Diffusion through Bifurcations in Oscillating Nano- and Microscale Contacts: Fundamentals and Applications

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Diffusion through Bifurcations in Oscillating Nano- and Microscale Contacts: Fundamentals and Applications

Ming Ma, Igor M. Sokolov, Wen Wang, Alexander E. Filippov, Quanshui Zheng, and Michael Urbakh

Phys. Rev. X 5, 031020 – Published 21 August 2015

See Focus story: Shaking Cleans Nanoscale Surface

Abstract

It has long been recognized that the diffusion of adsorbed molecules and clusters is the key controlling factor in most dynamical processes occurring on surfaces and in nanoscale-confined spaces. The ability to manipulate diffusion is essential for achieving efficient transport in nano- and microstructures and for many other applications. Through simulations and experiments, we found that under the influence of mechanical oscillations, the diffusion coefficient in nanoscale-confined regions can be greatly enhanced. This effect occurs due to bifurcations of particle trajectories caused by the reconstruction of the energy landscape during oscillations. We derive a parameter-free analytical model for the enhanced diffusion that is in excellent agreement with results of our numerical simulations. The oscillation-induced enhancement of diffusion may have interesting and promising applications in such areas as directed molecular transport, sorting of particles, and tribology. Here, our findings have been applied to studies of mechanical cleaning of surfaces from contamination. Through both experiments and simulations, we have shown that using an oscillating slider, one can significantly reduce the concentration of contaminants in a confined region, which is crucial for achieving superlow friction.

Received 4 May 2015

DOI:https://doi.org/10.1103/PhysRevX.5.031020

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Focus

Shaking Cleans Nanoscale Surface

Published 21 August 2015

An oscillatory motion dramatically reduces the number of contaminant molecules at the interface between two surfaces.

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Authors & Affiliations

Ming Ma¹, Igor M. Sokolov², Wen Wang^3,4, Alexander E. Filippov⁵, Quanshui Zheng^3,4, and Michael Urbakh^1,*

¹School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
²Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany
³Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
⁴Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
⁵Donetsk Institute for Physics and Engineering of NASU, 83114 Donetsk, Ukraine

^*urbakh@post.tau.ac.il

Popular Summary

It has long been recognized that the diffusion of adsorbed molecules and clusters is a key controlling factor in most dynamical processes occurring on surfaces and in nanoscale confined spaces. Molecular diffusion at surfaces is typically reduced compared with that in the gas or liquid phases because of the potential-energy landscape impeding the molecular motion. The ability to enhance or, more generally, to manipulate diffusion on the nanoscale presents a significant challenge for both fundamental studies and applications. Using simulations and experiments, we show that the diffusion coefficient in nanoscale-confined regions can be greatly enhanced via mechanical oscillations.

We conduct numerical simulations of molecular dynamics using a one-dimensional model of two rigid plates, where one plate oscillates harmonically; particles are embedded between the two plates. During a fraction of each period of oscillation, particles confined between two surfaces can move freely, which leads to a large enhancement ( $10^{- 10}$ ) in the diffusion. We simulate frequencies that range over 6 orders of magnitude, and we find that the diffusion coefficient is linearly proportional to the frequency of the oscillations. By simulating 200 periods, we find that the enhancement in diffusion in the confined region leads to a significant reduction in the contaminant concentration, which is difficult to achieve using conventional cleaning techniques alone. In situ cleaning of tribological contacts is crucial for achieving a superlow friction state (superlubricity) that may be destroyed by the presence of contaminations between the surfaces.

We expect that the oscillation-induced enhancement of diffusion may have many interesting and promising applications in areas such as directed molecular transport, surface nanostructuring, sorting of molecules and clusters, and tribology.

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Issue

Vol. 5, Iss. 3 — July - September 2015

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Images

Figure 1
Schematics of the studied systems and enhanced diffusion. (a) Schematic sketch of experimental configuration and (b) the model geometry, where red spheres represent particles embedded between two surfaces shown as black and yellow spheres (curves). The arrows in (b) indicate the directions of oscillations. (c) Dependence of normalized diffusion coefficient $D / D_{free}$ on frequency of oscillations $f / f_{0}$ calculated for commensurate ( $a_{sub} / a_{sld} = 1$ ) and incommensurate ( $a_{sub} / a_{sld} = 0.95$ ) surfaces, with $D_{free} = k_{B} T / η_{sub}$ being the free diffusion coefficient and the oscillation amplitude $A$ being $A / a_{sld} = 2$ . The inset shows this dependence in the high-frequency range.
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Figure 2
Mechanisms of enhanced diffusion. (a),(b) Trajectories of adsorbates calculated for commensurate surfaces oscillating with frequency $f / f_{0} = 1.26 \times 10^{- 2}$ and for incommensurate surfaces ( $a_{sub} / a_{sld} = 0.95$ ) with $f / f_{0} = 1.26 \times 10^{- 5}$ , respectively. The oscillation amplitude is $A = 2 a_{sld}$ . The time interval in (a) and (b) corresponds to two periods of oscillations. Note that different scales of the $Y$ axis are used for better visualization. (c),(d) Time evolution of the potential energy experienced by particles $U (x, t)$ for commensurate and incommensurate ( $ϵ = 0.05$ ) surfaces, respectively. Blue and red regions correspond to potential minima and maxima, respectively. The color bar is shown to the right of (d). The time interval in (c) and (d) corresponds to one period of oscillations. White curves in (c) show trajectories of adsorbates.
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Figure 3
Variation of potential energy barriers separating the neighboring minima in the particle-substrate energy landscape with time during one period of oscillations with the amplitude equal to $A = 2 a$ . The results are for commensurate surfaces.
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Figure 4
Diffusion coefficients with different damping coefficients for adsorbates confined between the (a) commensurate and (b) incommensurate ( $a_{sub} / a_{sld} = 0.95$ ) surfaces. The oscillation amplitude is $A = 2 a_{sld}$ . The damping coefficients for the overdamped case are two times larger than their values for the critical damping.
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Figure 5
Diffusion coefficient as a function of frequency at $T = 0.01 U_{sub} / k_{B}$ and $T = 0.2 U_{sub} / k_{B}$ for (a) commensurate and (b) incommensurate $ϵ = 0.05$ surfaces. Square dots connected by dashed lines are numerical results, and curves show theoretical results. The oscillation amplitude is $A = 2 a_{sld}$ . The normalization coefficient $D_{free}$ corresponds to $T = 0.01 U_{sub} / k_{B}$ .
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Figure 6
Mechanical cleaning of surfaces. (a)–(c) Schematic representation of the experimental procedure including (a) preparation of graphite mesas, (b) adsorption of contaminants, and (c) transferring of the cover of the right mesa to the top of the left one and mechanical cleaning. The top parts in blue are ${SiO}_{2}$ , and the rest in gray are graphite mesas. The black triangle stands for the tip of the microforce sensing probe, and the red arrows indicate the direction of the oscillation of the substrate. (d) Schematic sketch of the model used to simulate the cleaning process via mechanical oscillation. Golden spheres represent the slider surface that oscillates as indicated by the arrows, red spheres show adsorbed particles, which initially are uniformly distributed, and black spheres depict the substrate. (e),(f) Comparison between the values of $N^{conf} (t) / N^{conf} (0)$ measured in experiments (square symbols connected by dashed lines) and calculated in simulations (curves) for small ( $A \sim 0.1 L$ , where $L$ is the size of the slider) and large amplitudes ( $A \sim 1.0 L$ ) of oscillations, respectively. In (e), the curves from top to bottom have been calculated for $f / f_{0} = 1.26 \times 10^{- 2}$ , $5.03 \times 10^{- 5}$ , and $1.26 \times 10^{- 5}$ , respectively. In (f), the curves from top to bottom correspond to $f / f_{0} = 1.26 \times 10^{- 2}$ , $1.26 \times 10^{- 3}$ , and $5.03 \times 10^{- 5}$ , respectively. Simulations have been performed for incommensurate surfaces with $a_{sld} / a_{sub} = (1 + \sqrt{5}) / 2$ and $T = 0.2 U_{sub} / k_{B}$ .
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