pubs.acs.org/Langmuir © 2009 American Chemical Society
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Frictional Adhesion of Patterned Surfaces and Implications for Gecko and Biomimetic Systems Hongbo Zeng,† Noshir Pesika,‡ Yu Tian,†, Boxin Zhao,†,§ Yunfei Chen,† Matthew Tirrell,† Kimberly L. Turner,^ and Jacob N. Israelachvili*,† †
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Department of Chemical Engineering, Materials Department, and Materials Research Laboratory, University of California, Santa Barbara, California 93106, ‡Chemical & Biomolecular Engineering Department, Tulane University, New Orleans, Louisiana 70118, §Chemical Engineering Department, University of Waterloo, Ontario, Canada N2L 3G1, State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China, and ^Mechanical Engineering Department, University of California, Santa Barbara, California 93106 Received July 25, 2008. Revised Manuscript Received May 19, 2009
Geckos and smaller animals such as flies, beetles, and spiders have extraordinary climbing abilities: They can firmly attach and rapidly detach from almost any kind of surface. In the case of geckos, this ability is attributed to the surface topography of their attachment pads, which are covered with fine columnar structures (setae). Inspired by this biological system, various kinds of regularly structured or “patterned” surfaces are being fabricated for use as responsive adhesives or in robotic systems. In this study, we theoretically analyze the correlated adhesion and friction (frictional adhesion) of patterned surfaces against smooth (unstructured) surfaces by applying well-established theories of van der Waals forces, together with the classic Johnson-Kendall-Roberts (JKR) theory of contact (or adhesion) mechanics, to recent theories of adhesion-controlled friction. Our results, when considered with recent experiments, suggest criteria for simultaneously optimizing the adhesion and friction of patterned surfaces. We show that both the van der Waals adhesion and the friction forces of flexible, tilted, and optimally spaced setal stalks or (synthetic) pillars are high enough to support not only a large gecko on rough surfaces of ceilings (adhesion) and walls (friction) but also a human being if the foot or toe pads;effectively the area of the hands;have a total area estimated at ∼230 cm2.
1. Introduction Geckos and many insects such as flies, beetles, and spiders have extraordinary climbing abilities: They can firmly attach and easily detach from almost any kind of surface. In the case of small insects and flies, capillary forces have been shown to be responsible for their adhesion. In the case of larger animals such as geckos, the high adhesion and friction have been attributed to van der Waals forces coupled to the complex surface topography of their toes, which are covered with fine regular structures (setae and spatulae) with characteristic dimensions and geometries. The *To whom correspondence should be addressed. E-mail: jacob@engineering. ucsb.edu. (1) Arzt, E.; Gorb, S.; Spolenak, R. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 10603–10606. (2) Autumn, K. Am. Sci. 2006, 94, 124–132. (3) Autumn, K. Mrs Bull. 2007, 32, 473–478. (4) Autumn, K.; Dittmore, A.; Santos, D.; Spenko, M.; Cutkosky, M. J. Exp. Biol. 2006, 209, 3569–3579. (5) Autumn, K.; Liang, Y. A.; Hsieh, S. T.; Zesch, W.; Chan, W. P.; Kenny, T. W.; Fearing, R.; Full, R. J. Nature 2000, 405, 681–685. (6) Autumn, K.; Majidi, C.; Groff, R. E.; Dittmore, A.; Fearing, R. J. Exp. Biol. 2006, 209, 3558–3568. (7) Autumn, K.; Sitti, M.; Liang, Y. C. A.; Peattie, A. M.; Hansen, W. R.; Sponberg, S.; Kenny, T. W.; Fearing, R.; Israelachvili, J. N.; Full, R. J. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12252–12256. (8) Chan, E. P.; Greiner, C.; Arzt, E.; Crosby, A. J. Mrs Bull. 2007, 32, 496–503. (9) del Campo, A.; Greiner, C.; Alvarez, I.; Arzt, E. Adv. Mater. 2007, 19, 1973. (10) del Campo, A.; Greiner, C.; Arzt, E. Langmuir 2007, 23, 10235–10243. (11) Duncan, R. P.; Autumn, K.; Binford, G. J. Proc. R. Soc. B 2007, 274, 3049– 3056. (12) Gao, H. J.; Wang, X.; Yao, H. M.; Gorb, S.; Arzt, E. Mech. Mater. 2005, 37, 275–285. (13) Greiner, C.; del Campo, A.; Arzt, E. Langmuir 2007, 23, 3495–3502. (14) Huber, G.; Gorb, S. N.; Hosoda, N.; Spolenak, R.; Arzt, E. Acta Biomater. 2007, 3, 607–610. (15) Huber, G.; Mantz, H.; Spolenak, R.; Mecke, K.; Jacobs, K.; Gorb, S. N.; Arzt, E. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 16293–16296.
7486 DOI: 10.1021/la900877h
bioadhesion of these systems has received a lot of experimental and theoretical attention recently,1-38 especially the adhesion of geckos,1-37 which are the largest animals able to run on walls and ceilings.39 (16) Majidi, C. S.; Groff, R. E.; Fearing, R. S. J. Appl. Phys. 2005, 98, 10351. (17) Northen, M. T.; Turner, K. L. Nanotechnology 2005, 16, 1159–1166. (18) Northen, M. T.; Turner, K. L. Sens. Actuators, A 2006, 130, 583–587. (19) Northen, M. T.; Turner, K. L. Curr. Appl. Phys. 2006, 6, 379–383. (20) Persson, B. N. J. J. Chem. Phys. 2003, 118, 7614–7621. (21) Persson, B. N. J. J. Adhes. Sci. Technol. 2007, 21, 1145–1173. (22) Persson, B. N. J. Mrs Bull. 2007, 32, 486–490. (23) Persson, B. N. J.; Albohr, O.; Tartaglino, U.; Volokitin, A. I.; Tosatti, E. J. Phys.: Condens. Matter 2005, 17, R1–R62. (24) Persson, B. N. J.; Gorb, S. J. Chem. Phys. 2003, 119, 11437–11444. (25) Pesika, N. S.; Tian, Y.; Zhao, B. X.; Rosenberg, K.; Zeng, H. B.; McGuiggan, P.; Autumn, K.; Israelachvili, J. N. J. Adhes. 2007, 83, 383–401. (26) Reddy, S.; Arzt, E.; del Campo, A. Adv. Mater. 2007, 19, 3833. (27) Schubert, B.; Majidi, C.; Groff, R. E.; Baek, S.; Bush, B.; Maboudian, R.; Fearing, R. S. J. Adhes. Sci. Technol. 2007, 21, 1297–1315. (28) Spolenak, R.; Gorb, S.; Gao, H. J.; Arzt, E. Proc. R. Soc. London Ser. A; Math. Phys. Eng. Sci. 2005, 461, 305–319. (29) Tian, Y.; Pesika, N.; Zeng, H. B.; Rosenberg, K.; Zhao, B. X.; McGuiggan, P.; Autumn, K.; Israelachvili, J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19320– 19325. (30) Bhushan, B.; Peressadko, A. G.; Kim, T. W. J. Adhes. Sci. Technol. 2006, 20, 1475–1491. (31) Kim, T. W.; Bhushan, B. J. Adhes. Sci. Technol. 2007, 21, 1–20. (32) Lamblet, M.; Verneuil, E.; Vilmin, T.; Buguin, A.; Silberzan, P.; Leger, L. Langmuir 2007, 23, 6966–6974. (33) Majidi, C.; Groff, R. E.; Maeno, Y.; Schubert, B.; Baek, S.; Bush, B.; Maboudian, R.; Gravish, N.; Wilkinson, M.; Autumn, K.; Fearing, R. S. Phys. Rev. Lett. 2006, 97, 076103. (34) Kim, T. W.; Bhushan, B. J. R. Soc. Interface 2008, 5, 319–327. (35) Nosonovsky, M.; Bhushan, B. Mater. Sci. Eng., R 2007, 58, 162–193. (36) Creton, C.; Gorb, S. Mrs Bull. 2007, 32, 466–472. (37) Kustandi, T. S.; Samper, V. D.; Yi, D. K.; Ng, W. S.; Neuzil, P.; Sun, W. X. Adv. Funct. Mater. 2007, 17, 2211–2218. (38) Nosonovsky, M.; Bhushan, B. Adv. Funct. Mater. 2008, 18, 843–855. (39) Autumn, K.; Hsieh, S. T.; Dudek, D. M.; Chen, J.; Chitaphan, C.; Full, R. J. J. Exp. Biol. 2006, 209, 260–272.
Published on Web 06/12/2009
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Figure 1. SEM images of surface structures on real and synthetic attachment pads. (A) Beetle, (B) fly, (C) spider, and (D) gecko, (adopted from ref 1). (a-f) SEM images of typical fabricated patterned surfaces (adopted from ref 9). The adhesive pads are circled. In geckos, these are referred to as spatulae and are attached at the ends of the setae.
Although the adhesion mechanisms of the these animals at the micro- and nanoscales are not completely understood, it has been shown that the ever-present van der Waals forces can be enhanced by capillary forces, either due to capillary condensation from vapor or to natural secretions as occurs with flies. In the case of geckos in dry environments, the van der Waals forces between the finely structured toe pads and contacting surfaces dominate the adhesion (and friction) forces.7,15,21,22,28 However, regardless of the origin of the molecular forces, the proper functioning of the “system” depends on the coordinated movement of the feet and the fine structures on their toe pads. Figure 1A-D shows scanning electron microscope (SEM) images of these structures on the attachment pads of a beetle, fly, spider, and gecko. Inspired by the above biological systems, various kinds of patterned surfaces with large numbers of regular micro- to nanoscale structures, including cylindrical or conical pillars (columns or posts) with flat, spherical, toroidal, or concave ends, have been designed and fabricated (Figure 1) aimed at enhancing adhesion properties.9,10,13,26,27,40-42 Recently, the “frictional adhesion” of the attachment and detachment of gecko setal arrays was measured4,43 and theoretically analyzed,22,25,29 showing that the adhesion and friction forces of gecko toes are correlated and that both are used by the animal when it moves but in very different ways when it attaches and detaches. (40) Kim, S.; Aksak, B.; Sitti, M. Appl. Phys. Lett. 2007, 91, 221913. (41) Kim, S.; Sitti, M. Appl. Phys. Lett. 2006, 89, 261911. (42) Aksak, B.; Sitti, M.; Cassell, A.; Li, J.; Meyyappan, M.; Callen, P. Appl. Phys. Lett. 2007, 91, 061906. (43) Zhao, B. X.; Pesika, N.; Rosenberg, K.; Tian, Y.; Zeng, H. B.; McGuiggan, P.; Autumn, K.; Israelachvili, J. Langmuir 2008, 24, 1517–1524.
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Although various theoretical contact models have been established for the adhesion of bioinspired patterned surfaces,1,8,12,29,44-50 to our knowledge, there have been no systematic experimental studies or quantitative theoretical analyses (modeling) of the combined actions of adhesion and friction forces, which appear to be essential for producing responsive adhesives and especially interactive/articulated robotic systems. In this study, we theoretically analyze the adhesion and friction of an elastic patterned surface interacting with a rigid smooth substrate, mainly based on the classic Johnson-Kendall-Roberts (JKR) theory and the theory of van der Waals forces between surfaces. In the analysis, we have ignored any possible nonplanarity of the rigid base substrate supporting the pillars. The cracking or “peeling away” of the pillars from the boundary could occur when they detach, which has been analyzed in a previous work29 and is not considered here. The computed adhesion and friction forces are an upper bound.
2. Theoretical Background and Contact Geometry Experimental and theoretical work on the “contact mechanics” of surfaces has steadily progressed for more than 100 years, (44) Hui, C. Y.; Jagota, A. J.; Shen, L. L.; Rajan, A.; Glassmaker, N.; Tang, T. J. Adhes. Sci. Technol. 2007, 21, 1259–1280. (45) Jagota, A.; Hui, C. Y.; Glassmaker, N. J.; Tang, T. Mrs Bull. 2007, 32, 492– 495. (46) Lee, J.; Fearing, R. S. Langmuir 2008, 24, 10587–10591. (47) Lee, J. H.; Fearing, R. S.; Komvopoulos, K. Appl. Phys. Lett. 2008, 93, 191910. (48) Schubert, B.; Lee, J.; Majidi, C.; Fearing, R. S. J. R. Soc. Interface 2008, 5, 845–853. (49) Chen, B.; Wu, P. D.; Gao, H. J. R. Soc. Interface 2008, 6, 529–537. (50) Liu, J. Z.; Hui, C. Y.; Shen, L. L.; Jagota, A. J. R. Soc. Interface 2008, 5, 1087–1097.
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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r L þ 3πrW12 þ 6πrLW12 þ ð3πrW12 Þ2 K r pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ¼ 2L þ 3πrW12 þ 3πrW12 2K
a3 ¼
ð1Þ
The adhesion force (or maximum “pull-off” force) is given by (we omit the negative sign before the adhesion energy W, which is negative) 3 Fad ¼ πrW12 2
F ¼ μL þ Sc Areal
ð3Þ
where the first term is Amontons’ law for nonadhering surfaces in terms of the friction coefficient μ and Sc ≈εΔγ=δ
ð4Þ
is the shear strength, which depends on the adhesion energy hysteresis Δγ, the characteristic asperity or effective molecular bond length δ over which sliding must occur for the bonds of the two interacting surfaces to be broken, and the factor ε (εr>D0 or σ. The above equations show that the JKR/DMT theories can be used down to molecular dimensions (r f σ, N f R2/σ2), giving the correct theoretical values for the adhesion forces (or pressures) in these limits.51,68,69 The following plots illustrate some of the important and sometimes unexpected features of the above analysis. First, we note from eq 6 that the same total adhesion force can arise for quite different values of N and r, so long as Nr is constant. (68) Landman, U.; Luedtke, W. D.; Burnham, N. A.; Colton, R. J. Science 1990, 248, 454–461. (69) Landman, U.; Luedtke, W. D. J. Vac. Sci. Technol., B 1991, 9, 414–423.
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Figure 4. Total contact area vs pillar radius r for different values of pillar number N at zero external load.
However, the real contact area Areal does not remain constant when Nr is constant (eq 7), which is important for relating the adhesion to the friction forces, discussed later. The area vs load relationships for two different types of relationships between N and r for a gecko toe pad of constant base radius R=1 mm are shown in Figure 3. Figure 4 shows the variation of the total contact area Areal with the pillar radius r for fixed N at zero external load, again a useful plot for determining the friction forces (later). The displacement of the center of the elastic sphere d arises from both the applied load (as in the nonadhesive Hertzian case) and the adhesion energy, W12. The displacement can be expressed in a variety of ways, including pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð11Þ d ¼ a2 =r - 8πW12 a=3K where a is given by eq 1. Recent SFA force-distance measurements show that for randomly rough surfaces the repulsive force increases exponentially as the mean surface separation decreases.70 For patterned surfaces with a geometry as in Figure 2a, the relationship between the total normal load NL and the displacements d for the two cases of r=R/N and r ¼R=2ðNÞ1=2 (see Figure 3a,b) is given in Figure 5a,b, respectively. Our results suggest that there is no simple scaling (such as an exponential) relationship between NL and d for these types of patterned surfaces. Pillars with Flat Ends (Geometry of Figure 2b). Within the limits set by eqs 5a and 5b, r and N can vary independently, and for θ = 90, eq 5c gives r
