«UNIVERSITY OF CALIFORNIA Santa Barbara Design and Characterization of Fibrillar Adhesives A Dissertation submitted in partial satisfaction of the ...»
Chapter 5. Angled Semicircular Fibers oﬀ the cured PDMS by hand, taking care to only peel with the direction of tilt to avoid damage to the angled ﬁbers and to the photoresist mold.
This resulted in cm-scale PDMS samples with tilted microﬁbers and a photoresist mold that could be reused up to 15–20 times. The tilted ﬁbers were ≈13 µm in height, with a semicircular lateral proﬁle of average diameter ≈8.5 µm, although the radius varied with Z-axis height as seen in Figure 5.1(b) due to greater development of parts of the photoresist mold that were repeatedly directly exposed to deep UV light and the developer solution. The angle of tilt of the ﬂat side was observed by SEM to be ≈28◦ from the vertical, while the angle of tilt of the curved side was ≈15◦ from the vertical.
5.2.2 Adhesion and Friction Testing Adhesive testing was performed using a ﬂat-on-ﬂat testing geometry with the home-built friction and adhesion tester described in Chapter 3. The fourmillimeter diameter ﬂat glass puck contacted a maximum of 64,443 microﬁbers during testing. Load-drag-pull tests were performed to normally preload, laterally shear, and then pull oﬀ from the adhesive material. In each test, the sample was moved towards the glass puck at a vertical speed of 1 µm/s until a given compressive load, the preload, was reached. Before the surfaces were separated, the sample was then moved in the in-plane direction perpendicular to the straight Chapter 5. Angled Semicircular Fibers top edge of the ﬁbers at a horizontal speed of 3 µm/s. Motion of the sample in the +Y-direction generated movement with the tilt of the ﬁbers (and towards the ﬂat face), while motion in the −Y-direction was against the tilt (and towards the curved face). Once the desired sliding distance was achieved, the adhesive sample was then moved away from the glass puck at a vertical speed of 1 µm/s until complete separation occurred.
Load-drag-pull tests were performed on the sample at three diﬀerent preload values of 0.025 N, 0.1 N, and 0.18 N over a wide range of sliding lengths greater than 0.15 mm (up to 0.2 mm for the 0.18 N preload case) in both the positive and negative directions. Each test was performed 6 times, and the average values and standard deviations were calculated. The sample was subsequently tested for durability by performing 10,000 repeated tests in a single location without intermediate cleaning of either sample or glass puck surface. The testing procedure for durability was identical to the load-drag-pull procedure previously described, except that all durability tests were performed at the maximum preload value of
0.18 N and maximum positive (+Y) shear length of 0.2 mm. Temperature and humidity measurements were not taken during the testing period; however, later measurements taken every ﬁve minutes over a 2 month period showed an average laboratory temperature of 23.5 ◦ C with a standard deviation of 0.3 ◦ C, and an average relative humidity of 49.6% with a standard deviation of 5.3%.
Chapter 5. Angled Semicircular Fibers
5.3 Results and Discussion The tilted half-cylinder microﬁbers exhibited some adhesion even without lateral sliding for all the three preloads tested (0.025N, 0.1 N, and 0.18 N), as seen in Figure 5.3. The maximum adhesion pressure obtained without lateral sliding was
3.2±0.1 kPa, which is due to contact between the ﬂat top face of the microﬁbers (as seen in Figure 5.1(a)), and the ﬂat glass puck. In optical microscope images taken after preloading and before lateral sliding (a part of which is shown as Figure 5.4(a) for clarity) for a preload of 0.1 N, the contact area between the puck and the tops of the microﬁbers may be clearly observed as the darker regions. The outlines of the tilted ﬂat face of the microﬁbers are also visible, and observed to be not in signiﬁcant contact without sliding. This situation has also been illustrated in the schematic diagram in Figure 5.4(d).
Figure 5.3 illustrates how normal adhesion force may be easily controlled by laterally shearing the material along a preferred axis - either increasing adhesion after sliding (shear adhesion) to a maximum of 9.
3±0.1 kPa in the ﬁber tilt direction (+Y) from the zero-shear value of 3.2±0.2 kPa, or decreasing it to a steady state value of 1.5±0.2 kPa in the direction against tilt (−Y). Thus, the anisotropy in shear adhesion is 6.2, considerably higher than the anisotropy values previously obtained with purely vertical half-cylinder microﬁbers presented in Chapter 4. It Chapter 5. Angled Semicircular Fibers Figure 5.3: Shear adhesion force as a functions of the preload and shear length along the ±Y-axis. Shear adhesion forces can be controlled based on shear direction, with an anisotropy in shear adhesion forces of 6.2. A large µ′ value enables the material to generate normal adhesion of up to 4.7 times the preload with suitable shearing articulation. By using a shear length of −0.01 mm, the adhesive can be removed without any detachment force at any of the preloads tested. All data points depict average values with ±1 standard deviation error for 6 repeated tests.
Chapter 5. Angled Semicircular Fibers is also important to note that the adhesion force after sliding in the −Y-direction repeatedly showed a minimum force value of zero for a shear length of −0.
01 mm at all three values of the applied preload. Thus, with suitable articulation, it is possible to use this adhesive for strong attachment but very easy detachment in a manner similar to the gecko. The maximum ratio of shear adhesion to preload force (µ′ ), obtained for a preload of 0.025 N for sliding in the +Y-direction, is 4.7, a 571% increase when compared with 0.7 obtained with similar tests on both tilted micro-ﬂaps in Section 3.3 and vertical half-cylinder ﬁbers in Chapter 4. The reduction in initial preload required to 0.025 N contributes to increased operational stability in climbing applications on walls and ceilings due to a low corresponding reaction force from the substrate surface during preloading. A high value of µ′ is also likely to enhance reusability by preventing damage to ﬁbers during the preloading step.
The anisotropic adhesion behavior of the tilted microﬁbers can be explained by considering the anisotropic ﬁber shape in conjunction with the Kendall peel
model for the force required to peel a thin elastic adhesive ﬁlm from a surface :
where θpeel is the angle of peel between the ﬁlm and the substrate, w is the adhesive energy for the contact, b is the contact width of the ﬁlm, d is the thickness of the ﬁlm, and E is the Youngs modulus of the ﬁlm material. Tilted half-cylinder Chapter 5. Angled Semicircular Fibers microﬁbers may be expected to have diﬀerent values of contact width b as well as peel angle θpeel for peeling of the ﬂat face from a substrate versus peeling of the curved face from the same substrate, resulting in anisotropy in the peel force.
The half-cylinder microﬁbers are expected to have a larger area in contact with a substrate surface on the ﬂat face when compared with the curved face, and this was experimentally observed in optical microscope images taken after lateral sliding and before normal pull-oﬀ for the 0.1 N preload case (Figure 5.4(b) and Figure 5.4(c)). Destructive interference of reﬂected white light at the glass-PDMS interface enabled visualization of the ﬁber areas in contact as darker regions.
Figure 5.4(b) shows the area in contact between the puck and the sample after sliding towards the ﬂat face of the ﬁbers, in the +Y-direction.
For clarity, only a portion of the entire image taken has been shown in Figures 5.4(a), 5.4(b), and 5.4(c). Analysis of the full image indicates that the average contact width with the ﬂat face after sliding was ≈8.2 µm. This is in good agreement with the value obtained from analysis of SEM images of the microﬁbers (e.g. Figure 5.1(b)) which indicate an average value of the contact width of ≈8.5 µm. The curved face of the microﬁbers was designed to minimize contact area with a substrate. Although a cylinder forms only a lateral line contact with a ﬂat surface, since PDMS has a low Youngs modulus, the curved face of the microﬁbers is expected to signiﬁcantly deform and have a ﬁnite contact width. An approximate estimate for the contact Chapter 5. Angled Semicircular Fibers width on the curved face may be obtained by considering the equilibrium contact
width, ceq, of a cylinder in contact with a ﬂat surface [71, 32]:
Where W is the work of adhesion bet ween the two surfaces, R is the radius of the cylinder, and E ∗ is the eﬀective Youngs modulus of two materials 1 and 2 in contact, given by 1/E ∗ = (1 − ν1 )/E1 + (1 − ν2 )/E2, ν denoting the Poissons ratio.
For PDMS (E1 = 1.8 MPa)  in contact with glass (E2 = 50–120 GPa) , E ∗ ≈ E1 /(1 − ν1 ). Also, W = 100 mJ/m2 for PDMS in contact with glass, and ν1 = 0.5 for PDMS. Thus, Equation 5.2 predicts that the contact width with the curved face is 4.97 µm. This value is close to the experimentally observed value for the 0.1 N preload case - analysis of the optical microscope image in Figure 5.4(c) yields an average contact width of ≈ 4.7 µm.
Since the Kendall model in its original form applies to a ﬁlm with a rectangular cross section of width b and thickness d, and the microﬁbers in this case have a semicircular cross section of radius R, a small modiﬁcation was made to correct the cross sectional area, and the equation for peel force is re-derived as originally done in . Also, taking the vertical component of the peel force as the adhesion force, and multiplying the equation by the maximum number of ﬁbers N in contact with the puck, we may write an equation for the shear adhesion force Fad as shown Chapter 5. Angled Semicircular Fibers Figure 5.4: Schematic diagrams and optical microscope images illustrate the role of the tilt angle in obtaining adhesion anisotropy after lateral shearing along the ±Yaxis. The top view optical microscope images in ﬁgures (a), (b), and (c) correspond to the side view schematic diagrams in ﬁgures (d), (e), and (f), respectively. The optical microscope images were taken at the end of normal preloading in ﬁgure (a), and at the end of lateral sliding (itself performed after normal preloading) in ﬁgures (b) and (c). Areas of the ﬁbers in contact with the glass puck just before commencement of normal pull-oﬀ are seen as darker regions in these images.
Figure (d) depicts the angled ﬁbers before shearing, ﬁgure (e) depicts the ﬁbers after shearing along the +Y-direction, and ﬁgure (f) depicts the ﬁbers after shearing along the −Y-direction.
Chapter 5. Angled Semicircular Fibers below.
For the adhesive tested, N = 64,443. For the contact width, we may take b = 2R for the ﬂat face, while b = ceq as calculated earlier using Equation 5.2 for the curved face. The model still does not take into account bending energy or sliding of the ﬁbers.
In the absence of a mechanism to directly optically observe the peel angles of the ﬁbers after sliding in various directions, estimating Fad from Equation 5.3 requires the use of an estimate for the peel angle, θpeel. From the geometry of the ﬁbers, as shown in the schematic diagram in Figure 5.4(e), taking the peel angle f for the ﬂat face θpeel as the complementary angle of the tilt angle of this face from f the vertical (θpeel =62◦ ), we get a theoretical estimate of 89 mN for the adhesion force after sliding from Equation 5.3, a discrepancy of 17% from the experimental
The reasons for diﬀerences between theory and experiment are likely due to the fact that both the microﬁber surface (as seen in Figures 5.1(a) and 5.1(b)) as well as the glass puck surface are rough, while the theory is for smooth surfaces in contact. The glass puck surface was found to have an RMS roughness value of ≈ 160 nm by optical proﬁlometry (Wyko NT1100 Optical Proﬁling System).
Also, the actual peel angles with the adhesive engaged may not exactly match the geometric values as obtained by SEM observation of the ﬁbers when not engaged.
Values in the literature for the Youngs modulus of PDMS [22, 16, 29, 100, 3, 18, 103] span a range of values, and the values chosen may not perfectly match the system. The Kendall model also assumes no bending energy and no ﬁber sliding, both of which occur for the current adhesive. A constant ﬁlm thickness is also assumed, whereas the ﬁbers do not have this property in both the ±X- and ±Ydirections, as seen in Figures 5.1(a) and 5.1(b) - instead, average values for the cross sectional area and contact width as obtained from SEM analysis have been used in Equation 5.3.
The analysis, however, clearly provides certain guidelines for obtaining high adhesion force anisotropy, and provides an approximate estimate of the values Chapter 5. Angled Semicircular Fibers that may be obtained. In this case, both angle of tilt and ﬁber shape were found to have a signiﬁcant eﬀect on adhesion anisotropy. Use of half-cylinder microﬁbers with a higher Youngs modulus is expected to further lower the contact width ceq on the curved face from Equation 5.2, thereby increasing anisotropy. Use of larger tilt angles (from the vertical) is expected to result in a higher normal component of peel force on the face with the angle of tilt until a maximum is reached in accordance with Equation 5.3, before reducing again. Simultaneously, the normal component of the peel force on the face against the angle of tilt is predicted to continuously decrease for larger tilt angles, resulting in higher adhesion anisotropy.