Detachment Behavior of Mushroom-Shaped Fibrillar Adhesive

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Article pubs.acs.org/Langmuir

Detachment Behavior of Mushroom-Shaped Fibrillar Adhesive Surfaces in Peel Testing Craig K. Hossfeld,† Andreas S. Schneider,‡,∥ Eduard Arzt,‡,§ and Carl P. Frick*,† †

Mechanical Engineering Department, University of Wyoming, 1000 East University Avenue, Laramie, Wyoming 82071, United States ‡ Metallic Microstructures and Functional Surfaces Groups, INM - Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany § Saarland University, 66123 Saarbrücken, Germany ABSTRACT: Synthetic dry adhesive surfaces with mushroom-shaped pillars have been the subject of recent research investigation. This study is the first to systematically investigate the effect of peel angle, pillar diameter, and pillar aspect ratio on the force required for peeling. Explicit emphasis was placed on relatively large pillar structures to allow for in situ optical visualization in order to gain insights into fundamental mechanisms which dictate peeling. Traditional molding techniques were used to fabricate optical-scale mushroom terminated structures with pillar diameters of 1 mm and 400 μm and aspect ratios of 1, 3, and 5. Results were quantitatively compared to peel testing theory for conventional adhesives. It was convincingly demonstrated that the critical decohesion energy of a patterned surface changes as a function of angle and cannot be treated as a constant. Variability in the critical decohesion energy was linked to mechanistic differences in detachment through in situ observations and finite element analysis (FEA). Experimental results showed that smaller pillars do not necessarily lead to higher adhesion during peeling, and contact mechanics combined with optical observations were used to explain this phenomenon. Finally, unlike results from normal adhesion studies, aspect ratio was shown to play little role in peeling adhesive behavior due to the mechanics of peel testing. The results and conclusions from this study uncover the detachment mechanisms of mushroom-shape tipped dry adhesives under peel loading and serve as an outline for the design of these surfaces in peeling applications.

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INTRODUCTION

Contact splitting provides a quantitative description of the physical observations seen in natural dry adhesion systems and has been shown to predict normal adhesion results despite the simplifying assumptions necessary for its use.18,22 The overarching goal of research into smaller or hierarchical structures is to maximize the n value in eq 1 for a given contact area. The drawback to this line of research is the relative complexity and expense of making pillars on the micrometer or submicrometer range, reducing their usefulness for practical applications. A smaller number of research groups have investigated the effect of terminating shape on sample adhesion.15,23−27 Studies performed using vertical polydimethylsiloxane (PDMS) pillars, fabricated using a soft-molding technique, investigated the effects of pillar diameter, height, aspect ratio, backing layer thickness, ambient humidity, and repetitive measurements.15,23,24 These studies convincingly demonstrated that the “mushroom-shaped” tips display significantly higher adhesion compared to hemispherical or flat tip shapes.15 The proposed mechanism for this increase in adhesion is a relocation of the crack initiation point on mushroom-shaped

Over the past decade several researchers have worked to create synthetic adhesives that mimic the adhesion shown by geckos, spiders, and insects.1−4 These adhesives have been fabricated through small-scale photolithographic processes,1,5−7 ion etching,8−10 and vertical carbon nanotube arrays,11−14 with some more adhesive than the gecko itself.11,14−17 Synthetic adhesives have been proposed for many purposes including robots to climb vertical surfaces,18 self-assembling microdevices,8 and water adhesive surfaces.19 In an effort to increase the adhesion of synthetic surfaces, most researchers follow the path based on cumlative observations in nature: decreasing structure size and/or hierarchical structures.1,10,12,20 This research is based on wellestablished concepts of “contact splitting”.3,4,21 Contact splitting theory shows that adhesion of a unit area can be dramatically increased by breaking that area into multiple smaller contact areas. For example, consider a spherical body with radius R and an adhesive force of Fc. If this contact area were split into n self-similar contact points with radius R/√n, the new adhesive force would be3 Pc′ =

n Pc

Received: July 25, 2013 Revised: September 19, 2013 Published: November 7, 2013

(1) © 2013 American Chemical Society

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structures.25,26,28 On flat punch or hemispherical structures, debonding initiates through a crack formation at the edge of the structure where maximum stress occurs, followed by linear crack growth across the structure. The mushroom-shaped pillars eliminate the high stress at the pillars edge by the addition of a low-stress flange.26,28−30 The crack must then initiate underneath the pillar and propagate radially to detachment, requiring more input energy. This proposed mechanism has been shown analytically26 and numerically,29 but direct experimental observations of mushroom-shape tip detachment behavior have been complicated due to the micrometer or submicrometer sized pillars, e.g. ref 28. Unfortunately, there exists no standard technique for measuring adhesion of structured surfaces. This lack of standardization has allowed for research to be completed using vastly different fabrication and characterization methods, making comparison of results extremely difficult.23 A standard characterization technique would not only help push the limits of the field but is also a necessary step in the success of structured dry adhesive surfaces in an industrial setting. The most common method for characterizing the adhesion of dry adhesive surfaces is normal adhesion testing.15,17,18,23,31−34 In general, a glass probe is pressed on the sample normal to the adhesive surface and is subsequently retracted until separation occurs at a certain pull-off force. The popularity of normal adhesion testing is likely due to the ease of testing and the availability of analytical models. Normal adhesion testing is however, heavily dependent on probe size, shape, and preloading. For example, for conventional spherical probe testing, results are complicated by stepwise detachment and nonconstant contact areas.4,7,33,35 Flat probes have been used to circumvent some contact area issues,4 but as little as a 2° probe misalignment has shown to weaken adhesion dramatically.7 The dependence on alignment makes normal adhesion studies with a flat probe difficult to perform and requires complicated test fixtures. Peel testing is a well-established method for the characterization of conventional adhesives (e.g., Scotch tape, masking tape, duct tape, etc.) and is outlined in testing standards.36 For structured adhesive surfaces, however, peel testing is not widely used. This is most likely due to complexities in constant angle peel tests along with the difficulty of fabricating samples with sufficient length. Of the studies that investigated structured adhesives through peel testing, many examined either pure shear,1,11 90°/180° tests,5,32 or a varying angle throughout testing.11 Because of the infrequent use of peel testing on patterned adhesive surfaces, little is known about how structured samples react to peel loading. This includes load sharing among structures, sample detachment progression, and individual pillar detachment mechanisms as a function of peeling angle. Filling this gap in knowledge is critical, as peel testing behavior is important in the practical use of an adhesive. A study performed by Williams and Kauzlarich noted that resulting forces measured by peel testing of conventional adhesives are dependent on the following variables: peel angle, peel speed, rigidity of the substrate, and mechanical properties of the tape.37 Furthermore, the study determined a specific relationship for these variables and the peel-off force. For a linear elastic tape that is infinitely flexible in bending, the critical decohesion energy of the surface can be described by37−39 Gc = (1 − cos θ )

P P2 + 2 b 2b Eh

where Gc is the critical decohesion energy per unit area, θ is the angle of the applied loading, P is the magnitude of the peel off force, b is the width of the tape, h is the thickness of the tape, and E is the elastic modulus of the tape. Some researchers have attempted to extend eq 2 to include adhesion and friction mechanism in gecko attachment and detachment.39−41 However, it has not been extended to include any mechanisms specific to the detachment of mushroom-shape tip terminating structures. Equation 2 was derived for the peeling of conventional adhesives and does not account for the energy contributions of stepwise detachment, structure detachment mechanisms, bending of surface structures, and vertical displacement of the applied peeling loads due to surface structures. These energy contributions should dramatically affect the peel adhesion in structured surfaces, and their effects need to be characterized in order to extend conventional theory to encompass structured adhesives. For this study optical scale pillared surfaces (400 μm, 1 mm) were fabricated using traditional molding techniques and characterized using constant angle peel testing. The experimental results are compared to theories developed for conventional adhesives and optical observations with finite element analysis (FEA), revealing complex mechanics of detachment in mushroom-shape structured surfaces that are not encompassed by existing theory. Smaller diameter pillars were found to be not always more adhesive than larger ones in peeling applications, likely due to a decrease in contact area per row at most peel angles. Finally, aspect ratio is shown to play little role in peel adhesion for mushroom-shape tip surfaces peeled from a flat surface. This study serves as a preliminary approach for the design parameters of mushroom-shape adhesive surfaces in peeling applications.

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EXPERIMENTAL SECTION

Samples in this study were fabricated through casting of uncured PDMS onto aluminum molds. The aluminum used in mold fabrication was 6061 T6 aluminum alloy, and mold fabrication was completed through computer numeric controlled (CNC) milling. The molds were designed with a hexagonal pillar array in an effort to match previous small scale adhesion studies,15,23,24 as shown in Figure 1.

Figure 1. Hexagonal pillar array chosen to match previous small scale adhesion studies.15,23,24 All molds were machined with a two pillar diameter row-to-row and pillar-to-pillar spacing. The spacing was chosen to allow for the addition of mushroom tip terminating shapes to the pillars. The spacing between rows and columns was set at twice the diameter of the pillar for all fabricated samples. From this arrangement the 1 mm samples had 446 total pillars (26.2 pillars/cm2) and the 400 μm samples had 2979 pillars (175.2 pillars/cm2). The spacing of the structures in the hexagonal array was selected to allow for room between pillars to apply a mushroom-shape terminating shape. A recess was machined into the molds prior to machining the pillar holes to allow for fabrication of a 1.0 ± 0.2 mm backing layer on all samples.

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Molds with hole diameter of 400 μm and 1 mm were fabricated with aspect ratios of 1, 3, and 5. Molds were machined 1.7 cm wide by 20 cm long with 10 cm of flat sample to allow for load application and 10 cm of patterned length to adhere to the testing substrate. To facilitate demolding of PDMS from aluminum, a releasing agent layer was applied to the contact surfaces of the molds. To synthesize the releasing agent solution (91% n-hexane, 9% perfluooroctyltrichlorosilane (PFOTS)), 20 mL of n-hexane was mixed with 2 mL of PFOTS in a glass vile. The resulting mixture was shaken vigorously for 30 s and then placed in an ultrasound bath for 5 min to promote complete mixing. The coating was then applied to the surface of the aluminum molds as described in ref 23. Samples were fabricated using Dow Corning Sylgard 184 PDMS in a multistep process shown schematically in Figure 2. The PDMS

flange-to-pillar ratio was chosen because it created mushroom-shaped tips as large as possible without having pillars interconnect. Adhesion of the structured samples was measured using fixed-arm peel testing on a custom-built constant angle peel test fixture, schematically illustrated in Figure 3. The structured section of the test

Figure 3. Schematic representation of a fixed-arm peel test of a structured adhesive. Structured section is adhered to the substrate and the flat portion of the sample is affixed to a load cell. Adhesive sample is peeled at a constant velocity and angle while the required force is measured.

samples was adhered to the glass substrate, and the nonpatterned section was affixed to a load cell and displaced by the load frame. The linear actuator applies the peeling force while the substrate moves along the peeling angle the same distance to maintain a constant peeling angle. Peel tests began with minimal slack in the sample and were completed when all pillars detached from the substrate. The test fixture was designed to meet peel testing standard specifications.36 The only operational deviation from the testing standards was the ability to perform constant angle peel tests from 0 to 165°. For this study, a glass substrate was used because glass is the standard adhesion probe material used in previous normal adhesion studies.15,23,24 The test fixture operates in a MTS Mini-Bionix II hydraulic load frame using a MTS 100 N load cell with ±0.01 N resolution (load cell interchangeable for different maximum loads and resolutions). The displacement was controlled by the linear actuator of the load frame and was capable of movements accurate to ±0.01 mm with a stroke of 18 cm. The testing apparatus and data acquisition were controlled through LabView software. Prior to each test, the glass substrate was cleaned with deionized water followed by isopropanol. The structured adhesive samples were quickly rinsed with deionized water and then placed in an ultrasonic bath of isopropanol for 5 s prior to testing. Compressed air was immediately used to dry the sample and remove any remaining debris. Samples were then preloaded to the glass substrate by rolling a 164 g steel cylinder across the back of the sample. The mass of the steel cylinder was chosen to be high enough to ensure complete contact of the pillars but not so high to cause buckling. All tests were performed at a displacement rate of 0.3 mm/s, and the data sampling rate was 0.5 Hz. Testing was performed under ambient conditions at room temperature (22−25 °C). The relative humidity was measured to be 17−22% throughout the testing duration. Representative 90° peel tests were performed throughout the complete range of temperatures and humidity, and no quantifiable difference in peeling force was found. Five tests were performed at each angle from 0 to 165° in increments of 15°. Duplicate tests were performed on an additional sample of each diameter and aspect ratio to ensure repeatability and accurate averages. Testing is nondestructive, and therefore two samples of each type were sufficient to complete all testing. In order to better understand the stresses on the adhered surface of pillars with mushroom-shaped tips, a simple idealized finite element analysis was performed using a single 1 mm pillar connected to a square section of backing layer as illustrated in Figure 4. The section of

Figure 2. Process of fabricating samples where (a) the machined mold is (b) filled with PDMS and degassed. The sample is cured and (c) removed from the mold, and (d) the pillars are dipped in uncured PDMS and removed, leaving (e) small droplets of uncured PDMS on each pillar. After dipping, the sample is (f) placed on a flat aluminum plate. After curing, (g) the sample is removed and ready to be tested. solution was carefully poured into the metal mold and was degassed under vacuum (23 in.Hg, Alcatel Drytel vacuum pump) for 2 h to remove any air trapped in the holes (Figure 2a,b). The molds were then placed in a Fisher Scientific Isotemp oven at 95 °C for 1 h to cure the PDMS. Samples were removed from the aluminum molds (Figure 2c) and placed pillar down into a liquid sheet of PDMS approximately 500 μm thick (Figure 2d). The sheet of PDMS was created by spinning 1.5 g of uncured PDMS in a 6 in. Petri dish for 10 min at 300 rpm. Placing the pillars into the uncured PDMS creates small droplets of uncured PDMS on the tips of the pillars that allow for mushroomshaped flange creation (Figure 2e). Samples were then placed pillar side down on an aluminum sheet coated in releasing agent (Figure 2f). The sheet was placed in an oven at 95 °C for 1 h to cure the mushroom terminating shape (Figure 2f). Samples were then removed from the aluminum sheet and cleaned prior to testing (Figure 2g). The pillar dipping process was repeated as necessary in order to achieve a pillar to flange ratio of approximately 1.45:1 for all samples tested. The 15396

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backing layer was incorporated to allow for more accurate modeling of force transfer to the pillar.

Figure 5. (a) Naming convention used to discern samples used in this study. The aspect ratio is calculated by dividing structure height, H, by the structure diameter, d. (b) Optical image of a single AR1-D1000 pillar with pillar diameter, d, flange diameter, D, and height, H, denoted.

of an optical microscope and a charge-coupled device (CCD) camera. Twenty-five pillars were imaged across each sample in an equally spaced array in order to obtain representative averages. The averages and standard deviations of the pillar measurements are summarized in Table 1.

Figure 4. (top left) Optical image of a representative 1 mm pillar on a fabricated peel test specimen. (top right) Abaqus rendering of the fabricated pillar used in finite element analysis. (bottom) Abaqus rendering of the 0.01 N applied load to the backing layer for a 0° test model.

Table 1. Important Pillar Measurement Averages and Standard Deviations for All Tested Samples

The pillar was modeled in Abaqus using ten node quadratic tetrahedral elements (C3D10I). Improved surface stress elements were used because the surfaces of the elements adhered to the glass were of interest. Nonlinear geometry was used in this model due to the high degree of rotation of the pillar and because preliminary models displayed a 10% reduction in accuracy if a linear geometry was used. The pillar was attached to the backing layer using a constraint that required the face of the pillar to deform with the face of the backing layer and vice versa. Once the pillar and backing layer were appropriately meshed, the exposed mushroom-tip shape surface opposite the backing layer was fixed in space. This constraint was applied to model the condition of a pillar adhered to a substrate. Because of this constraint, all results model the stresses on the pillar under loading before a crack initiates at the surface. Three different boundary conditions were then applied to the backing layer in order to model a load of 0.01 N applied to one pillar during a 0°, 45°, and 75° peel test. The 0.01 N force was applied in the positive x direction to the side of the backing layer across the entire exposed surface, as shown in Figure 4. This was done to ensure that the model of stress application to the pillar most closely resembled the transition of stress from the peel arm to the backing layer molded to the adhered pillar. The three angles modeled were chosen to align with the three different detachment mechanisms observed during in situ optical measurements.

sample name

pillar diameter d (mm)

pillar height H (mm)

aspect ratio H/d

flange diameter D (mm)

AR1D1000 AR1D400 AR3D400 AR5D400

1.02 ± 0.01

1.32 ± 0.01

1.29 ± 0.01

1.45 ± 0.14

0.37 ± 0.01

0.39 ± 0.02

1.05 ± 0.01

0.56 ± 0.15

0.39 ± 0.01

1.16 ± 0.01

2.99 ± 0.01

0.56 ± 0.13

0.37 ± 0.01

2.08 ± 0.06

5.61 ± 0.04

0.54 ± 0.17

Shown in Figure 6 are peel force results from three representative 0°, 30°, and 90° tests performed on a single AR1-D1000 sample peeled at 0.3 mm/s. These results were chosen to represent the three peel mechanisms observed during in situ optical measurements. The 0° tests display a near linear initial loading where force is gradually applied to the sample, but no pillars detach from the substrate. After the linear loading phase the force stabilizes as pillars detach in large groups. Complete detachment of 0° tests occurs at displacements below 15 mm as a result of the groupwise pillar detachment along the sample. The 30° and 90° tests also display an initial near-linear loading phase where tension is applied to the sample without pillar detachment. The forces transition to plateau at a much lower force when compared to the 0° test because pillars in the two leading rows detach individually. Individual pillar detachment continues through the length of the sample until sample detachment occurs between 85 and 100 mm. Examination of the 30° tests in Figure 6 shows that there is a dip in the peeling force after the linear loading phase and prior to steady-state peeling. This dip is a result of the sudden detachment of the leading rows after the sample is initially loaded. The energy from this sudden movement is transferred along the backing

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RESULTS Samples with varying pillar diameters and aspect ratios were tested in this study; therefore, a naming convention was created for sample organization and quick reference and is outlined in Figure 5a. Pillars were characterized by their approximate aspect ratio (H/d) and pillar diameter. An optical image of a single AR1-D1000 pillar is shown in Figure 5b with the pillar diameter d, flange diameter D, and pillar height H noted. Important pillar measurements were obtained through the use 15397

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15°−165°. A representative 0° test result was not shown due to the large difference in magnitude from the rest of the angles tested. At peel angles above 60° the steady-state peel force values all converge to within 0.2 N of one another. Conversely, for angles below 60°, the peel force plateau values substantially increase. The general trends observed on the AR1-D1000 sample were seen in the results for all aspect ratios and pillar diameters tested. Figure 8a compares the steady-state peel force results for an AR1-D1000 sample to the force predicted by eq 2. For

Figure 6. Representative peel test results for a structured sample peeled at 0°, 30°, and 90° (0.3 mm/s). Each test displays an initial loading phase followed by a steady-state peeling phase. The 30° and 90° tests detach between 80 and 100 mm, and the 0° tests detach at approximately 10 mm. The average steady-state peel forces for each degree are noted by the dashed green lines.

layer and reduces the required peel force to detach the subsequent rows. It is shown in Figure 7 that this peel force dip

Figure 8. (a) Average steady-state peel force as a function of peel angle for an AR1-D1000 sample. Black points represent experimental data, and red line shows predictions of eq 2. Representative optical images of (b) normal detachment in a single pillar (c) shear detachment in a single pillar and (d) mixed detachment in a single pillar. Images are still frames taken during peel testing with the progression of detachment shown from left to right. Red arrows indicate locations of interest in pillar detachment.

Figure 7. Representative peel test results for an AR1-D1000 sample peeled from a glass substrate at 0.3 mm/s. All angles display an initial loading phase followed by a steady-state peel force to failure. It is seen that angles 75°−165° all fall within a 0.2 N range while peel tests from 60°−15° increase in magnitude as peel angle is decreased.

conventional adhesives, the term Gc in eq 2 is assumed to be constant for all angles38,42 and is solved for using experimental results at a chosen angle. In an effort to match this process, Gc was calculated for the structured sample using the average peel force at 75°. The decohesion energy was solved for at 75° because it was seen in experimental observations that the angle of the backing layer at the surface remains constant from 75° to 165°. This constant was then used to create the predictive curve (shown in red) in Figure 8a. Determining the constant at lower peel angles would shift the curve upward, but it would maintain the same shape. It is seen that eq 2 only qualitatively predicts

occurs for 15°, 45°, and 60° tests as well. This dip in required peel force is an artifact of peel testing angles below 75° and is removed by using steady-state peel force averages for comparisons in this text. The steady-state peel force for each angle is calculated by averaging the steady-state force plateaus for all tests at that angle, as shown by the dashed green lines in Figure 6. Figure 7 shows peel force versus displacement curves for a single AR1-D1000 sample peeled at 0.3 mm/s for peel angles of 15398

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the shape of the adhesive results, but deviations from the data are seen at low and high angles. The deviation from theory is shown to be a result of varying detachment mechanisms as a function of angle, as shown in Figure 8b−d. During peel testing, a CCD camera was used to gather 15 frames per second video of individual pillars as they detached. Analysis of these videos revealed three unique detachment mechanisms dependent on the peel angle. These detachment mechanisms occurred over three specific angle ranges, as shown in Figure 8a, and are referred to as normal detachment, shear detachment, and mixed detachment. Normal detachment, shown in Figure 8b, is representative of angles in the range of 75°−165°. The steady-state adhesive force over these angles reduces slightly as angle is increased, but all averages are within one standard deviation of another. Pillar detachment observed over this angle range closely resembles the progression of detachment seen in normal adhesion studies. Detachment is initiated by a combination of a vertical load and bending moment from the backing layer. This loading condition initiates a crack underneath the pillar shaft that grows radially to encompass the entire area under the pillar shaft. Failure occurs as the flange detaches, and the pillar is removed from the surface. Shear-based detachment, shown in Figure 8c, represents only 0° loading or the pure shear condition. The adhesive force at this peel angle is an order of magnitude larger than the average forces seen in normal detachment. Under this condition the applied load is transverse to the pillar shaft directly in line with the backing layer. This shear loading results in a large bending moment in the pillar itself with the highest tensile stress acting on the trailing edge of the pillar. A crack initiates at this high tensile location and propagates forward under the pillar shaft. This crack propagation is hindered by the compressive stresses created from the large bending moment on the pillar shaft. When crack growth encompasses approximately 50% of the pillar shaft, the tensile forces detach the trailing half of the pillar. Failure occurs when the shear stress is enough to buckle the leading flange of the pillar. Mixed detachment, as shown in Figure 8d, represents the angle range of 15°−60° where adhesive strength increases as peel angle is reduced. The failure of the pillars in this range contains qualitative similarities to both shear and normal detachment. Because of the angle of the applied loading, the pillar experiences both tangential and vertical applied loads. The tangential component of the applied load will cause a higher tensile stress at the trailing edge of the pillar and creates the site of crack initiation. The vertical component of mixed detachment will then propagate the crack to encompass the entire pillar area and failure occurs when the flange detaches. Optical observations of detachment revealed that crack initiation and propagation always progress in the same qualitative manner regardless of the angle tested. Detached areas in Figure 9 are noted by black arrows and appear darker in the image than areas where the pillar remains adhered. As shown in Figure 9, the crack almost always initiates at the location where the geometry of the structure changes from pillar to flange. This location has been analytically shown to be the location of a stress concentration.25 The crack then propagates to encompass the entire pillar shaft as noted in Figure 9b, and pillar failure occurs when the flange detaches as shown in Figure 9c. The main difference in this mechanism in the three modes of detachment is the side in which initiation occurs. For shear and mixed detachment, the crack initiates on

Figure 9. Optical images of a single pillar detachment from a glass substrate where (a) a crack nucleates at transition from pillar to flange (the detached area appears darker than the adhered areas and is noted by the black arrows), (b) the crack propagates radially to encompass the entire shaft, leaving only the flanges in contact, and (c) the pillar detaches from the surface.

the trailing edge of the pillar, contrary to normal detachment where the crack initiates on the leading edge of the pillar, as shown in Figure 8b. Also, it should be noted that for shearbased detachment final failure occurs as the leading flange buckles in shear because the applied loading does not allow for flange detachment from the surface (Figure 8c). Optical observations in Figures 8 and 9 are consistent with FEA results of a single pillar, as shown in Figure 10. For the finite element models, the individual pillars were fixed in space on the mushroom-shape tip surface to mimic the condition of a pillar adhered to a surface prior to detachment. A static tensile load of 0.01 N was applied in the desired peeling angle across the left surface of the backing layer, and the resulting stress on the mushroom-shape tip was measured perpendicular to the adhered surface. The measured stress is plotted graphically in Figure 10 with yellow indicating tensile stress, blue indicating compressive stress, and darker shades indicating areas of higher stress. Resulting stress values from the FEA were taken across the black line at the top of Figure 10; these results were then plotted over pillar geometry at the bottom of the figure. Regardless of the applied loading, the maximum stresses were located just inside the geometrical transition from pillar to shaft. It was also seen that the location of the tensile stress switched sides of the pillar when the loading angle changed 15399

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DISCUSSION

In Figure 8a, the steady-state peel force results for an AR1D1000 sample are compared to the predictions of eq 2. It is shown that eq 2 only qualitatively predicts the adhesive results, and deviations are seen at high and low angles. The equation does not predict the results completely because it does not include the specific energy contributions of structured surface detachment. During detachment, the number of pillars under loading, progression of detachment, and individual pillar mechanics were shown to vary as a function of peeling angle, regardless of pillar diameter tested. Equation 2 uses a constant critical decohesion energy for all angles and therefore does not capture mechanistic changes in structured adhesion. In order to extend eq 2 to predict the peel adhesion of structured surfaces, the critical decohesion energy would have to be modified to account for the differing adhesion mechanisms of the three different types of detachment observed. Normal-based detachment represents the mechanism for the angle range of 75°−165°. The average peel force over this angle range remains relatively constant, with the averages of all tested angles lying within one standard deviation. The peeling force remains relatively constant because of rigidity in the backing layer that causes the angle of the backing layer at the adhered surface to remain constant over this angle range, at approximately 75°. This is shown in Figure 8b, where the backing layer does not leave the pillar at the 90° angle applied globally to the sample. The effect of backing layer stiffness has been documented in conventional adhesives41 and is the driving mechanism for the constant steady-state peel force over the normal detachment range. Shear-based detachment represents the 0° loading condition where the applied load is transverse to the pillar, directly along the backing layer. The peeling forces at 0° are an order of magnitude higher than those observed in normal detachment. The cause of the large increase in adhesion is load sharing between multiple rows of pillars. The application of the applied load directly down the backing layer distributes the load along multiple rows of pillars, instead of the one or two rows carrying the load in normal detachment. This distribution of the applied load requires a far greater load be applied to the sample globally to reach the stresses required for detachment on each individual pillar. Load sharing is also the cause for the lower displacement to failure, as the large groups of pillars carrying the load reach detachment stresses simultaneously. Mixed detachment is the mechanism representative of the 15°−60° range. In this detachment range the average peel force increases as the peeling angle is reduced. This inverse relationship is due to an increase in the tangential loading. As the tangential load increases, the load is shared among more rows of pillars. Similar to shear detachment, this load sharing requires that more force is applied to reach the stresses high enough to detach individual pillars. As the applied loading angle is decreased, the number of rows controlling adhesion increases. The adhesive force does not reach the values observed in shear detachment because the loading is never applied directly down the backing layer and is therefore never distributed on as many rows of pillars as at 0°. Through in situ observation and FEA, it was concluded that cracks will almost certainly initiate at the transition from pillar to flange. The location of crack initiation can be further predicted based on the type of detachment. If the pillar is detaching under shear or mixed detachment mechanisms (0°−

Figure 10. (top) Predicted stress state on the adhered surface of a pillar during 0° peel test loading with the load applied to the left side of the backing layer. Tensile stresses are noted in yellow, and compressive stresses are noted in blue with darker shading indicating higher stress levels. The black line was the path used for stress analysis to create the stress gradients shown. (bottom) Stress gradients along the adhered surface for 0°, 75°, and 45° peel test loadings. The black lines represent the geometry of the modeled pillar superimposed over the stress results. Areas of high stress are predicted to be located just inside the transition from pillar to flange.

from 0° and 45° to 75°. It should also be noted from Figure 10 that even though the applied loading for all three angles was constant at 0.01 N, the maximum tensile stress varied greatly. The maximum tensile stress was largest for all cases on the 0° test. The 45° test showed the lowest tensile stress, and the 75° stress lies between the maximum found for the 45° and 0° tests. In Figure 11a, the steady-state adhesive values of the AR1D1000 and AR1-D400 samples are compared to a control flat sample. The structured samples are more adhesive than the flat sample at all angles excluding 0°. It is also shown that reducing the pillar size from 1 mm to 400 μm slightly decreases the steady-state adhesive force for all peel angles above 15°. The two samples are equally adhesive when tested at 15°, and when the angle is reduced to 0°, the 400 μm is more adhesive, as shown in Figure 11b. Figure 11c compares the three aspect ratios for the 400 μm samples. The steady-state peel force results for all angles between 15° and 165° lie within one standard deviation, indicating that aspect ratio plays a very small role in peel adhesion over that range. However, it is seen in Figure 11d that at 0° the 1:1 aspect ratio is approximately 50% more adhesive than the longer pillars. 15400

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Figure 11. Steady-state peel force with standard deviation error bars for all samples tested. (a) Comparison of samples with diameters 1 mm and 400 μm with aspect ratio of 1:1 to the flat sample, where (b) zooms in to the 0°, 15°, and 30° tests for these three samples. (c) Comparison of samples with 400 μm diameter and aspect ratios of 1:1, 3:1, and 5:1, where (b) zooms in to the 0°, 15°, and 30° tests for these three samples.

Figure 11a shows that both the AR1-D1000 and AR1-D400 samples are more adhesive than the flat sample at all angles excluding 0°. This behavior is notable because the addition of structures reduced the effective contact area of the sample from 17 cm2 for the flat sample to approximately 7.4 cm2 for a 1 mm pillared sample and 7.6 cm2 for a 400 μm sample. From this, it was determined that even with as much as a 56% decrease in contact area the addition of mushroom-shaped structures increased peel adhesion for angles of 15°−165°. The use of a smooth glass substrate assured that both the flat and structured samples attain the same conformance; therefore, the increased adhesion is solely due to the additional energy required to detach mushroom-shape terminated structures. As discussed above, addition of mushroom-shaped structures increases the adhesion compared to a flat sample, even with the use of relatively large scale pillars. Contact splitting theory predicts that an increase in contact points, or conversely a reduction in pillar diameter, should increase the adhesion of a sample.3,4,21 In Figure 11a, adhesive force results for 1 mm diameter samples (AR1-D1000) and 400 μm diameter samples (AR1-D400) are compared. The results show a small decrease in adhesion for the smaller diameter structured surfaces from 30° to 165°. In an effort to explain this decrease in adhesion, the adhesive force of each individual pillar on the sample can be estimated through contact mechanics. When concerned with flat tipped structural elements, the adhesion of a single pillar can be estimated using eq 3:43

60°) the crack will initiate on the trailing half of the pillar because the tangential component of the loading causes a bending moment on the pillar itself (Figure 8c,d). The stress from this bending moment is additive to the stress caused by the vertical component of the load (if any) and will therefore be the side of highest tensile stress. Conversely, if the pillar is detaching under normal detachment mechanisms, the crack will always initiate on the leading edge of the pillar due to the combination of applied bending moments from rotation of the backing layer and the vertical component of the applied load, causing tension on the leading edge (Figure 8b). The ability to predict the side of crack initiation can aid in the design of mushroom-shape tip pillars for peeling applications, as the design can be modified to reduce the stress concentration at the location of maximum stress. FEA modeling of a single pillar was shown to not accurately predict the peel test results. It was observed in Figure 10 that with a constant load applied on each test, the 0° test experienced the highest tensile stress followed by 75° and 45° angles. This means that finite element modeling of a single pillar predicts that the 45° loading would require the most force followed by the 75° and finally the 0° loading. Analysis of experimental results shows 0° to require the most load, followed by the 45° and then the 75° angles. The discrepancy between experiments and finite element modeling is due to load sharing when peeling. During a 45° or 0° peel test the load is shared among three or more rows of pillars, increasing its load bearing capacity, where in the 75° test the load is shared among a maximum of two rows of pillars. Therefore, in order to model peeling of structured adhesives, multiple rows or unique boundary conditions will be needed to produce accurate results.

P=

8πE*R3ω

(3)

where P is the adhesive force of the area, E* is the reduced elastic modulus, R is the contact radius of each subcontact, and ω is the surface energy of the contact area. It should be noted 15401

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because short and long pillars conform to a flat surface equally, and the increasing aspect ratio was not shown to increase the length of the cohesive zone. The conformance of the sample to the surface is not improved by increasing aspect ratio because the peeling surface is perfectly flat, and deformation of the backing layer accommodates any sample variation in pillar length. Figure 11d does show, however, that at 0° the 3:1 and 5:1 aspect ratio pillars are approximately 50% less adhesive than the 1:1 aspect ratio samples. The decrease in adhesion is due to the larger moment arm and the reduced effective stiffness of increased aspect ratio pillars. As a pillars aspect ratio increases, the applied load is displaced further from the adhered surface and the applied moment arm increases. The increase in moment arm dramatically increases the bending moment in the pillar and reduces the amount of load necessary for crack initiation. Also, because the effective stiffness is reduced in longer pillars, the pillar rotates more easily which aids in separation of the mushroom-shaped tip.

that eq 3 was derived with assumptions of a stiff pillar in contact with a compliant flat surface; however, the equation was used to describe biological attachments with conditions similar to the attachments in the text.43 To compare the expected peeling forces for each sample, eq 3 is multiplied by the number of contact points and a constant is used to relate the adhesion of the two samples, as shown in eq 4. (n 8πE*R3ω )AR1 − D1000 = C(n 8πE*R3ω )AR1 − D400

(4)

Equation 4 can be simplified for both force predictions because all variables, excluding the number of contact points and the contact radius, remain constant across the two samples, leaving eq 5: (n R3 )AR1 − D1000 = C(n R3 )AR1 − D400

(5)

In order to solve eq 5 for C, the number of contact points controlling the load during peeling was needed. During adhesion, a certain area of the sample at the peel front carries the load, which will be referred to as the “cohesive zone”. The length of the cohesive zone varies as a function of detachment mechanism, but for the normal detachment mechanism optical observations show that pillars detach in the first and second row, but never in the third row regardless of pillar size tested. From this, it is assumed that the first two rows of pillars carry the load and are considered to be the cohesive zone. With the two row cohesive zone assumption, 1 mm pillared samples have 9 contact points controlling adhesion, and the 400 μm pillared samples have 23. Substituting in these values for n, and the contact radius, R, from for each sample into eq 4, C is calculated to be approximately 1.6 ± 0.6. Comparison of experimental results at 75°−165°, where normal detachment mechanisms are observed, yields a C value of approximately 1.4 ± 0.6. The values of the experimental and theoretical constants are within 15% of each other, which analytically shows that the drop in contact area outweighs the increase in contact points in the smaller pillars, and in part is responsible for the reduction in adhesion. As the applied loading angle is reduced to 15°, the two samples perform nearly identically, and if the angle is further reduced to 0°, the 400 μm sample is more adhesive than the 1 mm sample (Figure 11b). This is because as the applied loading angle is reduced, the cohesive zone transitions from row controlled to area controlled. It was determined above that when the peel adhesion is controlled by a set number of rows, smaller pillars will always produce lower adhesion due to the large losses in contact area carrying the load. However, when a set length of the sample carries the applied loading (as in shear detachment) there is no loss in contact area for smaller pillars, and the increase in contact points, n, increases adhesion. This result is critical for the design of pillars for peeling applications, as it demonstrates that mushroom-shaped pillars can be designed to carry high loads at 0° and still be easily removed at higher peeling angles. Also, if the expected angle of peel loading for a mushroom-shaped tip surface is above 15°, larger pillars should be used for increased load bearing capacity. The aspect ratio has been shown to dramatically affect normal adhesion results of structured adhesive surfaces when using a spherical probe.1,34,44 However, results in Figure 11c show that an increase in aspect ratio does not have a large affect on the peel adhesion of structured samples for the angle range of 15°−165°. The aspect ratio over the range tested does not affect the peel adhesion of the mushroom-shaped pillars

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CONCLUSIONS 1. Peel testing theory developed for conventional adhesives is not sufficient to predict the adhesion of mushroom-shaped structured adhesives because the surface energy term does not account for the mechanistic changes in detachment as a function of angle. In order to extend this theory to encompass mushroom-shaped structured adhesives, the critical decohesion energy would have to vary as a function of angle to incorporate the load sharing and individual pillar detachment mechanisms of normal detachment, shear detachment, and mixed detachment. 2. Cracks most commonly initiate at the geometrical stress concentration of the transition from pillar to flange in mushroom-shaped structures. The location of crack initiation can be further predicted, as bending moments in the pillar create areas of high tensile stress on the leading or trailing edge of the pillar dependent on loading angle. Predicting the location of crack initiation can aid in the design of mushroom-shaped dry adhesion surfaces for peeling applications. 3. FEA analysis of a single pillar is not sufficient to predict the peel adhesion of a mushroom-shaped structured adhesive due to the load sharing effects during peeling. Instead, FEA modeling must incorporate multiple rows of pillars or repeating boundary conditions to accurately model the peeling forces of a pillared sample. 4. Mushroom-shaped pillars can increase the peel adhesion of a surface, even with very large reductions in contact area, due to the complex detachment mechanisms created by the addition of a low stress flange. 5. When designing mushroom-shaped structured adhesives for peeling applications, the expected loading angle will aid in the determination the optimal pillar size. If peeling angles of 15° or less are expected, smaller pillars should be used. However, if the loading angle is expected to be larger than 15°, larger pillars may allow for a higher load bearing capacity. 6. Adhesion in mushroom-shaped pillars exhibit large directionality during peeling due to the load sharing during peel-based detachment. Load sharing among pillars allows the sample to exhibit an order of magnitude higher adhesion at 0° than at 90°. Utilizing this directionality, a sample could be made with high load capacity at 0° that could still be easily removed at angles of 75° or more. 15402

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7. The aspect ratio of mushroom-shape tip dry adhesives plays no role in peel adhesion for applied loading angles between 15° and 165°. If the applied loading angle is expected to be less than 15°, shorter aspect ratio pillars should be used to maximize load capacity.

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AUTHOR INFORMATION

Corresponding Author

*Tel +1 307 766 4068; e-mail [email protected] (C.P.F.). Present Address ∥

A.S.S.: AG der Dillinger Hüttenwerke, Development and Plate Design, P.O. Box 1580, 66748 Dillingen. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.K.H. and C.P.F. gratefully acknowledge funding from the Wyoming NASA Space Grant Consortium, NASA Grant #NNX10A095H.

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