
  9. Johnson K, Greenwood J (1997) An adhesion map for the contact of elastic spheres. J Colloid Interface Sci 192:326–333CrossRefGoogle Scholar
  10. Pietrement O, Troyon M (2000) General equations describing elastic indentation depth and normal contact stiffness versus load. J Colloid Interface Sci 226:166–171CrossRefGoogle Scholar
  11. Requicha AAG (1999) Nanorobotics. In: Nof S (ed) Handbook of industrial robotics. Wiley, New York, pp 199–210CrossRefGoogle Scholar
  12. Shi X, Zhao YP (2004) Comparison of various adhesion contact theories and the influence of dimensionless load parameter. J Adhesion Sci Technol 18:55–68CrossRefGoogle Scholar
  13. Sitti M, Hashimoto H (2003) Teleoperated touch feedback from the surfaces at the nanoscale: modelling and experiments. IEEE/ASME Trans Mechatron 8:287–298CrossRefGoogle Scholar
  14. Stroscio JA, Eigler DM (1991) Atomic and molecular manipulation with the scanning tunneling microscope. Science 254:1319–1326CrossRefGoogle Scholar
  15. Sun Y, Akhremitchev B, Walker GC (2004) Using the adhesive interaction between atomic force microscopy tips and polymer surfaces to measure the elastic modulus of compliant samples. Langmuir 20:5837–5845CrossRefGoogle Scholar
  16. Tafazzoli A, Sitti M (2004) Dynamic behavior and simulation of nanoparticle sliding during nanoprobe-based positioning. In: ASME proceedings of International conference on mechanical engineering congress, pp 965–972Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Khadijeh Daeinabi
    • 1
    Email author
  • Moharam Habibnejad Korayem
    • 2
  1. 1.Department of Mechatronics Engineering, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Robotic Research Laboratory, College of Mechanical EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations