Article pubs.acs.org/Langmuir
Analysis of Preload-Dependent Reversible Mechanical Interlocking Using Beetle-Inspired Wing Locking Device Changhyun Pang,† Daeshik Kang,† Tae-il Kim,‡ and Kahp-Yang Suh*,†,‡ †
Division of WCU Multiscale Mechanical Design and ‡School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea S Supporting Information *
ABSTRACT: We report an analysis of preload-dependent reversible interlocking between regularly arrayed, high aspect ratio (AR) polymer micro- and nanofibers. Such a reversible interlocking is inspired from the wing-locking device of a beetle where densely populated microhairs (termed microtrichia) on the cuticular surface form numerous hair-to-hair contacts to maximize lateral shear adhesion. To mimic this, we fabricate various high AR, vertical micro- and nanopillars on a flexible substrate and investigate the shear locking force with different preloads (0.1−10 N/cm2). A simple theoretical model is developed based on the competition between van der Waals (VdW) attraction and deflection forces of pillars, which can explain the preload-dependent maximum deflection, tilting angle, and total shear adhesion force.
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INTRODUCTION Recently, a wide range of nature-inspired functional surfaces have been introduced for various applications such as water/oil repellence,1−3 water collection,4 dry adhesion,5−10 structural color,11−13 and biomedical patch.14,15 Multiscale, hierarchical structures are usually found on such surfaces, in which each structure has unique geometry and hierarchy to be useful in different environments for each living organism. To mimic structural functions of the above examples, micro- and nanopatterning methods have played a central role in creating single to multiple length scale structures by combining various top-down and bottom-up approaches.16 An additional interesting structural function is the directional and reversible interlocking of the beetle’s wing-fixation device with densely populated microhair arrays. Gorb and co-workers found that the wing fixation of a beetle is operated by bringing numerous microhairs on the cuticular surface in contact, thereby generating a high lateral shear friction while minimizing the force for vertical lift-off.17,18 The characteristic of this mechanical interlocking is quite different from the well-known hook-and-loop formation in burdock seeds (now commonly used in the fabric Velcro), and thus provides insight into a new binding mechanism toward reversible attachment and detachment. In addition to beetles, the reversible interlocking system is also found in a dragonfly’s head arrester consisting of unique fibrillar structures.19 In both cases, the locking is enabled by reversible fixation between microstructures (known as microtrichia), which are regularly arrayed, dense microfibers on the cuticular surface. Obviously, the functions of these microfiber arrays are directly related to their structural architecture, density, shape, shear or vertical directionality, and material properties at the interconnecting surfaces. © 2011 American Chemical Society
A variety of useful applications are conceivable based on the reversible adhesion or interlocking. First, an active control of the adhesion is possible with switching between maximum and minimum adhesion states. Previous studies have demonstrated that the adhesion force can be significantly enhanced or tuned by conformal alignment of micropillars and microholes with suitable geometry.20,21 Furthermore, a selective adhesion cycle can be established by utilizing a wrinkled surface of polydimethylsiloxane (PDMS) membrane with the help of phase-mismatch of the wavy surfaces.22,23 Similarly, the reversible interlocking between fibers could be used as an element for active control since the shear adhesion is considerably large compared to normal lift-off (i.e., high adhesion hysteresis). Second, the interconnected hairs can be used as a fastener or an electric connector. For example, several research groups reported core−shell type nanowires and CNTbased carbon forests as a permanent or reversible adhesive between surfaces.24,25 Furthermore, the adhesive can be used as an electric connector with the deposition of a thin metal film.26 To expand the utility of the interlocking-based adhesive presented here, we have recently demonstrated a polymerbased, flexible interlocking system by exploiting well-established soft lithography and adhesion tests.27 In this work, we fabricated various regularly arrayed, high aspect ratio (AR) polymer fibers made of UV-curable polyurethane acrylate (PUA) materials. In order to assess the effect of structural dimensions and materials properties, we used three PUA Special Issue: Bioinspired Assemblies and Interfaces Received: September 30, 2011 Revised: December 5, 2011 Published: December 13, 2011 2181
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Figure 1. (a) Schematic of folding and unfolding states of the wing-locking device of a beetle (Promethis valgipes) and SEM image for microtrichia on the cuticular surface. (b) Illustration of beetle-inspired interlocking structures with upper and lower fiber arrays. (c) Sequences of interlocking step: (Step 1) overlapping by a preload, (Step 2) paring of the fibers by VdW interactions, and (Step 3) distortion of the fibers upon application of an inlane stretch in the shear direction.
materials of different rigidity (elastic modulus: 3 MPa ∼ 10 GPa) with various hair radii and ARs, and found that the locking force increased with the decrease of hair radius and modulus and the increase of AR. In particular, the maximum shear locking force of ∼40 N/cm2 was observed for the nanopillar arrays of 50 nm radius and 1 μm height (AR = 10), which was probably the highest adhesion strength among the polymer adhesives reported to date.27 In this Article, we report on how the interlocking is mediated by different preloads in view of maximum deflection/angle and total adhesion force prior to detachment. It is readily expected that the total adhesion strength would be elevated with increasing the preload. Nonetheless, the degree of overlap between fibers and its respective deformation needs to be understood to accurately describe the interlocking behavior. To this aim, we used two types of high-AR pillars of PU elastomer (diameter = 3 μm, AR = 10, elastic modulus ∼ 3 MPa) and soft PUA (s-PUA, diameter = 100 nm, AR = 10, elastic modulus ∼ 19.8 MPa).28 Measurement of shear adhesion force demonstrated that the locking force was enhanced with the increase of preload for both materials. From the simulation, a typical stick− slip dynamic motion was predicted in response to an in-plane stretch, which can be interpreted as a competition between van der Waals (VdW) and deflection forces. Finally, a simple theoretical model was derived to incorporate the effect of the two competing forces, which was used to explain the preloaddependent behavior of the interconnected fibers. Figure 1a shows a scanning electron microscopy (SEM) image of the beetle’s wing-fixation microfiber array at its anterior field of thorax (Promethis valgipes) and illustrations for the interlocking mechanism. As seen from the image, the fixation unit is composed of dense, hexagonal microhair arrays of approximately 0.9 μm radius and 18 μm height with hexagonal packing (hair-to-hair distance divided by hair diameter ∼3). Such regularly arrayed microfibers are interconnected when the upper and lower layers are brought
in contact, which in turn generates a high shear locking force against an in-plane stretch (Figure 1a). Beetles use these structures when they need to stay on trees or grounds while protecting their large, intricate, and delicate wings. Also, the interlocking of cuticle microstructure made of β-keratin provides effortless folding with high shear adhesion and reversibility. According to the previous study,18 the function of this wing-fixation device is associated with body cleaning, food grinding, air holding, thermoregulation, and filtration with an aerodynamically or hydrodynamically active surface. A close examination of the SEM image reveals that the shape of microtrichia is tapered along the top with an inclination angle, displaying a pointed directionality toward a particular spatial axis. By contrast, the microfibers used here are straight with a uniform thickness. For better structural similarity, this deviation needs to be addressed in a future study. Inspired from this wing-locking device, artificial micro- and nanofiber arrays were prepared as shown in Figure 1b. The upper and lower layers having identical fiber arrays were interconnected in such a way that numerous hair-to-hair contacts were formed with a certain overlap. Due to some misalignment and collapse of fibers, the configuration of each interlocking would be different from single to multibody contacts. As shown shortly, the degree of overlap turned out to be a function of the applied preload. A schematic shown in Figure 1c shows the sequences of the interlocking step: (Step1) overlapping by a preload, (Step 2) paring of the fibers by VdW interactions, and (Step 3) distortion of the fibers upon application of an in-plane stretch in the shear direction.
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EXPERIMENTAL SECTION
Materials. Two PUA materials with different rigidity were purchased from Minuta Tech, Korea, and used throughout the experiment: PU elastomer for microfiber arrays (elastic modulus: 3 MPa) and soft PUA for nanofiber arrays (MINS 301 RM, elastic modulus: 19.8 MPa).28 2182
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Figure 2. (a,b) SEM images of microfiber (3 μm diameter with AR of 10) (a) and nanofiber arrays (100 nm diameter with AR of 10) (b). (c,d) Measurement of shear adhesion forces of paired microfiber (c) and nanofiber arrays (d) as compared to gecko-like contact (hair-to-flat surface) (see the insets of c and d). (e) Cross-sectional SEM images of preload-dependent interlocking between nanofiber arrays (1, 5, and 10 N/cm2), indicating overlap ratios of ∼50, ∼60, and ∼70%, respectively. Fabrication of Micro- and Nanopillars. The silicon masters with micro- and nanoholes were prepared by photolithography and subsequent reactive ion etching. The masters were treated with a fluorinated-self-assembled monolayer (SAM) solution ((tridecafluoro1,1,2,2-tetrahydrooctyl)-trichlorosilane: FOTCS, Gelest Corp.) diluted to 0.03 M in anhydrous heptane (Samchon Corp.) in an Ar chamber. The surface-treated masters were annealed at 120 °C for 20 min. Drops of UV-curable PU elastomer or soft PUA prepolymers were dispensed onto the master, and a flexible polyethylene terephthalate (PET) film (50 μm) was slightly pressed against the liquid drop to be used as a supporting backplane. After preparing a polymer replica by UV exposure and mold removal, the PUA replica was additionally exposed to UV for several hours for complete curing. Details on the synthesis and characterization of the PUA polymers can be found elsewhere.28,29 For the fabrication of hair arrays, two types of pillar structures were used: microfiber array with PU elastomer (3 μm diameter and 30 μm height, AR = 10) and nanofiber array with soft PUA (100 nm diameter and 1 μm height, AR = 10). The spacing ratio (= spacing/diameter) of each array was set at 3 with hexagonal packing, which is the same with that in the wing-locking device of a beetle. Adhesion Tests. The preload-dependent shear adhesion forces were measured by custom-built equipment at a relative humidity of 50%. Two layers of adhesion patch (1 × 1 cm2 area) were brought in contact with a preload of 0.1−10 N/cm2, and an in-plane strain was applied with strict alignment until a separation occurred (see the inset of Figure 2d and Supporting Information Figure S1). All measurements were repeated at least 10 times at ambient temperature and average values were used for the plots. Frictional coefficient (μ) was measured by a scratch/wear tester CP-4, CETR. Simulations. The simulations were performed using ABAQUS 6.91 program (SIMULIA). With 52469 mesh-elements for calculation, the following parameters were used for the soft PUA: Young’s
modulus (E) of 19.8 MPa, Poisson’s ratio (ν) of 0.4, and pillar AR of 10.28,30
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RESULT AND DISCUSSIONS Figure 2a,b shows SEM micrographs of dense micro- and nanofiber arrays formed on a flexible PET substrate. These well-defined structures were formed over a large area (9 × 13 cm2) without notable defects. In the case of microfiber arrays, the fibers are not straight with a tilting angle less than 5°. Although the effect of tilting angle on the interlocking behavior cannot be ruled out, such effects would be marginal in the quantitative analysis of preload-dependent interlocking. Also, the surfaces of the micro- and nanofibers are vertically smooth, suggesting that nanoscopic frictional resistance between rough surfaces would be minimal. Using these fiber arrays, shear adhesion forces were measured by varying the applied preload in the range of 0.1−10 N/cm2. As shown in Figure 2c,d, the interlocking-assisted shear adhesion (hair-to-hair) was compared with the gecko-like adhesion (hair-to-flat surface, see the inset of Figure 2c). With the increase of preload, the shear adhesion force ranged from 3 to 17 N/cm2 for the microfiber arrays, whereas it ranged from 3 to 40 N/cm2 for the nanofiber arrays. For the gecko-like attachment, the adhesion value was usually less than 40% of the interlocking adhesion. These observations strongly suggest that the shear adhesion is largely determined by the applied preload. In order to elaborate on the preload effect, we measured SEM images of interconnected nanofiber arrays with different preloads (1, 5, and 10 N/cm2). As expected, the degree of 2183
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Figure 3. Simulation snap shots for single paired hairs using the ABAQUS 6.9-1 program. When the shear load exceeds the VdW force, the hairs are separated and recover their original shape and internal stress (different colors denote different internal stress levels): αoverlap= (a) 0.3, (b) 0.6, and (c) 0.9.
2.09 × 10−20 by the measurement of materials properties (see Supporting Information). Additionally, from the geometric consideration illustrated in Figure 1c, one needs to consider the counterbalance by deflection (Fdef) of hairs, which is given by
overlap between upper and lower fibers was dependent on the preload; it ranged from ∼50, to ∼60, to ∼70% in the order of increasing the preload. A further increase of the preload (>10 N/cm2) was not effective, in the sense that the fibers were susceptible to collapse and the overlapping was not improved. A linear dependency was observed for both mechanical contacts, but the slope was much higher for the interlocking. Among various structures, the nanofiber array of 50 nm radius and 1 μm height showed a remarkable shear adhesion force as high as ∼40 N/cm2. To understand the preload-dependent mechanical interlocking of single fiber contacts, a series of simulation snap shots are present in Figure 3 using a multiscale mechanical simulation tool (ABACUS 6.9-1). Here, individual nanohairs of soft PUA (50-nm radius and 1-μm height) are brought in contact by a preload and then attracted by VdW forces (Fvdw) to form a reversible contact.31 Here, we assume that additional frictional resistance from, e.g., hook-and-loop formation between fibers can be neglected since the vertical fibers are carefully pressed with a preload. Also, the viscoelastic properties of fibers were not taken into consideration in the simulation. This assumption was partly supported by our experimental observations that a majority of fibers were restored to the initial vertical geometry even after repeating cycles of attachment and detachment.27 As mentioned earlier, the current reversible interlocking between high-AR fibers can be explained by the competition between the retaining VdW and disjoining deflection forces. According to the literature, Fvdw can be written as32
Fvdw =
Fdef =
l0 (2 − αoverlap)2 (4 + αoverlap)
(2)
where I is the moment of inertia (I = π·R4/4) and DS is the maximum displacement length. For simplicity, we assumed the condition of part-uniformly distributed load of beam deflection.33 As can be seen from the simulation snap shots, the hair-to-hair contact is maintained until the deflection force overcomes the VdW force upon application of an in-plane stretch. In all cases, the well-known stick−slip motion was observed.34 When the shear load exceeds the VdW force, then the hairs are finally separated and recover their original shape and internal stress (different colors denote different internal stress levels). It is noted that the maximum deflection displacement and angle of paired fibers were highly dependent on the overlap ratio, such that they were lowered with the increase of αoverlap. To obtain an expression for the maximum displacement of paired fibers before separation, we assume Amonton’s first law of friction (Ffriction = μFload).35According to the force balance, the interlocked hairs would maintain the merged state until Fdef sin θ < μ(Fvdw − Fdef cos θ), where μ is the friction coefficient of materials (μ = 0.04 for s-PUA) and θ is the tilted angle by shear adhesion force. When the dislocating force (Fdef sin θ) to the perpendicular direction is equal to μ(Fvdw − Fdef cos θ), the paired fibers would be separated, yielding a criterion as
A R · l0·αoverlap 16D0 2.5
48EIDs 3
(1)
Fdef sin θp = μ(Fvdw − Fdef cos θp)
where A is the Hamaker constant, R is the hair radius, D0 (0.4 nm) is the distance between hairs, l0 is the length of hair, and αoverlap(= l/l0) is the overlap ratio between upper and lower hairs. Here, the Hamaker constant of s-PUA is approximated to
(3)
where θp is the maximum titling angle via preload and can be simply written as 2184
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Figure 4. Plots of (a) Fvdw, Fdef, (b) θp, and (c) DS of single paired fibers and (d) Fshear as a function of αoverlap.
θp =
6DS l0(4 + αoverlap)
Here, the hair density (ρ) was ∼1.85 × 109 from the hair spacing and hexagonal layout used in the experiment. Using the estimated θp in Figure 4b, Fshear is plotted as a function of αoverlap in Figure 4d, indicating that the measured maximum shear adhesion (∼40 N/cm2) corresponds to αoverlap of 70% (dotted line), in good agreement with our experimental observations. The fundamental assumption here is that the shear strength is well distributed over dense nanofiber interconnects on a 1 cm2 patch with minimal edge failure that is associated with the fracture mechanics. As the measurement of shear adhesion was carried out under strict alignment and stretching, the major contribution of the shear adhesion would be from the separation of the merged fibers above the critical in-plane stretch (Supporting Information Figure S1).
(4)
After some algebraic manipulation, one can have the maximum displacement (DS), which is given by
DS ≅ 5.5 × 104
(4 + αoverlap) αoverlap
·
μR raspect
4
·
Fvdw Fdef
(5)
This relation indicates that DS can be determined by the competition between VdW and deflection forces with a friction coefficient μ and a geometric AR (raspect = l0/2R) of fiber arrays that differs from the structural AR of fibers. It is noted that the tensile force acting along the axial direction is considered the frictional force [μ(Fvdw − Fdef cos θ)], which competes with the disjoining bending force (Fdef sinθ). A schematic shown in Figure 1c illustrates the detailed force balance in vector forms in deriving the maximum θp and DS. Figure 4a−c shows plots of forces (Fvdw, Fdef), θp, and DS of single paired fibers as a function of αoverlap on the basis of the above equations. For the calculations, we used a nanofiber array of 50-nm radius and 1-μm height. As shown in Figure 4a, the VdW force is overwhelmingly higher than the deflection force for the entire range of αoverlap. Once the hairs are deflected, the contribution from the dislocating force (Fdef sin θ) becomes pronounced and ultimately equals the friction force of paired hairs (μ(Fvdw − Fdef cos θ)). A notable finding here is that both θp and DS are reduced with the increase of αoverlap since a larger deflection force is required for a higher αoverlap. Similarly, the total shear adhesion force per unit area (cm2) (Fshear) can be derived by multiplying the hair density (#/cm2) to the shear adhesion force per single hair:
Fshear = ρ· Fvdw cos θp
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SUMMARY
Inspired from the wing-fixation device in beetle, we have presented the preload-dependent reversible mechanical interlocking between regularly arrayed, high-AR polymer fiber arrays. Our experimental and theoretical studies demonstrated that the shear adhesion force is strongly affected by the applied preload (0.1−10 N/cm2); the higher the preload, the higher the shear adhesion force. From the cross-sectional SEM images of interconnected hairs, we have confirmed the increase of overlap ratio with the increase of preload, which supports the linear tendency of locking force as a function of preload. Furthermore, a simple theory was developed to explain the maximum deflection displacement/titled angle and total adhesion force, in good agreement with the experimental data. The current work provides insight into how densely populated hair arrays form reversible, interconnected structures, and the locking force varies with different preload in such paired structures.
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ASSOCIATED CONTENT
S Supporting Information *
Calculation of the Hamaker constant of soft PUA and optical images of the custom-built equipment for shear adhesion measurement. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Tel: +82-2-880-9103; fax: +82-2-883-1597; e-mail: sky4u@ snu.ac.kr.
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ACKNOWLEDGMENTS This work was supported by a National Research Foundation of Korea (NRF) grant (No. 20110017530), the World Class University (WCU) program (R31-2008-000-10083-0), and the Basic Science Research Program (2010-0027955). This work was supported in part by a Korea Research Foundation grant (KRF-J03003) and the Institute of Advanced Machinery and Design (IAMD) and Engineering Research Institute of Seoul National University.
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