Kellar Autumn The Gecko Adhesive System 1 of 39

Properties, Principles, and Parameters of the Gecko

Adhesive System

Kellar AutumnDepartment of BiologyLewis & Clark College

Portland, OR 97219-7899autumn@lclark.edu

10156 words + 130 references.6 figures, 2 tables.

“The designers of the future will have smarter adhesives that do considerablymore than just stick” –Fakley 2001

1. SummaryGecko toe pads are sticky because they feature an extraordinary hierarchy of structurethat functions as a smart adhesive. Gecko toe pads (Russell 1975) operate under perhapsthe most severe conditions of any adhesives application. Geckos are capable of attachingand detaching their adhesive toes in milliseconds (Autumn et al. 2005 (in press)) whilerunning with seeming reckless abandon on vertical and inverted surfaces, a challenge noconventional adhesive is capable of meeting. Structurally, the adhesive on gecko toesdiffers dramatically from that of conventional adhesives. Conventional pressure sensitiveadhesives (PSAs) such as those used in adhesive tapes are fabricated from materials thatare sufficiently soft and sticky to flow and make intimate and continuous surface contact(Pocius 2002). Because they are soft and sticky, PSAs also tend to degrade, foul, self-adhere, and attach accidentally to inappropriate surfaces. Gecko toes typically bear aseries of scansors covered with uniform microarrays of hair-like setae formed from !-keratin (Russell 1986; Wainwright et al. 1982), a material orders of magnitude stifferthan those used to fabricate PSAs. Each seta branches to form a nanoarray of hundreds ofspatular structures that make intimate contact with the surface.

Functionally, the properties of gecko setae are as extraordinary as their structure: thegecko adhesive is 1) directional, 2) attaches strongly with minimal preload, 3) detachesquickly and easily (Autumn and Peattie 2002; Autumn et al. 2000), 4) sticks to nearlyevery material, 5) does not stay dirty (Hansen and Autumn 2005) or 6) self-adhere, and 7)is nonsticky by default. While some of the principles underlying these seven functional

Preprint: Autumn, K. 2006. Properties, principles, and parameters of the gecko adhesive system. In Smith, A. and J. Callow, Biological Adhesives. Springer Verlag.��Do not copy or distribute without permission of the author (autumn@lclark.edu). Copyright (c) 2005 Kellar Autumn.

Kellar Autumn The Gecko Adhesive System 8 of 39

properties are now well understood, much more research will be necessary to fully mapout the parameters of this complex system.

2. Introduction

Over two millennia ago, Aristotle commented on the ability of the gecko to =run up anddown a tree in any way, even with the head downwards> (Aristotle @Thompson 1918).How geckos adhere has attracted substantial and sustained scientific scrutiny (Arzt et al.200J; Autumn and Peattie 2002; Autumn et al. 2000; Autumn et al. 2002b; Martier1872b; Oellit 19J4; Gadow 1901; Gennaro 1969; Hansen and Autumn 2005; Hiller 1968;Hiller 1969; Hiller 1975; Hora 192J; Huber et al. 2004; Irschick et al. 1996; Maderson1964; Mahendra 1941; Ruibal and Ernst 1965; Russell 1975; Russell 1986; Schleich andYZstle 1986; Schmidt 1904; Stork 198J; Weitlaner 1902; Williams and Peterson 1982).The unusual hairlike microstructure of gecko toe pads has been recognized for well overa century (Braun 1878; Martier 1872a; Martier 1872b; Martier 1874). Setal branches werediscovered using light microscopy (Schmidt 1904), but the discovery of multiple splitends (Altevogt 1954) and spatular nanostructure (Ruibal and Ernst 1965) at the tip ofeach seta was made only after the development of electron microscopy.

A single seta of the tokay gecko is approximately 110 microns in length and 4.2 micronsin diameter (Ruibal and Ernst 1965; Russell 1975; Williams and Peterson 1982) (]ig. 1).Setae are similarly oriented and uniformly distributed on the scansors. Setae branch atthe tips into 100-1000 more structures (Ruibal and Ernst 1965; Schleich and YZstle 1986)known as spatulae. A single spatula consists of a stalk with a thin, roughly triangular end,where the apex of the triangle connects the spatula to its stalk. Spatulae areapproximately 0.2 microns in length and also in width at the tip (Ruibal and Ernst 1965;Williams and Peterson 1982). While the tokay is currently the best studied of anyadhesive gecko species, there are over a thousand species of gecko (Han et al. 2004),encompassing an impressive range of morphological variation at the spatula, seta,scansor, and toe levels (Arzt et al. 200J; Autumn and Peattie 2002; Irschick et al. 1996;Maderson 1964; Peterson and Williams 1981; Roll 1995; Ruibal and Ernst 1965; Russell1975; Russell 1981; Russell 1986; Russell and Bauer 1988; Russell and Bauer 1990a;Russell and Bauer 1990b; Schleich and YZstle 1986; Stork 198J; Williams and Peterson1982). Setae have even evolved on the tails of some gecko species (Bauer 1998).Remarkably, setae have evolved convergently in iguanian lizards of the genus !"#$%&

(Braun 1879; Peterson and Williams 1981; Ruibal and Ernst 1965), and in scincid lizardsof the genus '()&%"#*)+,) (Irschick et al. 1996; Williams and Peterson 1982). Thischapter aims broadly at identifying the known properties of the gecko adhesive system,possible underlying principles, and quantitative parameters that affect system function.However, much of what is known is based on studies of a single species `the tokay gecko(-+..# 0+1.#)` and the degree of variation in function among species remains an openquestion that should be kept in mind.

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3. $dhesi*e +ro+erties of gec2o setae

T"o front feet of a tokay -ecko /Gekko gecko0 can "ithstand 2678 9 of force :arallel tothe surface "ith 22= mm2 of :ad area /?rschick et al7 899A07 The foot of a tokay Bearsa::roCimately 3EA66 tetrads of setae :er mm2E or 8FEF66 setae :er mm2 //Schleich andKIstle 89JA0K :ers7 oBs707 LonseMuentlyE a sin-le seta should :roduce an avera-e force ofA72 O9E and an avera-e shear stress of 67696 9 mmP2 /679 atm07 Qo"everE sin-le setae:roved Both much less sticky and much more sticky than :redicted By "hole animalmeasurementsE under varyin- eC:erimental conditionsE im:lyin- that attachment anddetachment in -ecko setae are mechanically controlled /Autumn et al7 266607

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Ssin- a ne"ly develo:ed microPelectromechanical systems /TUTS0 force sensor /Lhuiet al7 899J0E Autumn and collaBorators /26660 measured the adhesive and shear force of asin-le isolated -ecko seta7 ?nitial efforts to attach a sin-le seta failed to -enerate forcesaBove that :redicted By LoulomB friction Because of the inaBility to achieve the :ro:erorientation of the seta in siC de-rees of freedom7 The an-le of the setal shaft "as:articularly im:ortant in achievin- an adhesive Bond7 Stron- attachment occurred "henusin- :ro:er orientation and a motion Based on the dynamics of -ecko le-s durin-climBin- /Based on force :late dataK Vi-7 2K /Autumn et al7 266W /in :ress0007 A smallnormal :reload force yielded a shear force of XF6O9E siC times the force :redicted By"holePanimal measurements /?rschick et al7 899A07 The small normal :reload forceEcomBined "ith a WOm :roCimal shear dis:lacement yielded a very lar-e shear force of266O9E 32 times the force :redicted By "holePanimal measurements /?rschick et al7 899A0and 866 times the frictional force measured "ith the seta oriented "ith s:atulae facin-a"ay from the surface /Autumn et al7 266607 The :reload and dra- ste:s "ere alsonecessary to initiate si-nificant adhesion in isolated -ecko setaeE consistent "ith the loadde:endence and directionality of adhesion oBserved at the "holePanimal scale By Qaase/89660 and Yellit /893F07 The ratio of :reload to :ulloff force is the adhesion coefficientEOZE "hich re:resents the stren-th of adhesion as a function of the :reload /[hushan266207 ?n isolated -ecko setaeE a 27W O9 :reload yielded adhesion Bet"een 26 O9/Autumn et al7 26660 and F6 O9 /Autumn et al7 2662B0 and thus a value of OZ of Bet"eenJ and 8A7

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All A7W million /?rschick et al7 899AK Schleich and KIstle 89JA0 setae of a W6 -ram Tokay-ecko attached maCimally could theoretically -enerate 8366 9 /833 k- force0 of shearforce \enou-h to su::ort the "ei-ht of t"o humans7 This su--ests that a -ecko need onlyattach 3] of its setae to -enerate the -reatest forces measured in the "hole animal /269K/?rschick et al7 899A007 ^nly less than 676F] of a -eckoZs setae attached maCimally areneeded to su::ort its "ei-ht of W6 -rams on a "all7 At first -lanceE -ecko feet seem to Beenormously overBuilt By virtue of a safety mar-in of at least /26 9 _67W 90 P 8 ` 3966]7

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!hen lineari*ed (-.t.mn and Peattie 2332)5 yield a stron9 :orrelation ;et!een <or:e andadhesion ener9y <or !!!= >3?5 :onsistent !ith the @an der Aaals hypothesis.

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Do test dire:tly !hether :apillary adhesion or @an der Aaals <or:e is a s.<<i:ientme:hanism o< adhesion in 9e:Eos5 -.t.mn and :ollea9.es (-.t.mn et al. 2332;)meas.red the hydropho;i:ity o< the setal s.r<a:e and meas.red adhesion and <ri:tion ont!o polari*a;le semi:ond.:tor s.r<a:es that @aried 9reatly in hydropho;i:ity. F< :apillaryadhesi@e <or:es dominate5 !e eGpe:ted a la:E o< adhesion on the stron9ly hydropho;i:s.r<a:es. Fn :ontrast5 i< @an der Aaals <or:es are s.<<i:ient5 !e predi:ted lar9e adhesi@e<or:es on the hydropho;i:5 ;.t polari*a;le Ha-s and Ii JKJs s.r<a:es. Fn either :ase!e eGpe:ted stron9 adhesion to the hydrophili: IiL2 :ontrol s.r<a:es. Ae sho!ed thattoEay 9e:Eo setae are .ltrahydropho;i: (M>3.N?O (-.t.mn and Pansen 2335 (in press)O-.t.mn et al. 2332;))5 pro;a;ly a :onseR.en:e o< the hydropho;i: side 9ro.ps o< STEeratin (UereiterTPahn et al. MNV4). Dhe stron9ly hydropho;i: nat.re o< setae s.99eststhat they intera:t primarily @ia @an der Aaals <or:es !hether !ater is present or not.

Ihear stress o< li@e 9e:Eo toes on Ha-s (! X MM3?) and IiL2 (! X 3?) semi:ond.:tors!as not si9ni<i:antly di<<erent5 and adhesion o< a sin9le 9e:Eo seta on the hydrophili:IiL2 and hydropho;i: Ii :antile@ers di<<ered ;y only 2Y. Dhese res.lts reZe:t thehypothesis that polarity (as indi:ated ;y !!) o< a s.r<a:e predi:ts atta:hment <or:es in9e:Eo setae5 as s.99ested ;y Piller (MN>VO MN>N)5 and are :onsistent !ith reanalysis o< hisdata .sin9 adhesion ener9ies (-.t.mn and Peattie 2332). Iin:e @an der Aaals <or:e is theonly me:hanism that :an :a.se t!o hydropho;i: s.r<a:es to adhere in air (Fsraela:h@iliMNN2)5 the Ha-s and hydropho;i: semi:ond.:tor eGperiments pro@ide dire:t e@iden:ethat @an der Aaals <or:e is a s.<<i:ient me:hanism o< adhesion in 9e:Eo setae5 and that!aterT;ased :apillary <or:es are not reR.ired. Ietal adhesion is stron9 on polar andnonpolar s.r<a:es5 perhaps ;e:a.se o< the stron9ly hydropho;i: material they are madeo<5 and d.e to the @ery lar9e :onta:t areas made possi;le ;y the spat.lar nanoarray.He:Eo setae th.s ha@e the property o< "#$%&'#(!')*%+%)*%),%[ they :an adhere stron9ly toa !ide ran9e o< materials5 lar9ely independently o< s.r<a:e :hemistry.

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Property (4)5 material independent adhesion5 does not pre:l.de an e<<e:t o< !ater on9e:Eo adhesion .nder some :onditions. Aater is liEely to alter :onta:t 9eometry andadhesion ener9ies !hen present ;et!een hydropho;i: (e.9. spat.la) and hydrophili: (e.9.9lass) s.r<a:es5 ;.t it is eG:eedin9ly di<<i:.lt to predi:t !hat the e<<e:t !ill ;e in 9e:Eosetae ;e:a.se o< the :ompleGity o< the system. -n eG:ellent eGample o< the di<<i:.lty o<interpretin9 the e<<e:t o< !ater on 9e:Eo adhesion is a st.dy ;y I.n et al. (2335) that .seda model o< intera:tion o< t!o hydrophili: s.r<a:es as a <.n:tion o< h.midity to predi:t9reatest adhesion d.e to :apillary <or:es at \3 to V3Y relati@e h.midity (]P). I.n et al.meas.red 9reater adhesion in 9e:Eo spat.lae at \3Y ]P than in dry air. Po!e@er the

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6$),!()!8'#'.,'!"#':(2'*.,!()6#'<!&2.6(00&'@4?')+'-$%',$0.*,'.)'6$)!(6!B4'"'.,'('-/)6!.$)'$-!"#'1$0/+#'()*'2$0(%.P(3.0.!&'$-'!"#'+$0#6/0#,'.)1$01#*4

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

Kellar Autumn The Gecko Adhesive System 10 of 39

mechanics models, one might question the validity of models based on simple geometriesto the function of gecko setae.

3.5.4. JKR model of spatulae

The mechanics of contact have been modeled using continuum theory and highlysimplified geometries. For example the Johnson, Kendall, Roberts (JKR; (Johnson et al.1973)) model considers the force F required to pull an elastic sphere of radius R from aplanar surface. The predicted adhesion force is given by, F = (3/2)!R!, where ! is theadhesion energy between the sphere and the surface. Using values of R = 100 nm and ! =50 mJ/m2, the predicted force for a gecko spatula is F = 23.6 nN, approx. twice the valuemeasured by AFM (Huber et al. 2004) (Table 1).

Another test of the validity of the JKR model is to begin with the forces measured insingle setae, and then calculate the size of the JKR sphere (Autumn et al. 2002b).Adhesion is ~40 µN per seta on silicon cantilever surfaces (Table 1). The setal tip isapprox. 43 µm2 in area (Autumn and Gorb 2005, pers. obs.), therefore the adhesive stress(") was ~917 kPa. If the spatulae are packed tightly, " ! (3/2) !R! / !R2 = (3/2) ! / R.Using a typical adhesion energy for van der Waals surfaces (! = 50 to 60 mJ/m2), solvingfor the predicted radii (R) of individual spatulae using empirical force measurements: R =(3/2) ! / " = 82 to 98 nm, (164 to 196 nm in diameter). This value is remarkably close toempirical measurements of real gecko spatulae (200 nm in width) (Autumn et al. 2000;Ruibal and Ernst 1965) yet obviously spatulae are not spherical (Fig. 1E). Note that thepreceding estimate of R using the JKR model differs from that of Autumn andcolleagues’ (2002b) in that they estimated the area of one seta using setal density, andarrived at a similar but somewhat lower value for ". The confirmation that the JKRmodel predicts similar magnitudes of force as observed in setae suggested theextraordinary conclusion that adhesion can be enhanced simply by splitting a surface intosmall protrusions to increase surface density (Autumn et al. 2002b) and that adhesivestress is proportional to 1/R (Arzt et al. 2002). This model is supported by a comparativeanalysis of setae in lizards and arthropods (Arzt et al. 2003) (see Section 6.1).

3.5.5. Kendall peel model of spatulae

Spatulae may also be modeled as nanoscale strips of adhesive tape (Hansen and Autumn2005; Huber et al. 2004; Spolenak et al. 2004). Using the approach of Kendall (1975), F= !w, assuming there is negligible elastic energy storage in the spatula as it is pulled off,and where w is the width of the spatula, and ! is the adhesion energy as for the JKRmodel. Empirical measurements of spatular adhesion (Huber et al. 2004) suggest thateach spatula adheres with approx. 10 nN force. Using a value of ! = 50 mJ/m2, typical ofvan der Waals interactions the Kendall peel model predicts a spatular width of 200 nm,remarkably close to the actual dimension (Autumn et al. 2000; Ruibal and Ernst 1965).

Theoretical considerations suggest that generalized continuum models of spatulae asspheres or nanotape are applicable to the range of spatula size and keratin stiffness ofsetae found in reptiles and arthropods (Spolenak et al. 2004). Interestingly, at the 100 nm

Kellar Autumn The Gecko Adhesive System 11 of 39

size scale the effect of shape on adhesion force may be relatively limited (Gao and Yao2004; Spolenak et al. 2004). However, at sizes above 100 nm and especially above 1 µm,Spolenak et al. (2004) concluded that shape should have a very strong effect on adhesionforce. A phylogenetic comparative analysis of attachment force in lizards and insects willbe an important test of this hypothesis.

4. Anti-adhesive properties of gecko setae

Paradoxical as it may seem, there is growing evidence that gecko setae are strongly anti-adhesive. Gecko setae do not adhere spontaneously to surfaces, but instead require amechanical program for attachment (Autumn et al. 2000). Unlike adhesive tapes, geckosetae do not self-adhere. Pushing the setal surfaces of a gecko’s feet together does notresult in strong adhesion. Also unlike conventional adhesives, gecko setae do not seem tostay dirty.

4.1. Properties (5) self-cleaning and (6) anti-self-adhesion

Dirt particles are common in nature (Little 1979), yet casual observation suggests thatgeckos’ feet are quite clean (Fig. 1B). Sand, dust, leaf litter, pollen, and plant waxeswould seem likely to contaminate gecko setae. Hair-like elements on plants accumulatemicron-scale particles (Little 1979) that could come into contact with gecko feet duringclimbing. Indeed, insects must cope with particulate contamination that reduces thefunction of their adhesive pads (Gorb and Gorb 2002), and spend a significant proportionof their time grooming (Stork 1983) in order to restore function. On the other hand,geckos have not been observed to groom their feet (Russell and Rosenberg 1981), yetapparently retain the adhesive ability of their setae during the months between shedcycles. How geckos manage to keep their toes clean while walking about with sticky feethas remained a puzzle until recently (Hansen and Autumn 2005). While self-cleaning bywater droplets has been shown to occur in plant (Barthlott and Neinhuis 1997) and animal(Baum et al. 2002) surfaces, no adhesive had been shown to self-clean.

Gecko setae are the first known self-cleaning adhesive (Hansen and Autumn 2005).Tokay geckos with 2.5 µm radius microspheres applied to their feet recovered theirability to cling to vertical surfaces after only a few steps on clean glass. We contaminatedtoes on one side of the animal with an excess of 2.5 µm radius silica-aluminamicrospheres and compared the shear stress to that of uncontaminated toes on the otherside of the animal. Prior researchers had suggested that geckos’ unique toe peelingmotion (digital hyperextension) might aid in cleaning of the toe pads (Bauer et al. 1996;Russell 1979), so we immobilized the geckos’ toes and applied them by hand to thesurface of a glass force plate to determine if self-cleaning could occur without toepeeling. After only 4 simulated steps on a clean glass surface, the geckos recoveredenough of their setal function to support their body weight by a single toe (Hansen andAutumn 2005). To test the hypothesis that self-cleaning is an intrinsic property of geckosetae and does not require a gecko, we isolated arrays of setae and glued them to plastic

Kellar Autumn The Gecko Adhesive System 12 of 39

strips. We simulated steps using a servomanipulation system we called RoboToe. Wecompared shear stress in clean setal arrays to that in the same arrays with a monolayer ofmicrospheres applied to their adhesive surfaces. Self-cleaning of microspheres occurredin arrays of setae isolated from the gecko. Again as for live gecko toes, isolated setalarrays rapidly recovered the shear force lost due to contamination by microspheres. Wehypothesized that the microspheres were being preferentially deposited on the glasssubstrate, and did not remain strongly attached to the setae.

Contact mechanical models suggest that it is possible that self-cleaning occurs by anenergetic disequilibrium between the adhesive forces attracting a dirt particle to thesubstrate and those attracting the same particle to one or more spatulae (Fig. 3)(Hansenand Autumn 2005). The models suggest that self-cleaning may in fact require ! ofspatulae to be relatively low (equal to or less than that of the wall), perhaps constrainingthe spatula to be made of a hydrophobic material. So, geckos may benefit by having setaemade of an anti-adhesive material: decreasing ! decreases adhesion energy of eachspatula but promoting self-cleaning should increase adhesion of the array as a whole bymaximizing the number of uncontaminated spatulae. If ! were to be increased bysupplementing van der Waals forces with stronger intermolecular forces such as polar orH-bonding, it is likely that self-cleaning and anti-self properties would be lost. Thus theself-cleaning and anti-self properties may represent a sweet spot in the evolutionarydesign space for adhesive nanostructures.

4.2. Property (7) nonsticky default state

The discovery that maximal adhesion in isolated setae requires a small pushperpendicular to the surface, followed by a small parallel drag (Autumn et al. 2000),explained the load dependence and directionality of adhesion observed at the whole-animal scale by Haase (1900) and Dellit (1934), and was consistent with the structure ofindividual setae and spatulae (Hiller 1968; Ruibal and Ernst 1965). In their resting state,setal stalks are recurved proximally. When the toes of the gecko are planted, the setaemay become bent out of this resting state, flattening the stalks between the toe and thesubstrate such that their tips point distally. This small preload and a micron-scaledisplacement of the toe or scansor proximally may serve to bring the spatulae (previouslyin a variety of orientations) uniformly flush with the substrate, maximizing their surfacearea of contact. Adhesion results and the setae are ready to bear the load of the animal’sbody weight.

To test the hypothesis that the default state of gecko setal arrays is to be nonsticky,Autumn and Hansen (2005 (in press)) estimated the fraction of area able to make contactwith a surface in setae in their unloaded state. Only less than 6.6% of the area at the tip ofa seta is available for initial contact with a smooth surface, and 93.4% is air space. Thissuggests that, initially, during a gecko’s foot placement, the contact fraction of the distalregion of the setal array must be very low. Yet the dynamics of the foot must be sufficientto increase the contact fraction substantially to achieve the extraordinary values ofadhesion and friction that have been measured in whole animals (Autumn et al. 2002b;Hansen and Autumn 2005; Irschick et al. 1996) and isolated setae (Autumn et al. 2000;Autumn et al. 2002b; Hansen and Autumn 2005). Thus gecko setae may be nonsticky by

Kellar Autumn ,he Gecko Adhesive System 13 of 39

default because only a very small contact fraction is possible without mechanicallydeforming the setal array.

How much does the contact fraction increase during attachment? While there are noempirical measurements of the number of spatulae in contact as a function of adhesion(or friction) force, it is possible to estimate from measurements of single setae. Empiricalmeasurements and theoretical estimates of spatular adhesion (Arzt et al. 2003; Autumn etal. 2000; Autumn et al. 2002b; Hansen and Autumn 2005; Huber et al. 2004; Spolenak etal. 2004) suggest that each spatula generates approx. 10 to 40 nN with approx. 0.02µ2

area, or approx. 500 to 2000 kPa. A single seta on a Si MEMs cantilever can generateapprox. 917 kPa (Table 1). The value of 10 nN adhesion measured in single spatulaeusing an AFM (Huber et al. 2004) implies that 4000 spatulae would need to be attachedto equal the peak adhesion force (40µN) measured in single setae (Autumn et al. 2002b).However, each seta contains not more than approx. 100 to 1000 spatulae ((Ruibal andErnst 1965; Schleich and Kästle 1986)). Therefore a spatular force of 40 nN is moreappropriate for a conservative estimate of setal contact fraction during attachment. In thecase of a spatular adhesion force of 40 nN, the adhesive stress is 2000 kPa. Therefore acontact fraction of 46% is required to yield the setal stress. This suggests that unless theforce of adhesion of a spatula has been greatly underestimated, the contact fraction mustincrease from 6% to 46%, or by approx. 7.5-fold, following preload and drag.

5. Modeling adhesive nanostructures

!.#. %&&'()i+' ,-./0/1 -& 2 1')20 23324

The gecko adhesive is a microstructure in the form of an array of millions of high aspectratio shafts. The effective elastic modulus, !e##$ (Persson 2003; Sitti and Fearing 2003) ismuch lower than the Young's modulus (!) of !-keratin. Thus arrays of setae shouldbehave as a softer material than bulk !-keratin. ! of beta-keratin in tension is approx. 2.5GPa in bird feathers (Bonser and Purslow 1995) and 1.3 to 1.8 GPa in bird claws (Bonser2000). Young’s moduli of lizard beta keratins in general (Fraser and Parry 1996) andgecko beta keratins in particular (Alibardi 2003) remain unknown at present. Thebehavior of a setal array during compression and relaxation will depend on the mode(s)of deformation of individual setae. Bending is a likely mode of deformation(Simmermacher 1884) (Fig. 1D), and a simple approach is to model arrays of setae ascantilever beams (Glassmaker et al. 2004; Hui et al. 2004; Persson 2003; Sitti andFearing 2003; Spolenak et al. 2005). One might question the applicability of modelsbased on a simple geometry for the complex, branched structure of the seta. However, aswith the JKR and Kendall models (Sections 3.5.4 and 3.5.5) applied to spatulae, thesimple cantilever model is surprisingly well supported by empirical measurements ofsetal arrays (Geisler et al. 2005).

The cantilever model of a single seta (Campolo et al. 2003; Sitti and Fearing 2003) isbased on a cantilever beam under a lateral load, % at its tip. The resulting tip displacement

!"##$%&'()(*n ,-"&."c0o&'2-"si5"&67s)"* 89&o:&3<

due to bending is ! ! !L!

!E$, where ! is the length, " is the elastic modulus of the

material, and # is the area moment of inertia of the cantilever (Gere and Timoshenko1984) (Fig. 4A). The lateral bending stiffness $% is given by

Ky =!#$

%!=!!&"#

"%!

, (5.1)

for a cylindrical cantilever of radius &, ! ! !R!

!. For a cantilever at an angle ! to the

substrate and under a normal load, 'n, the resolved force lateral to the cantilever is ' =

'ncos! (Fig. 4B). This results in a lateral tip displacement of ! !Fn!"# "" #L$

$EI, and a

normal tip displacement of !n! ! cos" !

"ncos

2 "" ##3

3$%.

Next, to derive an effective elastic modulus (")**) for a model setal array, in the cantileversystem above, we use Hooke’s law, " = ")**#, where " and # are the applied stress andresulting strain in the normal axis, respectively. The normal strain is # = !n / !n (Fig. 4B),where !n = !sin!.

Now, for an array of cantilevers with density + (meter–2) in parallel at an angle ! andunder a normal stress ", the normal force acting on each cantilever tip is 'n = ",-,+. The

resulting normal displacement of the array is !n=" !"s$ #( )"%

%#$%. Thus,

! !" cos2 #" #!2

3"#$sin#, and the stress over the cantilever array is

! !!e##! cos

2 "( )$2

3!%&sin". Dividing by " and Solving for ")** we reach a general

equation for the effective stiffness of a cantilever array,

Eeff !3EIDsin!

cos2 !" #L2 . (5.2)

For a cylindrical cantilever, we can substitute "# in Eqn. 5.2 for !"#

3

3using Eqn. 5.1,

yielding,

Eeff !KyLDsin!

cos2 !

. (5.3)

For a tokay seta-size cylindrical cantilever of & = 2.1µm, ! = 110 µm, " = 1 GPa, thebending stiffness from Eqn. 5.1 is $% = 0.0344 N/m. For " = 2 GPa, $% = 0.0689 N/m.

I will now calculate the shaft angle ! (see Fig 4B) required to yield an effective stiffnessof 100 kPa (the upper limit of Dahlquist’s criterion) (Dahlquist 1969; Pocius 2002). A

Kellar Autumn The Gecko Adhesive System 19 of 39

typical tokay setal array has approx 14,000 setae per mm2 and ! 8 1.44 x 1010 m-2. ;singEqn. 5.3, a value of ! 8 50D is required for " 8 1 GPa, and ! 8 36.65D for " 8 2 GPa toyield "e$$ 8 100 kPa.

We measured the forces resulting from deformation of isolated arrays of tokay gecko(%e&&o gec&o) setae to determine "e$$ and test the validity of the cantilever model. Wefound that "e$$ of tokay gecko setae falls near 100 kPa, close to the upper limit ofDahlquist’s criterion for tack (Fig. 5)(Geisler et al. 2005). Additionally, we observedvalues of ! for tokay gecko setae near 43D, further supporting the validity of thecantilever model (Fig. 4; (Geisler et al. 2005)).

!"#"$%&'()$*'+f-.e$-01$-0234-2230($.&01323&0*

The cantilever model predicts that a high density of setae should be selected for inincreasing adhesive force of setal arrays. Firstly, it follows from the JKR model (Arzt etal. 2003; Autumn et al. 2002b) that packing in more spatulae should increase adhesion inan array of setae. Secondly, the cantilever model suggests that thinner setal shafts shoulddecrease Eeff, and promote a greater contact fraction on rough surfaces (Campolo et al.2003; Jagota and Bennison 2002; Persson 2003; Persson and Gorb 2003; Scherge andGorb 2001; Sitti and Fearing 2003; Spolenak et al. 2005; Stork 1983). The cantilevermodel also suggests that longer and softer setal shafts, and a lower shaft angle ! willresult in better adhesion on rough surfaces because these parameters will reduce "e$$. On arandomly rough surface, some setal shafts should be bent in compression (concave),while others will be bent in tension (convex). The total force required to pull off a setalarray from a rough surface should therefore be determined by the cumulative adhesiveforce of all the attached spatulae, minus the sum of the forces due to elastic deformationof compressed setal shafts.

If setae mat together (Stork 1983), it is likely that adhesive function will becompromised. Interestingly, the same parameters that promote strong adhesion on roughsurfaces should also cause matting of ad^acent setae (Glassmaker et al. 2004; Hui et al.2004; Persson 2003; Sitti and Fearing 2003; Spolenak et al. 2005). The distance betweensetae and the stiffness of the shafts will determine the amount of force required to bringthe tips together for matting to occur. It follows from the cantilever model that stiffer,shorter, and thicker stalks will allow a greater packing density without matting. As is thecase for self-cleaning (Hansen and Autumn 2005), setae should be made of materials withlower surface energy to prevent self-adhesion and matting. Satisfying both antimattingand rough surface conditions may require a compromise of design parameters. Spolenaket al. (2005) devised `design mapsa for setal adhesive structures, an elegant approach tovisualizing the parametric tradeoffs needed to satisfy the rough surface and antimattingconditions while at the same time maintaining structural integrity of the material.

!ellar Autumn The Gecko Adhesive System 16 of 39

6. Scaling

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8. Gecko-inspired synthetic adhesive nanostructures

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9. Future directions in the study of the gecko adhesive system

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Kellar Autumn The Gecko Adhesive System 20 of 39

Natural surfaces are rarely smooth, and an important next step will be to measureempirically the effect of surface roughness (Vanhooydonck et al. 2005) on friction andadhesion in gecko setae to test the predictions of the new generation of theoretical modelsfor rough surface contacts with micro and nanostructures (Persson and Gorb 2003).Under real-world conditions where surfaces are fractal (Greenwood 1992; Persson andGorb 2003), compliance is required at each level of the gecko adhesive hierarchy:spatula, seta, lamella, toe, and leg. Models including a spatular array at the tip of a setahave not yet been developed. Similarly, models of lamellar structure will be needed toexplain function on roughness above the micron scale.

Biological diversity of setal and spatular structure is high and poorly documented. Basicmorphological description will be required. Theory predicts that tip shape affects pulloffforce less at smaller sizes (Gao and Yao 2004), so it is possible that part of spatularvariation is due to phylogenetic effects, but material constraints such as tensile strength ofkeratin must be considered as well (Autumn et al. 2002b; Spolenak et al. 2005). Thecollective behavior of the setal array will be a productive research topic (Gao and Yao2004). Diversity of the array parameters, density, dimension, and shape is great but notwell documented. In particular, the shape of setal arrays on lamellae demands furtherinvestigation. Phylogenetic analysis (Harvey and Pagel 1991) of the variation in setalstructure and function will be required to tease apart the combined effects of evolutionaryhistory, material constraints, and adaptation (Autumn et al. 2002a).

The molecular structure of setae is not yet known. Setae are made primarily of !-keratin,but a histidine-rich protein or proteins may be present as well (Alibardi 2003). Onepossible role of non-keratin proteins is as a glue that holds the keratin fibrils together inthe seta (Fig. 1D) (Alibardi 2003). This suggests a possible role of genes coding forhistidine-rich protein(s) in tuning the material properties of the setal shaft. The outermolecular groups responsible for adhesion at the spatular surface will also be animportant topic for future research.

Clearly there is great desire to engineer a material that functions like a gecko adhesive,yet progress has been limited. A biomimetic approach of attempting to copy gecko setaeblindly is unlikely to succeed due to the complexity of the system (Fig. 1) and the factthat evolution generally produces satisfactory rather than optimal structures. Instead,development of biologically inspired adhesive nanostructures will require carefulidentification and choice of design principles (Table 2) to yield selected geckolikefunctional properties. As technology and the science of gecko adhesion advance, it maybecome possible to tune design parameters to modify functional properties in ways thathave not evolved in nature.

It is remarkable that the study of a lizard is contributing to understanding the fundamentalprocesses underlying adhesion and friction (Fakley 2001; Urbakh et al. 2004), andproviding biological inspiration for the design of novel adhesives and climbing robots.Indeed the broad relevance and applications of the study of gecko adhesion underscorethe importance of basic, curiosity based research.

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Kellar Autumn The Gecko Adhesive System 29 of 39

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'1)+s*-:!+:+$/,!'#!#)+!1*$#!p'$#*&(+!Y!sp'#%('!*:#+$.'&+@!':1!KRs!*s!#)+!?*1#)!-.!#)+!sp'#%('@':1!'ss%4*:/!:+/(*/*<(+!+('s#*&!+:+$/,!s#-$'/+5!Z)+!p%((-..!.-$&+!-.!#)+!1*$#!p'$#*&(+!.$-4'!p(':'$!?'((@!%s*:/!#)+![-):s-:@!F+:1'((@!R-<+$#s!7[FR9!4-1+(!7[-):s-:!+#!'(5!VWXM9!*s

!"# =3

"!$"" "# @!?)+$+!!pw *s!#)+!'1)+s*-:!+:+$/,!-.!#)+!p'$#*&(+!#-!#)+!?'((5!N!$+p$+s+:#s

#)+!:%4<+$!-.!sp'#%('+!'##'&)+1!s*4%(#':+-%s(,!#-!+'&)!1*$#!p'$#*&(+!#-!'&)*+3+!+:+$/+#*&+T%*(*<$*%45

Kellar Autumn The Gecko Adhesive System 30 of 39

!i#ure () "ree %ody dia+ram of .A0 cantilever %eam and .60 an+led cantilever %eam%ased on the model of Sitti and "earin+ .2;;30= This model is similar to that of ?ersson.2;;30 @ho used a sBrin+C%ased aBBroach=

!i#ure *) Doun+Es modulus .!0 of materials includin+ aBBroFimate values of %ulk !Ckeratin and effective modulus .!e##0 of natural setal arrays .Geisler et al= 2;;I0= A value of! ! J;; k?a .measured at J KL0 is the uBBer limit of the MahlNuist criterion for tackO@hich is %ased on emBirical o%servations of Bressure sensitive adhesives .?SAsPMahlNuist J9R9O ?ocius 2;;20= A cantilever %eam model .SNn= I=3P Sitti and "earin+2;;30 Bredicts a value of !e## near J;; k?aO as o%served for natural setae and ?SAs= Tt isnota%le that +eckos have evolved !e## close to the limit of tack= This value of !e## may %etuned to allo@ stron+ and raBid adhesionO yet Brevent sBontaneous or inaBBroBriateattachment=

!i#ure +) Stress versus area in the +ecko adhesive hierarchy= See Ta%le J for numericalvalues and literature sources= UKW and Kendall model Bredictions for sBatular adhesivestress .trian+les0 %ound the measured value of Ku%er et al= .2;;I0= TeFt %elo@ the XCaFissho@s the level in the +ecko adhesive hierarchy ."i+= J0

!a#le '( )caling o/ ad1esion and /riction stresses in tokay gecko setae( )tress decreases appro8i9ately e8ponentially :;ig( <=> or

appro8i9ately linearly on a log?log scale( !1e @endall peel 9odel prediction uses a sBuare spatula o/ 'CC n9 on a side( !1e D@E

9odel prediction uses a sp1erical spatula Fit1 'CC n9 radius( Got1 predictions use an ad1esion energy o/ H I JC 9DK9L( Mote t1at t1e

si9ilarity o/ area #etFeen single toe and single /oot is due to t1e use o/ larger geckos in t1e single toe 9easure9ents(

Scale &ode )orce Area Stress /k1a2 Stress /atm2

)ingle spatula :Nu#er et al( LCCJ= Od1esion 'C nM C(CL PL JCC Q(R

D@E 9odel prediction /or single spatula Od1esion LS(J< nM C(CS'Q PL TJC T(Q

@endall peel 9odel prediction /or single spatula Od1esion 'C(CC nM C(CQ PL LJC L(J

)ingle seta :Outu9n et al( LCCC= Od1esion LC PM QS(< PL QJU Q(J

)ingle seta :Outu9n et al( LCCL= Od1esion QC PM QS(< PL R'T R(C

)ingle seta :Outu9n et al( LCCC= ;riction LCC PM QS(< PL QJUJ QJ(L

)etal array :Nansen V Outu9n LCCJ= ;riction C(ST M C(RR 99L STC S(T

)ingle toe :Nansen V Outu9n LCCJ= ;riction Q(S M C('R c9L LL< L(L

)ingle /oot :Outu9n et al( LCCL= ;riction Q(< M C(LL c9L 'U< '(U

!Fo /eet :Wrsc1ick et al( 'RR<= ;riction LC(Q M L(LT c9L RC C(R

Table 2. Properties, principles, and parameters of the gecko adhesive system. This table lists known properties of the gecko adhesive,

proposed principles (or models) that explain the properties, and model parameters for each property. JKR refers to the Johnson,

Kendall, Roberts model of adhesion (Johnson et al. 1973).

!roperties !rinciples !arameters

!" Anisotro+ic attachment1Autumn et al" 25556

Shaft len9th: radius: density 1Sitti = >earin9

25536

2" @i9h !A 1+ulloffB+reload61Autumn et al" 25556

Shaft an9le 1Sitti = >earin9 25536

Shaft modulus 1Sitti = >earin96

3" CoD detachment force1Autumn et al" 25556

Eantilever Geam 1Autumn et al" 2555H Sitti =

>earin9 2553H S+olenak et al" 255JH Geisler =Autumn in +re+6

CoD effective stiffness1Sitti = >earin9 2553H Lersson 2553H Geisler =Autumn in +re+6

S+atular sha+e 1Lersson = GorG 2553H

S+olenak: GorG: Gao: ArMt 255J6

S+atular siMe1ArMt: GorG: S+olenak 25536

S+atular Sha+e1Gao = Nao 255JH S+olenak: GorG: Gao: ArMt255J6

J" Oaterial inde+endence1Autumn et al" 2552H @iller !9QR:96

van der Saals 1vdS6 mechanism1Autumn et al" 25526

TKVWlike contact mechanics1Autumn et al" 2552H ArMt et al" 2552:36

Xanoarray 1divided contact61Autumn et al" 2552H Gao et al" 255J6

S+atular density1ArMt: GorG: S+olenak 2553H Leattie 255J6

Y" SelfWcleanin91@ansen = Autumn 255Y6

S+atular Gulk modulus

Q" AntiWself Larticle siMe: sha+e: surface ener9y

7" Xonsticky default state 1Autumn =

@ansen in revieD6

Xanoarray 1divided contact6

Small contact area

Xontacky s+atulae

@ydro+hoGic: vdS s+atulae S+atular siMe: sha+e: surface ener9y

Fig. 1

"evel &lim)in+

"i$. &

Fig. 3

Fig. 4

Fig. 6