Article pubs.acs.org/Langmuir
Importance of Loading and Unloading Procedures for GeckoInspired Controllable Adhesives John Tamelier,* Sathya Chary, and Kimberly L. Turner Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, United States ABSTRACT: The importance of loading and unloading procedures has been shown in a variety of different methods for biological dry adhesives, such as the fibers on the feet of the Tokay gecko, but biomimetic dry adhesives have yet to be explored in a similar manner. To date, little work has systematically varied multiple parameters to discern the influence of the testing procedure, and the effect of the approach angle remains uncertain. In this study, a synthetic adhesive is moved in 13 individual approach and retraction angles relative to a flat substrate as well as 9 different shear lengths to discern how loading and unloading procedures influence the preload, adhesion, and shear/friction forces supported. The synthetic adhesive, composed of vertical 10 μm diameter semicircular poly(dimethylsiloxane) fibers, is tested against a 4 mm diameter flat glass puck on a home-built microtribometer using both vertical approach and retraction tests and angled approach and retraction tests. The results show that near maximum adhesion and friction can be obtained for most approach and retraction angles, provided that a sufficient shear length is performed. The results also show that the reaction forces during adhesive placement can be significantly reduced by using specific approach angles, resulting for the vertical fibers in a 38-fold increase in the ratio of adhesion force to preload force, μ′, when compared to that when using a vertical approach. These results can be of use to those currently researching gecko-inspired adhesives when designing their testing procedures and control algorithms for climbing and perching robots.
■
measurements on a single spatula2 and 2.3 cm2 for measurements on the two front feet6 have been performed, with larger test areas generally resulting in lower adhesion and shear stresses. This has been attributed to the inability to create equally good contact over the entire area as test areas are scaled upward in size. It has been discovered that setae that are first exposed to a compressive force and then pulled parallel to the surface have been shown to develop at least 10 times the adhesion force after shearing than those exposed to a compressive force without parallel movement.7 Shear forces, like adhesion forces, also required a parallel movement to generate maximum shear values.7 The shear and adhesion forces have been shown to behave differently in experiments where setal arrays are displaced along and against the direction of tilt,8,9 with theoretical approaches offering further evidence of the importance of adhesive movement.10−12 Single setae are able to adhere with a force of 20−40 μN using only a 2.5 μN preload, causing the ratio of adhesion force to preload force, μ′, to fall between 8 and 16.1,7 A variety of different approaches have been undertaken to mimic the main functions of the adhesive found on the gecko.13 The sizes of individual synthetic fibers can range from tens of nanometers to roughly a millimeter, with a variety of processes being utilized. Attempted processes for creating smaller
INTRODUCTION The ability of the Tokay gecko to climb on a variety of natural surfaces has attracted much attention and has primarily been attributed to van der Waals forces,1 with capillary forces playing an additional role.2 The strong adhesion/normal and shear/ lateral forces generated by van der Waals forces require large areas of real contact which are created by the hierarchical physical structure and the mode in which the structures are moved during adhesive placement/removal. The hierarchical structure of the Tokay gecko is composed at the largest scale of four legs, each of which has five toes. On the bottom of each toe are micro- and nanostructures arranged in millimeter arrays, lamellae. The individual components of the lamellae are made of β-keratin, E ≈ 1.6 GPa,3 in the shape of 5 μm diameter, 110 μm length stalks oriented at an angle of 45° with respect to the foot. Each of these individual stalks, setae, then breaks into hundreds of nanoscale structures, spatulae, which are triangular with 200 nm length, 200 nm width, and 5− 10 nm thickness.4 Each of these levels of hierarchy increases the compliance and enables the terminal structures to conform to surface roughness across a variety of size scales, ensuring safe operation of the adhesive. Tests on the gecko’s adhesive fibers have revealed the importance of how the structures are loaded and unloaded during adhesive engagement and disengagement in achieving many of their desirable properties. The adhesion pressures range from 48 kPa5 to 920 kPa,1 and shear pressures range from 88 kPa6 to 4.6 MPa.7 Test areas between 0.02 μm2 for © XXXX American Chemical Society
Received: March 5, 2013 Revised: July 2, 2013
A
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
structures include etching of polymer materials,14 molding nanostructured templates,15 drawing of polymer fibers,16 electron beam lithography,17 and carbon nanotube growth.18 Larger scale methods typically use molding to create vertical and angled fibers. The molds can be created in silicon using an angled etch for tilted structures,19 silicon-on-insulator using the notching effect for mushroom-tipped structures,20 poly(methylglutarimide) (PMGI) using angled lithography for angled fibers,21 SU-8 using dual-angle lithography for wedge structures, 22 and other more complex fabrication approaches.23,24 Research aimed at creating adhesives, such as those above, has received the majority of the attention, while the manner in which the adhesives are tested has received far less. Many synthetic adhesives are characterized with microtribometers built specifically for testing adhesion and/or friction forces. Precise control of the motorized positioners allows for specific testing procedures to be performed, which offers insight into the tribological properties of the adhesive. The testing surface can be either curved20,21,25 or flat26−28 depending on the microtribometer used. Curved surfaces do not suffer from alignment difficulties, although the area of contact between the two surfaces can be difficult to calculate and may require special techniques.29,30 Flat testing surfaces have the opposite problem; the test area is known from the size of the sample or test surface, but aligning the two surfaces to be parallel can be difficult, leading to irregular contact and decreased forces.31 One-dimensional microtribometer tests allow for the testing of either adhesion or shear forces. To measure adhesion using a load-pull test, the two surfaces are moved perpendicularly toward each other until a given condition, often the preload compressive force, is met and then moved perpendicularly away from each other. The adhesion force during this test is the maximum tensile force during separation. To measure shear using a load-drag test, the surfaces are brought together and a small preload is usually applied before the two surfaces are moved in-plane relative to each other. The maximum in-plane force resulting from the shear displacement of the two surfaces is called the shear force. A drawback of using one-dimensional tests is that the relationship between adhesion and shear forces is unable to be captured. To allow for the simultaneous measurements of both friction and adhesion forces, other adhesive characterization uses two-dimensional testing procedures. Two different types of two-dimensional microtribometer tests have been performed on gecko-inspired adhesives to investigate the effects of different testing procedures. The most common test used for determining the adhesion and friction force is the vertical load-drag-pull (vLDP) test. In the vLDP test, the two surfaces approach each other in the out-of-plane direction until a given condition is met, typically a preload force or distance. The out-of-plane approach motion then stops, and the surfaces are moved in-plane parallel to each other for a set distance, the shear length. Once the shear length has been reached, the surfaces are separated from each other in the outof-plane direction. The force values are calculated in the same manner, with the maximum tensile force supported still being called the adhesion force and the maximum in-plane force supported still being referred to as the shear force. Both vertical and angled synthetic adhesives have been characterized using a vLDP test. For vertical20,25 or angled32 fibers where contact is desired on the horizontal top face or
there is no benefit to in-plane shearing, referred to here as top contact fibers, a vertical load-pull test achieves the desired contact. In-plane movement during testing is only implemented to find maximum shear forces that the adhesive can sustain since excessive in-plane movement in a self-aligning tester33 and in a constant penetration depth tester34 has been shown to cause undesired side contact on the fiber and lower the adhesion and shear force values. Low preload forces, and consequently high μ′ values, are typical of top contact structures since very little force is needed to make sufficient contact across the top surface. For both vertical35−37 and angled27,29,38 fibers where contact is desired on the vertical or angled side or the adhesive benefits from in-plane shearing, reported in this paper as side contact fibers, the use of in-plane movement has allowed access to larger preferential areas of the fibers. Before shearing is possible, a preload force or distance must be applied. Since larger preload forces are required to compress the side contact fibers a greater amount, the preloads for maximum contact areas can be significant and risk low μ′ values. The preload forces per fiber during vertical loading for angled side contact fibers should be lower than those needed for vertical side contact fibers due to the replacement of only compression with compression and bending of the fibers, but the forces on even angled side contact fibers are usually more than those needed for top contact fibers. The angled load-drag-pull (aLDP) test uses an approach carried out at an angle, θapp, instead of a vertical approach to bring the surfaces in contact. The exact protocol used for the results presented in this paper can be seen in Figure 1. Unlike
Figure 1. The angled load-drag-pull test used for the results presented here follows the described testing protocol shown. A load, generated using a perpendicular approach, first establishes contact between the adhesive and glass puck testing surface. The adhesive is then moved using different approach angles, shear lengths, and retraction angles. For the vertical load-drag-pull tests, the approach angle and retraction angle are both perpendicular (θapp = θret = 90°). Positive directions, approach and retraction angles, and the zapproach depth are all defined in the manner indicated in the drawing. The glass puck is stationary, and the adhesive changes position during testing to match the way the adhesive would be engaged when integrated with a climbing robot.
the vertical test, a single preload cannot be specified to stop the approach because the maximum compressive vertical force supported by the fibers can lead to either buckling or insufficient surface contact, depending on the approach angle. An approach depth, zapproach, after contact must therefore be used to stop the approach. The two surfaces are then moved inplane parallel to each other over the shear length distance. After shearing is completed, the two surfaces are separated at the retraction angle, θret. For the aLDP results presented, the maximum adhesion (normal) and shear (lateral) forces from B
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
each test are reported. Angled approach and/or retraction tests targeting the testing procedure have been performed, but only drag speeds over various shear lengths,39 approach depths/ preload forces,22,27,40 and retraction angles22,27,40−42 have been systematically varied to characterize the adhesive. No information regarding the performance of different approach angles has been presented, and the parameters used could be suboptimal. Tests using angled approaches and/or retractions have not been performed on top contact structures since the inplane motion, as stated earlier, risks misorientation of the contact surface. Surprisingly, no characterization of side contact adhesives using approach angle variation have been presented up to this point. Therefore, this work is the first application of multiple-angle testing to vertical structures as well as the first systematic variation of the approach angle to be reported. Low preload forces during adhesive placement reduce the reaction forces from the substrate that a robot would have to counter and therefore increase a robot’s stability. When the adhesives are used with a climbing robot with g feet being placed at once during the fiber loading and f feet fully attached during the fiber loading, the minimum μ′ value to ensure that the robot has the ability to remain adhered to the wall is calculated as follows: g μ′min = f (1)
Figure 2. Scanning electron microscopy (SEM) image of vertical halfcylinder poly(dimethylsiloxane) (PDMS) microfibers of 15.0 μm height and 10.0 μm diameter which were used for the experimental results and as a model for the simulations. The cross-sectional shape is shown in white outline on the fiber below the x, y, and z axes. The ±x directions are the directions parallel to the straight long edge of the semicircle. Movement of the sample in the +y direction engages the flat face of the fibers. Movement of the sample in the −y direction engages the curved face of the fibers. +z is the (vertical) loading direction, and −z is the (vertical) unloading direction. Loading and unloading of the adhesive system to engage and release occurs in the y−z plane.
While a μ′min value for a four-legged robot could be as low as 0.33 with only one foot being placed at a time, the value for a robot mimicking the gecko’s foot placement pattern when climbing vertically would need to be at least 1.43 Many synthetic adhesives fall short of this value. To be able to achieve higher μ′ values when adhesion forces have reached their maximum value, the preload force must be lowered. Angled side contact fibers should achieve higher μ′ values than similar vertical fibers during vertical testing because the increased compliance of the tilted fibers lowers the applied preload force for a given contact requirement. As an alternative to using tilted fibers, which can be more difficult to reliably fabricate, ABAQUS simulations on vertical fibers, similar to those fabricated and shown in Figure 2, were used to determine the reduction in preload forces when using different approach angles. Using the Riks method solver in ABAQUS, the free tip of a single fiber, modeled as a two-dimensional wire with defined cross-sectional properties and Young’s modulus, E = 1.5 MPa, to match the fabricated fibers, was displaced at different angles to simulate fiber loading during approach. The base of the fiber was not allowed to rotate or move, while the free tip was allowed to rotate and was displaced over small incremental distances at a given approach angle. Tensile forces could form as in the experiments, and the maximum vertical compressive force supported by the fiber during approach was multiplied by the number of fibers in the testing area to compare with the experimental results. For approach angles parallel to the fiber’s axis, a linear perturbation buckling simulation was performed to find the critical buckling load. The results, shown in Figure 3, show that approach angles can have a significant effect on the preload forces, and the forces predicted by the simulation are in good agreement with the experimental results. For vertical fibers, a 90° approach resulted in the maximum reaction force across all approach angles, yet testing commonly uses this approach angle. Approach angles of less than 10° or greater than 170° resulted in the least amount of vertical compressive force during
Figure 3. Experimental and simulation values for the maximum vertical compressive reaction force supported during approach by the vertical and angled (20° from vertical) fibers using different approach angles. For vertical fibers, small (θapp ≤ 10°) or large (θapp ≥ 170°) approach angles significantly reduced the preload forces when compared to those using a vertical approach (θapp = 90°). The experimental and simulation values are in good agreement across all approach angles for the vertical fibers. To see if similar forces on the angled fibers could be achieved during approach, additional simulations were performed. The ranges of values for the angled and vertical fibers are similar, but for the angled fibers, a greater number of approach angles lead to low preload forces (θapp ≤ 30°) and there is no longer symmetry about a vertical approach. By using certain approach angles on vertical fibers, the lower preload forces of angled fibers can be achieved.
C
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
electron microscopy (SEM) image of the fibers can be seen in Figure 2. Adhesion and Shear Testing. Testing was performed using a custom-designed microtribometer, as previously described,35 with the flat face of a 4 mm diameter glass puck as the opposing surface (contact area 0.126 cm2). The adhesive sample was much larger than the glass puck, and testing was performed in the center of the sample to reduce edge effects. The testing surface was measured with whitelight interferometry (Wyko NT1100 Optical Profiling System) to find the surface characteristics. Over the area likely to contact the adhesive, a circular central area with a diameter of 3.9 mm, the puck was found to have an RMS roughness of ∼70 nm and a maximum height difference of 1.3 μm. Over the smoother central region of the puck, 3 mm diameter, the RMS roughness was ∼40 nm and the maximum height difference was ∼230 nm. The puck would be best described as having small-amplitude waves over large areas of the surface. Using glass as the opposing surface allows contact between the puck and adhesive to be visualized with the use of high-magnification zoom and a charge-coupled device (CCD) camera. The orientation of the puck can be controlled to match that of the adhesive with a three-point leveling system. Movement of the adhesive sample is generated in the vertical and horizontal directions by two dc motors with a minimum incremental motion of 60 nm. Forces and torques are recorded in the x, y, and z directions by a single six-axis load cell with a force resolution of 0.5 mN and a sensing range up to 12 N in-plane and 17 N out-of-plane. The sample is aligned parallel to the glass puck using three rotational stages. The z axis rotational stage aligns the sample to the horizontal stage’s direction of motion within 35 arcseconds. Two goniometers, with a sensitivity of less than 2 arcseconds, ensure flat-on-flat contact between the adhesive sample and glass puck. Humidity and temperature measurements were taken every 5 min while the tests were being performed. The controlled temperate ranged from 21.6 to 22.4 °C with an average temperature and standard deviation of 21.9 ± 0.2 °C. The uncontrolled relative humidity ranged from 51.2% to 67.5%, with the average and standard deviation being 62.9 ± 2.8%. The microtribometer was programmed using LabVIEW with data postprocessing performed in MATLAB. In the vLDP tests, the approach and retraction speed was 1 μm/s, the in-plane shear speed was 3 μm/s, preloads varied between 60 and 180 mN, and shear lengths varied between −150 and +150 μm. For the aLDP tests, a schematic of the test procedure is shown in Figure 1. The vertical component of the approach and retraction speed was 0.3 μm/s, the in-plane shear speed was 5 μm/s, the approach angle varied between 2.5° and 177.5°, the approach depth, zapproach, was 6.5 μm, the shear lengths varied between −40 and +40 μm, and the retraction angle varied between 2.5° and 177.5°. Testing parameters controlling the movements were set to be the same values for the vertical and angled tests, although the speeds achieved differed slightly between the two tests. The difference in vertical speed during approach and retraction is likely due to the additional horizontal motion when performing angled tests. Differences in force values for the horizontal speeds used in these tests are likely small.39 It should also be noted that these speed magnitudes and differences are small when compared to the wide range of speeds used to characterize synthetic adhesives.
approach. The lower preload forces are a result of bending the fibers as opposed to the compression that occurs at or near perpendicular approaches. Differences between the experiments and simulations at angles close to 90° are likely from the inability to include a flat top surface on the top of the fiber in the simulations. The flat top surface would reduce the rotation of the top of the fiber and therefore increase the forces that the fiber could sustain before buckling. Differences between the simulations and experiments could also arise due to the use of a glass puck (root-mean-square (RMS) roughness ∼160 nm), with small-amplitude peaks and valleys of roughness, that could unevenly load the fibers across the testing area. Additional simulations were performed on 70° tilted fibers with the same geometry to distinguish any advantages of the tilt during loading. The cross-sectional properties and length remained the same, but the angle that the fibers make with respect to the +z axis was changed from 0° to 20°. For the approach angles simulated, between 2.5° and 177.5°, the maximum and minimum vertical compressive forces for the 70° fibers, also shown in Figure 3, do not differ significantly from those achievable with the vertical fibers. When approaching in the same direction as the angle of tilt, the vertical compressive reaction forces were less than those of the vertical fibers and the range of approach angles leading to small preload forces was wider. However, when approaching against the angle of tilt, the reaction forces were higher for the tilted fibers. The simulations show that a vertical fiber can have preload forces that can be equal to those achieved using a 70° tilted fiber during attachment provided that the correct approach angle is used. It has been shown that an angled approach can greatly affect the preload forces during adhesive attachment. Side contact vertical fibers, which have been shown in the simulations to benefit from an angled approach, have yet to be characterized experimentally using an aLDP testing procedure. If adhesion and shear forces do not diminish with the new approach, the added benefits of specific adhesive movement, including higher μ′ values for side contact fibers, will be demonstrated. Unlike previous angled testing on fibers, the approach angle, shear length, and retraction angle, all of which describe the path taken during testing, have been systematically varied and the results, including the first reporting of the influence of the approach angle, are presented to find an optimal loading and unloading strategy.
■
EXPERIMENTAL SECTION
Microfabrication. The fibers are created using microfabrication and molding techniques previously described.35 To create the negative mold, photoresist is spin coated onto a clean silicon wafer. The fiber pattern is transferred onto the photoresist using projection lithography. After development of the photoresist to expose semicircular holes, the wafer is etched anisotropically using the Bosch process until a given etch depth is achieved. The photoresist is then removed from the silicon wafer using a stripping agent followed by an oxygen plasma. To facilitate separation after complete curing of PDMS, (1H,1H,2H,2H-perfluorodecyl)trichlorosilane (FDTS) was vapor-deposited and baked onto the silicon wafer before molding. PDMS (Sylgard 184, Dow Corning, Midland, MI) is prepared by mixing a 1:5 ratio by weight of curing agent to base elastomer. PDMS is degassed to remove any pockets of air introduced during mixing and then poured onto the silicon mold. The wafer and polymer are then degassed together to fill any voids created in the mold during pouring. To cure the PDMS, the wafer and polymer are placed in a convection oven for 15 min at 100 °C. The polymer is then carefully separated from the silicon wafer by hand to produce a reusable mold and a synthetic adhesive composed of semicircular fibers. A scanning
■
RESULTS The purpose of the experiments performed was not to highlight a new adhesive design, but to show how the testing procedure can influence key force values of the adhesive. Initial characterization of vertical semicircular fibers can be found in ref 35. However, the difference in composition between these and previous vertical semicircular fibers is likely to generate interest in how well this adhesive performs relative to a flat surface of the same material. For this reason, the adhesion and shear forces against an unpatterned portion of the 1:5 ratio curing agent to base elastomer PDMS is shown in Figure 4. Very little difference is seen in the adhesion forces, Figure 4a, D
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
Figure 4. Maximum adhesion and shear forces on an unpatterned PDMS sample for shear lengths between 0 and 190 μm and preloads between 60 and 180 mN using the vertical load-drag-pull test. Error bars show 1 standard deviation above and below the mean value based on five tests. (a) Across all shear lengths and preloads tested, a similar maximum adhesion value of 286 ± 1 mN is achieved when there is no in-plane shear displacement. The adhesion values are reduced with increasing shear displacements until a shear length of 90 μm is reached. At and above 90 μm shear lengths, there is almost no adhesion. (b) For the shear lengths tested, the 180, 140, 100, and 60 mN preloads have maximum shear values of 775 ± 1, 729 ± 1, 682 ± 0.4, and 635 ± 1 mN, respectively. The plateaued shear force values depend on the preload applied and occur at shear lengths between 70 and 90 μm.
Figure 5. Maximum adhesion and shear forces of the vertical semicircular fibers for shear lengths between 0 and 150 μm and preloads between 60 and 180 mN using the vertical load-drag-pull test. Error bars show 1 standard deviation above and below the mean value based on five tests. (a) Across all shear lengths tested, the 180, 140, 100, and 60 mN preloads have maximum adhesion values of 73.6 ± 0.3, 60.2 ± 1.7, 33.1 ± 1.2, and 20.2 ± 1.2 mN, respectively. The μ′ values at maximum adhesion force for the preloads tested range from 0.33 to 0.43 when using a vLDP test because of the high preloads necessary for large areas of contact. (b) For the shear lengths tested, the 180, 140, 100, and 60 mN preloads have maximum shear values of 237 ± 4, 163.6 ± 3.1, 86.2 ± 2.5, and 49.1 ± 0.7 mN, respectively. The highest shear force values occur when sufficient shear lengths have created large areas of contact with the flat face of the fiber.
for the four preloads tested. Maximum values reached as high as 286 ± 1 mN, an adhesion stress of 23 kPa, and as low as 1 mN at and above 90 μm shear lengths in either direction. At these higher shear lengths, the adhesive was not observed to reattach to the flat PDMS and no large scale stick−slip events were seen. The adhesion forces are roughly symmetric when equal shear lengths are applied in the positive and negative directions. The shear forces, Figure 4b, are also symmetric and, for all preloads, differ very little at shear lengths of 70 μm and below. At higher shear lengths, the shear forces separate from each other and each preload plateaus to its maximum value. The maximum shear forces are as high as 775 mN, a shear stress of 62 kPa, for the 180 mN preload. The maximum shear force for the 60 mN preload is 635 mN. The maximum shear force for the other two preloads falls between these two values. The adhesion and shear forces of the unpatterned PDMS are higher than the values of the fibrillar adhesive, which will be shown later. However, fibrillar adhesives offer significant advantages such as anisotropic attachment, lower sensitivity to roughness, self-cleaning, and a nonsticky default state. The adhesion forces supported by the fibers during a vLDP test can be seen for preloads of 60, 100, 140, and 180 mN in Figure 5a. Greater preloads compress the fibers a larger amount, leading to higher adhesion and shear forces when sheared due to more contact along the length of the fibers. The shear lengths tested during each set of preloads varied from 0 to 150 μm in both the positive and negative directions
perpendicular to the flat face of the fiber. Contact without shearing results in an adhesion stress of around 3 kPa. The adhesion stress can be reduced to a minimum of 0.5 kPa for easy detachment at small negative shear lengths. Large positive shear lengths resulted in longer contact lengths along the length of the fibers until a maximum value was reached. Depending on the preload, adhesion values reached maximum values for shear lengths between 20 and 50 μm, although values at shear lengths of 40 μm, the maximum shear length for the aLDP test, are quite similar to the maximum adhesion values for the same preload. The maximum adhesion force supported is 73.6 ± 0.3 mN, an adhesion stress of 6 kPa, and occurs at the maximum preload of 180 mN, μ′ = 0.41, and shear length of 50 μm. The μ′ values for maximum adhesion values across all preloads tested using a vLDP test fell between 0.33 and 0.43 because of the high preloads necessary to compress the fibers. Adhesion anisotropy, the ratio of forces in the positive direction to those in the negative direction, for the fibers is between 3 and 7.3, higher than the 3−4.9 anisotropy values seen with similarly shaped 1:10 curing agent to base elastomer ratio fibers.35 The maximum adhesion value in the +y direction is approximately the same for the two different polymer mixtures, but the maximum adhesion value in the −y direction is smaller for the 1:5 curing agent to base elastomer ratio polymer. This behavior was predicted for semicircular fibers in refs 35 and 38 since a higher modulus polymer should have a E
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
smaller contact width during pulloff, as was predicted for an initially vertical cylinder contacting with a flat surface.44 The shear forces supported by the fibers for the various preloads reached a maximum of 237 ± 4 mN, a shear stress of 19 kPa over the area of the glass puck, with a 180 mN preload as shown in Figure 5b. Higher preloads, through increased compression of the fibers, again lead to greater contact areas and therefore larger shear forces. This is in agreement with the current data, which also show increasing shear forces with larger preloads. The anisotropy ratio of shear forces in the +y direction to −y direction of 1.8−2.7 is slightly higher than the 1.8−2.4 value obtained with 1:10 curing agent to base elastomer ratio fibers.35 Under similar loading conditions, the curved face deformation for the higher modulus material should be less than that for the lower modulus due to its ability to resist deformation due to the applied forces. For this reason, there should be a small difference in the values of the shear force anisotropy. Tests on top contact fibrillar synthetic adhesives have been able to reach μ′ values up to 40,45 although most works fall very short of this impressive value. Angled side contact fibers have reached μ′ values as high as 13,27 while vertical side contact fibers have only achieved μ′ values between 0.2546 and 2.47 To increase the μ′ values for side contact adhesives, by reducing the preload forces during attachment, an angled approach, instead of a vertical approach, was investigated experimentally with vertical fibers. By loading a fiber at an angle, the high compression forces during attachment should be able to be reduced for side contact adhesives. The approach and retraction angles tested were 2.5°, 5°, 10°, 30°, 50°, 70°, 90°, 110°, 130°, 150°, 170°, 175°, and 177.5°, where angles of less than 90° cause +y direction movement toward the flat face of the fiber and angles greater than 90° cause −y direction movement toward the curved face of the fiber as shown in Figure 1. Using an angled approach and retraction, the adhesion forces supported by the adhesive without any additional shearing can be seen in Figure 6a. Three different regions, high, middle, and low adhesion values, can be seen and correspond to contacts with different parts of the fiber. The region with the highest values, reaching a maximum of 57 ± 1 mN due to large areas of contact on the flat side of the fiber, have approach and retraction angles of less than 10°. The region with the middle values occurs roughly along the diagonal of the approach angle−retraction angle plane. Since the net in-plane movement at pulloff is close to zero with a small approach angle and a large retraction angle, a large approach angle and a small retraction angle, or medium values of both the approach and retraction angles, contact remains on the top surface of the fiber. The top of the fiber has less available contact area than the flat face of the fiber, and the adhesion values therefore are less. Small adhesion force regions occur on either side of the tests leading to top contact when contact with just the edge of the fiber is made. Small forces can also occur at large approach and large retraction angles where the curved face of the fiber is the contacting surface. The maximum adhesion force of 57 ± 1 mN and the minimum adhesion force of 6 ± 1 mN are similar to the adhesion values obtained using a vertical test with a preload of 140 mN. The vertical test uses a shear length after the fibers are preloaded to increase the contact area, whereas the angled test bends the fibers during the approach into positions for maximum and minimum forces. The preloads required for the maximum and minimum adhesion values with
Figure 6. Adhesion and shear forces of the vertical semicircular fibers without additional shearing using the angled load-drag-pull test with various approach and retraction angles. By changing the loading and unloading conditions and contacting various parts of the fiber, very different adhesion and shear values can be achieved. Small approach and retraction angles result in higher adhesion and shear values than other angles due to contact with the flat face of the fiber. Error bars show 1 standard deviation above and below the mean value based on five tests. (a) The maximum adhesion value achievable with a shear length of 0 μm is 57 ± 1 mN. (b) Small approach and retraction angles also lead to large positive shear forces, while large approach and retraction angles result in smaller negative shear forces. Shear forces reach a maximum of +191 ± 6 mN and a minimum of −65 ± 2 mN.
an angled approach and retraction were 16−51% those needed for the vertical test. The shear force supported is also highly dependent on the approach and retraction angles as shown in Figure 6b. At low approach or low retraction angles, the maximum shear force experienced occurs during the shallow movement engaging the flat face. Maximum shear values without shearing reach 191 ± 6 mN using small approach and retraction angles and are higher than any shear value across all preloads except 180 mN using a vLDP test. A high approach angle or a high retraction angle engages the fiber’s curved face, reducing the maximum shear values in the negative direction. The engagement of the curved face has less surface area with which to make contact, and the shear force falls to a minimum value of −65 ± 2 mN . This minimum value is close to the shear values obtained with a 140 mN preload vLDP test. As was the case with the adhesion values, the preloads necessary for these maximum and minimum shear forces in each direction are 14−55% of the values needed for the 140 mN vertical test. The significant reduction in preload forces for maximum adhesion and shear forces with an angled approach and retraction prompted investigation into the ratio of adhesion force to preload force, μ′, across all tests. The results, shown in Figure 7, highlight that μ′ values can be significantly increased, up to 16.4 ± 1.8, by using an aLDP test. This value is approximately 38−55 times greater than the maximum μ′ values obtained with a vLDP test. Unlike the adhesion and shear force graphs, the high μ′ values are only possible by using F
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
Figure 7. μ′ values of the vertical semicircular fibers without additional shearing using the angled load-drag-pull test with various approach and retraction angles. Unlike adhesion and shear forces where small approach or retraction angles led to high forces, only small approach angles result in high μ′ values. Small approach angles were shown in the experiments and simulations of Figure 3 to reduce the preload forces during attachment, thereby increasing the μ′ values when similar adhesion values are achieved. The maximum μ′ value of 16.4 ± 1.8 represents a minimum 38-fold increase over a vertical load-drag-pull test and is the highest to date for a side contact fiber. Error bars show 1 standard deviation above and below the mean value based on five tests.
Figure 8. The addition of +40 μm of shear displacement increases the range of approach and retraction angles possible for large adhesion and shear forces when using the angled load-drag-pull test. The adhesion and shear forces of the vertical semicircular fibers are able to reach values similar to those obtained using a vertical load-drag-pull test. Error bars show 1 standard deviation above and below the mean value based on five tests. (a) The maximum adhesion force increases to 65.8 ± 0.3 mN, close to the vertical load-drag-pull test value of 73.6 ± 0.3 mN. (b) The minimum shear force reaches −59 ± 1 mN in the −y direction, and the maximum shear force reaches 225 ± 3 mN in the +y direction, close to the vertical load-drag-pull test value of 237 ± 4 mN.
approach angles of less than 10° with retraction angles of less than 170°. This is in agreement with the simulation results (Figure 3) which predicted low preload forces, an important component for high μ′ values, at approach angles of less than 10°. Depending on the approach and retraction angles used, the μ′ values can vary greatly, up to a factor of 520 for the data shown in Figure 7. The maximum μ′ value here, 16.4, exceeds the range, 8−16, of the gecko’s μ′ value. A μ′ value of this magnitude has not previously been achieved for vertical side contact, μ′ = 2,47 or angled side contact, μ′ = 13,27 fibers. Adding shear displacement to the test procedure has been used in many cases to increase the adhesion and friction forces of synthetic adhesives. In the vLDP test, increases in shear lengths caused higher adhesion and shear forces due to increased contact on the flat face of the fiber. Here, further testing of the adhesive with additional shearing in both the +y and −y directions is performed to see if even higher forces, μ′ values, and a larger optimal operating space (high adhesion force, high shear force, and high μ′ value) could be achieved. Shear lengths of −40, −30, −20, −10, 0, 10, 20, 30, and 40 μm have been performed for all approach and retraction angles, for a total of 1521 different loading and unloading combinations. Shearing in the negative direction for shear lengths of −40, −30, and −20 μm resulted in μ′ values of less than unity and smaller adhesion and shear forces than were achieved at other shear lengths. A small negative shear length of −10 μm gave a high maximum μ′ value of 13.9 ± 2.5, but adhesion and shear forces were lower than those achieved with large positive shear lengths. There was very little difference between the maximum forces for 20, 30, and 40 μm shear lengths, suggesting that the maximum force values have plateaued. The main difference between the larger positive shear lengths is the number of approach and retraction angles leading to high adhesion and shear forces. This number increased as the shear length became greater. For simplicity, the adhesion and shear values with the largest shear length (40 μm) are presented. The adhesion forces supported by the adhesive with 40 μm of positive shearing are shown in Figure 8a. The addition of positive shear allows a wider range of loading and unloading procedures to cause sufficient contact between the flat face of
the fiber and the glass puck for high adhesion forces. Instead of only having adhesion values above 50 mN at small approach or small retraction angles, as was the case without additional shear, the possible loading and unloading conditions now only exclude a few approach and retraction angles. The highest adhesion forces reached a maximum of 65.8 ± 0.3 mN. This value is higher than the value obtained without additional shearing using an aLDP test and is comparable to the maximum adhesion value using the vLDP test. As with the adhesion forces, the addition of shear length also increased the shear forces across additional approach and retraction angles as seen in Figure 8b. With a 40 μm shear length, shear forces above 150 mN are now possible with many different approach and retraction angles. Most testing procedures, using approach angles of up to 70°, can generate shear forces equal to the maximum shear force value without shearing. Significant increases in shear forces, up to the maximum shear force value of 225 ± 3 mN, are possible with the 40 μm shear length. This value is comparable to the 237 mN shear force achieved with a 180 mN preload using the vLDP test. In areas with μ′ values greater than unity for the 40 μm shear length, shear values are also high, between 180 and 215 mN. It should also be noted that frictional adhesion as described in ref 8 was observed for both the vertical and angled test results. Thus, neither test type could claim the advantage of having this key gecko-like characteristic over the other type of test. With increased adhesion and shear values across most approach and retraction angles, the μ′ values for the 40 μm shear length were calculated to determine if they behaved in a G
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
similar manner. The μ′ values, shown in Figure 9, did not significantly change for any approach or retraction angle despite
be used to reduce preload forces during loading. Since these designs typically suffer from low μ′ values, this important property can be improved. Unfortunately, adhesive designs with what has been defined as top contact structures, which do not benefit from in-plane motion, are unlikely to benefit from using angled testing procedures. Fiber clumping did not occur during testing because of the fiber-to-fiber distance of 25 μm. This suggests that the density of fibers can be increased. A higher fiber density should increase the forces the adhesive can support to reach the values achieved by other adhesives and close the gap relative to the flat sample. Previous work using higher density angled semicircular fibers38 showed force values approaching those of the gecko and a similar fiber density could be tested with these fibers. Likewise, the angled testing procedure used here could be implemented on the angled microfibers to test for increased fiber performance with higher μ′ values. Fiber geometry and polymer material will also be investigated to further increase force values in future designs.
Figure 9. The addition of +40 μm of shear displacement does not significantly change the μ′ values of the vertical semicircular fibers when using the angled load-drag-pull test despite the higher adhesion forces across many approach and retraction angles. For those testing procedures benefiting from the addition of shear length, the preload forces during attachment are too large to be able to reach the high μ′ values achieved when using small approach angles. The maximum μ′ value with a 40 μm shear length was 14.0 ± 2.7. The results show an angled load-drag-pull test can achieve similar adhesion and shear forces as a vertical load-drag-pull test while significantly increasing the μ′ values possible. Error bars show 1 standard deviation above and below the mean value based on five tests.
■
CONCLUSION The importance of loading and unloading procedures when testing dry adhesives has been experimentally investigated over a large range of approach angles, retraction angles, and shear lengths, a systematic study not previously performed. ABAQUS simulations modeling the approach predicted preload force dependence on approach angles, with certain approaches leading to significantly lower preload forces during attachment. The use of an angled approach, specifically the angled approaches shown in the simulations to reduce the preload forces on the adhesive, and angled retraction increased the μ′ values to previously unachievable levels, even surpassing the gecko’s range. Adding in-plane motion after attachment to the testing procedure retained these high μ′ values and led to nearly maximum adhesion and shear values for a larger range of approach and retraction angles. The maximum adhesion and shear values were very similar for both the vertical and angled testing methods, further evidence of the advantages of angled testing methods for certain synthetic adhesives. The experiments and simulations suggest that approach angles resulting in a large bending component, instead of compression, are part of an optimal loading and unloading scheme for the vertical fibers tested due to their ability to produce high adhesion forces, high shear forces, and high μ′ values.
the higher adhesion forces. Again, only the small approach angles with retraction angles of less than 170° have notable μ′ values. This trend was the same for all shear lengths tested between −10 and +40 μm. The negligible effect of increased adhesion forces on the μ′ values using the additional shear lengths suggests that the μ′ values for the vertical fibers presented here are limited by preload forces. It was found that preload forces for those testing procedures benefiting from the addition of shear could be as high as 185 mN, severely limiting the μ′ values possible. However, by combining the small approach angles with the correct shear length, an optimal loading and unloading strategy can be implemented to obtain high adhesion forces, high shear forces, and high μ′ values. Although the focus of this study is the importance loading and unloading procedures play in achieving maximal force values, durability is often a problem for synthetic adhesives. Typical durability results use a repeated test to show the performance of the adhesive over a given number of cycles. The highest durability tests have reached 10 000 cycles38,47 or more.22 Although a quantitative study of durability was not performed, the adhesive did survive over 8300 testing cycles without visible damage or noticeable drops to the adhesion or shear forces. The improvement in lifetime is significant when compared to that of previous testing of vertical semicircular fibers which survived 1080 tests.35 Future work aims to explicitly investigate the durability of the adhesive by using both vertical and angled testing procedures to compare how the placement and removal scheme influences durability. Since angled approaches and retractions were able to retain similar adhesion and shear forces while greatly increasing the adhesion to preload ratio, there exists a potential for future use with other adhesive designs. In this study, only a single design has been tested, but the testing application does not have to be limited to only these fibers. For side contact fibers, which were defined earlier to benefit from shearing, currently using vertical testing techniques, the results presented here should be able to
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was sponsored by Institute for Collaborative Biotechnologies Grant W911NF-09-0001 from the U.S. Army Research Office. The content of the information does not necessarily reflect the position or policy of the government, and no official endorsement should be inferred. Part of this work was done in the University of California, Santa Barbara (UCSB) Nanofabrication Facility, part of the NSF-funded National Nanotechnology Infrastructure Network (NNIN). H
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
■
Article
array displaying gecko-like dynamic adhesion, directionality and long lifetime. J. R. Soc., Interface 2009, 6, 1223−1232. (23) Murphy, M. P.; Aksak, B.; Sitti, M. Gecko-inspired directional and controllable adhesion. Small 2009, 5, 170−175. (24) Lee, J.; Bush, B.; Maboudian, R.; Fearing, R. S. Gecko-inspired combined lamellar and nanofibrillar array for adhesion on nonplanar surface. Langmuir 2009, 25, 12449−12453. (25) Greiner, C.; del Campo, A.; Arzt, E. Adhesion of bioinspired micropatterned surfaces: effects of pillar radius, aspect ratio, and preload. Langmuir 2007, 23, 3495−3502. (26) Gorb, S.; Varenberg, M.; Peressadko, A.; Tuma, J. Biomimetic mushroom-shaped fibrillar adhesive microstructure. J. R. Soc., Interface 2007, 4, 271−275. (27) Santos, D.; Spenko, M.; Parness, A.; Kim, S.; Cutkosky, M. Directional adhesion for climbing: theoretical and practical considerations. J. Adhes. Sci. Technol. 2007, 21, 1317−1341. (28) Tamelier, J.; Chary, S.; Turner, K. L.; Yu, J.; Das, S.; Israelachvili, J. N. Millimeter size patch behavior of gecko-inspired reversible adhesive. IEEE Sensors 2011; Limerick, Ireland, 2011; pp 1819−1822. (29) Lee, J.; Fearing, R. S.; Komvopoulos, K. Directional adhesion of gecko-inspired angled microfiber arrays. Appl. Phys. Lett. 2008, 93, 191910. (30) Aksak, B.; Murphy, M. P.; Sitti, M. Adhesion of biologically inspired vertical and angled polymer microfiber arrays. Langmuir 2007, 23, 3322−3332. (31) Long, R.; Hui, C.-Y.; Kim, S.; Sitti, M. Modeling the soft backing layer thickness effect on adhesion of elastic microfiber arrays. J. Appl. Phys. 2008, 104, 044301. (32) Murphy, M. P.; Aksak, B.; Sitti, M. Adhesion and anisotropic friction enhancements of angled heterogeneous micro-fiber arrays with spherical and spatula tips. J. Adhes. Sci. Technol. 2007, 21, 1281−1296. (33) Varenberg, M.; Gorb, S. Shearing of fibrillar adhesive microstructure: friction and shear-related changes in pull-off force. J. R. Soc., Interface 2007, 4, 721−725. (34) Kim, S.; Aksak, B.; Sitti, M. Enhanced friction of elastomer microfiber adhesives with spatulate tips. Appl. Phys. Lett. 2007, 91, 221913−3. (35) Tamelier, J.; Chary, S.; Turner, K. L. Vertical anisotropic microfibers for a gecko-inspired adhesive. Langmuir 2012, 28, 8746− 8752. (36) Lee, J.; Majidi, C.; Schubert, B.; Fearing, R. S. Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behaviour. J. R. Soc., Interface 2008, 5, 835−844. (37) Qu, L.; Dai, L.; Stone, M.; Xia, Z.; Wang, Z. L. Carbon nanotube arrays with strong shear binding-on and easy normal lifting-off. Science 2008, 322, 238−242. (38) Chary, S.; Tamelier, J.; Turner, K. A microfabricated geckoinspired controllable and reusable dry adhesive. Smart Mater. Struct. 2013, 22, 025013. (39) Gravish, N.; Wilkinson, M.; Sponberg, S.; Parness, A.; Esparza, N.; Soto, D.; Yamaguchi, T.; Broide, M.; Cutkosky, M.; Creton, C.; Autumn, K. Rate-dependent frictional adhesion in natural and synthetic gecko setae. J. R. Soc., Interface 2010, 7, 259−269. (40) Day, P.; Cutkosky, M.; Greco, R.; McLaughlin, A. Effects of He++ ion irradiation on adhesion of polymer microstructure-based dry adhesives. Nucl. Sci. Eng. 2011, 167, 242−247. (41) Soto, D.; Hill, G.; Parness, A.; Esparza, N.; Cutkosky, M.; Kenny, T. Effect of fibril shape on adhesive properties. Appl. Phys. Lett. 2010, 97, 053701. (42) Kim, S.; Spenko, M.; Trujillo, S.; Heyneman, B.; Santos, D.; Cutkosky, M. Smooth vertical surface climbing with directional adhesion. IEEE Trans. Rob. 2008, 24, 65 −74. (43) Autumn, K.; Hsieh, S. T.; Dudek, D. M.; Chen, J.; Chitaphan, C.; Full, R. J. Dynamics of geckos running vertically. J. Exp. Biol. 2006, 209, 260−272. (44) Majidi, C. S.; Groff, R. E.; Fearing, R. S. Attachment of fiber array adhesive through side contact. J. Appl. Phys. 2005, 98, 103521.
REFERENCES
(1) Autumn, K.; Sitti, M.; Liang, Y. A.; Peattie, A. M.; Hansen, W. R.; Sponberg, S.; Kenny, T. W.; Fearing, R.; Israelachvili, J. N.; Full, R. J. Evidence for van der Waals adhesion in gecko setae. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12252−12256. (2) Huber, G.; Mantz, H.; Spolenak, R.; Mecke, K.; Jacobs, K.; Gorb, S. N.; Arzt, E. Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 16293−16296. (3) Peattie, A. M.; Majidi, C.; Corder, A.; Full, R. J. Ancestrally high elastic modulus of gecko setal beta-keratin. J. R. Soc., Interface 2007, 4, 1071−1076. (4) Ruibal, R.; Ernst, V. The structure of the digital setae of lizards. J. Morphol. 1965, 117, 271−293. (5) Gravish, N.; Wilkinson, M.; Autumn, K. Frictional and elastic energy in gecko adhesive detachment. J. R. Soc., Interface 2008, 5, 339− 348. (6) Irschick, D. J.; Austin, C. C.; Petren, K.; Fisher, R. N.; Losos, J. B.; Ellers, O. A comparative analysis of clinging ability among padbearing lizards. Biol. J. Linn. Soc. 1996, 59, 21−35. (7) Autumn, K.; Liang, Y. A.; Hsieh, S. T.; Zesch, W.; Chan, W. P.; Kenny, T. W.; Fearing, R.; Full, R. J. Adhesive force of a single gecko foot-hair. Nature 2000, 405, 681−685. (8) Autumn, K.; Dittmore, A.; Santos, D.; Spenko, M.; Cutkosky, M. Frictional adhesion: a new angle on gecko attachment. J. Exp. Biol. 2006, 209, 3569−3579. (9) Zhao, B.; Pesika, N.; Rosenberg, K.; Tian, Y.; Zeng, H.; McGuiggan, P.; Autumn, K.; Israelachvili, J. Adhesion and friction force coupling of gecko setal arrays: implications for structured adhesive surfaces. Langmuir 2008, 24, 1517−1524. (10) Zhao, B.; Pesika, N.; Zeng, H.; Wei, Z.; Chen, Y.; Autumn, K.; Turner, K.; Israelachvili, J. Role of tilted adhesion fibrils (setae) in the adhesion and locomotion of gecko-like systems. J. Phys. Chem. B 2009, 113, 3615−3621. (11) Tian, Y.; Pesika, N.; Zeng, H.; Rosenberg, K.; Zhao, B.; McGuiggan, P.; Autumn, K.; Israelachvili, J. Adhesion and friction in gecko toe attachment and detachment. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19320−19325. (12) Sitti, M.; Fearing, R. S. Synthetic gecko foot-hair micro/nanostructures as dry adhesives. J. Adhes. Sci. Technol. 2003, 17, 1055− 1073. (13) Autumn, K.; Gravish, N. Gecko adhesion: evolutionary nanotechnology. Philos. Trans. R. Soc., A 2008, 366, 1575−1590. (14) Northen, M. T.; Turner, K. L. A batch fabricated biomimetic dry adhesive. Nanotechnology 2005, 16, 1159. (15) Majidi, C.; Groff, R. E.; Maeno, Y.; Schubert, B.; Baek, S.; Bush, B.; Maboudian, R.; Gravish, N.; Wilkinson, M.; Autumn, K.; Fearing, R. S. High friction from a stiff polymer using microfiber arrays. Phys. Rev. Lett. 2006, 97, 076103. (16) Jeong, H. E.; Lee, S. H.; Kim, P.; Suh, K. Y. Stretched polymer nanohairs by nanodrawing. Nano Lett. 2006, 6, 1508−1513. (17) Geim, A. K.; Dubonos, S. V.; Grigorieva, I. V.; Novoselov, K. S.; Zhukov, A. A.; Shapoval, S. Y. Microfabricated adhesive mimicking gecko foot-hair. Nat. Mater. 2003, 2, 461−463. (18) Zhao, Y.; Tong, T.; Delzeit, L.; Kashani, A.; Meyyappan, M.; Majumdar, A. Interfacial energy and strength of multiwalled-carbonnanotube-based dry adhesive. J. Vac. Sci. Technol., B 2006, 24, 331 − 335. (19) Jeong, H. E.; Lee, J.-K.; Kim, H. N.; Moon, S. H.; Suh, K. Y. A nontransferring dry adhesive with hierarchical polymer nanohairs. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 5639−5644. (20) Kim, S.; Sitti, M. Biologically inspired polymer microfibers with spatulate tips as repeatable fibrillar adhesives. Appl. Phys. Lett. 2006, 89, 261911. (21) Yu, J.; Chary, S.; Das, S.; Tamelier, J.; Pesika, N. S.; Turner, K. L.; Israelachvili, J. N. Gecko-inspired dry adhesive for robotic applications. Adv. Funct. Mater. 2011, 21, 3010−3018. (22) Parness, A.; Soto, D.; Esparza, N.; Gravish, N.; Wilkinson, M.; Autumn, K.; Cutkosky, M. A microfabricated wedge-shaped adhesive I
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
Langmuir
Article
(45) Davies, J.; Haq, S.; Hawke, T.; Sargent, J. A practical approach to the development of a synthetic gecko tape. Int. J. Adhes. Adhes. 2009, 29, 380−390. (46) Schubert, B.; Lee, J.; Majidi, C.; Fearing, R. S. Sliding-induced adhesion of stiff polymer microfibre arrays. II. Microscale behaviour. J. R. Soc., Interface 2008, 5, 845−853. (47) Gillies, A. G.; Fearing, R. S. Shear adhesion strength of thermoplastic gecko-inspired synthetic adhesive exceeds material limits. Langmuir 2011, 27, 11278−11281.
J
dx.doi.org/10.1021/la400835n | Langmuir XXXX, XXX, XXX−XXX
