Preprint: Autumn, K. 2006. Properties, principles, and parameters of the gecko adhesive system. In Smith, A. and J. Callow, Biological
Adhesives. Springer
KellarVerlag.
Autumn
The Gecko Adhesive System
1 of 39
Do not copy or distribute without permission of the author ([email protected]). Copyright (c) 2005 Kellar Autumn.
Properties, Principles, and Parameters of the Gecko
Adhesive System
Kellar Autumn
Department of Biology
Lewis & Clark College
Portland, OR 97219-7899
[email protected]
10156 words + 130 references.
6 figures, 2 tables.
“The designers of the future will have smarter adhesives that do considerably
more than just stick” –Fakley 2001
1. Summary
Gecko toe pads are sticky because they feature an extraordinary hierarchy of structure
that functions as a smart adhesive. Gecko toe pads (Russell 1975) operate under perhaps
the most severe conditions of any adhesives application. Geckos are capable of attaching
and detaching their adhesive toes in milliseconds (Autumn et al. 2005 (in press)) while
running with seeming reckless abandon on vertical and inverted surfaces, a challenge no
conventional adhesive is capable of meeting. Structurally, the adhesive on gecko toes
differs dramatically from that of conventional adhesives. Conventional pressure sensitive
adhesives (PSAs) such as those used in adhesive tapes are fabricated from materials that
are 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, selfadhere, and attach accidentally to inappropriate surfaces. Gecko toes typically bear a
series of scansors covered with uniform microarrays of hair-like setae formed from !keratin (Russell 1986; Wainwright et al. 1982), a material orders of magnitude stiffer
than those used to fabricate PSAs. Each seta branches to form a nanoarray of hundreds of
spatular structures that make intimate contact with the surface.
Functionally, the properties of gecko setae are as extraordinary as their structure: the
gecko adhesive is 1) directional, 2) attaches strongly with minimal preload, 3) detaches
quickly and easily (Autumn and Peattie 2002; Autumn et al. 2000), 4) sticks to nearly
every 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
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properties are now well understood, much more research will be necessary to fully map
out the parameters of this complex system.
2. Introduction
Over two millennia ago, Aristotle commented on the ability of the gecko to =run up and
down 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; Martier
1872b; 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; Maderson
1964; Mahendra 1941; Ruibal and Ernst 1965; Russell 1975; Russell 1986; Schleich and
YZstle 1986; Schmidt 1904; Stork 198J; Weitlaner 1902; Williams and Peterson 1982).
The unusual hairlike microstructure of gecko toe pads has been recognized for well over
a century (Braun 1878; Martier 1872a; Martier 1872b; Martier 1874). Setal branches were
discovered using light microscopy (Schmidt 1904), but the discovery of multiple split
ends (Altevogt 1954) and spatular nanostructure (Ruibal and Ernst 1965) at the tip of
each 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 microns
in 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 at
the 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 are
approximately 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 any
adhesive 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; Russell
1975; Russell 1981; Russell 1986; Russell and Bauer 1988; Russell and Bauer 1990a;
Russell and Bauer 1990b; Schleich and YZstle 1986; Stork 198J; Williams and Peterson
1982). 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 lizards
of the genus '()&%"#*)+,) (Irschick et al. 1996; Williams and Peterson 1982). This
chapter 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 open
question that should be kept in mind.
!e##ar '(t(mn
,he .ec0o 'dhesi5e 67stem
3 of 3:
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 to
the surface "ith 22= mm2 of :ad area /?rschick et al7 899A07 The foot of a tokay Bears
a::roCimately 3EA66 tetrads of setae :er mm2E or 8FEF66 setae :er mm2 //Schleich and
KIstle 89JA0K :ers7 oBs707 LonseMuentlyE a sin-le seta should :roduce an avera-e force of
A72 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 animal
measurementsE under varyin- eC:erimental conditionsE im:lyin- that attachment and
detachment in -ecko setae are mechanically controlled /Autumn et al7 266607
!.#. %ro()rti), -#. /ni,otro(ic /tt/c23)nt /nd -2. 2i62 /d2),ion co)77ici)nt -89.
Ssin- a ne"ly develo:ed microPelectromechanical systems /TUTS0 force sensor /Lhui
et al7 899J0E Autumn and collaBorators /26660 measured the adhesive and shear force of a
sin-le isolated -ecko seta7 ?nitial efforts to attach a sin-le seta failed to -enerate forces
aBove that :redicted By LoulomB friction Because of the inaBility to achieve the :ro:er
orientation 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 "hen
usin- :ro:er orientation and a motion Based on the dynamics of -ecko le-s durinclimBin- /Based on force :late dataK Vi-7 2K /Autumn et al7 266W /in :ress0007 A small
normal :reload force yielded a shear force of XF6O9E siC times the force :redicted By
"holePanimal measurements /?rschick et al7 899A07 The small normal :reload forceE
comBined "ith a WOm :roCimal shear dis:lacement yielded a very lar-e shear force of
266O9E 32 times the force :redicted By "holePanimal measurements /?rschick et al7 899A0
and 866 times the frictional force measured "ith the seta oriented "ith s:atulae facina"ay from the surface /Autumn et al7 266607 The :reload and dra- ste:s "ere also
necessary to initiate si-nificant adhesion in isolated -ecko setaeE consistent "ith the load
de: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 coefficientE
OZE "hich re:resents the stren-th of adhesion as a function of the :reload /[hushan
266207 ?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"een
J and 8A7
!"#"#" %arge sa+e,- +ac,or +or a0hesion an0 +ric,ion4
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 shear
force \enou-h to su::ort the "ei-ht of t"o humans7 This su--ests that a -ecko need only
attach 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 are
needed to su::ort its "ei-ht of W6 -rams on a "all7 At first -lanceE -ecko feet seem to Be
enormously overBuilt By virtue of a safety mar-in of at least /26 9 _67W 90 P 8 ` 3966]7
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!ellar '(t(mn
,-e .ec01 'd-e3i5e 673tem
8 19 :;
!hen lineari*ed (-.t.mn and Peattie 2332)5 yield a stron9 :orrelation ;et!een <or:e and
adhesion ener9y <or !!!= >3?5 :onsistent !ith the @an der Aaals hypothesis.
!"#"$%&'()&*+$,-.$/0*)&102$134)()34)3*$045)61'3
!"#"$"%&'()*+,%)-'%./+%0'1%2//3(%/+0%4/5*33/16%/0-'(*7+%-657)-'('(
Do test dire:tly !hether :apillary adhesion or @an der Aaals <or:e is a s.<<i:ient
me: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 on
t!o polari*a;le semi:ond.:tor s.r<a:es that @aried 9reatly in hydropho;i:ity. F< :apillary
adhesi@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 that
toEay 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< ST
Eeratin (UereiterTPahn et al. MNV4). Dhe stron9ly hydropho;i: nat.re o< setae s.99ests
that 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 the
hypothesis that polarity (as indi:ated ;y !!) o< a s.r<a:e predi:ts atta:hment <or:es in
9e:Eo setae5 as s.99ested ;y Piller (MN>VO MN>N)5 and are :onsistent !ith reanalysis o< his
data .sin9 adhesion ener9ies (-.t.mn and Peattie 2332). Iin:e @an der Aaals <or:e is the
only me:hanism that :an :a.se t!o hydropho;i: s.r<a:es to adhere in air (Fsraela:h@ili
MNN2)5 the Ha-s and hydropho;i: semi:ond.:tor eGperiments pro@ide dire:t e@iden:e
that @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 and
nonpolar s.r<a:es5 perhaps ;e:a.se o< the stron9ly hydropho;i: material they are made
o<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< "#$%&'#(!')*%+%)*%),%[ they :an adhere stron9ly to
a !ide ran9e o< materials5 lar9ely independently o< s.r<a:e :hemistry.
!"#"8"%&-'%173'%79%:/)'1%*+%,'4;7%/0-'(*7+
Property (4)5 material independent adhesion5 does not pre:l.de an e<<e:t o< !ater on
9e:Eo adhesion .nder some :onditions. Aater is liEely to alter :onta:t 9eometry and
adhesion ener9ies !hen present ;et!een hydropho;i: (e.9. spat.la) and hydrophili: (e.9.
9lass) s.r<a:es5 ;.t it is eG:eedin9ly di<<i:.lt to predi:t !hat the e<<e:t !ill ;e in 9e:Eo
setae ;e:a.se o< the :ompleGity o< the system. -n eG:ellent eGample o< the di<<i:.lty o<
interpretin9 the e<<e:t o< !ater on 9e:Eo adhesion is a st.dy ;y I.n et al. (2335) that .sed
a model o< intera:tion o< t!o hydrophili: s.r<a:es as a <.n:tion o< h.midity to predi:t
9reatest adhesion d.e to :apillary <or:es at \3 to V3Y relati@e h.midity (]P). I.n et al.
meas.red 9reater adhesion in 9e:Eo spat.lae at \3Y ]P than in dry air. Po!e@er the
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=0!#%.):'!"#'6"#+.6(0'6$+2$,.!.$)'$-'$)#'$%'3$!"',/%-(6#,'6()'(0!#%'=8'7".6"'6()'3#'(,
0$7'(,'(22%$Q4'$)#'"(0-'!$'$)#'!".%*'!".,'1(0/#'-$%',$+#'2$0&+#%92$0&+#%'.)!#%(6!.$),
<#4:4'EKRS'$%'2$0&,!&%#)#B8'()*'(,'".:"'(,'-.1#'!.+#,'!".,'1(0/#'-$%',$+#'+#!(09$)9+#!(0
.)!#%(6!.$),4'D)'7(!#%8'"'6()'3#'%#*/6#*'3&'()'$%*#%'$-'+(:).!/*#4'T#1#%!"#0#,,8'!"#
1(%.(!.$)'.)'"'.,'$)0&'(3$/!'()'$%*#%'$-'+(:).!/*#'7".0#':(2'*.,!()6#'()*'6$)!(6!'(%#(
+(&'1(%&'3&',.Q'$%'+$%#'$%*#%,'$-'+(:).!/*#'7.!"$/!'+(6%$,6$2.6(00&'1.,.30#'6"():#,'(!
!"#'.)!#%-(6#4'U$%#$1#%8'!"#'#--#6!,'$-':(2'*.,!()6#'(%#'#Q2$)#)!.(0'!$'('2$7#%'$-'(!'0#(,!
!7$4'K"/,'(*"#,.1#',/%-(6#'#--#6!,'*/#'!$'1()'*#%'5((0,'.)!#%(6!.$),'(%#'('-/)6!.$)
2%.+(%.0&'$-':#$+#!%&')$!'6"#+.,!%&4'='1()'*#%'5((0,'+#6"().,+'-$%'(*"#,.$)'.)':#6;$
,#!(#',/::#,!,'!"(!'6$)!.)//+'!"#$%&'+$*#0,'$-'!"#'+#6"().6,'$-',/%-(6#'6$)!(6!
<I$"),$)'FGJAB'+(&'3#'(220.6(30#4'K"#)'(:(.)8',.)6#'!"#'6$+20#Q',!%/6!/%#'$-',#!(#'()*
,2(!/0(#'*.--#%,'*%(+(!.6(00&'-%$+'!"#'.*#(0'6/%1#*'()*'20()(%',/%-(6#,'/,#*'.)'6$)!(6!
Kellar Autumn
The Gecko Adhesive System
10 of 39
mechanics models, one might question the validity of models based on simple geometries
to the function of gecko setae.
3.5.4. JKR model of spatulae
The mechanics of contact have been modeled using continuum theory and highly
simplified 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 a
planar surface. The predicted adhesion force is given by, F = (3/2)!R!, where ! is the
adhesion 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 value
measured by AFM (Huber et al. 2004) (Table 1).
Another test of the validity of the JKR model is to begin with the forces measured in
single 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 is
approx. 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), solving
for 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 to
empirical 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 the
preceding estimate of R using the JKR model differs from that of Autumn and
colleagues’ (2002b) in that they estimated the area of one seta using setal density, and
arrived at a similar but somewhat lower value for ". The confirmation that the JKR
model predicts similar magnitudes of force as observed in setae suggested the
extraordinary conclusion that adhesion can be enhanced simply by splitting a surface into
small protrusions to increase surface density (Autumn et al. 2002b) and that adhesive
stress is proportional to 1/R (Arzt et al. 2002). This model is supported by a comparative
analysis 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 Autumn
2005; 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 JKR
model. Empirical measurements of spatular adhesion (Huber et al. 2004) suggest that
each spatula adheres with approx. 10 nN force. Using a value of ! = 50 mJ/m2, typical of
van 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 as
spheres or nanotape are applicable to the range of spatula size and keratin stiffness of
setae 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 Yao
2004; 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 adhesion
force. A phylogenetic comparative analysis of attachment force in lizards and insects will
be 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 antiadhesive. Gecko setae do not adhere spontaneously to surfaces, but instead require a
mechanical program for attachment (Autumn et al. 2000). Unlike adhesive tapes, gecko
setae do not self-adhere. Pushing the setal surfaces of a gecko’s feet together does not
result in strong adhesion. Also unlike conventional adhesives, gecko setae do not seem to
stay dirty.
4.1. Properties (5) self-cleaning and (6) anti-self-adhesion
Dirt particles are common in nature (Little 1979), yet casual observation suggests that
geckos’ feet are quite clean (Fig. 1B). Sand, dust, leaf litter, pollen, and plant waxes
would seem likely to contaminate gecko setae. Hair-like elements on plants accumulate
micron-scale particles (Little 1979) that could come into contact with gecko feet during
climbing. Indeed, insects must cope with particulate contamination that reduces the
function of their adhesive pads (Gorb and Gorb 2002), and spend a significant proportion
of 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), yet
apparently retain the adhesive ability of their setae during the months between shed
cycles. How geckos manage to keep their toes clean while walking about with sticky feet
has remained a puzzle until recently (Hansen and Autumn 2005). While self-cleaning by
water 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 their
ability to cling to vertical surfaces after only a few steps on clean glass. We contaminated
toes on one side of the animal with an excess of 2.5 µm radius silica-alumina
microspheres and compared the shear stress to that of uncontaminated toes on the other
side of the animal. Prior researchers had suggested that geckos’ unique toe peeling
motion (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 the
surface of a glass force plate to determine if self-cleaning could occur without toe
peeling. After only 4 simulated steps on a clean glass surface, the geckos recovered
enough of their setal function to support their body weight by a single toe (Hansen and
Autumn 2005). To test the hypothesis that self-cleaning is an intrinsic property of gecko
setae 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. We
compared shear stress in clean setal arrays to that in the same arrays with a monolayer of
microspheres applied to their adhesive surfaces. Self-cleaning of microspheres occurred
in arrays of setae isolated from the gecko. Again as for live gecko toes, isolated setal
arrays rapidly recovered the shear force lost due to contamination by microspheres. We
hypothesized that the microspheres were being preferentially deposited on the glass
substrate, and did not remain strongly attached to the setae.
Contact mechanical models suggest that it is possible that self-cleaning occurs by an
energetic disequilibrium between the adhesive forces attracting a dirt particle to the
substrate and those attracting the same particle to one or more spatulae (Fig. 3)(Hansen
and Autumn 2005). The models suggest that self-cleaning may in fact require ! of
spatulae to be relatively low (equal to or less than that of the wall), perhaps constraining
the spatula to be made of a hydrophobic material. So, geckos may benefit by having setae
made of an anti-adhesive material: decreasing ! decreases adhesion energy of each
spatula but promoting self-cleaning should increase adhesion of the array as a whole by
maximizing the number of uncontaminated spatulae. If ! were to be increased by
supplementing van der Waals forces with stronger intermolecular forces such as polar or
H-bonding, it is likely that self-cleaning and anti-self properties would be lost. Thus the
self-cleaning and anti-self properties may represent a sweet spot in the evolutionary
design space for adhesive nanostructures.
4.2. Property (7) nonsticky default state
The discovery that maximal adhesion in isolated setae requires a small push
perpendicular to the surface, followed by a small parallel drag (Autumn et al. 2000),
explained the load dependence and directionality of adhesion observed at the wholeanimal scale by Haase (1900) and Dellit (1934), and was consistent with the structure of
individual 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 setae
may become bent out of this resting state, flattening the stalks between the toe and the
substrate such that their tips point distally. This small preload and a micron-scale
displacement of the toe or scansor proximally may serve to bring the spatulae (previously
in a variety of orientations) uniformly flush with the substrate, maximizing their surface
area of contact. Adhesion results and the setae are ready to bear the load of the animal’s
body 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 contact
with a surface in setae in their unloaded state. Only less than 6.6% of the area at the tip of
a seta is available for initial contact with a smooth surface, and 93.4% is air space. This
suggests that, initially, during a gecko’s foot placement, the contact fraction of the distal
region of the setal array must be very low. Yet the dynamics of the foot must be sufficient
to increase the contact fraction substantially to achieve the extraordinary values of
adhesion 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 mechanically
deforming the setal array.
How much does the contact fraction increase during attachment? While there are no
empirical 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. Empirical
measurements and theoretical estimates of spatular adhesion (Arzt et al. 2003; Autumn et
al. 2000; Autumn et al. 2002b; Hansen and Autumn 2005; Huber et al. 2004; Spolenak et
al. 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 generate
approx. 917 kPa (Table 1). The value of 10 nN adhesion measured in single spatulae
using an AFM (Huber et al. 2004) implies that 4000 spatulae would need to be attached
to 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 and
Ernst 1965; Schleich and Kästle 1986)). Therefore a spatular force of 40 nN is more
appropriate for a conservative estimate of setal contact fraction during attachment. In the
case of a spatular adhesion force of 40 nN, the adhesive stress is 2000 kPa. Therefore a
contact fraction of 46% is required to yield the setal stress. This suggests that unless the
force of adhesion of a spatula has been greatly underestimated, the contact fraction must
increase 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 aspect
ratio shafts. The effective elastic modulus, !e##$ (Persson 2003; Sitti and Fearing 2003) is
much lower than the Young's modulus (!) of !-keratin. Thus arrays of setae should
behave as a softer material than bulk !-keratin. ! of beta-keratin in tension is approx. 2.5
GPa in bird feathers (Bonser and Purslow 1995) and 1.3 to 1.8 GPa in bird claws (Bonser
2000). Young’s moduli of lizard beta keratins in general (Fraser and Parry 1996) and
gecko beta keratins in particular (Alibardi 2003) remain unknown at present. The
behavior 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 as
cantilever beams (Glassmaker et al. 2004; Hui et al. 2004; Persson 2003; Sitti and
Fearing 2003; Spolenak et al. 2005). One might question the applicability of models
based on a simple geometry for the complex, branched structure of the seta. However, as
with the JKR and Kendall models (Sections 3.5.4 and 3.5.5) applied to spatulae, the
simple cantilever model is surprisingly well supported by empirical measurements of
setal arrays (Geisler et al. 2005).
The cantilever model of a single seta (Campolo et al. 2003; Sitti and Fearing 2003) is
based 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 Timoshenko
1984) (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 ' =
F !"#"" # L$
'ncos! (Fig. 4B). This results in a lateral tip displacement of ! ! n
$EI , and a
" cos 2 "" # #3
normal tip displacement of ! n ! ! cos " ! n
3$% .
Next, to derive an effective elastic modulus (")**) for a model setal array, in the cantilever
system above, we use Hooke’s law, " = ")**#, where " and # are the applied stress and
resulting 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 ! and
under a normal stress ", the normal force acting on each cantilever tip is 'n = ",-,+. The
" !"s$ (# ) "%
resulting normal displacement of the array is ! n =
%#$% . Thus,
2
2
" cos "# # !
, and the stress over the cantilever array is
!!
3"#$sin #
! ! cos2 (" ) $2
. Dividing by " and Solving for ")** we reach a general
! ! e##
3!%&sin "
equation for the effective stiffness of a cantilever array,
E eff ! 3EIDsin !
cos 2 "! # L2 .
For a cylindrical cantilever, we can substitute "# in Eqn. 5.2 for
yielding,
E eff !
K y LDsin !
cos 2 !
.
(5.2)
! " #3
3 using Eqn. 5.1,
(5.3)
For a tokay seta-size cylindrical cantilever of & = 2.1µm, ! = 110 µm, " = 1 GPa, the
bending 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 stiffness
of 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. ;sing
Eqn. 5.3, a value of ! 8 50D is required for " 8 1 GPa, and ! 8 36.65D for " 8 2 GPa to
yield "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. We
found that "e$$ of tokay gecko setae falls near 100 kPa, close to the upper limit of
Dahlquist’s criterion for tack (Fig. 5)(Geisler et al. 2005). Additionally, we observed
values of ! for tokay gecko setae near 43D, further supporting the validity of the
cantilever model (Fig. 4; (Geisler et al. 2005)).
!"#"$%&'()$*'+f-.e$-01$-0234-2230($.&01323&0*
The cantilever model predicts that a high density of setae should be selected for in
increasing adhesive force of setal arrays. Firstly, it follows from the JKR model (Arzt et
al. 2003; Autumn et al. 2002b) that packing in more spatulae should increase adhesion in
an array of setae. Secondly, the cantilever model suggests that thinner setal shafts should
decrease Eeff, and promote a greater contact fraction on rough surfaces (Campolo et al.
2003; Jagota and Bennison 2002; Persson 2003; Persson and Gorb 2003; Scherge and
Gorb 2001; Sitti and Fearing 2003; Spolenak et al. 2005; Stork 1983). The cantilever
model also suggests that longer and softer setal shafts, and a lower shaft angle ! will
result in better adhesion on rough surfaces because these parameters will reduce "e$$. On a
randomly 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 setal
array from a rough surface should therefore be determined by the cumulative adhesive
force of all the attached spatulae, minus the sum of the forces due to elastic deformation
of compressed setal shafts.
If setae mat together (Stork 1983), it is likely that adhesive function will be
compromised. Interestingly, the same parameters that promote strong adhesion on rough
surfaces 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 between
setae and the stiffness of the shafts will determine the amount of force required to bring
the 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 the
case for self-cleaning (Hansen and Autumn 2005), setae should be made of materials with
lower surface energy to prevent self-adhesion and matting. Satisfying both antimatting
and rough surface conditions may require a compromise of design parameters. Spolenak
et al. (2005) devised `design mapsa for setal adhesive structures, an elegant approach to
visualizing the parametric tradeoffs needed to satisfy the rough surface and antimatting
conditions 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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Kellar Autumn
The Gecko Adhesive System
20 of 39
Natural surfaces are rarely smooth, and an important next step will be to measure
empirically the effect of surface roughness (Vanhooydonck et al. 2005) on friction and
adhesion in gecko setae to test the predictions of the new generation of theoretical models
for rough surface contacts with micro and nanostructures (Persson and Gorb 2003).
Under real-world conditions where surfaces are fractal (Greenwood 1992; Persson and
Gorb 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 seta
have not yet been developed. Similarly, models of lamellar structure will be needed to
explain function on roughness above the micron scale.
Biological diversity of setal and spatular structure is high and poorly documented. Basic
morphological description will be required. Theory predicts that tip shape affects pulloff
force less at smaller sizes (Gao and Yao 2004), so it is possible that part of spatular
variation is due to phylogenetic effects, but material constraints such as tensile strength of
keratin must be considered as well (Autumn et al. 2002b; Spolenak et al. 2005). The
collective behavior of the setal array will be a productive research topic (Gao and Yao
2004). Diversity of the array parameters, density, dimension, and shape is great but not
well documented. In particular, the shape of setal arrays on lamellae demands further
investigation. Phylogenetic analysis (Harvey and Pagel 1991) of the variation in setal
structure and function will be required to tease apart the combined effects of evolutionary
history, 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). One
possible role of non-keratin proteins is as a glue that holds the keratin fibrils together in
the seta (Fig. 1D) (Alibardi 2003). This suggests a possible role of genes coding for
histidine-rich protein(s) in tuning the material properties of the setal shaft. The outer
molecular groups responsible for adhesion at the spatular surface will also be an
important 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 setae
blindly is unlikely to succeed due to the complexity of the system (Fig. 1) and the fact
that evolution generally produces satisfactory rather than optimal structures. Instead,
development of biologically inspired adhesive nanostructures will require careful
identification and choice of design principles (Table 2) to yield selected geckolike
functional properties. As technology and the science of gecko adhesion advance, it may
become possible to tune design parameters to modify functional properties in ways that
have not evolved in nature.
It is remarkable that the study of a lizard is contributing to understanding the fundamental
processes underlying adhesion and friction (Fakley 2001; Urbakh et al. 2004), and
providing biological inspiration for the design of novel adhesives and climbing robots.
Indeed the broad relevance and applications of the study of gecko adhesion underscore
the importance of basic, curiosity based research.
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!oology 23), 2+9-3...
Rosenberg 67 and Rose R. (1999). =olar adhesive pads of the feathertail glider,
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Kellar Autumn
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':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 !C
keratin 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 .?SAsP
MahlNuist 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 is
nota%le that +eckos have evolved !e## close to the limit of tack= This value of !e## may %e
tuned to allo@ stron+ and raBid adhesionO yet Brevent sBontaneous or inaBBroBriate
attachment=
!i#ure +) Stress versus area in the +ecko adhesive hierarchy= See Ta%le J for numerical
values and literature sources= UKW and Kendall model Bredictions for sBatular adhesive
stress .trian+les0 %ound the measured value of Ku%er et al= .2;;I0= TeFt %elo@ the XCaFis
sho@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 attachment
Shaft len9th: radius: density 1Sitti = >earin9
1Autumn et al" 25556
25536
2" @i9h !A 1+ulloffB+reload6
1Autumn et al" 25556
3" CoD detachment force
1Autumn et al" 25556
Eantilever Geam 1Autumn et al" 2555H Sitti =
>earin9 2553H S+olenak et al" 255JH Geisler =
Autumn in +re+6
Shaft an9le 1Sitti = >earin9 25536
CoD effective stiffness
Shaft modulus 1Sitti = >earin96
1Sitti = >earin9 2553H Lersson 2553H Geisler =
Autumn in +re+6
S+atular sha+e 1Lersson = GorG 2553H
S+olenak: GorG: Gao: ArMt 255J6
van der Saals 1vdS6 mechanism
1Autumn et al" 25526
J" Oaterial inde+endence
1Autumn et al" 2552H @iller !9QR:96
TKVWlike contact mechanics
1@ansen = Autumn 255Y6
Q" AntiWself
1ArMt: GorG: S+olenak 25536
S+atular Sha+e
1Autumn et al" 2552H ArMt et al" 2552:36
1Gao = Nao 255JH S+olenak: GorG: Gao: ArMt
255J6
Xanoarray 1divided contact6
S+atular density
1Autumn et al" 2552H Gao et al" 255J6
Y" SelfWcleanin9
S+atular siMe
Xanoarray 1divided contact6
Small contact area
1ArMt: GorG: S+olenak 2553H Leattie 255J6
S+atular Gulk modulus
Larticle siMe: sha+e: surface ener9y
Xontacky s+atulae
7" Xonsticky default state 1Autumn =
@ansen in revieD6
@ydro+hoGic: vdS s+atulae
S+atular siMe: sha+e: surface ener9y
Fig. 1
"i$. &
"evel
&lim)in+
Fig. 3
Fig. 4
Fig. 6