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

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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.

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Abbreviations

a :

Spherical contact-radius

a0(α):

Contact-radius at zero applied force

b :

Cylindrical contact-radius

E :

Young’s moduli

E p :

Nano-particle Young’s moduli

E*:

Elastic constant

F :

Applied load

F ad :

Adhesion force

F s :

Particle–substrate force in contact area

F T :

Pushing force

F t :

Tip–particle force in contact area

F Y :

Lateral tip force

F y :

Bending force of the cantilever

F Z :

Normal tip force

F z :

Bending force of the cantilever

G :

Shear modulus

H :

Probe height

I p :

Moment of inertia

K :

Elastic modulus

K y :

Lateral spring constant of the cantilever

K z :

Normal spring constant of the cantilever

K θ :

Torsional spring constant of the cantilever

L :

Length of the cantilever

M θ :

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

R p :

Nano-particle radius

R t :

Spherical tip radius

t :

Thickness of the cantilever

V :

Shear force

w :

Width of the cantilever

y p :

Horizontal deflection of the probe

y s :

Horizontal displacement of substrate

y T :

Horizontal displacement of tip

z p :

Vertical deflection of the probe

z s :

Vertical displacement of substrate

z T :

Vertical displacement of tip

α :

Dimensionless parameter dependent on λ

δ :

Indentation depth

δ s :

Indentation depth between nano-particle and substrate

δ t :

Indentation depth between tip and nano-particle

\( \phi \) :

Angle of tip–particle contact

\( \varphi \) :

Half angle of conical tip

γ t :

Tip surface energy

γ p :

Nano-particle surface energy

γ tp :

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

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Authors and Affiliations

  1. Department of Mechatronics Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Khadijeh Daeinabi

  2. Robotic Research Laboratory, College of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

    Moharam Habibnejad Korayem

Authors
  1. Khadijeh Daeinabi
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  2. Moharam Habibnejad Korayem
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Correspondence to Khadijeh Daeinabi.

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Daeinabi, K., Korayem, M.H. Indentation analysis of nano-particle using nano-contact mechanics models during nano-manipulation based on atomic force microscopy. J Nanopart Res 13, 1075–1091 (2011). https://doi.org/10.1007/s11051-010-0096-y

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  • DOI: https://doi.org/10.1007/s11051-010-0096-y

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