Contact-area dependence of frictional forces: Moving adsorbed antimony nanoparticles

Claudia Ritter, Markus Heyde, Bert Stegemann, Klaus Rademann, and Udo D. Schwarz

Phys. Rev. B 71, 085405 – Published 8 February 2005

Abstract

Antimony nanoparticles grown on highly oriented pyrolytic graphite and molybdenum disulfide were used as a model system to investigate the contact-area dependence of frictional forces. This system allows one to accurately determine both the interface structure and the effective contact area. Controlled translation of the antimony nanoparticles (areas between 10 000 and $110 000 {nm}^{2}$ ) was induced by the action of the oscillating tip in a dynamic force microscope. During manipulation, the power dissipated due to tip-sample interactions was recorded. We found that the threshold value of the power dissipation needed for translation depends linearly on the contact area between the antimony particles and the substrate. Assuming a linear relationship between dissipated power and frictional forces implies a direct proportionality between friction and contact area. Particles about $10 000 {nm}^{2}$ in size, however, were found to show dissipation close to zero. To explain the observed behavior, we suggest that structural lubricity might be the reason for the low dissipation in the small particles, while elastic multistabilities might dominate energy dissipation in the larger particles.

Received 3 June 2004

DOI:https://doi.org/10.1103/PhysRevB.71.085405

Authors & Affiliations

Claudia Ritter^*, Markus Heyde^†, Bert Stegemann^‡, and Klaus Rademann

Institute of Chemistry, Humboldt Universität zu Berlin, Brook-Taylor-Strasse 2, D-12489 Berlin, Germany

Udo D. Schwarz

Department of Mechanical Engineering, Yale University, P. O. Box 208284, New Haven, Connecticut 06520-8284, USA

^*Corresponding author. Electronic address: claudia@chemie.hu-berlin.de
^†Present address: Fritz-Haber Institute of the Max Planck Society, D-14159 Berlin, Germany.
^‡Present address: Federal Institute of Materials Research and Testing (BAM), D-12200 Berlin, Germany.

Calculations of the threshold force and threshold power to move adsorbed nanoparticles

Dhavide A. Aruliah, Martin H. Müser, and Udo D. Schwarz

Phys. Rev. B 71, 085406 (2005)

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Vol. 71, Iss. 8 — 15 February 2005

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Images

Figure 1
SFM $(2.5 \times 2.5 {μ m}^{2})$ and TEM $(0.66 \times 0.66 {μ m}^{2})$ images of the two sample surfaces (a) Sb on HOPG and (b) Sb on $Mo S_{2}$ . The insets show bright field TEM images of typical flower-shaped Sb particles on each surface. The dark contour lines inside the particles are bending contours produced by the strained crystalline particles.Reuse & Permissions
Figure 2
Illustration of the manipulation procedure (SFM images, Sb on HOPG, image size $1 \times 1 {μ m}^{2}$ , height of particle $a$ is 26 nm). (a) Overview of the particle of interest (labeled with $a$ ) and the surrounding area. A white and a gray arrow indicate the path of the subsequent tip motion and the resulting dislocation of the particle, respectively. (b) Topography after the manipulation. Comparison with (a) shows that the particle $a$ experienced a lateral translation of 83 nm and an in-plane rotation of 58°. For the next manipulation step, another contact point between the particle and the tip was selected, visualized again by a white arrow. (c) Result of the second manipulation step, revealing a translation of 211 nm and an in-plane rotation of 77°. (d) Final result after the third manipulation step. This time, the translational motion of 175 nm was accompanied only by a small in-plane rotation of about 3°. In (c) it is visible that particle $b$ was accidentally translated during the imaging process. The contact area of this particle is slightly below $10 000 {nm}^{2}$ and thus in the range of very low power dissipation. In contrast, power dissipation during the manipulation of particle $a$ with a contact area of about $62 000 {nm}^{2}$ is much higher, and stable imaging is easily achieved.Reuse & Permissions
Figure 3
Formation of the letters “H” and “U” (for Humboldt University) as an example for an intentionally composed two-dimensional nanostructure. (a)–(c) illustrate different steps of the assembly process, (d) the final result. The final structure consists of 50 Sb nanoparticles; the substrate is HOPG. The average particle height is about 30 nm, and the size of all images is $4 \times 4 {μ m}^{2}$ .Reuse & Permissions
Figure 4
Plot of the minimum values of power dissipation needed for translation of different-sized Sb nanoparticles on HOPG (filled triangles) and $Mo S_{2}$ (empty circles), respectively. The threshold values for both substrates are in the same range and scale linearly with the contact area of the translated particles. The straight lines represent linear fits of the measured data. The heights of the translated particles were between 21.3 and 28.0 nm with an average value of 26.2 nm for the 23 particles moved on HOPG and between 17.9 and 24.0 nm with an average of 21.5 nm for the 12 particles moved on $Mo S_{2}$ .Reuse & Permissions
Figure 5
Sketch of the tip-particle coupling. The impact angle $α_{t}$ between tip and antimony particle determines the normal $(z)$ and lateral $(x)$ components of the acting force.Reuse & Permissions

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