pubs.acs.org/Langmuir © 2009 American Chemical Society
Adhesion of Biologically Inspired Polymer Microfibers on Soft Surfaces Eugene Cheung and Metin Sitti* Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received March 21, 2009. Revised Manuscript Received May 8, 2009 Polymer microfiber arrays with mushroom-shaped tips are shown to adhere well to a soft, smooth substrate. An existing model describing the effect of backing layer thickness is also shown to be applicable to the adhesion of fibrillar arrays on soft surfaces. Simulations showed that adhesion can be enhanced by increasing the compliance of the microfibers in addition to maximizing single-fiber adhesion. This model can be used to guide the development of optimized microfiber adhesives for use on soft surfaces such as biological tissues or textiles.
Introduction
Materials
Recently there has been significant progress in the design and fabrication of polymer fibrillar temporary adhesives with potential applications in many fields. Inspired by the fibrillar attachment mechanisms employed by geckos,1,2 researchers have focused on understanding dry adhesion and using this knowledge to design synthetic fibrillar adhesives. Fibers can be used to enhance adhesion through contact splitting3 and crack trapping.4 These insights combined with work on the influence of tip shape5 have led to several promising polymer microfiber designs with mushroom-shaped tips that perform similarly to gecko foot hairs on smooth, rigid surfaces.6,7 The vast majority of work done in this area has focused on adhesion to rigid substrates. However, there are many applications that require adhesion to soft substrates, most notably in the biomedical field. Many mobile medical robots that work on or inside the human body need to adhere to soft tissues.9,10 The development of reliable repeatable fibrillar adhesives would benefit performance and robustness in addition to reducing power requirements and cost. Similarly, surgical graspers must hold tissue securely. Fibrillar adhesives could be used to reduce the applied pressure required to maintain this grip, reducing tissue trauma. Another promising application is use as a one-sided fastener for textiles or soft packaging materials. This letter explores the use of existing polymer fibrillar adhesives on controlled soft substrates. An existing model is shown to be applicable to this situation, providing a useful design tool for the development of fibrillar adhesives.
The polymer microfiber arrays used in this work were fabricated using previously developed techniques.11 The microfiber stalks and backing layer were molded in a soft rubber negative mold of lithographically formed master template structures. During this process, a spacer between the mold and a flat surface was used to determine the thickness of the backing layer, resulting in a stand-alone large-area array of polymer microfibers. Alternatively, a small volume of uncured polymer was placed on the mold, on top of which was placed a small acrylic peg that was 2 mm in diameter (cut out of an acrylic sheet with a laser cutter). Capillary forces pull the peg toward the mold, resulting in complete coverage of the peg with microfibers and a very thin backing layer (on the order of 100 μm). A dip-transfer process was then used to mold mushroom-shaped structures on the tips of the microfibers for both the large-area arrays and the acrylic pegs. This work uses two fiber geometries (50 μm diameter, 120 μm center-to-center spacing, 100-μm-tall fibers with 100-μm-diameter tips, as seen in Figure 1, and 25 μm diameter, 80 μm centerto-center spacing, 100-μm-tall fibers with 50-μm-diameter tips). Two polyurethanes (BJB Enterprises, Tustin, CA) with different Young’s moduli (E) were chosen: ST-1060 (E = 2.9 MPa) and ST-1087 (E = 9.8 MPa). Only one polyurethane was used in a single sample; both fiber and tips were made from the same polyurethane. Soft substrates were fabricated from the F-15 polyurethane (BJB Enterprises, Tustin, CA), chosen for its low Young’s modulus of 200 kPa as well as its transparency for imaging purposes. F-15 was molded into a 6-mm-diameter hemisphere using a soft rubber negative mold of a glass hemispherical lens. Flat substrates of varying thicknesses (0.7, 1.5, 3.0, and 5.5 mm) were created by molding the F-15 between two smooth, flat, plastic surfaces separated by an acrylic spacer of the corresponding thickness. Thinner flat F-15 substrates (0.02, 0.03, 0.05, and 0.14 mm) were fabricated by spinning the uncured polyurethane onto glass slides.
*E-mail:
[email protected]. (1) Autumn, K.; Liang, Y. A.; Hsieh, S. T.; Zesch, W.; Chan, W. P.; Kenny, T. W.; Fearing, R.; Full, R. J. Nature 2000, 405, 681–685. (2) 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. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12252–12256. (3) Arzt, E.; Gorb, S; Spolenak, R. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 10603–10606. (4) Hui, C. Y.; Glassmaker, N. J.; Tang, T.; Jagota, A. J. R. Soc. Interface 2004, 1, 35–48. (5) Spuskanyuk, A. V.; McMeeking, R. M.; Deshpande, V. S.; Arzt, E. Acta Biomater. 2008, 4, 1669–1676. (6) Aksak, B.; Murphy, M. P.; Sitti, M. Langmuir 2007, 23, 3322–3332. (7) Gorb, S.; Varenberg, M.; Peressadko, A.; Tuma, J. J. R. Soc. Interface 2007, 4, 271–275. (8) Kim, S.; Sitti, M. Appl. Phys. Lett. 2006, 89, 26911–26913. (9) Glass, P.; Cheung, E; Sitti, M. IEEE Trans. Biomed. Eng. 2008, 55, 2759– 2767. (10) Ota, T.; Patronik, N.; Riviere, C.; Zenati, M. A. Innovations Phila. PA 2006, 1, 227–231.
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Hemispherical Adhesion Experiment A typical tensile adhesion measurement with a load cell involves contacting the adhesive sample with a hemispherical substrate to eliminate any alignment errors.6 The first set of experiments performed in this work employed this method to investigate the viability of polymer microfiber adhesives on soft substrates. The 25-μm-diameter ST-1060 large-area microfiber arrays were brought into contact with 6-mm-diameter glass and (11) Murphy, M. P.; Aksak, B.; Sitti, M. J. Adhes. Sci. Technol. 2007, 21, 1281– 1296.
Published on Web 05/18/2009
DOI: 10.1021/la900997p
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Figure 1. Scanning electron microscope image of fabricated polyurethane fibers with mushroom-shaped tips. The stalks of the fibers have a diameter of 50 μm and are arranged in a square array with a 120 μm center-to-center distance. The tips of the fibers have a diameter of 100 μm. The total height of the fibers and tips is 100 μm. F-15 hemispheres with varying preloads and then retracted at 5 μm/s until separation. Adhesion measurements were also performed on a flat polyurethane sample for comparison. Each test was repeated three times, with the results plotted in Figure 2. As previously reported, the polymer microfibers enhance adhesion to the rigid glass substrate over the flat control.8,11 The results for adhesion to the soft F-15 substrate are promising, showing a greater enhancement over the flat control and almost as much adhesion as for the microfibers on glass.
Figure 2. Adhesion between 6-mm-diameter hemispheres and polyurethane adhesive samples (flat control and 25 μm diameter, ST-1060 microfibers), performed at a speed of 5 μm/s. Each marker represents three experimental values. The polymer microfibers enhance adhesion to both rigid and soft substrates.
Model Single-fiber adhesion models are clearly still applicable to soft substrate adhesion, but modeling the adhesion of an array of microfibers contacting a soft substrate is not simply the sum of the adhesions of all fibers in contact. The deformation of the substrate as the fibers pull off couples the adhesion of neighboring fibers, resulting in a decrease in adhesion. This situation is nearly identical to the backing layer thickness theory reported by Long et al. in 2008.12 Their numerical model describes the adhesion between a rigid cylindrical punch contacting an array of microfibers with an elastic backing layer. By altering the separation interface from the fiber punch to fiber backing layer, the model can also be seen to describe the adhesion of an array of microfibers to a soft substrate as shown in Figure 3. Complete equivalence requires a zero thickness backing layer between the fibers and cylindrical punch. Because this is not the case, there will be an added effect due to this backing layer. However, in this work the backing layer is much stiffer than the soft substrate and thin enough (less than 100 μm) that its effect is negligible. The only remaining difference is the interface that separates during pull off, but this is immaterial to the analysis and thus the equations can be used with no alterations. The normalized pull-off force F p was found to depend on a single dimensionless parameter β:12 2 F p ¼ pffiffiffi π β
ð1Þ
The dimensionless parameter β is a function of the material and geometrical properties of the substrate and fibers β ¼
4 2 / 0 χ0 ðηÞη / / C ðR Þ R C ðR Þ 1 f¥ f¥ π2 π2 1 þ χðηÞ
ð2Þ
(12) Long, R.; Hui, C. Y.; Kim, S; Sitti, M. J. Appl. Phys. 2008, 104, 044301.
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Figure 3. Drawing of the adapted model. In the backing layer theory, the fibers are connected to the substrate and adhere to the rigid punch.12 In this work, the fibers are connected to the rigid punch with a thin backing layer and adhere to the soft substrate.
where C f¥ ðR/ Þ ¼
π2 ðR/ Þ2 þ 46:4R/ þ 16 4R/ þ 16
R/ ¼
χðηÞ ¼
ka 2πG½1 þ χðηÞ
1:095η þ 1:3271η2 þ 0:1431η3 0:9717 η ¼
a h
ð3Þ
ð4Þ
ð5Þ
ð6Þ
In the above equations, a is the radius of the flat punch, h is the thickness of the substrate, k is the stiffness of the fiber array, and G is the shear modulus of the substrate material. The fiber array stiffness k can be calculated as k ¼ Fkf ¼ F
Ef A L
ð7Þ
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where F is the number of fibers per unit area, kf is the stiffness of a single fiber, Ef is the Young’s modulus of the fiber material, A is the cross section of a single fiber, and L is the length of a single fiber. In the case of a zero-thickness substrate, each fiber in the entire array contributes its full pull-off force, a condition known as equal load sharing (ELS). F P in eq 1 is normalized by the array pull-off force under this ELS condition such that 2 Fp ¼ F p πa2 FPf ¼ pffiffiffi a2 FPf β
ð8Þ
where Pf is the single fiber pull-off force. Thin substrates where most of the fibers are subject to approximately the same stress are said to be in the ELS regime.
Comparison with Experiments Because this model uses a flat circular contact area, experimental verification required the use of acrylic pegs with microfibers molded onto one end. An acrylic peg was placed on a soft F-15 substrate with the fibers in contact, ensuring perfect alignment through gravity. The load cell was then lowered into position, and quick-setting glue was employed to fix the peg to the load cell while still aligned on the substrate. Once the glue dried, adhesion measurements were performed. This process was repeated for each fiber sample and substrate thickness. All of these tests were conducted with a high preload of 50 mN and a slow retraction speed of 10 μm/s. Figure 4 shows the measurement results along with the model predictions. As done in the earlier backing-layer thickness paper, the single fiber pull-off force was fit to the four largest substrate thickness results where the system is considered to be in the nonELS regime.12 Table 1 shows the mean and standard deviation of the fitted pull-off force for each fiber material and geometry, with the fits found to be independent of the substrate thickness. The model correctly captures the increasing adhesion as the substrate thickness decreases, but the very thin substrate experiments do not follow the model exactly. We hypothesize that this discrepancy in the ELS regime is due to the deterministic nature of the model, as posited earlier in the backing-layer effect paper.12 The model expects the fibers to reach their critical pull-off force simultaneously, whereupon the entire interface fails instantaneously. However, the fiber failure observed during the experiments was more stochastic (Supporting Information). The single fiber pull-off force is not uniform across the entire array as the model requires, primarily because of differences in the local surface roughness as well as differences in fiber structure. When a fiber fails, the stresses on all other fibers still in contact must increase to compensate, causing them to fail earlier, resulting in a reduced pull-off force for the entire array. Porwal and Hui performed a recent statistical study on the effects of the aforementioned differences in the single-fiber pull-off force, demonstrating decreased pull-off for an array of fibers in the ELS limit with Monte Carlo simulations.13 For large thickness substrates in the non-ELS regime, the substrate deformation is dominant, leading to a failure of the interface on the edge of the flat punch that propagates toward the center (Supporting Information). Because this does not require a large number of fibers to detach simultaneously, the non-ELS regime is not affected by the small variations in pull-off force between fibers, and the model is expected to perform better. (13) Porwal, P. K.; Hui, C. Y. J. R. Soc. Interface 2008, 5, 441–448.
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Figure 4. Adhesion between 2-mm-diameter circular arrays of polyurethane microfibers on soft F-15 substrates of varying thicknesses, measured with a speed of 10 μm/s. Each marker represents five experimental values. Model results are plotted as lines, with the single-fiber adhesion fitted to the high-thickness experiments. The inset zooms in on the thinner substrates, showing that the model does not fit this regime well but still captures the correct trends. Table 1. Single-Fiber Pull-Off Force Values Used to Fit Equation 8 to the Large-Thickness Experimental Results Shown in Figure 4 fiber material ST-1060 ST-1060 ST-1087 ST-1087
fiber stalk diameter ( μm)
single fiber pull-off force (mN)
50 25 50 25
1.26 ( 0.06 0.44 ( 0.04 1.01 ( 0.02 0.33 ( 0.01
Discussion and Summary Even though the model in its current form is not as accurate in the ELS regime as in the non-ELS regime, the trends are still correct. Therefore, the model can be used to identify changes to an adhesive design that will increase its performance. It should be noted, however, that the majority of soft surface applications occur on very compliant surfaces, resulting in operation in the non-ELS regime where the model is more predictive. The foremost area for improvement is the single-fiber pull-off force, Pf, in eq 8. Increasing the adhesion of an individual fiber can be achieved in ways such as optimized tip shape5,14 and surface coatings.15 Another possible improvement that is not immediately obvious from the equations but was revealed through simulation is increasing the compliance of the fibers. This can be accomplished by altering the bulk material properties (lower the Young’s modulus) or changing the geometry of the fiber (increase length, decrease radius). However, there is a limit to the amount that the compliance can be lowered because fibers that are too soft suffer from lateral collapse issues.16 This compliance change is part of the more general minimization of the nondimensional parameter β. A target of future research is the inclusion of an accurate single-fiber pull-off force model. Simple geometries such as hemispheres and cylindrical flat punches have well-defined adhesion models, but one does not yet exist for a mushroom-shaped tip. Furthermore, the extension of this work from flat-flat contact to more complex/realistic contact modes would be very (14) Gao, H.; Yao, H. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 7851–7856. (15) Lee, H.; Lee, B. P.; Messersmith, P. B. Nature 2007, 19, 338–342. (16) Glassmaker, N. J.; Jagota, A.; Hui, C. Y.; Kim, J. J. R. Soc. Interface 2004, 1, 23–33.
DOI: 10.1021/la900997p
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useful. Surface roughnesses on a scale smaller than the tip size can be incorporated into the single-fiber adhesion model. Larger-scale surface roughnesses similar to the hemispherical adhesion test performed in this work present an interesting scenario. For this case, the substrate deformation may be beneficial by facilitating more fibers to make contact for a given preload in addition to allowing more fibers to maintain contact for a longer period of time. In summary, the adhesion of polyurethane microfibers with flat mushroom-shaped tips to soft substrates was investigated. The microfibers were found to enhance adhesion over a flat control in a similar manner to their performance on rigid substrates. Furthermore, the recently proposed backing layer theory model was found to be directly applicable to soft substrate adhesion and experimentally verified. Simulations using this model identified
6616 DOI: 10.1021/la900997p
increased fiber compliance and single-fiber adhesion as important means of increasing the soft surface adhesion of an array of microfibers. This work shows that the model can be a useful tool in the design of adhesives for soft substrates. Acknowledgment. This work was supported by Defense Threat Reduction Agency Project No. 8R22GA under the auspices of the U.S. Army Research Office Scientific Services Program administered by Batelle (delivery order 0068, contract no. W911NF-07-D-001). Supporting Information Available: Video showing the difference in pull-off behavior of fiber arrays between the ELS and non-ELS regime. This material is available free of charge via the Internet at http://pubs.acs.org.
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