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Dynamic modeling of submerged nanoparticle pushing based on atomic force microscopy in liquid medium

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Abstract

This article introduces a theoretical analysis of submerged nanoparticle manipulation in liquid medium using the atomic force microscopy, and gives a review of the major differences between dry and submerged manipulation processes. In this regard, the manipulation is modeled by adding the influences of the hydrodynamic forces surface forces to the manipulation model in dry air. Then, the pushing of a gold nanoparticle of 50-nm radius on a silicon substrate at a velocity of 100 nm/s is simulated, and the dynamic behaviors of the tip and nanoparticle are investigated. The results show that, in water (as compared to air), the required manipulation force and time for nanoparticle sliding and rolling increase by 3.5 and 6.5%, for sliding and 2 and 4.3% for rolling, respectively. Also, in liquids with different viscosities, the critical values related to sliding and rolling have a maximum variation of 17 and 32% for the manipulation time, and 6 and 22% for the manipulation force, respectively, as compared to the critical values related to particle manipulation in air. Moreover, for various submerged lengths of the cantilever in water, the critical values related to sliding and rolling show a maximum time variation of 9 and 10.5%, and 7 and 7.2% (for the manipulation force), respectively. Qualitative comparisons between the obtained results and those of the existing experimental investigations show the advantages of the liquid medium for the manipulation purposes.

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Abbreviations

R t :

Tip radius

L :

Length of cantilever

w :

Width of cantilever

t :

Thickness of cantilever

H :

Probe height

R P :

Radius of nanoparticle

P T :

Pushing force

ψ :

Pushing force angle

K y :

Lateral spring constant of the cantilever

Kc :

Normal spring constant of the cantilever

\( K_{\theta } \) :

Torsional spring constant of the cantilever

F y, F z :

Bending forces of cantilever

M θ :

Torsional torque of cantilever

v :

Shear force

F Y , F Z :

Vertical and horizontal forces of the probe tip

θ :

Torsion angle of cantilever

y P :

Horizontal deformation of cantilever

z P :

Vertical deformation of cantilever

a :

Radius of the contact area

A :

Contact area

δ :

Indentation depth

K :

The reduced elasticity modulus between two contacted materials

F :

Normal force in contact area

f t, f s :

Tip–particle and particle–substrate frictions

F t, F s :

Tip–particle and particle–substrate normal forces in contact area

R ′ :

Effective radius of two contacted surfaces

E :

Young’s modulus

G :

Shear modulus

ν :

Poisson’s coefficient

ω :

Work of adhesion (energy per unit area of two flat surfaces)

\( \gamma \) :

Surface energy

\( \varphi_{0} \) :

Initial deformation of cantilever

\( \varphi \) :

Probe/nanoparticle Contact angle

Z P0 :

Initial normal deflection

m :

Constant parameter depending on the tip geometry

μ and τ :

Friction constants

τ :

Shear strength of the particle/substrate or tip/particle contact area

μ d :

Friction coefficient (stationary state)

μ s , μ r :

Sliding/rolling friction coefficient

τ s, τ r :

Shear strength of contact area in the sliding/rolling operation

d :

Critical rolling displacement

σ :

The mean distance between neighboring atoms

P cr :

Critical force (tip force on the particle to overcome adhesion forces)

t cr :

Critical time (the moment nanoparticle begins to move on the substrate)

V sub :

Substrate velocity

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Authors and Affiliations

  1. Robotic Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

    M. H. Korayem, A. Motaghi & M. Zakeri

Authors
  1. M. H. Korayem
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  2. A. Motaghi
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  3. M. Zakeri
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Correspondence to M. H. Korayem.

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Korayem, M.H., Motaghi, A. & Zakeri, M. Dynamic modeling of submerged nanoparticle pushing based on atomic force microscopy in liquid medium. J Nanopart Res 13, 5009 (2011). https://doi.org/10.1007/s11051-011-0482-0

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  • DOI: https://doi.org/10.1007/s11051-011-0482-0

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