Flexibility and Poisson effect on detachment of gecko-inspired adhesives

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Abstract

Geckos and some insects can easily adhere to and detach from surfaces with micro/nanoscale hair structures on their foot, called setae and spatulas. Here, a model is developed to describe the detachment of the seta. In this model, the seta is assumed to be a beam whose tip adheres to a surface. When normal and tangential forces are applied to the root of the beam, a moment is generated at the contact tip and detachment occurs. The detachment conditions depend heavily on flexibility of the hair. The effects of Young's modulus and aspect ratio of length versus thickness of the beam on the detachment condition are theoretically investigated. The Poisson effect on the detachment conditions was also examined with the experimental results using fabricated silicone rubber beam arrays.

Introduction

Microstructures on surfaces have the potential to change the surface properties of the materials regarding adhesion phenomena, as observed especially in biological structures such as beetles' and geckos' feet [1], [2], [3]. Geckos have thousands of micro/nanoscale hairs on their feet to obtain excellent adhesion, especially for gripping surfaces [4]. The structures of the geckos' foot hairs can be divided into two types: microscale inclined curved hairs called setae and nanoscale flat hairs called spatulas on the tips of the setae.

Recently, many micro-fabricated adhesives mimicking geckos' foot hairs have been manufactured and dramatic increases in adhesion force have been reported [5], [6], [7], [8], [9], [10], [11]. The asymmetric adhesion property of the setae has been experimentally reported [4] and justified by finite element analysis considering a contact tip as a cohesive element [12]. Understanding the asymmetric behavior of the setae is important for the easy and rapid detachment of micro/nanoscale adhesive structures. As a simple theoretical model of the setae, the tip has been assumed to be a ball and Johnson–Kendall–Roberts (JKR) theory [13] was utilized to calculate adhesive forces [14], [15], [16]. This assumption is useful for the prediction of adhesion force (normal force), but the stiffness of the hair is neglected in the model. Elastic contact theory including stiffness has been proposed by Takahashi, Mizuno and Onzawa (TMO) extending JKR theory from the perspective of thermodynamic analysis [17]. Utilizing TMO theory in the seta model, the relationship between the flexibility of the hair and the ability to accommodate surface roughness was discussed [18]. When the amplitude of the roughness is smaller than the tip width, enough contact area cannot be created and size reduction of the structure is required, what the geckos is doing. In contrast, compliance of the hair becomes important when the tip is smaller. Because more tips can be kept in contact with the surface if the compliance is large enough, the total adhesion force does not decrease significantly compared to the non-roughness condition. JKR theory was also extended to the JKR friction model to discuss the effect of friction [19]. In this model, the friction force is assumed to be proportional to the real contact area obtained from JKR theory. JKR-related models, however, cannot explain how the deformation of the hair affects the asymmetric detachment of the hairs because the normal stress distribution at the contact is considered to be symmetrical.

When a tangential force acts at the root of the hair, a moment is presented at the contact, and the normal stress distribution becomes asymmetric. An asymmetric detachment mechanism due to the moment has been theoretically proposed assuming the hair to rigid [18] and has been experimentally investigated [20], [21]. It was clarified that the inclination of the hair and the direction of the tangential force play important roles in easy detachment. However, when normal and tangential forces are applied at the root, the hairs should deform, generating a change in the moment at the contact, which plays an important role in detachment. Thus, the flexibility of the structure has been discussed, introducing torsional springs into the root and the tip of the rigid beam [22]. This assumption is one of the techniques utilized to calculate the deflection of a cantilever beam. In the case of discussing curved beams with a varying moment of inertia and modulus, this model is quite profitable because the effect of shape can be discussed by adjusting spring constants. In contrast, most gecko mimicking adhesives have a simple straight structure with unchanged bending stiffness. Thus, it would be more practical to express the deformation of the structure using Euler beam theory.

The beam theory has been used for the discussion of the geckos' adhesion mechanism [23], [24], [25], [26], considering the adhesion at the side surface of the beam. These discussions focus on the peeling behavior of the spatulas. In contrast, different criterion has to be introduced to model the detachment behavior of the setae even though the beam theory is also used to explain the deformation of the hairs.

As an advantage of a simpler model utilizing Euler beam theory, the moment at a contact tip can be given as a closed-form solution. Therefore, the effects other than the flexibility, such as the Poisson effect, on the adhesion criterion can be also introduced to the previously proposed model [18]. Additionally, the effect of each parameter, which is important for the design of the devices, on the adhesion force can be theoretically discussed. In this paper, the central role of flexibility of the hair in the detachment of an adhered hair is theoretically elucidated applying Euler beam theory and experimentally examined using a fabricated beam array with silicone rubber.

Section snippets

Model

When the normal and tangential forces, Fn and Ft, are applied to the root of a seta, the tip of the seta that is adhered to a flat surface is supported by a moment at the contact, Mc (see Fig. 1). The moment depends on the applied forces and the rigidity of the seta. The stress distribution generated by the normal force and the moment is schematically drawn in Fig. 2, assuming the case of a linear distribution. The normal stress generated by the normal force is given byσn=Fn/A

and the normal

Experimental

Beam array structures were prepared by pouring silicone rubber into a metal mold (see Fig. 6). Commercially available two-component rubber (Base resin KE-106, Hardener CAT-RG, Shin-Etsu Chemical Co., Ltd., Japan) was utilized. The curing time was 3 h at 140 °C. To prepare devices with different stiffness, the mixing ratio of the base resin and hardener was set to 100:4, 100:5, and 100:6. The Young's moduli of the devices were measured by tensile test, as shown in Fig. 7. The dimensions of the

Results and discussion

The normal and tangential force results at detachment are plotted in Fig. 9a. Compared with the other two, the results of the mixing ratio 100:4 had smaller values overall, which might reflect a difference of material properties especially related to adhesion phenomenon. The value of the y intercept is theoretically 3l times larger than the x intercept when θ=90°. Although the aspect ratio of the prepared beams was l=3, the experimentally obtained values of the y intercept were smaller than the

Conclusion

A theoretical model of an adhesive beam, the tip of which adheres to a substrate, is proposed considering the deformation of the beam and the adhesion criterion. It is clarified that the Young's modulus and aspect ratio of length versus thickness are effective parameters for the detachment condition. With lower Young's modulus and smaller aspect ratio, the adhesion region increases. Upon inclining the beam, the adhesion region becomes asymmetric, and an easy detachment mechanism can be

Acknowledgments

This work was supported by JSPS KAKENHI Grant number 25889020.

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