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Mechanics of Load−Drag−Unload Contact Cleaning of GeckoInspired Fibrillar Adhesives Uyiosa A. Abusomwan† and Metin Sitti*,†,‡ †

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, United States ‡ Max-Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany S Supporting Information *

ABSTRACT: Contact self-cleaning of gecko-inspired synthetic adhesives with mushroom-shaped tips has been demonstrated recently using load−drag−unload cleaning procedures similar to that of the natural animal. However, the underlying mechanics of contact cleaning has yet to be fully understood. In this work, we present a detailed experiment of contact self-cleaning that shows that rolling is the dominant mechanism of cleaning for spherical microparticle contaminants, during the load−drag−unload procedure. We also study the effect of dragging rate and normal load on the particle rolling friction. A model of spherical particle rolling on an elastomer fibrillar adhesive interface is developed and agrees well with the experimental results. This study takes us closer to determining design parameters for achieving self-cleaning fibrillar adhesives.

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we believe that either particle rolling or sliding at the fibrillar interface contributed to the cleaning performance, in which case the contaminants rolled or slid off from individual microfiber tips (for particles smaller than the spacing between adjacent microfiber tips) or from the entire microfiber array (for larger particles). In this paper, we present results from a detailed investigation of LDU-based cleaning of fibrillar adhesives and show that particle rolling is the dominant cleaning mechanism during the drag step. The LDU cleaning procedure was used to clean fibrillar adhesive samples contaminated with a single microparticle, and the corresponding force and visual data were analyzed. We studied the effects of normal load and the rate of lateral displacement on the rolling friction of the microparticle, and developed an analytical model that well represents the experimental results.

INTRODUCTION Despite the significant progress that has been made in the design and fabrication of gecko-inspired fibrillar adhesives and the demonstration of such adhesives in numerous areas of applications, such as in robotics,1−4 manufacturing,5 and biological devices,6 fibrillar adhesives are yet to be seen in practical real-world applications. One of the potential limitations to the use of fibrillar adhesives is the adverse effect of contaminants, which have been shown to reduce their adhesive strength and overall performance.5 Several studies of self-cleaning and antifouling of fibrillar adhesives have been conducted to tackle the contamination problem.7−15 Some initial studies of self-cleaning focused on the use of water droplets to remove contaminants from the fiber tips as a result of the hydrophobicity of the array, a process labeled as wet selfcleaning8,9,15 (similar to the popular lotus effect). Dynamic cleaning approaches have also been taken to tackle the contamination problem through the process of digital hyperextention14 and sample vibration.15 Recently, we demonstrated a traction based cleaning of fibrillar adhesives using a load−drag− unload (LDU) contact cleaning procedure similar to that demonstrated for the natural Gecko.10 The cleaning process implemented involved a cycle of loading, dragging, and unloading of a microfiber adhesive sample contaminated with microspheres, against a smooth rigid substrate. We showed that fibrillar adhesives could recover up to 100% of initially lost adhesion after a few steps, with over 95% of the cleaning taking place during the dragging step; however, the details of the underlying cleaning mechanism for the LDU procedure have not been fully understood. Similar to other investigators,11,12 © 2014 American Chemical Society

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EXPERIMENTAL SECTION

The cleaning experiments were performed with a custom-designed two-axis force measurement system. As shown in Figure 1, the system consists of automated linear actuated stages (MFA-CC and VP-25XA, Newport) for motion control, manual rotational stages (GON40-U, Newport) for angular alignment correction, and two load cells (GSO50 and GSO-10, Transducer Techniques) for normal and tangential force measurements, respectively. The experimental setup was mounted onto an inverted optical microscope (ECLIPSE TE200, Nikon), and a colored digital video camera (DFW-X710, Sony) was Received: June 14, 2014 Revised: August 11, 2014 Published: September 22, 2014 11913

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Figure 1. Images of the experimental system showing (a) the inverted microscope and (b) the experimental setup: (A) camera, (B) light source, (C) goniometer, (D) manual two-axis linear stage, (E) motorized y-axis linear stage, (F) motorized z-axis linear stage, (G) motorized x-axis linear stage, (H) vertical axis load cell, (I) horizontal axis load cell, (J) glass substrate, and (K) microscope objective. The contaminated sample (not shown) is mounted onto the horizontal axis load cell and brought into contact with the glass substrate during the experiment.

Figure 2. A schematic of an ideal case of contamination of a microfiber adhesive sample by spherical particles, showing the motion and corresponding displacements of an individual particle after a cleaning step with a drag distance of Δ. (a) Initial position of the particle before cleaning (note the markers on the fiber tip−marker spacing = Δ/2; green markers indicate starting position and red markers indicates final position). After dragging, (b) the particle remains in the same position relative to the fiber when sliding occurs only at the substrate interface, (c) the particle displacement is equal to the drag distance when sliding occurs only across the fiber tip, or (d) the particle displacement is equal to one-half the drag distance under pure rolling condition. Here, R is the particle radius, F is the respective friction force for the various motions, V is the drag speed, and ρ is the normalized particle displacement given by eq 1.

used to capture the visual data at a rate of 15 frames/s and to observe the contact area during the experiments. Custom software was used to control the system and to record the time-stamped visual and force data. A monochromatic light source (DC-950, Fiber-Lite) was channeled through the microscope onto the contact interface to get a view of the real contact area. Experiments were conducted using elastomer microfiber adhesive samples with mushroom-shaped tips.10,16−18 The samples were made from polyurethane elastomer (ST-1060, BJB Enterprises; Young’s modulus Ef = 2.9 MPa, Poisson’s ratio νf = 0.5) and fabricated using a previously published lithography and soft-molding technique.16 The microfibers were laid out in a square-packing pattern, with a center-tocenter spacing of 118 μm, microfibers tip diameter of 95 μm, microfiber stem diameter of 45 μm, microfiber height of 105 μm, mushroom tip angle of 45°, and an aspect ratio (fiber tip diameter to fiber height ratio) of 1.1. During the experiment, a clean glass substrate was brought into contact with the contaminated adhesive sample and preloaded to a desired normal load. Next, the glass substrate was dragged relative to the adhesive until a desired drag distance was reached. Finally, the substrate was pulled away from the adhesive. The samples were cut into 10 × 10 mm2 square patches and contaminated with a single fused silica microparticle (FSB Swiss Jewel Co.). A single 250 μm diameter particles was used in the experiment to study the cleaning mechanism for cases where the particles are larger than the microfiber tips (large contaminants regime) and for cases where the particles are smaller than the microfiber tips (small contaminants regime).10 In the latter case, a flat polyurethane elastomer sample was used. Using a 250 μm diameter particle allowed for observation of the particle motion type (rolling or sliding), in the video images. However, to study the effect of normal load and drag speed, we used a large 1 mm diameter fused silica particle due to the force resolution limit of the 10 g load cell in order to clearly capture the rolling friction values for a single particle, as well as to obtain a clear view of the contact area. Our use of spherical microparticles as contaminants makes the current work consistent with, and applicable to previous studies.7−15

three cases of particle motion are possible when the glass substrate is dragged: Case I: The particle slides across the substrate without moving relative to the fiber tips ⇒ ρ = 0 (Figure 2b); Case II: The particle slides across the fiber tips without moving relative to the substrate ⇒ ρ = 2 (Figure 2c); and Case III: The particle rolls with respect to both surfaces ⇒ ρ = 1 (Figure 2d). A combination of any two or all three cases is also possible when the critical forces required for each of the particle motions are similar. For example, the particle could roll with intermittent slipping across the fibrillar adhesive when the critical shear force for particle rolling is close to the critical shear force for particle sliding across the microfiber, in which case ρ will be slightly greater than 1. In logical terms, any one of the cases of particle motion (Figure 2b−d) is a suf f icient condition for obtaining ρ. However, the value of ρ in and of itself is not sufficient to know the particle motion. For example, under pure rolling motion, ρ is equal to 1, but ρ = 1 does not necessarily imply that the particle motion is pure rolling, as it could be the result of a combination of several particle motions. Thus, a visual inspection is also necessary to ascertain the particle motion. Figure 3 shows a graph of the normalized displacement measured at various normal loads for a 250 μm diameter particle positioned between a microfiber array and a glass substrate. In the experiment, the substrate was displaced for 3 mm at a speed of 20 μm/s. From the graph, it is observed that ρ is approximately equal to 1 for all loads, which suggests that rolling dominates the cleaning process. Analysis of the videos recorded during the experiments confirmed that particle rolling is the dominant cleaning mechanism (see Videos S01 and S02

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RESULTS AND DISCUSSION Evidence of Particle Rolling. Let us define the normalized particle displacement, ρ, as ρ = 2δ /Δ

(1)

where δ is the particle displacement relative to the adhesive and Δ is the drag distance applied to the substrate. Evidently, ρ is also a measure of the cleaning performance. Larger values of ρ indicate large particle displacement relative to the adhesive after each cleaning step, which results in better cleaning performance. For a spherical particle sandwiched between a glass substrate and a fibrillar adhesive sample, as shown in Figure 2a, 11914

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contaminated with multiple particles (results of a preliminary study with three contaminant particles can be found in Video S03 and Figure S04 in the Supporting Information). Effect of Dragging Rate and Normal Load on Particle Rolling Friction. The effect of drag rate and normal load on particle rolling was studied by measuring the rolling friction during the LDU process. During the experiment, it was important that the microfibers were not in direct contact with the substrate, so that the measured tangential force was solely due to the friction at the particle−fiber and particle−substrate interfaces. The use of a 1 mm diameter particle also helped to eliminate such loading scenario. A sample plot of the normal (line AKLMG in black) and tangential (line ABCDEFG in red) forces measured during a single cleaning experiment is shown in Figure 4. Line AB is the cross-talk on the tangential force

Figure 3. Graphs of the normalized particle displacement measured at various normal loads for a 250 μm diameter particle sandwiched between a microfiber array and a substrate and dragged at a speed of 20 μm/s. (a) The normalized displacement is approximately equal to 1 at all normal loads less than 50 mN, which suggests that particle rolling dominates the cleaning process. Analysis of the videos recorded during the experiments confirmed that particle rolling was the dominant cleaning mechanism (particle rolling can be seen in the Videos S01 and S02 of the Supporting Information). Each data point represents the mean and one standard deviation obtained from two experiments (error bars smaller than the marker size are not visible). (b) Graph showing a decreasing normalized displacement as the normal load is increased. The decreasing performance is due to the increasing occurrence of particle sliding at the substrate interface. Here, ρ is the normalized particle displacement given by eq 1.

Figure 4. (Top) Graph of the normal and tangential forces measured during a single cleaning experiment with a 1 mm diameter silica microparticle rolling across a flat polyurethane adhesive sample, for an applied normal load of 120 mN and a drag speed of 10 μm/s. Line AKLMG (black line) is the measured normal force, while line ABCDEFG (red line) is the measured tangential force. During the experiment, the contaminated sample was pressed against a smooth and flat glass slide until a preload of 120 mN was reached (line AK). A contact time of 10 s was observed before the substrate was dragged horizontally, while the indentation was kept constant (line LM). After a drag distance of 3 mm, the sample was pulled from the glass substrate (line MG). The cross-talk on the measured tangential force due to the normal load is recorded as the average of line BC and subtracted from the rest of the tangential force data to obtain the actual rolling friction. (Bottom) The increasing rolling friction observed at the initial phase of rolling is attributed to the growth of the contact area at the onset of rolling.

in the Supporting Information). At very small normal loads of less than 10 mN, ρ is slightly greater than 1, as can be seen in Figure 3a. This suggests that there was some sliding at the microfiber interface, although rolling occurred most of the time. At large normal loads greater than 50 mN, ρ becomes less than 1 and decreases with increasing normal load, as shown in Figure 3b. This result indicates the occurrence of sliding at the substrate interface. At higher normal loads, the particle significantly indents the fiber array (or fiber tip for the small contaminants regime), which begins to act as an obstacle, so that and sliding at the substrate (case I) becomes the dominant particle motion, and cleaning is inhibited. Also, the observed dependence of ρ on the normal load is intuitive since friction in this case is a function of both the applied load and contact area. By increasing the normal load, the contact area at the adhesive interface increased significantly (for soft polyurethane) compared to the contact area at the substrate interface (for hard glass). This leads to a significantly higher friction resistance at the adhesive interface so that sliding occurs along the substrate. The results lead us to conclude that a low normal load is favorable for the LDU cleaning procedure. Although a single particle was used in the analysis above, the result obtained is also applicable for the case of a sample

sensor during normal loading. The average tangential force measured at the end of the loading step (B, C) is subtracted from the tangential force measured during the dragging step (C−F) to obtain the actual rolling friction without the crosstalk. Analysis of the rolling friction curve reveals two distinct regions. The first is observed at the onset of rolling (C−E) during which the rolling friction (or rolling resistance) increases gradually until it saturates. In the second region (E, F), the rolling friction remains constant for the remaining drag time. The increase in rolling friction in the first region is believed to be the result of an increasing contact area at the onset of rolling (see contact area insets in Figure 4). Rolling friction curves for various drag speeds ranging from 10 to 500 μm/s at a constant normal load of 100 mN are shown in Figure 5a. At low drag speeds, the rolling friction increased gradually until it reached a steady-state value. 11915

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where ξ is the critical rolling displacement before a readjustment of the contact zone (or irreversible rolling occurs), and is a fraction of the contact radius,22,23 W is the work of adhesion of the interface, and R is the effective radius of the particles given as R = [(1/R1) + (1/R2)]−1, where R1 and R2 are the radii of the contacting particles. In the present study, the particle is in contact with two surfaces, so the total rolling resistance moment can be obtained as the sum of the resistances from the individual surfaces and given as M T = 6πR(Wpf ξpf + Wpsξps)

(3)

where the subscripts “ps” and “pf” refer to the particle−fiber and particle−substrate interfaces, respectively, and R is the radius of the particle. By assuming a conservative value of ξ equal to the contact radius and calculating the work of adhesion and contact radii at both interfaces, we observed that Wpfξpf for the soft polyurethane interface was over an order of magnitude greater than Wpsξps for a rigid glass interface. Thus, for simplicity, we can neglect the contribution of the substrate from eq 3, so the critical rolling friction force (Fc) can be obtained, after substituting MT = 2FcR from the static equilibrium, as

Fc = 3πWpf ξpf

Although eq 4 does not show a direct dependence on the drag speed, the work of adhesion is known to be dependent on crack propagation speed through a power law relationship12 of the form

Figure 5. Graphs showing the dependence of rolling friction on the drag speed and normal load for a 1 mm diameter particle. (a) Rolling friction plotted against drag distance for various drag speed at a constant normal load of 100 mN shows an increasing steady-state rolling friction as the drag speed was increased. An initial peak rolling friction with overshoots of up to 160% of the steady state value was observed for drag speeds greater than 50 μm/s. (b) Graph of rolling friction plotted against drag distance for various normal loads and at a constant drag speed of 10 μm/s shows an increasing steady-state rolling friction as the normal load was increased.

⎡ ⎛ ν ⎞n ⎤ ⎢ W = G0 1 + ⎜ ⎟ ⎥ ⎢⎣ ⎝ ν0 ⎠ ⎥⎦

(5)

Here, ν is the crack propagation speed, which is equal to the particle displacement speed (or one-half of the drag speed for pure rolling motion); G0 is the work of adhesion as ν approaches zero; ν0 is the crack propagation speed at which G0 is doubled; and n is a fitting parameter. We expect ξ to be dependent on normal load and nonzero when the normal load is zero. We propose ξpf as a function of the normal load Fz in the form

However, for higher drag speeds, the rolling friction increased past the steady-state value to an initial peak value before decreasing to a steady-state rolling friction. The peak of this overshoot was also observed to increase as the drag speed increased and rose up to 160% of the steady-state rolling friction for a drag speed of 500 μm/s. Finally, the average steady-state rolling friction increased as the drag speed was increased. The steady-state rolling friction is believed to be due to an increase in the work of adhesion, which is known to be a function of the crack propagation speed,19,20 and further discussed later in this paper. The observed overshoot is believed to be a result of the enhanced adhesion at the initial contact area before the onset of rolling (a relaxation phenomenon), in addition to the rate effect on the work of adhesion mentioned above. Rolling friction curves from cleaning experiments at a 10 μm/s drag speed, under various normal loads (10−150 mN), are shown in Figure 5b. The curves had a similar trend for different loads but reached a higher steady-state rolling friction as the normal load was increased. The observed increase in the rolling friction with normal load can be attributed to the increase in contact area at higher normal load. Using the Johnson−Kendall−Roberts (JKR) theory, Dominik and Tielens21 previously derived the rolling resistance moment M at the interface of two contacting microparticles in the presence of adhesive interactions, assuming pure rolling, as

M = 6πRWξ

(4)

ξpf = ξ0 + CFz

(6)

such that ξpf = ξ0 when Fz is zero and increases linearly with Fz by a compliance parameter C (m/N).24 We anticipate that ξ0 is a function of the particle size and will increase for larger particles;22,23 C, on the other hand, will depend on the effective modulus of the contact interface and the contact radius. By substituting eqs 5 and 6 into eq 4, we obtain the equation for the rolling friction force as a function of both the normal load and drag speed as 21,22

Fc = 3πG0(ξ0 + CFz)[1 + (v /ν0)n ]

(7)

A graph of the average steady-state rolling friction plotted against Fz for a 5 μm/s rolling speed is shown in Figure 6a. The graph shows a linear relationship between rolling friction and normal load. The experimental data was fitted to eqs 4 and 6 to obtain ξ0 = 0.4 ± 11 μm and C = 1.85 ± 0.13 μm/mN, where Wpf = 140 mJ/m2 for a polyurethane-fused silica interface. Due to the relatively high load values we investigated, the value of ξ0 given here is statistically insignificant, and experiments at very small normal load and with a high-resolution force sensor will be required to obtain a more accurate value.22,23 By fitting the theoretical model in eq 7 to the experimental results in Figure

(2) 11916

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spherical contaminants. This work takes us closer to obtaining design parameters that can be implemented in order to achieve self-cleaning fibrillar adhesives for robust real-world applications. Although our use of spherical silica microparticles as idealized contaminants in this work is consistent with previous studies, future efforts in this topic will incorporate contaminants of various geometries and materials.

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ASSOCIATED CONTENT

S Supporting Information *

Video S01, showing a 250 μm radius particle rolling between a flat elastomer and a glass substrate; Video S02, showing a 250 μm radius particle rolling between a fibrillar elastomer and a glass substrate; Video S03, showing the LDU experiment with three particles simultaneously rolling between a fibrillar elastomer and a glass substrate; and Figure S04, a graph of the normalized displacement of the particles shown in video S03, where the error bars represents one standard deviation of the mean of four data points. 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.

Figure 6. Experimental and theoretical results from eq 7 of the dependence of rolling friction on both normal load and drag speed. (a) Graph of rolling friction as a function of normal load for a 5 μm/s rolling speed. Each data point represents the average steady-state rolling friction for a single experiment. The dashed line is a fitted line from eqs 4 and 6, where ξ0 = 0.38 μm and C = 1.9 μm/mN are obtained after fitting to the empirical data. (b) Experimental results of the average steady-state rolling friction measured at various drag speeds and for normal loads of 20, 50, and 100 mN. The theoretical results (dashed line) were obtained from eq 7 and agree well with the experimental results at various loads and drag speed values where n = 0.63, G0 = 140 mJ/m2, and ν0 = 104.4 μm/s.

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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation Grant No. CMMI-1130520. U.A. was funded by the National Science Foundation Graduate Research Fellowship under Grant No. 0946825. We thank Soohyun (Soo) Park for her help during the experiments.

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REFERENCES

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5a, we obtained n = 0.63, where G0 = 140 mJ/m2 and ν0 = 104.4 μm/s. Experimental results of the average steady-state rolling friction measured at various drag speeds are shown in Figure 6b for normal loads of 20, 50, and 100 mN. For each normal load, the theoretical rolling friction obtained from eq 7 using the parameter values listed above was also plotted and fits well with the experimental data. It is important to note that although the theoretical plots were obtained from fitted parameters n and C, those parameters were obtained from a single loading case (100 mN) but they agree well with experimental results at differing loads and drag speeds.

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CONCLUSIONS By studying the mechanics of cleaning using a single contaminating particle, we have shown that particle rolling is the underlying cleaning mechanism for contact cleaning of microfiber adhesives with spherical contaminants using the load−drag−unload procedure. The experimental and model results suggest that rolling friction is strongly dependent on the applied normal load and the drag rate. Increasing the applied normal load or the drag rate leads to an increase in the rolling resistance, resulting in a reduction in the cleaning performance. On the basis of this analysis, we suggest that low normal load and low drag rates are more favorable for contact cleaning of 11917

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(10) Mengüc,̧ Y.; Röhrig, M.; Abusomwan, U.; Holscher, H.; Sitti, M. Staying Sticky: Contact Self-Cleaning of Gecko-Inspired Adhesives. J. R. Soc. Interface 2014, 11, 20131205. (11) Hui, C.; Shen, L.; Jagota, A.; Autumn, K.Mechanics of AntiFouling or Self-Cleaning in Gecko Setae. Proceedings of the 29th Annual Meeting of the Adhesion Society; Adhesion Society: Bethesda, MD, 2006; pp 29−31 (12) Gillies, A. G.; Puthoff, J.; Cohen, M. J.; Autumn, K.; Fearing, R. S. Dry Self-Cleaning Properties of Hard and Soft Fibrillar Structures. ACS Appl. Mater. Interfaces 2013, 5, 6081−6088. (13) Lee, J.; Fearing, R. S. Contact Self-Cleaning of Synthetic Gecko Adhesive from Polymer Microfibers. Langmuir 2008, 24, 10587− 10591. (14) Hu, S.; Lopez, S.; Niewiarowski, P. H.; Xia, Z. Dynamic SelfCleaning in Gecko Setae via Digital Hyperextension. J. R. Soc. Interface 2012, 9, 2781−2790. (15) Sethi, S.; Ge, L.; Ci, L.; Ajayan, P. M.; Dhinojwala, A. GeckoInspired Carbon Nanotube-Based Self-Cleaning Adhesives. Nano Lett. 2008, 8, 822−825. (16) Aksak, B.; Murphy, M. P.; Sitti, M. Adhesion of Biologically Inspired Vertical and Angled Polymer Microfiber Arrays. Langmuir 2007, 23, 3322−3332. (17) Gorb, S.; Varenberg, M. Mushroom-Shaped Geometry of Contact Elements in Biological Adhesive Systems. J. Adhes. Sci. Technol. 2007, 21, 1175−1183. (18) Cheung, E.; Sitti, M. Adhesion of Biologically Inspired Polymer Microfibers on Soft Surfaces. Langmuir 2009, 25, 6613−6616. (19) Shull, K. Contact Mechanics and the Adhesion of Soft Solids. Mater. Sci. Eng., R 2002, 36, 1−45. (20) Abusomwan, U.; Sitti, M. Effect of Retraction Speed on Adhesion of Elastomer Fibrillar Structures. Appl. Phys. Lett. 2012, 101, 211907. (21) Dominik, C.; Tielens, A. Resistance to Rolling in the Adhesive Contact of Two Elastic Spheres. Philos. Mag. A 1995, 72, 783−803. (22) Heim, L.; Blum, J.; Preuss, M.; Butt, H. Adhesion and Friction Forces between Spherical Micrometer-Sized Particles. Phys. Rev. Lett. 1999, 83, 3328−3331. (23) Blum, J. Experiments on Sticking, Restructuring, and Fragmentation of Preplanetary Dust Aggregates. Icarus 2000, 143, 138−146. (24) Minshall, H.; Greenwood, J. A.; Tabor, D. Hysteresis Losses in Rolling and Sliding Friction. Proc. R. Soc. London, Ser. A 1961, 259, 480−507.

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