Relationship between Asperity-Mediated Surface Forces and

Mar 19, 2014 - Topography Alteration of Silica Microspheres Sliding on Mica, ... Dan Zhang,. † .... mica, glass, and sapphire are chosen to study th...
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Relationship between Asperity-Mediated Surface Forces and Topography Alteration of Silica Microspheres Sliding on Mica, Sapphire, and Glass Substrates under Ambient Conditions: Atomic Force Microscopy and Theoretical Studies Dan Zhang,† Xin-qiang Chen,† You Wang,‡,§ Fei-hu Zhang,∥ and Yang Gan*,† †

School of Chemical Engineering and Technology, ‡Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Ministry of Education, §Materials Physics and Chemistry Department, and ∥School of Mechanical Engineering, Harbin Institute of Technology, Harbin 150001, China S Supporting Information *

ABSTRACT: Contact geometry significantly influences adhesive force measurements and modeling for adhesion/friction studies where an AFM colloidal probe technique has been extensively employed. Here we present a systematic study on the topography alteration of silica microspheres sliding on mica, sapphire, and glass substrates under ambient conditions at a relative humidity of 30−55% and the consequential adhesion behaviors of worn microspheres through AFM direct force measurements and theoretical modeling. The wearing of microspheres creates a truncated platform, which is largest for sliding on glass substrates. On the platform are nanoasperities consisting of wear debris and airborne particulate contaminants. Variations in adhesive forces with sliding time and testing modes as well as the effect of surface roughness of substrates are explained within the theoretical framework of nanoasperity-mediated capillary and van der Waals forces. The drawbacks of the present reverse-imaging method for microsphere topography examination, and numerous sources of errors associated with the extraction of key parameters for force modeling, are discussed in detail. The results will also have important implications for more reliable AFM colloidal probe technique and its application in adhesion and tribological studies.

I. INTRODUCTION Atomic force microscopy (AFM) has been widely used for high-resolution surface characterization and direct surface force measurements under ambient conditions.1−6 The AFM-based colloidal probe technique (CPT), realized by attaching a micrometer-sized spherical particle to a cantilever, facilitates quantitative and reproducible force measurements as well as theoretical modeling for colloidal stability, adhesion, and tribological studies7−13 under various environmental conditions. The general procedure for carrying out force measurements, using either a routine AFM probe with a sharp tip or a CPT probe, requires direct hard contact with or controlled sliding against a substrate. Consequently, it is expected that the tip or attached particles may be blunted, worn, and contaminated. Indeed, for routine sharp AFM probes, there are numerous reports regarding the topography alteration of tips after force measurements or sliding tests.14−18 Much to our surprise, however, for CPT probes modified with a microsphere, only scarce reports of the evidence of topography alteration, surface contamination, and related theoretical explorations of surface forces can be found.19−26 This is first because of the common dogmatic impression that microspheres can remain intact even © 2014 American Chemical Society

after being in loaded contact or sliding against solid substrates because of their larger size (in micrometers) compared to that of sharp tips (in nanometers). Only in recent years have the overlooked topography change in CPT probes and the effects on force measurements been paid some attention.19−25 Unfortunately, the topography and surface contamination of microspheres are seldom examined using standard microscopy techniques such as SEM, presumably because it is by no means conveniently accessible in most laboratories. In this regard, the novel AFM-based reverse-imaging method27 stands out for the quick, convenient, and affordable evaluation of microspheres’ topography and surface contamination as our preliminary results demonstrated,20 yet admittedly this method may sacrifice resolution in comparison to that of more elaborate direct imaging methods.28,29 The adhesive force required to detach a microsphere from a flat substrate completely, under ambient conditions, is the sum of capillary and van der Waals (vdW) forces provided that short-range chemical interactions are absent. Capillary force is Received: October 6, 2013 Revised: March 19, 2014 Published: March 19, 2014 3729

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Figure 1. Illustrations of various sphere−plate contact geometries for (a−c) the capillary force and (d, e) vdW force modeling. (a) The sphere−plate geometry, (b) the corrugated/truncated sphere−plate geometry, and (c) the corrugated/truncated sphere−corrugated plate geometry for capillary force modeling. (d) The truncated sphere−plate geometry and (e) the spherical cap−plate geometry for vdW force modeling. See the text for the meaning of symbols.

mica, glass, and sapphire are chosen to study the effects of substrate hardness and roughness because of their distinct difference in terms of hardness (Mohs’ hardness from 2 to 9) and surface roughness (atomic vs nanometer scale), with all exhibiting good hydrophilicity. The topography−adhesion relationships were investigated experimentally with AFM, including the sliding mode and sliding time dependence, and explored theoretically through modeling vdW and capillary forces by considering local asperities on the microspheres and the surface roughness of substrates.

caused by the attractive action of a water meniscus between the microsphere and substrate. Capillary force is the major contribution for hydrophilic surfaces when the atmospheric relative humidity (RH) is >20%.26,30,31 Under mild RH conditions (30−60%), the height of the water meniscus is only on the order of 1 nm, leading to a strong contact geometry dependence of the capillary force.11 Therefore, accurate contact geometry information such as the contact area and topography of asperities on both the microsphere and substrate is crucial for correctly modeling capillary forces and comparing with experimental results.32−34 At the same time, the vdW force is also sensitive to surface roughness and contact geometry because of the rapid decay of the vdW force with separation.35 Especially for CPT probes, the nanoscale topography of a few protruding asperities on a microsphere, instead of averaged parameters such as surface roughness, is crucial to determining the overall surface forces. It is thus very important to obtain accurate topographic information about individual asperities on CPT probes. Therefore, a valid adhesive force model for CPT probes should quantitatively take into account the contact geometry dependence of capillary and vdW forces. In this regard, quantitative adhesive force measurements and accurate topography characterizations of both microspheres and substrates will be highly desirable to enable one to evaluate proposed models critically. We carried out a systematic study on the topography change of CPT silica microspheres caused by loaded sliding against mica, sapphire, and glass substrates under ambient conditions with the relative humidity ranging from 30 to 55%. Silica microspheres have been frequently used to prepare CPT probes thanks to their uniform size, subnanometer surface roughness, and well-defined surface chemistry. Silica is also an important type of abrasive for the chemical mechanical polishing of hard optical materials such as sapphire and SiC. Three substrates of

II. THEORETICAL FRAMEWORK A. Capillary Force Model for the Corrugated/ Truncated Sphere−Plate Geometry. For smooth sphere− plate geometry (Figure 1a), the attractive capillary force Fc can be calculated according to the well-known equation11,36 Fc(sphere/plane geometry) = −

4πRγw cos θ 1+

D d

(1)

where γw is the surface tension of water (0.072 N/m), R is the radius of microspheres, and θ is the contact angle between the surface and water assuming an identical contact angle for both sphere and substrate. θ is set to 30° for all capillary force calculations. D is the closest separation between the sphere and the substrate, usually taken as 0.17 nm for dry surfaces and 0.3 nm for wet surfaces because of existence of water molecules on the surfaces.37 d is the height of the spherical cap immersed in the water meniscus: d = 2r1 cos θ − D. r1 is the local radius of curvature of the water meniscus intersecting with the sphere and substrate. Because r1 is usually taken to be the Kelvin radius rk (0.43, 0.57, and 0.87 nm for RH values of 30, 40, and 55%), r1 ≪ r2 holds even for nanoscale spheres or asperities; therefore, for example, d is 0.69 nm for θ = 30°, D = 0.3 nm, 3730

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40% RH at 25 °C. By substituting d into eq 1, an equivalent expression is Fc(sphere/plane geometry) ⎛ D ⎞ = − 4πRγw cos θ ⎜1 − ⎟ 2r1 cos θ ⎠ ⎝

and a plate; however, this equation cannot be reduced to the case of a sphere because it was not derived analytically for a truncated sphere. Then, for asperities shown in Figure 1b, it is straightforward to write down the separation-dependent FvdW(D) by assuming Da ≪ Ra and da ≪ Ra

(2)

FvdW (spherical cap of asperity/plane geometry)

For the corrugated/truncated sphere−plate geometry (Figure 1b), asperities are present on the truncated platform of the sphere, eqs 1 and 2 are assumed to be valid for each individual asperity with its profile being approximated by a sphere Fca(asperity/plane geometry) = −

=−

Da da

(3)

⎛ ⎞ rca 2 ⎜1 + ⎟ R a(Da + da) ⎠ ⎝

where Rca is the radius of curvature of the asperity, da is the height of asperities immersed in the water meniscus, and Da is the closest separation between the asperity and the substrate. The total capillary force is the sum of contributions from individual asperities. For a more complex corrugated/truncated sphere−corrugated plate geometry (Figure 1c), where interacting asperities are assumed to be present both on the sphere and plate with identical contact angles, an equation such as eq 3 still holds except that Rca is now the effective radius of curvature of interacting asperities. B. vdW Force Model for the Corrugated/Truncated Microsphere−Plate Geometry. The well-known expression38 for the attractive vdW force between a sphere and plate is FvdW (sphere/plane geometry) = −

AR 6D2

(7)

III. EXPERIMENTAL DETAILS (4)

A. Materials and Substrate Cleaning. Commercial silica microspheres with a uniform nominal diameter of 5.0 μm (Bangs Laboratories Inc., Fishers, IN) were used to prepare colloid probes. The morphology of fresh microspheres was characterized with FESEM (Zeiss Sapphire Supra 55, Germany) operated in low acceleration voltage mode to enable the coating-free observation of raw surfaces. High-purity polished epi-ready (0001) sapphire substrates (Epistone Inc., Shenzhen, China) were used at a size of 10 mm × 10 mm × 0.43 mm and a misorientation angle of 0.2°. Glass slides (JWFU Inc., Shanghai, China) were cut into 10 mm × 10 mm × 1.0 mm pieces. Muscovite mica substrates (Zhongjingkeyi Technol., Beijing, China) were cut into 10 mm × 10 mm pieces. Mica substrates were freshly cleaved before tests. Analytical-grade chemical reagents were used. Deionized (DI) water with a resistivity of 18.2 MΩ/cm was used throughout. Sapphire substrates were carefully cleaned following a modified RCA method42 and then irradiated with low-pressure air plasma for 20−30 min before experiments.43 Glass substrates were sonicated in a detergent solution for 30 min, rinsed with a copious amount of DI water, and treated consecutively with the standard RCA protocols,44 followed by rinsing in DI water and blowing dry with nitrogen gas, irradiated with a home-built UV cleaner (equipped with a model UVGL-55 lamp, UVP Inc., Upland, CA) for 20 min immediately before use. Static water contact angles were measured using the sessile drop method with a commercial system (model SL200B, Shanghai SuoLun Tech Inc., Shanghai, China). The volume of the water droplet is 1 μL. Five measurements were taken, and mean values were reported. B. AFM and Colloidal Probe Preparation. A MultiMode AFM system including a NanoScope IIIa controller (Veeco Instruments Inc., Santa Barbara, CA) was used in contact mode for sliding tests and reverse imaging of silica microspheres and in tapping mode for the topographical characterization of substrates. The controller functions

AR a 6Da 2

(6)

where rca is the radius of the round platform of the truncated sphere of the asperity. Now we are able to compare the relative contributions of the spherical cap and truncated sphere to the total vdW force of an asperity at Da = 0.3 nm. The spherical cap part (height da = 2 nm) contributes to as much as 95% of the total vdW force for the asperity. In other words, the contribution from the part of truncated sphere of the asperity is only marginal. This is not unexpected because of the rapid decay of the vdW force with separation according to eqs 6 and 7. Later, eqs 6 and 7 will be used to calculate vdW forces with inputs of da, Da, and Ra from analyzing topographic images of fresh and worn microspheres.

where A is the Hamaker constant, R is the radius of the microsphere, and D is the closest separation between the microsphere and plate. Equation 4 holds for D ≪ R. The literature values of A are 1.2 × 10−20 J for silica/water/mica,39 1.4 × 10−20 J for silica/water/sapphire,40 and 6.5 × 10−21 J for silica/water/glass.41 For individual asperities interacting with a plate such as those shown in Figure 1b, it is straightforward to write down the expression based on eq 4 provided that Da ≪ Ra holds and the profile of each asperity is approximated by a sphere FvdW (asperity/plane geometry) = −

6Da 2 (Da + da)3

FvdW (truncated sphere of asperity/plane geometry) ⎛ AR a 2da ⎞ AR a =− + 1 ⎜ ⎟≈ 2 Da + da ⎠ 6(Da + da) ⎝ 6(Da + da)2

4πR caγw cos θ 1+

AR a 3Da da 2 + da 3

(5)

where Da is the closest separation for the asperity and Ra is the radius of curvature of the asperity. It is, however, desirable to determine quantitatively the relative vdW contributions from two parts of an asperity: (1) part from the truncated sphere of the asperity and (2) part from the spherical cap of the asperity, as illustrated for two asperities in Figure 1b. In this way, the dominating contribution of the spherical cap part of the asperity will be revealed. The first step is to derive vdW force expressions for two simpler geometries (Figure 1d−e): (1) a single truncated sphere−plate geometry and (2) a spherical cap−plate geometry. Lengthy derivations are given in the Supporting Information. It should be pointed out that, for a single truncated sphere−plate geometry, Parsegian38 and Israelachvili36 gave an expression of (−Arc2/ 6D3) for the vdW force between a cylinder (the area is πrc2) 3731

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Figure 2. (a−e) Schematic illustrations of the experimental procedures for colloidal probe preparation and topography characterization of microspheres and three different sliding tests. Steps for (f−j) I1, (k−p) I2, and (q−s) NI sliding test modes. emphasized that the variation in RH was carefully accounted for as a known input parameter into the models. During sliding tests, a constant loading force was applied to press the microsphere against the substrate. For I1 and NI modes, the loading force was 1200 nN for mica and 800 nN for sapphire and glass substrates; for I2 mode, the loading force was 2500 nN for mica and 800 nN for sapphire and glass substrates. Adhesive forces (Fad) were derived from force curves and calculated with one of two formulas: for weak forces, Fad = k × Dj, where Dj (nm) is the snap-off deflection; Fad = k × ΔE, where ΔE (nm) is the piezo tube retraction displacement for the tip to disengage from the substrate, used for strong force cases where the retracting hard contact curve was no longer linear. The set point for reverse imaging was 1 to 2 V so that the contact force was 100−200 nN, which was much smaller than the sliding load force. The procedure for a typical nonintermittent (NI) sliding test consisted of the following: First, the colloidal probe was engaged with the substrate to scan at a specific loading force over a 1 μm × 1 μm area at 2 Hz for 120−180 min without any break (Figure 2q). Second, force curves were taken for this tested colloidal probe with the same substrate but at a new site (Figure 2r). Last, the topography of the worn microspheres was characterized with the reverse-imaging method (Figure 2s). The procedure for a typical intermittent-I (I1) sliding test is as follows: In contrast to NI tests, a colloidal probe scans for a certain time and then disengages for force measurements. Steps were repeated on a new substrate site until the total sliding time reached 120−180 min. The procedure for a typical intermittent-II (II2) sliding test is as follows: In contrast to NI and I1 tests, after each round of sliding and force measurements the surface topography of this microsphere was examined with the reverse-imaging method. Note that for tests on glass substrates adhesive forces were also measured on freshly cleaved mica substrates to study the effect of the substrate’s surface roughness. D. Extraction of Contact Geometry from AFM Topography: Histogram Analyses. Histogram analyses were used to derive contact geometry from AFM images of microspheres. After a raw topographic image was loaded into the SPIP software, a square area including the contact area of microspheres was selected and enlarged for further inspection. With the software’s histogram module, parts of any asperity between the highest point of the whole image (M2 value) and a single threshold height value (M1 value, the value of d in eqs 1 and 3, d = 2r1 cos θ − 0.3), again for the whole image, were identified

with three independent 16-bit DACs. The scanner (model AS130VLR), featuring a 125 μm × 125 μm × 5 μm sampling range, enables vertical engagement with minimum XY tilts. All topographical images were captured and saved in the raw format with routine 512 × 512 lines. Three-dimensional-rendered images were visualized using free WSxM software (version 5.0−64).45 Commercial SPIP software (Image Metrology A/S, version 6.0.14) was used to carry out some profile and all histogram (flooding) analyses. Silicon probes (NSG10, NT-MDT Co., Moscow, Russia) with a nominal spring constant of 11.5 N/m were used for sliding tests. The actual spring constant of each cantilever was calibrated with the reference cantilever method (reference cantilever model CLFCNOBO, Veeco, Santa Barbara, CA). The calibrated spring constant is 9.8−12.0 N/m. Colloidal probes, three to five for each sliding test, were prepared by gluing a silica microsphere to the cantilever following the cantilevermoving procedure.12 Because the tip height (∼10 μm) of an asreceived probe is larger than the size of silica microspheres (5.0 μm), the microsphere, if attached directly to the cantilever, fails to touch the substrate. Therefore, before microsphere attachment, a probe’s tip was shortened by loaded sliding against a cleaned glass substrate (Figure 2a,b). Then a silica microsphere was glued to the base of the shortened tip in order to secure a strong attachment (Figure 2c). After the curing of UV-curable glue (Norland Products Inc., Cranbury, NJ) using the same UV light unit mentioned above, the surface topography of the microsphere was inspected by scanning over a silicon calibration grating with super-sharp spikes (TGT1, NT-MDT Co., Moscow, Russia; Figure 2d). Force curves were taken for a fresh microsphere and a substrate with a 1 Hz approaching frequency (Figure 2e). Probes were irradiated with UV light for another 10 min to remove organic contaminants before tests. C. Sliding Tests and Adhesive Force Measurements. Three modes of sliding tests (intermittent-I (I1), intermittent-II (II2), and nonintermittent (NI) mode) were carried out to investigate the effects of sliding mode and sliding time. During tests, the cantilever scans along the slow-scan axis without monitoring the lateral force (friction force). The temperature of the AFM laboratory was around 25 °C. The natural RH of the laboratory was monitored and recorded for each experiment. Although the RH during this study ranged from 30 to 55%, throughout each experiment the RH was approximately constant. RH was 40% for all tests on mica and glass substrates and 55%/ 45%/42% for I1/I2/NI tests on sapphire substrates. It should be 3732

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Figure 3. Histogram analysis of an experimental AFM topographic image. M2 is the highest z value, and M1 is moved to a defined M2 − M1 value to determine the area sliced by this M1 plane.

Figure 4. Morphology and topography images of gratings, silica microspheres, and three substrates. SEM images of (a) gratings and microspheres at (b) lower and (c) higher magnification. AFM topography of a fresh silica microsphere: (d) 3D view, (e) deflection image, and (f) height image (bow removed) of the squared area in plot e with a z height scale of 7.56 nm. AFM height images and profile analysis of (g) mica, (h) sapphire, and (i) glass substrates. for further geometrical analysis. Note that more than one asperity with a different individual highest height value (Mx) might be found. An example is given in Figure 3, where a large M2 − M1 value was set only for demonstration purposes and all histograms were given in Figures S1−S3. Then the pixels occupied by these parts of any asperity were selected as polygons, and other pixels were set to be voids. Two key parameters for each asperity were then determined: the area of polygons and the height range. Each polygon was approximated as the base of a spherical cap, and the equivalent diameter was calculated. The height range (Mx − M1) was taken as the height of the spherical cap. In this way, each asperity was taken to consist of a spherical cap and a truncated sphere sharing the same base.

and topography, on several length scales, of a typical fresh silica microsphere and also periodically arranged sharp spikes in the gratings. Note that apparent multiple identical images of spheres or half spheres in d and e were caused by the same microsphere scanning against several sharp spikes of the gratings. Only contaminant-free microspheres such as this one were used for sliding tests. The typical surface roughness of microspheres shown in Figure 4f is Rq = 0.75 nm and Rmax = 2.54 nm over a 1 μm2 area. Mica substrates are featureless with Rq = 0.06 nm and Rmax = 0.36 nm over a 500 × 500 nm2 area. Sapphire substrates are atomic-scale smooth with Rq = 0.10 nm and Rmax = 0.62 nm without step-terrace features; pits are caused by plasma etching.43 Glass substrates are rougher, showing typical nanoscale-etched topography with Rq = 0.91 nm and Rmax = 4.28 nm. A few airborne dust particles can be

IV. RESULTS A. Topography Characterization of Substrates and Fresh Silica Microspheres. Figure 4 shows the morphology 3733

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Figure 5. AFM 3D-rendered images of microspheres before and after I1, I2, and NI sliding tests for specific duration on mica, sapphire, and glass substrates. Images designated as 0 min are for fresh microspheres.

found randomly scattered on these substrates. Contact angles for the three substrates are less than 5°, indicating high hydrophilicity. B. Topography Characterization of Microspheres before and after Sliding Tests. Figure 5 shows clearly that, regardless of sliding modes and substrates, a topography change in the microspheres occurs after sliding tests. The region where the microsphere contacted the substrate was somewhat flattened for mica/sapphire and truncated significantly for glass substrates, which is further confirmed through profile analyses (examples for Figure 5-I1-ab and Figure 5-I2-f are shown in Figure 6). Here we call this region a platform. The shape of this platform is irregular for mica/sapphire and close to circular for a glass substrate. If a polygon is drawn along the border of the platform, then the equivalent radius of a circular area that equals the area of a polygon is ca. 200−400 nm for mica, 120−230 nm for sapphire, and 350−530 nm for glass. The profile and more histogram analyses indicated that there are a few asperities, up to 200 nm in diameter and 5−10 nm in height, protruding further out for both fresh and worn microspheres, and this is common for all sliding modes. Besides, we emphasize that each fresh microsphere is different in apparent surface topography. C. Adhesive Force Measurements. Capillary forces were calculated with eq 3, and vdW forces were calculated with eqs 6 and 7 for asperities with the contact geometry information obtained using histogram analyses, with all substrates assumed to be ideal featureless plates. The effects of surface roughness will be discussed later in section V.C. Numerical values of all experimental and calculated adhesive forces as well as force curves for three substrates are given in the Supporting Information as Tables S1−S3 and Figure S8. Calculations show that for all tests capillary forces dominate adhesive forces and vdW forces contribute only marginally (ca. 4%). Note that although adhesive forces for one microsphere were given for each sliding mode a similar trend with numerically different values was found for the repeated experiments. Figure 7a shows that for mica substrates the calculated forces (Fcal) satisfactorily reproduce the overall trends in the

Figure 6. AFM height topography, a corresponding deflection image, and profile analyses (for height images, drawn along two vertical lines 1 and 2) of microspheres (a−c) before and (d−f) after the intermittent-I sliding test on the mica substrate and (g−i) after the 120 min intermittent-II sliding test on the glass substrate. Note the different length and height scales in the three line profiles.

experimental adhesive force (Fexp) for three sliding tests. Force curves show sharp snap-in on the approaching curves and also sharp snap-off on the retracting curves for I1 and NI modes but a sharp snap-in and a gradual snap-off for the I2 mode. For the NI mode, Fcal shows a total 6.7-fold jump against 2.7-fold for Fexp. The relative magnitude of Fexp agrees with Fcal at 0, 120, and 180 min (i.e., I1 > NI at 0 and 180 min, I1 > I2 at 120 min). For sapphire substrates, Figure 7b shows that the overall trends in Fcal compare favorably with Fexp for I1 and NI modes 3734

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Figure 7. Experimental (mean and standard deviation) and calculated adhesive forces between microspheres and (a) mica, (b) sapphire, and (c) glass substrates for I1, I2, and NI sliding tests. Note that calculations for glass substrates assume an ideal featureless smooth surface.

but poorly with the I2 mode. For the I2 mode, Fexp increases sharply up to 60 min and then decreases linearly until 120 min. Fcal fluctuates with the sliding time (the 120 min point is missing because of inadvertent damage to the cantilever). Force curves are similar to those for mica substrates. Unlike mica, the relative magnitudes of Fexp at 0 and 180 min are not well reproduced (i.e., for 0 min, the order of Fcal is I1 ≈ I2 > NI, whereas Fexp shows NI > I1 > I2; for 180 min, the order is reversed as Fcal shows NI > I1 against I1 > NI for Fexp). For glass substrates, adhesive forces were measured immediately after each sliding test on the freshly cleaved mica substrateFexp(mica) for all sliding modes to study the effect of surface roughness. Figure 7c shows that the overall trends in Fcal compare favorably with Fexp(glass) and Fexp(mica) for three modes. It is interesting that for the NI mode Fexp(glass) is close to Fexp(mica) and Fcal decreases after all tests, in distinct contrast to mica and sapphire. Force curves show (1) similar sharp snap-in and snap-off for mode I1, (2) snap-in for 0−60 min tests and a repulsive barrier for 90 and 120 min tests for mode I2, and (3) sharp snap-in without any repulsive barrier and sharp snap-off except for 120 min for mode NI. The order for Fcal at 0 min is NI > I1 > I2 against I2 > I1 > NI for Fexp(glass). For 120 min, the order for Fcal is I1 > I2 ≈ NI against I1 > I2 > NI for Fexp(glass). In summary, a topographical examination of silica microspheres after sliding tests on all substrates unambiguously indicates a morphology change in the microspheresthe appearance of a platform, asperities, and particulate matter. We observed a strongly positive sliding time correlation of Fexp for all I1 and NI tests on mica and sapphire substrates and no apparent sliding time correlation for most I2 and NI tests on

glass substrates. At the same time, using histogram analyses, we identify and quantify the geometry of protruding asperities that were approximated as rigid spherical caps. Their geometrical parameters were input into models for adhesive force calculations. Capillary forces dominate adhesive forces for all tests. Good general qualitative agreement is found between Fexp and Fcal for three substrates, strongly suggesting that contacting asperities the control adhesion behavior between microspheres and substrates. Nevertheless, it is more than common that Fexp and Fcal values are unequal or even quite different, though the difference is within an order of magnitude. Consequently, we will discuss below the origin of platform and asperities, the sliding mode and time dependence of adhesive forces, the effects of substrate roughness, errors associated with modeling and force calculations, and problems with the current reverse-imaging method.

V. DISCUSSION A. Origin of Platform and Asperities on Microspheres. i. Constant Loading Force Condition. Let us consider how the deflection of the cantilever varies during sliding. Because all sliding tests were carried out under constant force mode (with very high values of ∼1000 nN), the vertically applied force and deflection of the cantilever should remain constant regardless of whether materials were removed from microspheres during sliding, even for the case of a spherical cap of up to a few tens of nanometers being removed after tests on glass substrates. ii. Origin of the Platform and Its Geometrical Features. One of the most outstanding topographical changes after sliding tests is the appearance of the platform, which is especially prominent for these severely worn microspheres 3735

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Figure 8. Cartoons illustrating how a platform on a microsphere is created by loaded sliding on a solid substrate for (a) symmetrically and (b) misaligned mounted positions on an inclined cantilever, viewed from both the y and x axes. The xy plane is a horizontal plane parallel to the substrate. The symmetrical axis of microspheres is given as a solid line. (c−e) Histograms of microspheres after a sliding test on the glass substrate.

sliding on glass substrates. Two interesting findings deserve close scrutiny: (1) the size of platform shows a substrate dependence and (2) the peculiar geometrical features of platforms after sliding on glass substrates. Topographical images of microspheres (Figure 5) show that the platform is largest for glass, smaller for mica, and at a minimum for sapphire under comparable test conditions. Although sapphire is harder than glass and mica (Mohs’ hardness of 9 vs 6 and 2), the large platform for glass substrates can be confidently attributed to accelerated material removal caused by a water-mediated tribochemical reaction between silica and glass.46,47 Histograms for glass substrates, such as those shown in Figure 8c−e, indicate that not every platform falls on a leveled contour plane, instead being inclined to the horizontal plane a front rim or side rim is much higher than other parts of a platform. The cantilever with an attached microsphere is inclined at a certain angle against the substrate before and during sliding tests. The leading edge of the cantilever remains parallel to the substrate thanks to the vertical movement capability of the scanner used in this study. Different mounting positions of a microsphere on the cantilever induce different geometrical features of platforms. Figure 8a shows the process of platform formation where the microsphere is symmetrically mounted on the cantilever. The symmetrical axis of the microsphere can rotate only within the xz plane and perpendicular to the y axis during engagement and sliding. A platform is created by wear, and it is parallel to the xy plane during sliding. The formed platform is thus inclined against the horizontal plane. The front rim of the platform, viewed from the x axis, becomes the topographically highest region responsible for adhesion as shown in Figure 8c. Note that microspheres wear may occur upon initial engagement with a large set point because the loaded longitudinal displacement of the microsphere along the x axis causes microsphere sliding (and thus wearing) against the substrate, as demonstrated by Cannara et al.48 This contribution is certainly non-negligible but minor as a result of the short engagement interval in comparison with the much longer sliding test span. Figure 8b

shows the other case where the microsphere is misalignedly mounted on the cantilever. Now the symmetrical axis can rotate not only within the xz plane but also is inclined to the y axis. After disengagement, however, the formed platform is inclined against both the horizontal plane and the xz plane, and the adhesive area should be confined to the far left rim of the platform. Nevertheless, Figure 8d shows the adhesive region change from the front rim to the side rim for 90 and 120 min tests. Figure 8e shows the region located on the unexpected area of the platform. The discussions above deal with only a platform’s geometrical features; the actual topography may be complicated by asperities and contamination, to be discussed below. iii. Asperity Formation and Contamination. Asperities and particulate matter of as large as 200 nm in width and 5−10 nm in height are found on and around the platform, which is most noteworthy for tests on glass substrates (Figure 6g). We argue that these asperities and particulate matter originate from airborne contaminants and wear debris. This argument is tested by examining a mica substrate that was exposed to laboratory air for 180 min sliding tests. Figure S8 shows a few aggregates of as large as 450 nm accumulated along the borders of the sliding region. Smaller particles are scattered rather evenly over the outskirt area. Also shown is the particle size statistics of dust particles from four outskirt square regions (2 μm × 2 μm). Most particles are 20−50 nm in size. The above observation leads us to reason that air-borne particles will deposit on the surface of substrates during tests, though we did not examine sapphire and glass substrates after tests. Consequently, large aggregates along the borders very likely consist of smaller particles such as those in the outskirt area and wear debris. It is hard to discriminate between dust particles and wear debris, however. Because the size of these large aggregate is on the same scale as those found on the platform of worn microspheres, we thus believe that asperities and particulate matter on microspheres are wear debris and aggregated dust particles or even air-borne organic matter.49,50 Larger asperities and particulate matter on microspheres after tests on glass substrates can be explained by the larger amount of debris 3736

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For NI sliding tests, a microsphere slides continuously over the same area of the substrate for 120 min without any adhesion evaluation or topography examination until the end of the test. The structure of the layer of debris and particles formed during sliding is neither as uniform as that for the I1 mode without repeated compression nor reconstructed to be as loose and nonuniform as that for the I2 mode without repeated scrubbing by sharp spikes. With the size of the platform getting larger with sliding time, the actual contact area depends largely on the asperities’ topography on a particular microsphere, thus causing different changes in adhesive forces for three substrates, though adhesive forces are generally less than that of the I1 mode. C. Effect of Surface Roughness. Mica and sapphire substrates are atomically smooth, so it is reasonable to assume an ideal smooth and featureless surface. In contrast, glass substrates are much rougher, showing a typical nanoscale corrugated topography (Figure 4i). The capillary force model (eq 3) predicts a roughness effect for a corrugated substrate (i.e., a smaller adhesive force due to a reduced contact area, which is also what one intuitively perceives for this effect). To investigate if this indeed occurs for glass substrates, adhesive forces were measured immediately after each sliding round on the freshly cleaved mica substrates as control samples. A combined inspection of Figure 7c1,c2 reveals a very interesting finding: Fexp(mica) < Fexp(glass) for low forces (small contact area) and Fexp(mica) > Fexp(glass) for high forces (large contact area). In other words, it seems that the effect of surface roughness is the contact area sensitive. This can be qualitatively explained in terms of variations in contact geometry between corrugated glass substrates and microspheres when the contact area varies. We studied the statistics of the separation and size of surface asperities of the glass substrate available for capillary interaction (Figure S9). A bimodular distribution of separation between asperities is found with two peaks of 20 and 41 nm, indicating the discreteness of these eligible asperities. Treating the tip shape of each surface asperity as a spherical cap, we find a 210 nm mean radius of curvature for them. Consequently, because most asperities on a microsphere are small enough to dip between the asperities on the glass substrate, multiple water bridges may form between each asperity on the microsphere with the substrate, as illustrated in Figure 1c. In contrast, only a single water bridge forms between each asperity with the mica substrate, thus causing Fexp(mica) to be lower than Fexp(glass). Instead, if a few asperities on the microsphere are large enough to cover several asperities on the glass substrate, then the net capillary action is weaker on the glass substrate because of reduced contact area than on the smooth mica substrate, resulting in Fexp(mica) being greater than Fexp(glass). Nevertheless, in this regard, Fcal given in Figure 7, derived assuming a smooth and featureless surface, seems to average over two extreme situations discussed above. The discrepancy between Fcal and Fexp(glass) and Fexp(mica) may be due to errors associated with force calculations and other factors to be discussed below. However, the overlooked change in contact geometry caused by the deformation of asperities28 under high adhesive force deserves more attentions in the future. It is interesting to point out that the accelerated removal rate with glass or silica under ambient or liquid conditions47 may be exploited to prepare truncated microspheres with defined topography.

generated and the greater chance of this debris be snatched from the platform, which is on the micrometer scale in diameter. Changes in the locations of the topographically highest regions in Figure 8e can thus be attributed to the nonuniform accumulation of wear debris and contaminants on a certain part of the platform. This change may occur only when the effect of a slight misalignment of microspheres (Figure 8b) is amplified for large platforms. Consequently, the topographically highest region on microspheres, which are responsible for adhesion between microspheres and substrates, is determined both by the geometrical features of the platform (an inclined plane against the substrate) and asperities consisting of wear debris and contaminants on the platform. Insights into the formation of the platform and its geometrical/ topographic features help us to address the other two questions raised at the beginning of this section: (1) the sliding mode dependence of the adhesive forces for each substrate and (2) the quantitative difference between Fexp and Fcal values. B. Sliding Mode Dependence of Adhesive Forces. The variation of Fexp with sliding time is distinctly different for three sliding modes on each substrate as shown in Figure 7. For all I1 sliding tests, Fexp increases with time to a rather high value but at a lower increasing rate at prolonged time. No sliding time correlation is found for most I2 sliding tests. For NI tests, Fexp increases with time on mica and sapphire but decreases on glass substrates. The difference can be attributed to the evolution of a microsphere’s topographic features. For I1 sliding tests, after each sliding run for a specific time, a layer of wear debris and (single or aggregated) air-borne particles deposits on the platform area of a worn microsphere. This layer may be disrupted by high shearing stress so that fresh surface is exposed, but simultaneously new wear debris and airborne particles are picked up again. During the following adhesion evaluation on a new site, these debris and particles are more likely pressed hard against the microsphere to adhere more tightly rather than being dropped down or attracted to the substrate. A rather uniform and robust layer thus forms on the platform, as evidenced by sharp snap-in and the steep hard contact part of approaching force curves. (The exception for glass substrates will be discussed later.) With the size of platform increasing, the actual contact area increases with sliding time, thus leading to higher adhesive forces. For I2 sliding tests, after sliding for a specific time the probe was disengaged for force measurements on a new site, and then the topography of the microsphere was examined by scanning over the gratings in contact imaging mode. Although only the first good topography image was used for histogram analysis, two or three images were usually taken to allow the optimization of scanning parameters. Consecutive topographies of the same microsphere (Figure S7) indicate discernible blurring or the disappearance of features for tests on all substrates. Consequently, in each round of topography examination, some loosely attached wear debris and aggregates that accumulated in the former round may be mechanically pushed/scrubbed away by the sharp spikes of the gratings20 or relocated to a new location on the platform to expose fresh surface. Therefore, the layer of debris and particles may be artificially reconstructed after each round to be rather loose and nonuniform, giving rise to retarded snap-in and the compliant contact part of the approaching force curves, especially for sapphire and glass substrates. When the platform becomes larger with sliding time, the actual contact area fluctuates a lot, thus causing increases and decreases in adhesive forces. 3737

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D. Errors Associated with Contact Geometry Extraction and Force Calculations. The first type of error comes from the assumption that each asperity is approximated as a spherical cap. Although it is admittedly impossible to obtain the true shape of an asperity because of the finite resolution and the tip convolution effect, the spherical cap approximation is still widely used by many because of actual rounding of the sharp apex of asperities as well as feasible analytical treatments. Studies32 show that the difference in capillary force between a sphere, cone, or cylinder tip and a plate can be more than an order of magnitude, which is much larger than the difference observed between our experimental and modeling results. The second type of error is associated with the sampling and pixel resolution of the AFM instrument. Because the controller functions with three independent 16-bit DACs, the z-range sampling precision is thus 5000 nm/65 536 = 0.075 nm. A rough estimate shows that this may cause a maximum 30% error in the area determination over an area of 10 000 nm2. However, the lateral pixel resolution is ca. 10 nm for a 5 μm × 5 μm image (512 lines × 512 lines), thus leading to an area uncertainty of 100 nm2, equivalent to a force uncertainty of 15 nN. The third source of error is the distortion of topographic images due to an environmental disturbance such as vibration/ noise, the thermal drift of the scanner, and so forth. Unfortunately, the contact geometry extraction is vulnerable to these disturbances because histogram analyses requires nanometer-scale precision (M2 − M1 value in Figure 3). Images for histogram analyses are all raw ones without being subjected to flattening or bow removal modification because, unlike for flat samples, no routines are available to detect and compensate for these distortions perfectly in images with rich nanoscale features on a spherical background. The fourth source of error is the uncertainty in the contact angles. Contact angles are set to a unique value of 30° for capillary force calculations. Nevertheless, initial contact angles (less than 10°) of substrates and microspheres can change after prolonged exposure to laboratory air. Moreover, the contact angle of microspheres is unknown and can be as high as 30° as cited by Yang et al.29 and references therein. Although this treatment indeed causes errors in force calculations, this error is systematic so that the overall trends will not change. E. Difference between Experimental and Calculated Adhesive Forces. It has been found that Fexp and Fcal are frequently unequal or even quite different numerically. Besides various assumptions and errors associated with force calculations, there are other contributing factors. First, there is inequivalence in two types of contact geometries that determine Fexp and Fcal correspondingly: one type of contact geometry is actually not accessible when force curves are captured for Fexp determination. The other type is derived from the topography image so that the asperities’ topography is extracted to derive Fcal. The difference in the two types renders our comparison between Fexp and Fcal, which was based on the implicit assumption of two types contact geometry being identical, vulnerable to errors. Second, there is the destructive nature of the contact-mode reverse-imaging method: frankly speaking, the process of examining the topography of worn microspheres in contact mode cannot be claimed as nondestructive as discussed before. The actual weakly bonded asperities on the microspheres may be disrupted by the mechanical “scrubbing” action of spikes during the topography examination. Then the derived contact geometry is very likely

different from the actual geometry, thus giving rise to errors. In the future, semicontact or noncontact imaging modes may be tried to render damage-free imaging of worn microspheres. In this regard, the direct imaging method developed by Yang et al.28,29 through examining the topography of disengaged microspheres directly with a tapping-mode AFM probe has merits of higher resolution and less topography alteration but with the drawback of low efficiency.

VI. CONCLUSIONS (1) Sliding induced topography change of silica microspheres for colloidal probe applications (i.e., being truncated to form a platform due to the removal of materials), examined by the reverse-imaging technique, is great for glass, notable for mica, and moderate for sapphire substrates. Nanosized asperities on the platform originate from accumulated wear debris and contaminants under ambient conditions. (2) The theoretical capillary force and vdW force were calculated according to expressions derived analytically for a rigid corrugated/truncated sphere interacting with a featureless or corrugated plate. Capillary force dominates the adhesion. The variation in the relative humidity for each test was satisfactorily accounted for as a known input parameter into the models. Good qualitative correlation is thus found between calculated and experimental adhesive forces, revealing strong asperity-mediated adhesion. (3) The sliding-mode dependence of adhesive forces is explained on the basis of the structural evolution of the asperity layer on microspheres. The importance of the structure of the asperity layer and the destructive nature of the present contactmode reverse-imaging method are revealed. (4) The effect of surface roughness, especially for corrugated glass substrates, reflects a change in the asperity−asperity contact density for small and large asperities on microspheres. (5) In the future, more studies will be carried out on the effects of loading force, the deformation of asperities, and environmental factors such as media, humidity, temperature and contamination level, substrate roughness, relationships between asperity-mediated frictional forces and microsphere topography. The preparation of truncated colloidal probe microspheres with defined topography may be useful for adhesion, tribology, and indentation studies.

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ASSOCIATED CONTENT

S Supporting Information *

Derivations of vdW force expressions. Numerical values of adhesive forces. Histograms of microspheres. Experimental force curves. AFM images showing the topography change of microspheres. AFM images of wear debris and particles on mica substrates. Distribution and separation statistic of asperities for glass substrates. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was sponsored by the National Basic Research Program of China (973 Program) under grant nos. 3738

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2012CB934100 and 2011CB013200, the Natural Scientific Research Innovation Foundation in HIT (HIT.NSRIF.2009/ 20), the Specialized Research Fund for the Doctoral Program of Higher Education (20102302120035), and Interdisciplinary Basic Research of Science-Engineering-Medicine in HIT.

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