Design of taper shape

Young‘s modulus is a fairly important parameter for us to forecast the adhesive ability and whether the hairy structures bunch themselves or not. Conventional adhesives, such as those used in adhesive tapes, must be soft enough. It means that low Young‘s modulus materials (E < 100 kPa) were used for satisfying Dahlquist‘s criterion to inherit intimate and continuous surface contact [8]. Definitely, the Young‘s modulous will vary by the deformation and geometry to fit the criterion as shown in Fig. 2.27. Facile fabrication of high-AR and taper nanostructures by replica molding requires the optimization of mechanical properties of a structured material. If the material is too soft (such as polydimethylsiloxane so called PDMS, with a Young‘s modulus of 1.8 MPa), the resulting high-AR nanostructure is prone to clump and collapse after molding which will reduce the real area of contact between the adhesive and surface. In contrast, if the material is too stiff (such as carbon nanotube), the

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high-AR nanostructure can readily be fabricated, despite a high preloading force and a significant reduction in the adaptability for a rough surface are still the major concern.

Hence, the material we using is sufficiently rigid for high-AR replica molding with its modulus 19.8 MPa but low preloading force.

In short summary, in theory, smaller features will generate higher levels of adhesion, and such materials with a higher modulus of elasticity will resist clumping and fouling.

The taper shape is beneficial for its ―longer length‖, ―higher stability‖, ―higher adhesion‖ and better ―self-cleaning‖ ability compared with other shapes, showing the profile and SEM image of taper pillars in Fig. 4.7a, c. Pillars cannot survive at the same conditions of density and length compared with taper shape pillar, that is, the life time or cycles can be improved without additional deposition such as Pt compared with other shapes of nanohairs as shown in Fig. 4.8. Eq. 6 [9] and Eq. 7 [11-12]

explain the maximum height of polymer nanohair (H) and the adhesion energy of the fibrils, respectively.

. . . ( 6 )

where R is the radius of hair, r_s is the surface energy, W is the distance of 2 neighboring hairs, E is the elastic modulus of hair, and ν is the Poisson‘s ratio.

. . . ( 7 )

where L is the length of the fibrils, Pcr 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.

 

 

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Figure 4.7 (a) Taper shaped pillars profile sketch map. (b) Pillar shape profile sketch map. (c) SEM image of taper shaped pillars and (d) illustration of taper‘s advantage.

Figure 4.8 Force measurements versus cycles of attachment and detachment, and the force remained the same for over hundreds of time.

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According to Eq. 7, the larger the density (area fraction) or length of the fibrils, which means the high-AR fibrils accompany the high adhesion energy. Taper shape has the advantages compared with pillar shape in both of density and length. The advantage is showing here via this equation, the taper shaped pillar can keep high density of fibrils which referred to adhesion ability while length increasing. Because if the pillar shape reach the same optimal length level as taper shaped pillar, the space between only pillar shapes should be widen in case of bunching, that is, density and area fraction must be decreased dramatically which reduce the adhesion force.

Consequently, taper pillar has a better performance than others. Gradient diameter of taper shaped pillar can firmly support whole weight from bottom, and avoids bunching due to wider interval from top. Evidently, taper shaped pillar can did increase the pillar height compared to pillar shape in the same material as shown in Fig. 4.7d. It is also noted that the maximum height of taper shaped and pillar shaped nanohairs in Eq. 6 are in the range of 1.3~1.8 μm and 0.7~1.2 μm (γs ~ 40 mJ/m² and ν = 0.5), respectively, corresponding to the height of taper shaped hairs presented here (~1.4 μm and 800 nm). As shown in Fig. 4.9 and Fig. 4.10, different lengths and profiles are fabricated by replicating, and the optimal lengths are 1.4 μm and 800 nm, respectively, which are both fit to the theoretic value.

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Figure 4.9 Taper pillars with different lengths. (a) 600 nm from tilted SEM image (b) 600 nm from cross SEM image. (c) 1.4 μm from cross SEM image. (d) 1.4 μm from cross SEM image. The insets showed the molds of replicating or SEM images of high magnification, respectively.

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Figure 4.10 SEM images of taper and pillar nanohairs. (a) Low magnification of our structure, and the inset is the top view image that displays the taper edge and hexagonal arrays. (b) Tilted SEM image of the pillar shape showing this type cannot support the same height as the taper shape and (c) SEM image from cross. (d) Stable pillar with decreasing the length.

Gecko‘s adhesive system is massively reusable and stable because of its multilevel hierarchy that distributes the load and generates such high levels of adhesion because of the smaller features (Fig. 4.11a) [8]. We can easily understand that taper shape could achieve stable and reusable than others due to the gradient diameter from bottom to top of the pillar. The larger diameter at bottom can support longer length and offer a better fundamental base of the pillar in case of breaking by external force, and smaller diameter at top is responsible for higher contact area

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related to the adhesion and also avoids clumping which we discussed previously (Fig.

4.7d). We can split the taper shape into several layers staked up one by one as shown in Fig. 4.11b. Moreover, each layer can regard as a sum of hundreds of thousands pillars to support the layer above themselves that is just like the gecko‘s multilevel hierarchy. In another way, due to the ―optimal‖ Young‘s modulus in gecko‘s feet, the multilevel hierarchy can easily acquire by gecko. Eq. 8 [10] shows the lowest Young‘s modulus needed for different conditions (as shown in Fig. 4.11c).

. . . ( 8 )

Obviously, we can find out the Young‘s modulus needed for taper shape pillar is much lower than sheer pillar shape used in the most of synthetic gecko adhesives. The result revealed the taper shape can break the limitation of material characteristics (such as Young‘s modulus limitation) through successfully designed structure and shows an optimal model which enhanced the stability and lifetime within the high adhesion, for any kind of material.

Figure 4.11 Illustrate hierarchy (a) of gecko and (b) of taper shape as a hierarchy-like by “cake‖ model. (c) Illustration of Eq. 8.

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