Contribution of Capillary Adhesion to Friction at Macroscopic Solid--Solid Interfaces

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Contribution of Capillary Adhesion to Friction at Macroscopic Solid–Solid Interfaces

Feng-Chun Hsia, Chao-Chun Hsu, Liang Peng, Fiona M. Elam, Chen Xiao, Steve Franklin, Daniel Bonn, and Bart Weber

Phys. Rev. Applied 17, 034034 – Published 11 March 2022

Abstract

Capillary adhesion is commonly present in ambient conditions. It can be measured in single-asperity contacts through atomic force microscopy using a sharp probe that is pulled off a smooth substrate. However, for macroscopic multiasperity interfaces, the measured adhesive force is always close to zero because of the elastic energy stored into the deformation of surface roughness; this is known as the adhesion paradox. Here, we experimentally show how capillary adhesion influences friction between macroscopic $Si$ -on- $Si$ interfaces, covered with native oxide, in two vapor environments: humid air and isopropyl alcohol (IPA) vapor. To quantify the adhesion contribution to friction, we present a boundary element method that successfully models the interplay between capillary adhesion, surface topography, and friction without adjustable parameters and show that the evolution of the surface topography during sliding dramatically increases capillary adhesion and thus friction. Replacing the water vapor with an organic (IPA) vapor, we find a lower adhesion due to the smaller surface tension.

Received 28 October 2021
Revised 13 January 2022
Accepted 9 February 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.034034

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Physics Subject Headings (PhySH)

Adhesion Capillary interactions Elasticity Friction Surface & interfacial phenomena

Atomic force microscopy Finite-element method Rheology techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Feng-Chun Hsia ^1,2, Chao-Chun Hsu³, Liang Peng², Fiona M. Elam¹, Chen Xiao^1,2, Steve Franklin ^1,4, Daniel Bonn², and Bart Weber^1,2,*

¹Advanced Research Center for Nanolithography (ARCNL), Science Park 106, 1098 XG Amsterdam, Netherlands
²Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
³Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
⁴Department of Materials Science and Engineering, The University of Sheffield, Sheffield S1 3JD, United Kingdom

^*b.weber@arcnl.nl

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Issue

Vol. 17, Iss. 3 — March 2022

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Images

Figure 1
Single nanoasperity and macroscopic multiasperity pull-off force measurements and calculations. (a) A typical force-displacement (F-D) curve measured at a relative humidity (RH) of 58%, showing the tip-sample normal force measured as the tip approaches the sample and as the tip is retracted. (b) An F-D curve measured in an isopropyl alcohol (IPA) rich vapor environment. The inset (a) and lower inset (b) display an F-D curve measured while the tip-sample interface is immersed in liquid water and IPA, respectively. The upper inset (b) illustrates a capillary bridge and the capillary and tension forces exerted at such a bridge. (c) External force (F_ex) as a function of time (T) measured during the retraction of a $Si$ ball from a $Si$ wafer surface; the inset shows a close-up. (d) The calculation of capillary adhesion (F_c) exerted at the $Si$ ball-on- $Si$ wafer interface as a function of the average interfacial gap relative to the average interfacial gap corresponding to an elastic force of 40 mN. The inset shows that as the elastic force (F_elastic) decreases to zero the capillary adhesive and external force, both of the order of µN, cancel each other. The experiments and calculations in (c) and (d) were conducted at an RH of 53 ± 1.4% and 50%, respectively.
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Figure 2
Atomic force microscopy (AFM) surface topography of $Si$ balls. The AFM topography of (a) a pristine $Si$ ball and (b) an artificially worn $Si$ ball. The AFM topography of a pristine $Si$ ball (c) before sliding and (d) after 190 µm sliding at a velocity of 1 µm/s and a normal force of 40 mN. The AFM topographies are measured over a 31 µm × 31 µm scan area with 430.6 nm² pixel size. (e) The cross-section height profile (H) of the topographies shown in (a)–(d). (f) Zoom-in height profile corresponding to the orange boxes in (e). Scale bar 10 µm.
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Figure 3
Macroscopic siding experiment. (a) The $Si$ ball-on- $Si$ wafer friction measurements are performed using a customized rheometer that measures the normal force and torque exerted on a geometry to which the $Si$ ball is clamped while it is slid at a constant externally applied normal force (F_ex) and angular velocity (ω). A plastic tube is mounted right next to the 3 mm ball to perform IPA vapor-phase lubrication friction experiments. The tube directs a gas flow of dry $N_{2}$ that is passed through a gas wash bottle filled with IPA towards the interface at a rate of 5 l/min (see Appendix pp5 for more details). (b) The static and dynamic coefficient of friction (COF) are measured in ambient (41 ± 1% RH) and water-immersed environments. The inset of (b) shows the COF measured in IPA vapor as described above and immersed in IPA. All measurements are performed at a normal force of 40 mN and a sliding velocity of 1 µm/s.
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Figure 4
$Si$ ball-on- $Si$ wafer capillary adhesion calculations and experiments. (a) Calculated capillary adhesion (F_ad) at 40 mN external load in ambient (40% relative humidity, blue line) and 10%–70% partial pressure of IPA vapor (green lines) environments as a function of wear volume (V). The adhesive forces in (a) were calculated based on the topographies of four independent $Si$ balls; we report the average and the standard deviation of the results. The experimental estimates of the capillary adhesion and wear volume are reflected by the blue (ambient) and green (IPA) shaded squares. The capillary adhesion is plotted against the rms roughness (R_q) of the artificially worn $Si$ ball in the inset of (a). The BEM contact calculations of solid–solid contacts (red) and capillary-wetted areas (grey, W = 4 nm) are shown for the pristine (V = 0 nm³) $Si$ ball (b) and the artificially worn (V = 4 × 10⁹ nm³) $Si$ ball (c). Scale bar 10 µm.
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