Nanotribology

Abstract

Nanotribology is a study on friction phenomena occurring at nanometer scale. The distinction between nanotribology and conventional tribology is primarily due to the effect of surface forces in the determination of the adhesion and friction behavior of the system. Commercial bearings and lubricating oils reduce friction in the macroscopic machines; however, the tribological issues on small devices such as microelectromechanical systems and nanoelectromechanical systems require other solutions. Their high surface-to-volume ratio leads to severe adhesion and friction issues, which dramatically reduce their reliability and lifetime. This chapter reviews the basic concepts for handling the adhesion and friction issues at nanoscale. A brief summary on analytical models of single-asperity contact as well as the basic concepts on the surface forces occurring at nanometer gap are discussed in the first two sections, followed by three case studies: (1) experimental measurements on adhesion and friction at single-asperity contact, (2) experimental measurements on adhesion at multi-asperity contact, and (3) biomimetics: controlling nano-adhesion and nano-friction.

Appendices

Problems

• 1. For a ball-on-flat elastic half space contact, discuss the difference in the radii of contact for the Hertz, JKR, and DMT models.

• 2. Explain why the capillary force under single-asperity contact depends on the water-wetting angles of the surfaces.

• 3. If an AFM tip made of conductive silicon is approaching onto a gold surface in vacuum, jump-to-contact usually occurs. Explain this using the surface force interaction between the AFM tip and the gold surface.

• 4. Explain the origin of the nonzero friction at zero applied load.

• 5. Suppose you are designing a micro-ball. If you know the material properties, you may calculate the adhesion force with the 3D drawings by using Hertz, JKR, and DMT models. Can you estimate the accuracy of the calculated values?

• 6. Define the meaning of biomimetics.

Solutions

• 1. Hertzian model: ${a}^3=\frac{3 FR}{4{E}^{*}}$

  where F is the applied load, R is the radius of the ball, and the E^* is given by

  $$ \frac{1}{E^{*}}=\frac{1-{\nu}_1^2}{E_1}+\frac{1-{\nu}_2^2}{E_2} $$

  where E ₁ and E ₂ are the elastic moduli and ν₁ and ν₂ are the Poisson’s ratios of the contacting bodies.

  JKR model: ${a}^3=\frac{3R}{4{E}^{*}}\left(F+6\gamma \pi R+\sqrt{12\gamma \pi R F+{\left(6\gamma \pi R\right)}^2}\right)$

  where γ is the surface energy per unit area.

  DMT model: ${a}^3=\frac{3R}{4{E}^{*}}\left(F+2\varDelta \gamma \pi R\right)$

• 2. The adhesion force could be represented as the sum of the JKR adhesion force contribution and the capillary force as represented in (15.16). This adhesion force could be normalized with the tip radius (R), and then it may be possible to eliminate the tip radius effect. Equation (15.17) represents the adhesion force normalized with the tip radius:

  $$ {F}_{\mathrm{ad}}=2\pi R{\gamma}_{\mathrm{L}}\left( \cos {\theta}_1+ \cos {\theta}_2\right)+\frac{3}{2}\pi \gamma R $$

  (15.16)
  $$ \frac{F_{\mathrm{ad}}}{R}=2\pi {\gamma}_{\mathrm{L}}\left( \cos {\theta}_1+ \cos {\theta}_2\right)+\frac{3}{2}\pi \gamma $$

  (15.17)

  In (15.17), if the capillary force dominates the adhesion, Fad/R may increase linearly with cos θ ₁. Measured results are normalized with the tip radius and are summarized in Fig. 15.9. Figure 15.9 shows that Fad/R increased linearly with cos θ ₁. That means when the surface becomes more hydrophobic, the adhesion force would decrease.

• 3. Jump-to-contact in AFM usually occurs when F_s/z (where F_s is the surface force, and z is the gap distance) becomes greater than the stiffness of AFM cantilever. The surface force usually increases with decreasing gap distance. Thus, when the AFM tip is far out from the sample surface, k_c > F_s/z and the AFM tip do not exhibit jump-to-contact. When approaching the AFM tip onto the surface, the cantilever stiffness, k_c, is constant but F_s/z increases. At a threshold point where F_s/z = k_c, jump-to-contact occurs.

• 4. Figure 15.6b shows that the friction at zero applied load is not zero.

  The friction occurs when there is load on it. That means some other, nonmechanical load is already given onto the AFM tip. Figures 15.8 and 15.9 clearly show that it is capillary force.

• 5. Only a rough estimate of the force can be obtained. This is because the real contacting surfaces including the micro-ball are inherently rough. One example is shown in Fig. 15.12 where it is seen that the deviation range is unbelievably large.

• 6. Biomimetics is an interdisciplinary subject which involves the study of the structure and function of biological systems as models for the design and engineering of materials and machines.