Chapter 3: Experiments
4.2 Dry adhesive
4.2.2 Unidirectional force through slanted angle slanted angle
In addition to high AR and small radius of structures, a directional angle of nanostructure is another crucial factor for anisotropic, reversible dry adhesive. It is because an angled structure significantly lowers the effective modulus of the surface from Eq. 9 [9].
. . . ( 9 )
where E is the elastic modulus, I is the moment of inertia (I = 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. According to Dahlquist criterion we have mentioned previously, the effective modulus should be less than 100 kPa for ensuring a tacky surface. Ιf the structures are slanted, the effective modulus can be greatly reduced without the need of structures with extremely high AR, which we mentioned in Chapter 2.3, including the risk of self-matting and structural buckling within the limited modulus of polymers. As shown in Fig. 4.12, for 80 nm nanohairs with AR of 15 (E = 19.8 MPa, D = 6.3×108 cm−2, μ = 0.25), the effective modulus decreases less than 100 kPa when the structures are slanted with less than 73° angle with respect to the horizontal plane.
Another fascinating property of the slanted structures is a controllable adhesion by varying the applied shear force. Efficient climbing relies on this behavior. By contrast, materials such as pressure-sensitive adhesive tapes require a substantial preload to achieve adhesion and a similarly large force to achieve detachment. The attached and detached mechanism of our slanted taper is shown in Fig. 4.13.
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Figure 4.12 Displays the simulation of Eeff versus slanted angle. Clearly, the Eeff drop below 100 kPa, which fit the Dahlquist criterion, with decreasing slanted angle after 73°.
Figure 4.13 Theoretical analysis of directional adhesion mechanism of the slanted taper shaped pillars. An illustration showed the change of leaning angle of the slanted taper nanohairs when the adhesive is pulled in (a) the gripping, (b) initial state and (c) releasing direction.
We hypothesize that the observed anisotropic behavior arises primarily due to
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the stresses caused by the moment created when the taper is sheared. This can be understood by analysis of the rotation of the tip during shear loading in each direction (Fig. 4.13). The original angle, φ, introduces a moment that is relative to the magnitude of the angle change from its undeformed state. The peeling moment is increased if the tapered pillar is sheared in the releasing direction because it increases the already present tip rotation to a larger angle (φr), increasing Δφ as seen in Fig.
4.13c. This increased moment peels the leading edge, eventually detaching and overturning the fiber tip. However, when sheared in the gripping direction, the fiber tip begins to return to its original angle, reducing the moment to zero (Fig. 4.13a).
When the magnitude of the moment is near zero, the normal stress distribution at the interface is more evenly distributed, reducing the chances of detachment. After this point, if the shearing in the gripping direction is continued, Δφ changes and begins to increase in magnitude, eventually causing the leading edge (left) in detachment. The initial decrease in moment for shearing in the gripping direction increases the allowable displacement before detachment occurs, which means adhesion increased when shear force is applied in a preferred direction, in contrast to the releasing direction where the moment increases immediately. The increased displacement in the gripping direction allows the fibers to stretch and maintain contact, leading to high interfacial shear strength and anisotropy. All the shear and normal forces were recorded at the adhesive‘s failure point within our experiment. Taper shaped pillars we fabricated with slanted angle by pressure technique are shown in Fig. 4.14.
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Figure 4.14 Taper shaped pillars with slanted angle we fabricated by pressure technique. (a) Low magnification. (b) High magnification of tilted SEM image of the structure. (c) Low magnification and (d) high magnification from cross-view.
The shear force was greatly reduced to 2.1 N/cm2 when the sample was pulled in releasing direction, suggesting that the dry adhesive presented here can be used as a smart, directional adhesive patch with strong attachment (~21.5 N/cm2) and easy detachment (~2.1 N/cm2), with the hysteresis close to 13 as shown in Fig. 4.15. A simple peeling model can also explain the strong directional adhesion capability.
According to the Kendall peeling model, the critical peel-off force (Fc) of a nanohair can be estimated with an assumption that the tip of slanted taper nanohairs forms intimate contact with the substrate as in an elastic tape, yielding [11-12]
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. . . ( 1 0 )
where γ = 100 mJ/m2 is the adhesive energy, θ is the peel-off angle, and b = 50 nm, t,= 100 nm and E = 19.8 MPa are the width, thickness, and elastic modulus of the tape,
respectively. Thus, the peel-off force can be expressed as a function of peeling angle for given parameters and the total peel-off force per unit area can be expressed by
. . . ( 1 1 )
where D = 6.46*108 cm-2 represented the hair density. Fig. 4.15 presented the peel-off force per unit area with varying peeling angles. As shown in Fig. 4.15, the peel-off force increased gradually with a stronger shear adhesion force. When the adhesive was pulled in the reverse direction, however, the leaning angle of nanohairs is increased from its initial value of 60° to 180°, and thus the peel-off force is greatly reduced. According to Eq. 11, the peel-off forces are 21.5, 3.4, and 2.1 N/cm2 for 0°, 90°, and 180°, respectively. The value of simulation is not quite fit with experimental data at a glance; however, the maximum value of simulation takes place at the angle around 0° which is scarcely possible on average day. Hence if the slanted angle was extended to 54°, the adhesion force will be around 8 N/cm2 which agrees fairly well with our experimental results (maximum shear adhesion of ~8 N/cm2 in the forward direction and ~1.4 N/cm2 in the reverse direction as shown in Fig. 4.16).The diagram in Fig. 4.17 gave us a comparison between taper shape and pillar shape, then we can find out the higher adhesion of taper shape than pillars‘. There is still remaining a
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possible reason which restricts the extension of slanted angle may be the way to measure is not efficient enough.
Figure 4.15 Simulation of critical peeling-off forces as a function of peeling angle.
Figure 4.16 Measurement of shear force for various cases with an adhesive patch of
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1.0 cm2. The taper nanohairs were composed of soft PUA.
Figure 4.17 Giving a comparison between taper shape and pillar [5] shape, we can find out the higher adhesion of taper shape than pillars‘ can account for the higher density, longer length or adhere efficiently we discuss previously.
Taking the density and Hmax parameter into Eq. 11 (Eq. 12) to show how the Young‘s modulus work in the motion, we can find out Young‘s modulus with a few effects on Pcr in the same condition of length and density as shown in Fig. 4.18. That is, taper pillar is such a great solution, which isn‘t from material but structure, for polymer-based adhesives.
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. . . ( 1 2 )
where the φmax stands for the maximum area fraction of a given hair pattern. It can be shown that φmax = π/2 for a triangular lattice (Fig 4.10a).
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