«UNIVERSITY OF CALIFORNIA Santa Barbara Design and Characterization of Fibrillar Adhesives A Dissertation submitted in partial satisfaction of the ...»
Chapter 6 Fiber Articulation Chapters 3, 4, and 5 all used ﬁber geometry to enhance adhesive performance.
Chapter 6, instead, investigates the eﬀect of testing procedure on adhesive performance. The ﬁbers used were similar to the vertical semicircular ﬁbers presented in Chapter 4, but they were slightly shorter and composed of PDMS using a different ratio curing agent to base elastomer. Testing procedures commonly use a vertical approach and retraction where the two surfaces are brought together perpendicular to their testing surfaces. This procedure has not been shown to be ideal for all gecko-inspired adhesives and was compared with non perpendicular approach and retractions. The testing procedures used diﬀerent approach angles, shear lengths, and retraction angles to ﬁnd the inﬂuence of movement, or articulation, on important adhesive properties of vertical semicircular ﬁbers.
Chapter 6. Fiber Articulation
6.1 Introduction Tests on the gecko’s adhesive ﬁbers have revealed the importance of articulation, how the structures are manipulated or moved during adhesive testing or placement, in achieving many of their desirable properties. It was discovered that setae that are ﬁrst exposed to a compressive force and then pulled parallel to the surface have been shown to develop at least ten times the adhesion force after shearing, shear adhesion force, than those exposed to a compressive force without parallel movement, pure adhesion force . Shear forces, like adhesion forces, also required a parallel movement in order to generate maximum shear values . The shear and adhesion forces have been shown to behave diﬀerently in experiments where setal arrays are articulated along and against the direction of tilt [7, 120], with theoretical approaches oﬀering further evidence of the importance of articulation [121, 111]. Single setae are able to adhere with a force of 20–40 µN using only a 2.5 µN preload, causing the ratio of adhesion force to preload force, µ′, to fall between 8–16 [12, 10].
A variety of diﬀerent approaches have been undertaken in order to mimic the main functions of the adhesive found on the gecko . The sizes of individual synthetic ﬁbers can range from tens of nanometers to roughly a millimeter with a variety of processes being utilized. Attempted processes for creating smaller Chapter 6. Fiber Articulation structures have included etching of polymer materials , molding nanostructured templates , drawing of polymer ﬁbers , electron beam lithography , and carbon nanotube growth . Larger scale methods typically have used molding techniques to create vertical and angled ﬁbers. The molds have been created in silicon using an angled etch for tilted structures , in silicon-on-insulator using the notching eﬀect for mushroom-tipped structures , in PMGI using angled lithography for angled ﬁbers , in SU-8 using dual angle lithography for wedge structures  and other more complicated fabrication approaches [78, 63].
Work aimed at creating adhesives, such as those above, has received the majority of the workload while the manner in which the adhesives are tested has received far less.
Both vertical and angled synthetic adhesives have been characterized using a vertical load-drag-pull test (vLDP) test (Section 3.2.3). For vertical [54, 37] or angled  ﬁbers where contact is desired on the horizontal top face or there is no beneﬁt to in-plane shearing, referred to here as top contact ﬁbers, a vertical load-pull test achieves the desired contact. In-plane movement during testing is only implemented to ﬁnd maximum shear forces that the adhesive can sustain since excessive in-plane movement has been shown to cause undesired side contact and lower the adhesion and shear force values [114, 53]. Low preload forces, and consequently high µ′ values, are typical of top contact structures since very little Chapter 6. Fiber Articulation force is needed to make suﬃcient contact across the top testing surface. For both vertical [109, 66, 88] and angled [98, 65, 19] ﬁbers where contact is desired on the vertical or angled side or the adhesive beneﬁts from in-plane shearing, referred to here as side contact ﬁbers, the use of in-plane movement has allowed access to larger preferential areas of the ﬁbers. Before shearing is possible, a preload force or distance must be applied. Since larger preloads are required to compress the side contact ﬁbers a greater amount, the preloads for maximum contact areas can be signiﬁcant and risk low µ′ values. The preload forces per ﬁber during vertical loading for angled side contact ﬁbers should be lower than those needed for vertical side contact ﬁbers due to the replacement of only compression with compression and bending of the ﬁbers, but the forces on even angled side contact ﬁbers are usually more than those needed for top contact ﬁbers.
Angled approach and/or angled retraction tests, here referred to as angled load-drag-pull tests (aLDP) even though all testing stages may not be angled or in-plane shearing may not occur, targeting articulation have been performed.
Drag speeds over various shear lengths , patch areas , He++ ion irradiation doses , approach depths/preload forces [83, 98, 26] and retraction angles [83, 98, 26, 107, 55] have been systematically varied to characterize the adhesive, but no information regarding the performance of diﬀerent approach angles was presented and the parameters used could be suboptimal. Tests using angled approach and/or Chapter 6. Fiber Articulation retractions have not been performed on top contact structures since the in-plane motion, as stated earlier, risks misorientation of the contact surface. Surprisingly, no characterization of vertical ﬁber adhesives using approach angle variation have been presented up to this point. Therefore, the result shown in this chapter are the ﬁrst application of multiple angle testing to vertical structures as well as the ﬁrst systematic variation of approach angle to be reported. A schematic of the testing procedure, with deﬁnitions for approach angle, θapp, approach depth, zapproach, and retraction angle, θret, shown in Figure 6.1.
Low preload forces during foot placement reduce the reaction forces from the substrate that a robot would have to counter, and therefore increase a robot’s stability. When adhesives are used with a climbing robot with g feet being placed at once during the ﬁber loading and f feet fully attached during the ﬁber loading, the minimum µ′ value of the adhesive to ensure that that the robot has the ability to remain adhered to the wall is given by Equation 6.1.
While a µ′min value for a four-legged robot could be as low as 0.33 with only one foot being placed at a time, the value for a robot mimicking the gecko’s foot placement pattern when climbing vertically would need to be at least 1 . Many synthetic adhesives fall short of µ′ being greater than 1. To be able to achieve Chapter 6. Fiber Articulation Figure 6.
1: The angled load-drag-pull test used for the results presented here follows the described testing protocol shown. A load, generated using a perpendicular approach, ﬁrst establishes contact between adhesive and glass puck testing surface. The adhesive is then articulated using diﬀerent approach angles, shear lengths, and retraction angles. For the vertical load-drag-pull tests, the approach angle and retraction angle are both perpendicular (θapp = θret = 90◦ ). Positive directions, approach and retraction angles, and the zapproach depth are all deﬁned in the manner indicated in the drawing. The glass puck is stationary and the adhesive is articulated during testing to match the way the adhesive would be engaged when integrated with a climbing robot.
Chapter 6. Fiber Articulation higher µ′ values when adhesion forces have reached their maximum value, the preload force must be lowered.
Angled side contact ﬁbers should achieve higher µ′ values than similar vertical ﬁbers during vertical testing because the increased compliance of the tilted ﬁbers lowers the applied preload force for a given contact requirement. As an alternative to using tilted ﬁbers, which can be more diﬃcult to reliably fabricate, ABAQUS simulations on vertical ﬁbers, similar to those fabricated and shown in Figure 6.2, were used to determine the reduction in preload forces when using diﬀerent approach angles.
Using the modiﬁed Riks method solver in ABAQUS, the free tip of a single ﬁber, modeled as a two-dimensional wire with deﬁned cross-sectional properties and Young’s modulus to match the fabricated ﬁbers, was displaced at diﬀerent angles to simulate ﬁber articulation during approach. Tensile forces could form as in the experiments, and the maximum vertical compressive force supported by the ﬁber during approach was multiplied by the number of ﬁbers in the testing area to compare with the experimental results. For approach angles parallel to the ﬁber’s axis, a linear perturbation buckling simulation was performed to ﬁnd the critical buckling load. The results, shown in Figure 6.3, show that approach angles can have a signiﬁcant eﬀect on the preload forces and the forces predicted by the simulation are in good agreement with the experimental results.
Chapter 6. Fiber Articulation Figure 6.
2: Scanning electron microscope (SEM) image of vertical half-cylinder PDMS micro-ﬁbers of 15.0 µm height and 10.0 µm diameter which were used for the experimental results and as a model for the simulations. The cross-sectional shape is shown in white outline on the ﬁber below the X-, Y-, and Z-axes. The ±Xdirections are parallel to the straight long edge of the semicircular ﬁbers; movement of the sample in the +Y-direction engages the ﬂat face of the ﬁbers; movement of the sample in the the −Y-direction engages the curved face of the ﬁbers; +Z is the (vertical) loading direction, and −Z is the (vertical) unloading direction.
Articulation of the adhesive system to engage and release occurs in the Y-Z plane.
Chapter 6. Fiber Articulation For vertical ﬁbers, a 90◦ approach resulted in the maximum reaction force across all approach angles, yet testing commonly uses this approach angle.
Approach angles less than 10◦ or greater than 170◦ resulted in the least amount of vertical compressive force during approach. The lower preload forces are a result of bending the ﬁber as opposed to the compression that occurs at or near perpendicular approaches. Diﬀerences between the experiments and simulations at angles close to 90◦ are likely from the inability to include a ﬂat top surface on the top of the ﬁber in the simulations. The ﬂat top surface would reduce the rotation of the top of the ﬁber and therefore increase the forces that the ﬁber could sustain before buckling. Diﬀerences between the simulations and experiments could also arise due to the glass puck (root mean square (RMS) roughness ≈ 70 nm), with peaks and valleys of roughness, that could unevenly load the ﬁbers across the testing area.
Additional simulations were performed on 70◦ tilted ﬁbers with the same geometry to distinguish any advantages of the tilt during loading. The cross-sectional properties and length remained the same, but the angle that the ﬁbers made with respect to the +Z-axis was changed from 0 to 20◦. For approach angles between 0 and 180◦, the maximum and minimum vertical compressive forces for the 70◦ ﬁbers, also shown in Figure 6.3, do not diﬀer signiﬁcantly from that of the vertical ﬁbers. When approaching in the same direction as the angle of tilt, the Chapter 6. Fiber Articulation Figure 6.
3: The experimental and simulation values for the maximum vertical compressive reaction force supported during approach by the vertical and angled (20◦ from vertical) ﬁbers using diﬀerent approach angles. For vertical ﬁbers, small (θapp ≤ 10◦ ) or large (θapp ≥ 170◦ ) approach angles signiﬁcantly reduced the preload forces when compared to those using a vertical approach (θapp = 90◦ ). The experimental and simulation values are in good agreement across all approach angles for the vertical ﬁbers. The range of force values for the angled and vertical ﬁbers are similar, but for the angled ﬁbers, a greater number of approach angles lead to low preload forces (0 ≤ θapp ≤ 30) and there is no longer symmetry about a vertical approach.
Chapter 6. Fiber Articulation vertical compressive reaction forces are less than the vertical ﬁbers and the range of approach angles leading to small preload forces was wider.
However, when approaching against the angle of tilt, the reaction forces were higher for the tilted ﬁbers. The simulations show that a vertical ﬁber can have preload forces that can be equal to those achieved using a tilted ﬁber during attachment provided that the correct approach angle is used.
It has been shown that an angled approach can greatly aﬀect the preload forces during adhesive attachment. Side contact vertical ﬁbers, which have been shown in the simulations to beneﬁt from an angled approach, have yet to be characterized experimentally using an aLDP testing procedure. If adhesion and shear forces do not diminish with the new approach, the added beneﬁts of articulation, including higher µ′ values for side contact ﬁbers will be demonstrated. Unlike previous angled testing on ﬁbers, the approach angle, shear length, and retraction angle, all of which describe the path taken during testing, have been systematically varied and the results, including the ﬁrst reporting of the inﬂuence of approach angle, are presented in order to ﬁnd an optimal articulation strategy.
Chapter 6. Fiber Articulation