Gecko-Inspired Artificial Structure for Adhesion

Van der Waals forces are unspecific and therefore omnipresent between practically any solid surfaces; the reason why we do not experience them in everyday life is their extremely short range: the surfaces have to be in intimate contact over large areas to exert strong forces. Nature utilizes these forces in animal locomotion.

The prime example, which has aroused scientific interest especially over the last decade, is the adhesion and friction of the gecko pad for example during running, climbing, and traversing ceilings. It is now known that the gecko owes its extreme reversible adherence to a fine structure of hierarchically arranged fibrils, which enable it to exploit van der Waals and capillary forces with great efficiency.^7-10

Dry adhesion mechanism in gecko lizards has attracted much attention since it provides strong, yet reversible attachment against surfaces of varying roughness and orientation. Such unusual adhesion capability is attributed to arrays of millions of fine microscopic foot hairs (setae), splitting into hundreds of smaller, nanoscale ends (spatulae), which form intimate contact to various surfaces by van der Waals forces with strong adhesion (10 N/cm²).^7,9 Recent advances of nanofabrication via top-down and bottom-up approaches have made it possible to develop synthetic, high-performance dry adhesives based on a range of different materials. Of these, polymeric nanohairs and carbon nanotubes (CNTs) have been largely used as attachment tip materials, since they allow for robust, high aspect ratio structures in a simple and reproducible manner.^11-16 In fact, researchers have already demonstrated that artificial dry adhesives can be applied to climbing robot and biomedical

patch.^17-18

For fabricating gecko-inspired artificial dry adhesives, a number of methods have been proposed, which can be classified into two main streams: polymer-based dry adhesives and carbon nanotube (CNT)-based dry adhesives. These two kinds of adhesives have been developed independently by utilizing different fabrication principles. In general, the polymer-based adhesives have been fabricated by a top-down approach. For example, conventional topdown nanofabrication techniques such as electron-beam lithography, photolithography and etching techniques were utilized for fabricating nanohairs directly from a substrate.¹¹ In parallel, polymer molding techniques were adopted by using a master with straight nanoholes.12,14,19-20

As to CNT-based dry adhesives, a bottom-up approach in which the CNT arrays were grown from the catalyst layer deposited on a substrate by chemical vapor deposition.

Due to different process characteristics and materials properties used in the fabrication, the polymer-based and the CNT-based dry adhesives demonstrate different adhesion capability and parameters.

One of the biggest advantages of the polymer-based methods is that they offer a simple and scalable approach to fabricating gecko-mimicking nanohairs with tailored geometry (angle, radius, height, shape of tip and hierarchy) and tunable material properties (modulus, surface energy, etc.) in a fast and cost-effective manner. Large area fabrication can be also achievable with the polymer-based approaches. The adhesion strength, however, is usually lower than that of the CNT-based adhesives because the resolution and aspect-ratio of polymer nanostructures are restricted by low mechanical strength of polymer materials. In contrast, the CNT-based dry adhesives usually have high level adhesion strength since the CNTs have superior structural features such as high AR, extremely small radius (10 nm) and high modulus (1000 GPa).^15-16 Despite these advantages, the CNT-based methods are potentially

limited by complicated process for CNT growth and small patterning area (4 mm × 4 mm).^15,21 Several exemplary works are in order to demonstrate how nanofabrication methods have been utilized to achieve synthetic dry adhesive with these two materials.

The gecko‘s high aspect-ratio nanohairy structures can maximize the contact area by a large number of pillars at the time of contact and a smaller effective modulus, which in turn increases the adhesion force against various surfaces. To achieve high aspect-ratio structures, Geim et al. presented a prototype of gecko tape having polyimide nanohairs (as small as 200 nm diameter) fabricated by e-beam lithography.¹¹ By fabricating high aspect-ratio polyimide hairs, relatively high normal adhesion (3 N/cm²) was obtained. The slow and expensive process of e-beam lithography, however, is a major shortcoming of this approach. In this work, they reported that the flexibility of the substrates was a crucial factor for obtaining high pull-off force. In these studies, researchers demonstrated that a small thickness of the substrate enhances the actual adhesion significantly as it allows flexibility and equal load sharing and prevents edge stress concentration.²² After the work by Geim et al., alternative approaches have been developed to overcome the limitations of e-beam lithography. The proposed approaches are mostly based on nanomolding methods, as they allow for a facile process with minimal time and cost. In these methods, various substrates (e.g., Si, SiO2, poly-Si, PAA, polycarbonate film, etc.) having nanoholes are prepared by e-beam lithography, photolithography, etching or electrochemical reactions. Subsequently, nanohairs are replicated by molding polymers against the substrates. The fabricated substrates can be re-used as a template for nanomolding, allowing for significant reduction of time and cost. For example, Majidi et al. reported polypropylene nanohairs.¹³ The hairy structures were fabricated by casting polypropylene film into a commercially available polycarbonate filter at an elevated

temperature (at 200°C for 25 min) in a vacuum condition. In spite of high elastic modulus (1 GPa) of the polypropylene, the hair arrays exhibited the coefficient of friction greater than 5 N/cm² due to the enhanced compliance of the high aspect-ratio nanostructures. PAA also has been utilized as a mold for generating high aspect-ratio polymer nanohairs. The PAA template has highly ordered nanoholes whose diameters and depths can be easily controlled by varying the electrochemical parameters without the need of expensive e-beam or photolithography. Cho et al. presented a gecko mimicking adhesives by molding from PAA but with a low adhesion (0.05 N/cm²).

High aspect-ratio polymer nanostructures could be easily obtained by simply molding the templates with thermoplastic or UV cured polymers.^19-20 However, the resulting nanohairs molded from the PAA usually suffer ,from self-matting problem due to wet chemical etching during template release or too high packing density and aspect-ratio of the nanostructures, which diminishes the resulting adhesion force significantly. ^19-20 Jeong et al. suggested a nanodrawing method for fabricating high aspect-ratio polymer nanohairs (80 nm in diameter, 2 μm in height and aspect-ratio > 20) on a solid substrate by sequential application of molding and drawing of a thin polymer film with 3 N/cm².¹²

Fibrillar surfaces with a slanted angle show smaller effective elastic modulus than planar surfaces. As a result, they deform easily and form contact effectively, especially when adhering to rough substrates. The elastic-strain energy stored in slanted single fibrils during pull-off is dissipated and, as a consequence, the separation work is higher than for a planar contact of similar material.^23-24 From the point of view of fracture mechanics, fibrillar structures with a slanted angle require frequent re-initiation of the interface crack and the failure of the interface therefore occurs at higher stresses.²⁴ Spatular tips at angles between 0 and 900 with respect to the substrate were obtained on tilted PU fibers by applying a controlled load to the tilted

fibrils during curing, causing bending of the fibrils.²⁵ This design, containing two independent tilted components (fiber and spatula), represents the most complex structure obtained to date with artificial systems. Slanted fibrillar structures were obtained by double replication of tilted SU-8 fibrillar arrays obtained by photolithography. This process involved tilted exposure of the resist layer to obtain fibrils forming angles between 0 and 500 with the substrate and exhibiting dimensions of 4 to 35 μm in diameter and ARs of up to 10. A mold of silicone rubber containing angled holes is then fabricated by soft-molding against the SU-8 template and subsequently used to obtain PU microfibers from liquid precursors.²⁶ Alternatively, arrays of PP microfibers were fabricated by first filling PC membranes with PP to obtain vertical fibrils and then tilting them by processing the patterned film through two heated rollers.²⁷ Tilted fibrils with 0.6 mm diameter, 18 to 20 mm length, and a 45° tilting angle were obtained. Coarser structures with 1mm length, 380 μm diameters and a tilt angle of 20° with a top face inclined at 450 with respect to the vertical were obtained by casting a PU precursor onto a mold fabricated by micromachining. Tilted structures were also prepared by a post-molding electron-beam irradiation step. The irradiated fibril surfaces shrink more than the opposite surface, resulting in bending of soft-molded fibrils.¹⁴ In this method, PUA nanopillars (100 nm in diameter and with an aspect-ratio of 10) were fabricated with tilting angles between 30° and 80°.

Ge et al. suggested dry adhesives with micropatterned CNT arrays.¹⁵ Interestingly, they reported that micropatterned CNT arrays with optimized geometry have four to seven times higher shear adhesion (~36 N/cm²) strength than nonpatterned CNT arrays. Moreover, the adhesion strength was maintained over thousands of cycles. Qu et al. also reported similar adhesion strength (15 N/cm² for shear adhesion and 30 N/cm² for normal adhesions) by growing single walled CNTs

(SWCNTs).²⁸ Following this work, they further enhanced the performance of the dry adhesive using MWCNTs.¹⁶ With use of vertically aligned MWCNT having curly entangled end segment, they could obtain extremely high shear adhesion (~100 N/cm²), which was ten times higher than gecko‘s adhesion strength. The strong shear adhesion comes from shear-induced alignment of the nonaligned top layer of the nanotubes enhancing the contact line length.¹⁶ As a result, increasing the CNT length greatly enhanced the shear adhesion. In contrast, the normal adhesion force was almost insensitive to the nanotube length as a result of point contact. Interestingly, there have been seemingly opposite reports on repeatability and robustness of CNT-based dry adhesives. Ge et al. and Qu et al. reported that CNT arrays maintained the strength for long attachment/detachment cycles whereas Zhao et al. reported that the adhesion strength was decreased with repeated use due to an interface failure between CNT arrays and the substrate.^15-16 Recently, Wirth et al. investigated the structural changes of vertically aligned CNT arrays (10 nm in diameter and 100 μm in length) after attachment.²⁹ They observed that the applied force for preloading leads to the collapse of the CNT arrays limiting the repeatable use of the dry adhesives. It seems that the interfacial strength between CNTs and the substrate is important for ensuring robustness and repeatability of the CNT-based adhesives. In general, CNT-based dry adhesives have higher adhesion strength than polymer-based adhesives due to outstanding structural properties such as extremely high aspect-ratio (> 104, diameters around 10nm and heights over 100 μm). With extraordinary high AR, the effective modulus of CNT is reduced below Dahlquist criterion (E ~100 kPa) in spite of its high mechanical modulus (~103 GPa). However, the patterned area of CNT arrays is usually small (~1.6 mm²) due to the complicated process (photolithography, catalyst deposition and chemical vapor deposition at high temperature, e.g., ~750^◦C). It is worthwhile noting in this regard that the adhesion

force per area can be enhanced greatly by reducing the contact area.³⁰ Also, the adhesion force of single nanohair measured by AFM might be misleading as it would not scale linearly into the bulk adhesion strength. In addition to the complicated and expensive process as well as small patterning area, another major concern of the CNT-based adhesives is that it requires a high preload (50~500 N/cm²) compared to that of polymer-based adhesives (< 0.5 N/cm²), potentially limiting the widespread use of the CNT-based adhesives.

Learning from nature creatures, we can find that nanostructures are essential in fabricating super hydrophobic surfaces with high CA, and multiscale structure can effectively reduce the angle of hysteresis of water droplets. In general, surfaces with a static CA (contact angle) higher than 150° are defined as super hydrophobic surfaces.

As for the details of CA hysteresis,^31-33 five states are possible for super hydrophobic surfaces: Wenzel‘s state, Cassie‘s state, the so-called ―Lotus‖ state, the transitional state between Wenzel‘s and Cassie‘s states, and the ―Gecko‖ state.

The phenomenon of self-cleaning in gecko setae is out of general thinking because setae are adhesive and can self-clean when dry. Adhesion in gecko setae is a consequence of many divided contact points (spatulae) that deform to achieve intimate, high-density contact with the surface, whereas lotus-like surfaces remain slippery because their rough, and in some cases waxy, cuticle prevents intimate contact. Lotus-like surfaces require water as a cleaning agent,^34-35 whereas self-cleaning in gecko setae may occur because it is energetically favorable for particles to be deposited on the surface rather than remain adhered to the spatula. We can model spatulae as curved surfaces with approximately spherical geometry at the interface, and also work at flexible strips. In each case, we compare the magnitude of attraction between a spherical dirt particle and a planar wall to the combined attraction of the same particle to a number of spatulaeas. This model suggests that >

26 spatulae would need to be attached simultaneously to a single 2.5 μm-radius dirt particle in order for self-cleaning not to occur, assuming similar Hamaker constants (Α) and gap distances. Hamaker constants are unlikely to vary by more than a factor of 2; if we take the worst case where Aps ~ 2Apw, (where p and w refer to particle and wall, respectively) energetic equivalence occurs with 13 spatulae attached. Gap distance remains an unknown parameter in the model. Until measurements are available, we will assume that D_pw and D_ps have similar probability distributions, and thus can be assumed to be approximately equal.

Adhesion is the result of attractive forces between two solids with surfaces in close proximity. The opponent of adhesion is the elastic strain energy of the solids as they deform to optimize their contact. A well-known model that treats this energy balance for two contacting spheres is the Johnson–Kendall–Roberts theory.³⁶ It predicts the force necessary for producing a contact area with radius a between two spherical solids of radius R as

... (1)

where E* is the Young modulus of the contact pair, and γ is the work of adhesion. The first term in Eq. 1 corresponds to the Hertz solution in the absence of attractive surface forces. The assumption of such forces leads to the prediction of a theoretical pull-off (or adhesion) force between a sphere and a plane given by

... (2)

identical apparent contact area, the adhesion force rises by a factor n^1/2. This principle is reflected in the design of the attachment pads of different natural species. Heavier animals with different lineage (including flies, beetles, spiders, and lizards) display progressively finer contact elements. Assuming that the adhesion force is proportional to body mass, a theoretical dependence of number of contacts versus animal mass has been derived which matches the observed correlation.³⁷ An additional feature in gecko locomotion is the rapid switching between attached and detached states.

Understanding this mechanism is essential for producing responsive adhesives.

Recent studies have revealed that geckos move by utilizing both adhesion in the normal direction and friction in the lateral direction.^38-39 These two components are strongly coupled: the friction enhances the adhesion when geckos grip onto substrate surfaces, called ‗‗frictional adhesion‘‘, while both forces fall to almost zero during detachment with little expenditure of energy by the gecko (‗‗directional adhesion‘‘).

This mechanism arises if the fibrils are not vertical, but tilted with respect to the surface. It is because an angled structure significantly lowers the effective modulus of the surface.⁴⁰ According to a previous study, the effective modulus should be less than 100 kPa for ensuring a tacky surface (so called ‗‗Dahlquist criterion‘‘), which is given by

... (3)

where E is the elastic modulus, I is the moment of inertia (πR4/4, R is the radius of hair), D is the hair density, L is the hair length, μ is the friction coefficient, and θ is the slanted angle. For vertical nanostructures, it is extremely difficult to meet the

AR should be larger than 2×10² for the vertical nanohairs with 100nm diameter assuming the slanted angle of 89^◦ (E = 1 GPa, D = 1.1 × 1013 m⁻², μ = 0.25).³⁷

This value is not easily achievable using polymeric materials with current fabrication techniques. Even if possible, the self-matting problem or structural buckling will occur due to too high aspect-ratio and limited modulus of polymers.^40-41 On contrast, if the structures are slanted, the effective modulus can be greatly reduced without the need of structures with extremely high AR. For 100 nm nanohairs with aspect-ratio of 20 (E = 1GPa, D = 1.1×1013 m⁻², μ = 0.25), the effective modulus decreases less than 100 kPa when the structures are slanted with less than 60° angle with respect to the horizontal plane. Most solid surfaces are not perfectly smooth and have some degree of roughness. Therefore, the height of nanohair should be long enough to ensure adaptation of rough surface with varying amplitude and topography.

The maximum height of polymer nanohair (h_max), however, is restricted by a critical value that is involved in lateral collapse of hairy structures due to relatively low elastic modulus of polymers. The value of h_max for given elastic modulus, size and surface energy of nanohairs is given by ⁴⁰

... (4)

where R is the radius of hair, γs is the surface energy, W is the distance of two neighboring hairs, E is the elastic modulus of hair, and ν is the Poisson‘s ratio.

According to Eq. 4, the maximum aspect-ratio of polymeric nanohairs without self-matting is about 10~20, limiting the absolute height of nanostructures significantly. In this regard, micro/nanoscale combined hierarchical structures could be useful, as they increase adhesion strength against a rough surface either by enhancing structural height or by reducing structural stiffness without structural

 

 

instability observed in high aspect-ratio nanostructures.⁴² As to the adhesion, the adhesion energy, which consists of the energy dissipated along the interface and the elastic energy stored in the fibril volume, should be concerned without doubt.

... (5)

where L is the length of the fibrils, P_cr is the critical force required to peel an elastic thin film off a rigid surface, W is the width of the film, H is the thickness of the film and φ is the area fraction of the fibril array. According to Eq. 5,^42-43 the larger the length of the fibrils are, the higher will be the adhesion energy. Taking L = 120 μm as the length of a seta, we can find γe >> γ. For φ~1, when the peeling angle of the spatula pad is θ = π/2, we have γe = 10 J and γ = 0.1 J; when the peeling angle of the spatula pad is slightly smaller than θ = π/6, we find γ_e = 924 J and γ = 9.24 J.

Therefore, extending the spatula pads to the length of the seta gives rise to a structural unit with much higher adhesion energy than the van der Waals interaction energy. The increase in adhesion energy is tremendous. At the same time, the effect of orientation dependent adhesion energy for peeling at different angles is magnified through the term P²cr in Eq. 5. Thus, at the scale of the seta, the adhesion energy for attachment is almost two orders of magnitude higher than that for detachment.