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\title{MicroWedges: microfabricated arrays displaying geckolike dynamic adhesion, directionality, and long life}

\author{Aaron Parness\thanks{To whom correspondence should be addressed.  E-mail: ski4ever@stanford.edu}\affil{1}{Stanford University, Stanford, CA}, Daniel Soto\affil{1}{}, No\'e Esparza\affil{1}{}, Nick Gravish\affil{2}{Lewis and Clark College,Oregon}, Matt Wilkinson\affil{2}{}, Autumn Kellar\affil{2}{} \and Mark Cutkosky\affil{1}{}}


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\contributor{Submitted to Proceedings of the National Academy of Sciences 
of the United States of America}

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\begin{article}

\begin{abstract}      % TBD
Gecko adhesion has become a paradigmatic example of bio-inspired engineering, yet among  the many geckolike synthetic adhesives (GSAs), truly geckolike performance has been elusive.  Many GSAs have previously demonstrated one or two features of the gecko adhesive.  We have developed a new GSA, MicroWedges, that exhibits many geckolike properties simultaneously: directional features, zero force at detachment, a high \gm', a non-adhesive default state, the ability to be scaled to large areas, massive reusability, and `dynamic adhesion'--MicroWedge fibers independently detach and reattach during sliding, providing high levels of both shear and normal adhesion during drag.  This behavior provides a non-catastrophic failure mechanism crucial for high risk applications like climbing robots and devices for human climbing.  Large 1 cm\textsuperscript{2} patches showed adhesive pressures greater than 5.1 kPa while simultaneously supporting more than 17.0 kPa of shear, and patches were found to be effective for over 30,000 attachment/detachment cycles without requiring cleaning. 20 \gm m and 50 \gm m diameter MicroWedges are manufactured in a molding process where molds are fabricated using a dual-side, dual-angle lithography process on quartz wafers with SU-8 photoresist as the mold material and PDMS as the cast material.
\end{abstract}


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\keywords{ dry adhesion | fibrillar adhesive | gecko }


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\section{Introduction}

\dropcap{T}he gecko inspires a great deal of attention because of its incredible ability to use a very stiff material, \gb-keratin (E$\sim$1.6GPA)\cite{Peattie2007}, to create something soft and tacky. Seven major functional properties of the gecko adhesive were identified in 2005.  The gecko adhesive is 1) directional 2) attaches strongly with minimal preload 3) detaches quickly and easily, 4) sticks to nearly every material, 5) does not stay dirty or 6) self-adhere, and 7) is nonsticky by default \cite{Autumn2006Book}. We believe another critical attribute of the gecko's adhesive is missing from this list: the ability to engage and sustain high levels of adhesion while sliding. Because gecko setae and spatulae are able to independently detach and reattach, a consistent level of friction and adhesion is maintained as samples are dragged in their preferred direction across surfaces\cite{Autumn2006}. The gecko employs this 'dynamic adhesion' to help engage and load the many terminal spatulae evenly. Dynamic adhesion also provides a non-catastrophic failure mechanism during climbing.

GSAs potential applications in robotics, biomedical devices, manufacturing, consumer products, and in devices for human climbing, have spawned a large number of attempts to create usable materials. Although many of these synthetics have some geckolike attributes, a structure that replicates all of the gecko adhesive's properties, and its subsequent utility, remains a holy grail of sorts in the field. MicroWedges further work towards that goal as seen in Table \ref{GSAComparison}.

Many groups have successfully exploited the contact splitting aspect of the gecko adhesive\cite{Yurdumakan2005,Zhao2006,Tsai2006,Ge2007,Geim2003}. Interesting work has also been done on hierarchical structures and actively switchable adhesives by \cite{Northen2005,Northen2006conf}. However, these structures had been fabricated at right angles to the substrate despite the fact that that real gecko setae are angled, permitting largely linear elastic deformation and low effective modulus\cite{Autumn2006a}. One recent GSA addressed directionality by fabricating fibers at an oblique angle to the substrate\cite{Aksak2007}. While these angled pillars lowered the effective stiffness of the sample and showed great promise, the tips of the fibers were coplanar with the base of the surface, creating a situation in which fibers likely pivoted onto a single point contact during drag.  Tip shape has been shown to have a drastic affect on adhesion for contact diameters on the order of 1 \gm m or more\cite{Gao2004} and non-directional synthetics utilizing spatular tips\cite{Gorb2007, Kim2006} achieved much greater adhesive pressures than the original angled GSAs, likely due to this phenomenon. However, the latest work on these angled stalks improved the tip geometry through a dipping procedure, dramatically increasing performance \cite{Murphy2007}, although even further improvement might be achieved if the spatular tips could also be fabricated at an angle. High aspect ratio, stiff polypropylene fibers have recently been shown to develop high shear forces despite a vertical orientation when loaded in shear \cite{Fearing1, Fearing2}.  Our group previously created an adhesive that combined both directional stalks and non-coplanar tips\cite{Santos2007,SantosJAST} that performed very well on a climbing robot\cite{Kim2007}, but this result was fabricated at a fiber diameter (d = 380 \gm m) much larger than the gecko setae. Theory suggests that smaller features and features with a low modulus of elasticity will perform better\cite{Arzt2003, Dai2006}. Recent work has also shown increased adhesion on both wet and dry substrates through the use of surface coatings\cite{Lee}. 

MicroWedges, seen in figure \ref{SEM}, overcome several of the recent challenges in the field of GSAs. Large arrays of MicroWedges retain nearly 100\% of their adhesion during sliding, showing dynamic adhesion for the first time in a flat punch test.  Using a flat punch instead of a spherical tip is important for sliding tests because it insures that fibers detach and reattach across a large contact area as opposed to simply engaging new fibers with the leading edge of the sphere. {Fearing1, Fearing2} show continuous shear during drag, but require a positive normal force rather than producing steady levels of adhesion.  MicroWedges asymmetric features follow the directional adhesion model observed in the gecko\cite{Autumn2006}. This means that adhesion increases as shear force is applied in a preferred direction, allowing the amount of adhesion to be controlled.  Additionally, when the shear loading is removed, MicroWedges can be detached with virtually zero force.  The sharp tip shape helps engage the adhesive at low attachment forces, and only very large patch sizes that would be useful in real applications were tested. MicroWedges also set a new standard of reusability for GSAs, retaining 56\% of their initial adhesion after a battery of 30,000 test cycles, more than 2 orders of magnitude better than any previous result.

MicroWedges were fabricated and tested at two characteristic stalk diameters, 20 \gm m and 50 \gm m.  MicroWedges were also fabricated out of three different materials of varying bulk properties in order to begin forming empirical relationships between feature size, stiffness, adhesion, clumping, and self cleaning.  

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\section{Results and Discussion}    
\subsection{Dynamic Adhesion}
Data from a flat punch load-drag-pull (LDP) test are shown in Figure \ref{mwForceTrace} (LDP tests consisted of a 45$^\circ$ preload trajectory to a depth of 80 \gm m followed by a 1mm horizontal drag and finishing with a vertical pulloff\cite{AutumnGravish2008}). These data are for a 1 cm$^2$ patch of 50 \gm m stalks made from Dow Corning's Sylgard 170 silicone encapsulant with a backing thickness of 600\gm m, but are representative of all 6 sample types tested. The most striking phenomenon observed is the continuous adhesion during the 1 mm drag phase between points 2 and 3.  Unlike spherical indenter tests which engage new fibers as the probe moves horizontally across the sample, these data indicate that stalks are detaching independently and reattaching, a property previously unreported for any GSA.  Previous flat punch results, in contrast, pass through point 2 and immediately drop to near zero adhesion. The gecko also exhibits dynamic adhesion as shown in the flat punch LDP data for a gecko setae, see Figure  \ref{geckoForceTrace}.

Dynamic adhesion is a very significant result for MicroWedges not only because it more accurately mimics the gecko, but because the prominent failure mode is no longer a catastrophic detachment event, but a slow and predictable slip.  The gradual sliding contact allows time for an animal/robot to compensate by reattaching the slipping foot in another location or by placing additional feet on the surface to secure overall grip. In geckos, the sliding phenomenon also helps to orient all of the terminal spatulae for good contact while not damaging individual contacts, and thereby reduces the demand on the accuracy of foot presentation to the climbing surface. We believe contacts may self align by sliding into their preferred alignment, relieving stress concentrations through frictional loss. This behavior helps MicroWedges' adhesion scale to large patch sizes, and will be even more valuable to future versions of GSAs that are hierarchical and require a similar ability to passively distribute a foot's load to individual contacts. 

%Figure \ref{mwForceTrace} is representative of data seen for all 6 sample types tested, although overall adhesion and shear values varied somewhat between sizes and materials as reported below.

\subsection{Directionality}

Similar to the behavior observed in individual gecko setae and whole gecko toes, MicroWedges follow the frictional adhesion model\cite{Autumn2006} by demonstrating more adhesion when loaded in a preferred shear direction. This property makes an adhesive particularly well suited to climbing vertical surfaces, where the body weight of an animal or robot induces a large downward shear loading on the contacts, and where feet must be detached without disturbing the overall purchase of the remaining legs.

Data was collected for MicroWedges by running a series of flat punch load-pulloff (LP) tests\cite{Santos2007} which all began with a preload of 45$^\circ$ that terminated at a depth ranging from 0\% to 80\% of the stalks' height. The preload phase was immediately followed by a pulloff trajectory at a specified angle that ranged from 0$^\circ$ to 180$^\circ$. Shear and normal forces were recorded at the failure event, which was determined to be the point that the adhesive either popped off or began sliding. Shear and normal force results for the entire series of tests are plotted together in Figure \ref{FrictionAdhesion50s}, creating a limit surface inside of which contact will be maintained.  The shape of this plot shows the directional behavior of MicroWedges; maximum adhesion is reached only when a large value of shear is present. Additionally, because the limit surface intersects the origin, when no shear is applied to a sample, MicroWedges detach without any pulloff forces. These two facts allow Microwedges to act as a programmable adhesive, effectively controlled by the amount of shear loading imposed upon a given patch.  High performance climbing applications require this programability. There exist many materials that provide enough adhesion to support a gecko or a small robot (i.e. duct tape), but of these solutions, only materials that can switch on and off are useful. A robot climbing with non-directional adhesives would experience large pull off forces at detachment that consume large amounts of energy and create vibrations that could cause the robot to fall.  Non-directional adhesives are also incapable of the rapid attachment/detachment cycles observed in the gecko (15 ms 25 ms)\cite{?}.

While easy detachment of feet is crucial to climbing quickly and efficiently, easy attachment of an adhesive patch is equally important.  The gecko, utilizing a four-tiered hierarchy, exhibits a \gm' of between 8 and 16 depending on conditions\cite{Autumn2000}, which means that it can pull with 8 to 16 times the normal force with which it has preloaded its' feet.  \gm' values for GSAs range from 0.02 to 7.5 \cite{Zhao2006, Gorb2007}.  The highest \gm' observed for MicroWedges was 2.1 and occurred when stalks were loaded at an incoming angle of 30$^\circ$ to avoid buckling fibers.  Adhesion during this trial was 4.9 kPa, very near the maximum adhesive pressure observed. It is interesting to keep in mind that a four legged climbing robot has a theoretical minimum \gm' of 0.33 because the attached feet must support the preload of the next step.      

The MicroWedge data presented show some bi-directional behavior.  This is attributable to the thin tip at the end of the wedge, which is capable of flopping over in the anti-preferred direction and creating a significant area of contact when loaded in such a way.  However, the desirable functions of directionality are attained, 1) adhesion increases with shear loading and 2) the limit surface passes through the origin.  It is these two properties that the gecko relies on to activate and release the adhesion of its feet while climbing. For contrast, flat control patches were also tested with the same trajectories and are shown in Figure \ref{FrictionAdhesionFlat}.  These data fit embedded friction cone behavior, which is isotropic and exhibits the strongest adhesion under no shear loading.

\subsection{Long Life}

There has been little data presented on the reusability of GSAs in the literature to this point, and where it is present, it is almost always seen that performance has dropped significantly after only a few tests because structures have broken or become dirty\cite{Geim2003, Yurdumakan2005, Zhao2006, Northen2005, Kim2006}.  Some exceptions to this, Directional Polymer Stalks\cite{Santos2007, SantosJAST} and The Max Planck Institute's mushroom shaped adhesive\cite{Gorb2007}  claim reusability for over 100 attachment/detachment cycles before performance degraded and cleaning was required.  After this cleaning, some samples were shown to regain their initial performance. UC Berkeley's polypropylene hairs\cite{Fearing1, Fearing2} retained a high level of performance for over 150 cycles.  MicroWedges performed well for over 30,000 trials without cleanings before the experiment was stopped.  

A high value of \gm' helps a GSA's reusability by preventing damage to stalks during the loading procedure.  In the case of MicroWedges, durability is also a result of the elastomeric materials ability to bend rather than break.  While a gecko's adhesive system is massively reusable with a very stiff material, \gb-keratin (E $\sim$ 1.6GPa \cite{Peattie2007}), it only achieves this because of the multi-level hierarchy that distributes the load to individual spatulae.  Setae and spatulae also avoid overload damage by detaching and resticking as needed, the dynamic adhesion property also observed in MicroWedges. Without these attributes, it is not surprising that many single level, stiff, non-sliding GSAs only show good levels of adhesion for a few tests before suffering irreparable damage.

Figure \ref{mwLongevityTest} shows data for a 1 cm$^2$ patch of Sylgard 170 over a battery of 30,000 Load-Drag-Pull cycles.  The drag phase of these tests was extended from 1 mm to 10 mm in order to increase the rate of wear on the stalks.  A preload depth of 100 \gm m was used and the average values of shear and normal adhesion during the drag phase were taken as representative data points for each trial and plotted.  Clearly, MicroWedges are massively reusable without frequent cleanings. The gecko's adhesive system is also massively reusable, as it must climb for long periods of time before new growth replaces the setae and terminal spatular elements of its toe pads.  %Similar data from a battery of LDP cycles performed on a patch of harvested gecko setae is presented in figure \ref{GeckoLongevity}.

Based on the durability data for MicroWedges and assuming a robot stride length of 5 cm, a 1500 meter building could be scaled using MicroWedges. %Current research is focussing on the development of a hierarchical system for MicroWedges to make this scenario a reality and move from the tightly controlled parameters of an experimental stage to climbing robots and mechanisms for human climbing.  Work is also ongoing to manufacture MicroWedges at even smaller sizes and with more complicated geometries that could enhance their performance. 

\subsection{Material Choice and Size Considerations}

MicroWedges were fabricated at two characteristic stalk diameters, 50 \gm m and 20 \gm m, both at a 25\% fill factor in a square pattern.  Assuming a similar loading trajectory scaled by the stalk size, the array of 20 \gm m features have the same real area of contact, but with a 2.5$\times$ increase in the summed perimeter of contacting elements.  Results for similar patches fabricated from Sylgard 170 at these two characteristic size scales with identical backing layers are plotted in a force space representation below in Figure \ref{sizeComparison}.  It has been reasoned that contact splitting will increase overall adhesion in a vertical preload/vertical pulloff experiment\cite{Arzt2003}, and although similar behavior is observed in Figure \ref{sizeComparison} for directional tests, this was not the case across all materials tested and results varied based on the backing thickness of samples as well.  Further research on a broader variety of samples is needed for conclusive comparisons on feature size, backing thickness, and overall levels of adhesion.   The general directional behavior of the stalks, their ability to adhere dynamically, and the shape of the limit surface did remain consistent at both characteristic sizes across all trials.  

In total, six sample types were fabricated and tested extensively, 50 \gm m and 20 \gm m diameter wedges of 3 material types: Silicones Inc. P-20, Dow Corning Sylgard 170, and Silicones Inc. P-70.  Bulk material properties for these elastomers were measured using thin, flat control samples and macroscale cubes of material.  The Young's Moduli for the materials were measured as 340kPa, 760kPa, and 930kPa for P-20, Sylgard 170, and P-70 respectively.  It was expected that the softest material, P-20, would show the strongest levels of adhesion, but would be susceptible to dirt and fouling.  Although samples were successfully fabricated and tested using this soft polymer, the material proved to be too soft and widespread clumping of wedges was observed in both the 50 \gm m and 20 \gm m arrays of stalks, resulting in significantly reduced performance. Arrays of Sylgard 170 and P-70 cast from the same mold did not clump extensively, but performed similarly to one another at both size scales.  This led to the recognition of a need to test more drastically different materials if a quantitative empirical relationship between effective stiffness and adhesion is to be achieved.

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\section{Materials and Methods}

\subsection{Design and Fabrication}
Taking cues from Directional Polymer Stalks \cite{Santos2007,SantosJAST}, the wedge shape was chosen as a viable anisotropic geometry with a sharp tip shape that would promote high levels of adhesion.  For fabrication, we were inspired by work on angled microstructures unrelated to adhesion that used multiple angled exposures in SU-8 to create interesting three dimensional structures\cite{Yoon2, Sato1, Han1}, and developed a process based on innovative lithography and molding techniques. Using thick films of SU-8, arrays of wedge-shaped cavities were created as a reusable mold into which soft, elastomeric polymers were poured and released.  

To create the SU-8 mold, a 2 mask angled exposure technique was developed where an angled backside exposure was sequentially followed by a vertical topside exposure before development to create a 3D structure in the film. After several early failures, care was taken in the final mask designs to reduce volumes in the film that would be unmasked during both exposures. A custom built tilting stage was used to orient the wafer at a repeatable and precise angle under a collimated UV lamp for the angled exposure. This angle was subject to a correction factor to account for the refraction effect due to SU-8's high index of refraction (n=1.61) \cite{Hung1}. For the structures presented here, the target angle was 14.8$^\circ$ to create a 4:1 aspect ration, which required an exposure angle of 23.5$^\circ$. After the molds were created, various silicone based elastomers were cast under vacuum, spun to a desired backing layer thickness, heat cured, and pulled out of the mold by hand. Molds typically exhibited reusability for over 10 cast/peel cycles. The fabrication sequence is shown in Figure \ref{Fabsteps}.

\subsection{Test Equipment and Experimental Methods}

Data was collected using two different experimental test setups. Each setup is capable of moving a flat glass substrate and sample into and out of contact along trajectories in both the normal and tangential direction simultaneously. One setup is the local test stand for the Biomimetics Dexterous Manipulation Laboratory (BDML) at Stanford University, Stanford, CA. The BDML setup consists of a 3-axis linear stage, force transducer and 2-axis manual tilt stage. The motion stage (Velmex, MAXY4009W2-S4 and MA2506B-S2.5) has a 10 \gm m positioning resolution in the tangential direction and a 1 \gm m positioning resolution in the normal direction. The flat glass substrate is attached to the motion stage while the sample is placed upon a 6-axis force/torque sensor (ATI Industrial Automation, Gamma Transducer SI-32-2.5). The force transducer is mounted onto a manual 2-axis tilt stage (Newport, 30 Series Tilt Platform) which is used for manual alignment of the sample relative to the substrate. The second setup is located at Lewis and Clark College, Portland, OR. The Lewis and Clark setup consists of a 2-axis linear stage, force transducer and 2-axis tilt stage. The motion stage is formed by two Aerotech ANT-50L (Aerotech, Pittsburgh, PA) linear actuators, which provide positioning control on the nanoscale, and the flat glass substrate is attached rigidly to the motion stage. The sample is mounted onto a Kistler9328A three-axis piezoelectric force sensor (Kistler, Winterthur, Switzerland). Two Newport goniometers, GON65L and TR120BL, (Newport, Irvine, CA) are used to align the sample and substrate. 

In total, three different types of experiments were performed, LDP tests \cite{AutumnGravish2008}, LP test series \cite{Santos2007}, and longevity tests as described in Results and Discussion.  These experiments were designed to explore MicroWedges' dynamic adhesion, directionality (and the contact limit surface), and reusability, among other properties.

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\begin{acknowledgments}
-- text of acknowledgments here, including grant info --
\end{acknowledgments}


%% Add your bibliography items here.  PNAS requires that bibliography items
%% be entered directly into the article rather than called from a BibTeX
%% environment.  Contact pnas@nas.edu if you need assistance with your
%% bibliography.

% Sample bibliography item in PNAS format:
%\bibitem{Ch} D. Chae (2003) {\it Nonlinearity} {\bf 16}, 479-495.
%\bibitem{Ch} Author Names (year published){\it Journal Name} {\bf Volume #}, %start page-end page

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\begin{thebibliography}{10}

\bibitem{Ge2007} L. Ge, S. Sethi, L. Ci, P.M. Ajayan \& A. Dhinojwala (2007) Carbon nanotube-based synthetic gecko tapes. {\it PNAS} {\bf 104} 10792-10795

\bibitem{Autumn2006Book} K. Autumn (2006) {\it Biological Adhesives}, 225-256.

\bibitem{Peattie2007} A. Peattie, C. Majidi, A. Corder \& R.J. Full (2007) Ancestrally high elastic modulus of gecko setal \gb-keratin  {\it J. R. Soc. Interface} {\bf }, 1071-1076.

\bibitem{Aksak2007} B. Aksak, M.P. Murphy \& M. Sitti (2007) Adhesion of biologically inspired vertical and angled polymer microfiber arrays. {\it Langmuir} {\bf 23}, 3322-3332.

\bibitem{Gao2004} H. Gao \& H. Yao (2004) Shape insensitive optimal adhesion of nanoscale fibrillar structures. {\it PNAS}  {\bf101}, 7851-7856.

\bibitem{SantosJAST} D. Santos, M. Spenko, A. Parness \& M. Cutkosky (2007) Directional adhesion for climbing: theoretical and practical considerations. {\it J. Adhesion Science and Technology} {\bf21}, 1317-1341.

\bibitem{Tsai2006} Y. Tsai, W. Shih, Y. Wang, L. Huang \& P. Shih (2006) E-Beam photoresist and carbon nanotubes as biomimetic dry adhesives. {\it IEEE MEMS} {\bf  }, 926-929.

\bibitem{Arzt2003} E. Arzt, S. Gorb \& R. Spolenak (2003) From micro to nano contacts in biological attachment devices. {\it PNAS} {\bf100}, 10603-10606.
 
\bibitem{Dai2006} Z. Dai, M. Yu \& S. Gorb (2006) Adhesion characteristics of polyurethane for bionic hairy foot. {\it Journal of Intelligent Material Systems and Structures} {\bf 17}, 737-741. 
 
\bibitem{Autumn2000} K. Autumn et al (2000) Adhesive force of a single gecko foot-hair. {\it Nature} {\bf 405}, 681-685.

\bibitem{Autumn2006} K. Autumn, A. Dittmore, D. Santos, M. Spenko \& M. Cutkosky (2006)  Frictional adhesion: a new angle on gecko attachment. {\it Journal of Experimental Biology} {\bf 209} 3569-3579

\bibitem{Autumn2006a} K. Autumn et al (2006) Effective elastic modulus of isolated gecko setal arrays. {\it Journal of Experimental Biology} {\bf 209} 260-272

\bibitem{Geim2003} A. Geim et al (2003) Microfabricated adhesive mimicking gecko foot-hair. {\it Nature Materials} {\bf 7} 461-463 

\bibitem{Hansen2005} W.R. Hansen \& K. Autumn (2005) Evidence for self-cleaning in gecko setae. {\it Proceedings of the National Academy of Science} {\bf 102} 385-389.

\bibitem{Lee} H. Lee, B.P. Lee \& P.B. Messersmith (2007) A reversible wet/dry adhesive inspired by mussels and geckos. {\it Nature} {\bf 448}, 338-342.

\bibitem{Kim2007} S. Kim et al (2007) Whole body adhesion: hierarchical, directional and distributed control of adhesive forces for a climbing robot.  {\it IEEE ICRA}, 1268-1273.

\bibitem{Yurdumakan2005} B. Yurdumakan, R. Raravikar, P. Ajayanb \& A. Dhinojwala (2005) Synthetic gecko foot-hairs from multiwalled carbon nanotubes. {\it Chem. Commun.} {\bf 30} 3799-3801.

\bibitem{Zhao2006} Y. Zhao et al (2006) Interfacial energy and strength of multiwalled-carbon-nanotube-based dry adhesive. {\it J. Vac. Sci. Technol. B} {\bf 24} 331-335.

\bibitem{Northen2005} M. Northen \& K. Turner (2005) A batch fabricated biomimetic dry adhesive. {\it Nanotechnology} {\bf 16} 1159-1166 

\bibitem{Northen2006conf} M. Northen, K. Turner, C. Greiner \& E. Arzt (2006) A hierarchical gecko-ispired switchable adhesive. {\it Hilton Head} 43-46

\bibitem{Kim2006} S. Kim \& M. Sitti (2006) Biologically inspired polymer microfibers with spatulate tips as repeatable fibrillar adhesives. {\it Appl. Phys. Lett} {\bf 89}, 
261911.

\bibitem{Sato1} H. Sato, Y. Houshi \& S. Shoji (2004) Three-dimensional micro-structures consisting of high aspect ratio inclined micro-pillars fabricated by simple photolithography. {\it Microsystem technologies} {\bf 10}, 440-443.

\bibitem{Han1} M. Han, W. Lee, S.K. Lee \& S.S. Lee (2004) 3D microfabrication with inclined/rotated UV lithography. {\it Sensors, Actuators A} {\bf 111}, 14-20.

\bibitem{Yoon2} Y.K. Yoon, J.H. Park \& M. G. Allen (2006) Multidirectional UV Lithography for complex 3D MEMS structures. {\it Journal of Microelectricalmechanical Systems} {\bf 15} 1121-1130.

\bibitem{Gorb2007} S. Gorb, M. Varenberg, A. Peressadko \& J. Tuma (2007) Biomimetic mushroom-shaped fibrillar adhesive microstructure. {\it J. R. Soc. Interface} {\bf 4}, 271-275.

\bibitem{Santos2007} D. Santos, S. Kim, M. Spenko, A. Parness \& M. Cutkosky
(2007) Directional adhesive structures for controlled climbing on smooth vertical surfaces. {\it IEEE ICRA} 

\bibitem{Hung1} K.Y. Hung, H.T. Hu \& F.G. Tseng (2004) Application of 3D glycerol-compensated inclined-exposur technology to an integrated optical pick-up head. {\it Journal of micromechanics, microengineering} {\bf 14} 975-983.

\bibtem{Fearing1} J. Lee, C. Majidi, B. Schubert \& R.S. Fearing (2008) Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behviour. {\it J. R. Soc. Interface} doi:10.1098/rsif.2007.1308  

\bibtem{Fearing2} B. Schubert, J. Lee, C. Majidi \& R.S. Fearing (2008) Sliding-induced adhesion of stiff polymer microfibre arrays. I. Microscale behviour. {\it J. R. Soc. Interface} doi:10.1098/rsif.2007.1309

\end{thebibliography}

\end{article}
% figures and tables here

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/SEM.pdf}
\caption{SEM images of MicroWedges  a) side view of 20 \gm m diameter MicroWedges  b) diagonal view of large array of 50 \gm m diameter MicroWedges \label {SEM}}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/mwForceTrace.pdf}
\caption{MicroWedge load-drag-pull data from a single trial.  Preload occurs from point 0 to 1 consisting of a 45 degree approach angle to a depth of 80 \gm m.  This was followed by a 1 mm drag (points 2-3) and a vertical pulloff (points 3-4).  The substrate moved at a constant 500 \gm m/s over the course of the trial.  Notice the sustained dynamic adhesion and shear between points 2 and 3, indicating independent detachment and reattachment of single wedges.  \label{mwForceTrace}}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/geckoForceTrace.pdf}
\caption{Gecko setae load-drag-pull data from a single trial.  Comparison with figure 3 shows the strong behavioral similarity between MicroWedges and gecko setae, especially the dynamic adhesion observed between points 2 and 3.  \label{geckoForceTrace}}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/FrictionalAdhesion_Sylgard170_50s_225um.pdf}
\caption{Limit surface of a Sylgard 170 sample of 50 \gm m stalks on a 225 \gm m backing layer.  Points indicate contact failures either through slipping or detachment from the surface.  Important to note: adhesion is only achieved in the presence of shear loading, following the frictional adhesion model \cite{Autumn2006}.  Also, the limit surface intersects the origin, indicating that when no shear is present, MicroWedges can be detached with zero force. \label{FrictionAdhesion50s}}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/flatLimitSurface.pdf}
\caption{Limit surface of a flat patch of Sylgard 170.  This set of data follows the imbedded cone model \cite{??} exhibiting the strongest adhesion when no shear loads are present.
\label{FrictionAdhesionFlat}}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/sizeComparison.pdf}
\caption{Size Comparison Adhesion  \label{sizeComparison}}
\end{center}
\end{figure}


\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/mwLongevityTest.pdf}
\caption{Lifetime data for a single sample of 50 \gm m stalks made from Sylgard 170.  MicroWedges are massively reusable, retaining over \%50 of their adhesion after 30,000 trials.  This is more than two orders of magnitude longer than any other published data on GSAs. \label{mwLongevityTest}}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=0.8\columnwidth]{./figures/Fabsteps.pdf}
\caption{Fabrication Sequence 1) Deposit aluminum on quartz wafer 2) Pattern aluminum to create self-aligned mask 3) Deposit SU-8 on top of aluminum 4) Angled self-aligned UV exposure from backside 5) Align mask to topside and UV expose 6) Develop 7) Cast and spin PDMS 8) Peel out cast microwedges and backing layer\label{Fabsteps}}
\end{center}
\end{figure}

\begin{table}
\newcommand{\colsize}{0.60in}
\begin{tabular}{ p{1.0in} p{\colsize} p{\colsize} p{\colsize} p{\colsize} p{\colsize}
p{\colsize} p{\colsize} p{\colsize} c}
 &  gecko toe & Parness & Lee &  Gorb &  Ge & Kim & Murphy & Northen \\
 & & Cutkosky  & Fearing & & Dhinojwala & Sitti & Sitti & Turner\\
 \hline
adhesion (kPa) & 10? & 5.1  & 0.3 & 78 & N.M. & 180 & 20 & 0.022\\
shear stress (kPa) & 100? & 25 & 0.9 & N.M. & 360 & N.M. & 33 &  N.M.\\
\gm'  & 8 to 16 & 2  & 0.6 & 7.1 & <0.1 & 1.5 & 2 & 22\\
tested area(cm$^2$)  & 0.22 & 4  & 0.01 & 0.066 & 0.16 & 0.03 & 0.007 &
0.002\\
max adh. force (N) & 4.6? & 2.04 & 0.003 & 0.52  & N.A. &  0.54 & 0.014 & 0.0000044
durability (cycles) & >30000 & >30000 & >150 & unknown & unknown & unknown & >15 & 10\\
directional & yes & yes & no & no & no & no & yes &  no\\
zero force detach & yes &  yes & yes & no & no & no & no & no\\
non-adh. default & yes & yes & yes  & no & no &  no & no & no\\
dynamic adhesion & yes & yes & no & no & no & no & sphere & no\\
\hline
\end{tabular}
\caption{GSA Comparison \label{GSAComparison}}
\end{table}

%\begin{table}
%\newcommand{\colsize}{0.50in}
%\begin{tabular}{ p{1.0in}  p{\colsize} p{\colsize} p{\colsize} p{\colsize}
%p{\colsize} p{\colsize} p{\colsize}p{\colsize} p{\colsize} c}
%& adhesion (kPa) & shear stress (kPa) & \gm' & tested area (cm$^2$) & durability (cycles) & directional & zero force detach & non-adhesive default & dynamic adhesion\\
%tokay gecko &  10 & 100 & 8 to 16 & 1 & ? & yes & yes & yes & yes\\
%Parness & 5 & 25 & 2 & 4 & 30,000 & yes & yes & yes & yes\\
%\hline
%\end{tabular}
%\caption{GSA Comparison \label{GSAComparison}}
%\end{table}

\end{document}
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%% Adding Figure, Table References
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%%, before \end{document}
%% For figures, put the caption below the illustration.
%% \begin{figure}
%% \caption{Almost Sharp Front}\label{afoto}
%% \end{figure}
%% For Tables, put caption above table
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%%, not have a period at the end
%% Using @{\vrule height ?? depth ?? width0pt} in the preamble will
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%% \caption{Repeat length of longer allele by age of onset class}
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%% \end{tabular}
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%% For two column figures, tables, use the following:
%% \begin{figure*}
%% \caption{Almost Sharp Front}\label{afoto}
%% \end{figure*}
%% \begin{table*}
%% \caption{Repeat length of longer allele by age of onset class}
%% \begin{tabular}{ccc}
%% table text
%% \end{tabular}
%% \end{table*}
