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12: Shear tests were performed on the vertical and angled ﬂaps to compare the anisotropy and shear forces. The vertical ﬂaps had an anisotropy value of 1.1 and similar shear values were obtained when shearing in the positive and negative directions. The angled ﬂaps had an anisotropy value of 1.6 with higher shear forces obtained when sliding in the negative direction at small shear lengths.
The angled ﬂaps also had higher shear forces than the vertical ﬂaps when sliding in the positive direction despite having half the ﬁber density.
Chapter 3. Friction and Adhesion Tester property of the gecko’s adhesive.
Although trying to minimize contact by shearing until an edge is in contact, as shown here with the vertical ﬂaps and elsewhere on wedge structures , is possible, the simplicity of shearing against the tilt direction over a large range of shear lengths requires less precision for detachment and therefore is a more attractive option.
3.3.4 Conclusion An initial comparison over millimeter sized areas between vertical and angled ﬂaps using a simple rectangular geometry was presented. From the diﬀerences obtained during load-pull and load-drag-pull tests, it is possible to ascertain advantages of incorporating tilt for gecko-like synthetic adhesives. The tilted rectangular ﬂaps had the pure adhesion property of a non-sticky default state. The angled ﬂaps had large anisotropy in shear adhesion forces. Shearing with the tilt caused maximum shear adhesion values and shearing against the tilt caused almost no shear adhesion. When compared to the vertical structures, the shear adhesion and shear forces per ﬂap of the angled ﬂaps were greater. Tilt improved the ﬂap’s shear force performance by adding anisotropy based on shearing direction.
Although equal density comparisons are needed, the use of tilt and rectangular structures are promising alternatives for gecko-like adhesives.
Chapter 3. Friction and Adhesion Tester
3.4 Established Tester Comparison Although the initial testing on the rectangular ﬂap structures was encouraging, there was no veriﬁcation of the adhesive characteristics. The adhesive and shear pressures were within an order of magnitude when compared to other completely diﬀerent adhesives and rough calcuations. However, the range of values for geckoinspired adhesives can vary and a better comparison was needed.
Work done in collaboration with the Isrealachvili group tested the rectangular ﬂap adhesive using the surface forces apparatus (SFA) . The SFA was created by D. Tabor, R.H.S. Winterton, and J.N. Israelachvili during the 1970s and has since been modiﬁed to work in a variety of environments. The experiments on rectangular ﬂaps used a SFA 2000 with a recently developed 3D force displacement attachment  to characterize the adhesive. The attachment allows for movement and force measurement in both the normal and in-plane directions.
Both load-drag and load-drag-pull tests were performed on the rectangular ﬂaps using the SFA. Diﬀerences between the Bio-F and SFA testing apparatus are shown in Table 3.2. SFA tests used a spherical glass disk with a 2 cm radius as the testing surface contacting the ﬂat patterned adhesive. Unlike the ﬂat glass puck used with the Bio-F, only a small portion of the sphere comes in contact with the adhesive, limiting the contact area to 0.1–1 mm2. A signiﬁcant advantage of Chapter 3. Friction and Adhesion Tester
Table 3.2: The Bio-F and SFA testers each characterized the rectangular ﬂap adhesives.
The diﬀerence in testing surface shape and size allowed the adhesive’s properties to be compared at two size scales.
using a spherical testing surface is that the sphere does not need to be aligned to the testing surface since the contact will be the same regardless of the sphere’s orientation. Out-of-plane speeds were slightly slower, 0.06 µm/s, and in-plane speeds were slightly higher, 20 µm/s, than those the Bio-F tester used.
The force values and important parameters for the angled ﬂap structures tested in the SFA and Bio-F were in good agreement as seen in Table 3.3. The shear adhesion values with both the positive and negative shear displacements were within a factor of three for both directions. Strong shear adhesion when sliding with the tilt angle and low shear adhesion when sliding against the tilt angle gave Chapter 3. Friction and Adhesion Tester
Table 3.3: The Bio-F and SFA tests showed similar behavior for important geckoinspired adhesive properties when testing the angled rectangular ﬂaps.
high anisotropy values for both sets of tests. The pulloﬀ to preload ratio, µ′, for the two testers was also similar and diﬀered by a factor of roughly two. The ﬂaps exhibited a low detachment force and a non-sticky for both sets of testing. The shear forces for the testers were also fairly close with a maximum force diﬀerence under four fold. The durability tests for adhesion were performed 50 times on the Bio-F tester while tests for the SFA were repeated eight times.
Chapter 3. Friction and Adhesion Tester The agreement between the two test apparatuses allowed future testing of various ﬁber geometries with conﬁdence in the values obtained by the Bio-F.
In the following chapters, two separate investigations will be discussed. Chapters 4 and 5 implemented a diﬀerent structure shape, semicircular ﬁbers, to determine if further improvements in force values and anisotropy can be achieved. Chapter 6 used non-perpendicular approaches and retractions to study the inﬂuence of articulation, or how the ﬁbers are moved, on key gecko-synthetic properties.
Chapter 4 Vertical Semicircular Fibers The construction of the Bio-F test apparatus discussed in Chapter 3 allowed characterization of micrometer rectangular ﬂap adhesive structures. Similar adhesive properties and force values were seen when the same micrometer rectangular ﬂaps were tested with the established surface forces apparatus (SFA). The agreement between testers resulted in independent testing of new adhesive ﬁber designs using the Bio-F.
Chapter 4 describes the testing of a vertical semicircular ﬁber to ascertain if ﬁber shape, like ﬁber tilt, could be used to gain anisotropy in forces when shearing in a single axis. A ﬁber shape commonly used for gecko-inspired adhesives was vertical cylindrical pillars which lack anisotropy when shearing. A semicircular shape was chosen to see if high friction and adhesion could be generated when contact was made with the ﬂat face of the ﬁber and low friction and adhesion could be generated when contact was made with the curved face of the ﬁber. It Chapter 4. Vertical Semicircular Fibers was also desired that the ﬁber be simple to create as an alternative to the complex ﬁbers becoming common in the literature. Should the semicircular ﬁber work as predicted, other research groups using symmetric ﬁber shapes might change to an asymmetric design such as the semicircular ﬁber.
4.1 Introduction A key feature of the gecko system is the signiﬁcant high reversibility and controllability of adhesion and friction, enabling both sticking and easy, rapid peeling. Recent experimental and theoretical ﬁndings have demonstrated that the setae on the gecko’s feet are highly anisotropic in shape and naturally exhibit anisotropy in their adhesion and friction forces when engaged and displaced along opposing directions [120, 121]. Depending on articulation direction, either large numbers of nano-scale spatulae are brought into contact with the substrate for strong adhesion and friction or the natural adhesive is able peel oﬀ with very low pull-oﬀ forces. Thus, gecko setal arrays already exhibit desirable directional behavior of strong adhesion and friction in the gripping direction and almost zero adhesion and low friction in the releasing direction.
To design dry, responsive adhesive systems inspired by the gecko, various kinds of patterned surfaces of diﬀerent shapes and materials with micro- to nano-scale Chapter 4. Vertical Semicircular Fibers structures have been fabricated [2, 65, 47, 56]. These structures use cylindrical micro-ﬁbers with a symmetrical geometry, and introduce structural asymmetry
- and thereby friction and adhesion anisotropy - by fabricating the ﬁbers with a preset angle from the vertical, resulting in a complex fabrication process. When purely vertical ﬁber-based adhesives have been previously reported in the literature, friction anisotropy has only been shown after the addition of a second material to half of the ﬁber . Testing performed on vertical ﬁbers with anisotropic tops have also shown anisotropy depending on loading direction with peel tests [59, 95]. These asymmetric tipped structures can be complex to fabricate and generate anisotropy from the shape of the tip, not the ﬁber. Adhesion and friction force anisotropy has yet to be demonstrated with any purely vertical ﬁber of a single material articulated in a single direction [116, 30, 33, 81, 96, 95, 59, 36].
Further, the use of cylindrical ﬁbers results in only a line contact with the adhering surface when sheared, limiting the real surface contact area for the van der Waals forces to develop. In the absence of other interactions and for molecularly smooth surfaces, the van der Waals adhesion force Fc between a cylinder (of
where AH is the Hamaker constant, and D is the intermolecular separation for close contact. In comparison, the van der Waals adhesion force Ff between two Chapter 4. Vertical Semicircular Fibers ﬂat molecularly smooth surfaces, one of length L and width 2R, and the other an inﬁnite plane, is given below .
For close contact with D=0.2 nm over the entire contact area, and for the geometry used here with R=5 µm and L=19 µm, the expected ratio of adhesion forces generated between a ﬂat substrate and a ﬂat surface, and that between a ﬂat substrate and a curved surface is 190.
While Equations (4.1) and (4.2) assume no deformation of the contacting surfaces, PDMS has a low modulus of elasticity and therefore might be expected to deform signiﬁcantly when in contact against a relatively rigid glass surface. To model this deformation, Majidi  found that for stable attached equilibrium of an initially vertical cylinder to a horizontal ﬂat surface, the contact width is
where W is the work of adhesion between two surfaces, ν is Poisson’s ratio for the cylinder, and E is the elastic modulus. For W =60 mJ/m2, ν=0.5, and E=1.82 MPa , the contact width, ceq is 4.7 µm.
The ﬁbers have an aspect ratio (height/radius) of ≈4, and are bent over upon shearing. During separation the ﬁbers are likely inclined at some angled with respect to the testing surface and removal of the ﬁbers could generate forces Chapter 4. Vertical Semicircular Fibers similar to elastic ﬁlms peeling from rigid substrates as modeled by Kendall .
The force, Fpeel, needed to peel a strip of ﬂexible adhesive is given by
where b is the tape width, d is the tape thickness, E is the Young’s modulus of the ﬁlm material, w is the adhesive energy for the contact (w=100 mJ/m2 ), and α is the angle the tape is being pulled at with respect to the substrate . As stated in Chapter 2, the Kendall peel model neglects bending energy and the adhesive ﬁlm is not assumed to move. Despite these limitations which contradict the behavior of the semicircular ﬁbers, the model agrees fairly well with the experimental values. Applying Equation (4.4) and assuming that α is the same in both the shearing directions, it can be seen that the peel force is proportional to the tape width. Using b= 10 µm for the ﬂat side and 4.7 µm for the curved side, the anisotropy pull-oﬀ forces is 2.1, much lower than the value of 190 computed using Equations (4.1) and (4.2).
Adhesion forces can also strongly inﬂuence the friction/shear forces which are important for climbing on vertical surfaces. A general equation describing the friction force, F, between two adhesive surfaces is 
Chapter 4. Vertical Semicircular Fibers where τ is the shear strength, and Areal is the real contact area.
For non-adhering surfaces, F is a linear function of the load, L, and can take the common form F = µL where µ is the coeﬃcient of friction. For adhering surfaces, Equation (4.5) remains the same, however the friction force is no longer a linear function of the load because of the adhesive component of the load. Therefore, the real area of contact will determine the friction force.
The above equations demonstrate that a ﬂat surface in contact with a ﬂat substrate is expected to generate higher adhesion and friction forces than a curved surface against the same substrate. It is important to note that this approach can be extended to higher modulus materials as well. Since the contact width on the curved face will be lower, it should be possible to achieve higher anisotropy ratios.
In order to create an anisotropic adhesive, arrays of half-cylinder micro-ﬁbers that can change their contact area with the substrate have been fabricated. A ﬂat face (for strong adhesion and friction) or a cylindrical face (for weak adhesion and friction) can be obtained by externally shearing forwards or backwards along a single axis. By spacing the ﬁbers far apart to avoid self-matting, the forces are reduced compared to higher density designs, but insights into the force anisotropy can still be retained.