# «UNIVERSITY OF CALIFORNIA Santa Barbara Design and Characterization of Fibrillar Adhesives A Dissertation submitted in partial satisfaction of the ...»

The region with highest values, reaching a maximum of 57±1 mN due to large areas of contact on the ﬂat side of the ﬁber, had approach and retraction angles less than 10◦. The region with the middle values occurred roughly along the diagonal of the approach angle-retraction angle plane. Since the net in-plane movement at pulloﬀ was close to zero with small approach angle and large retraction angle, large approach angle and small retraction angle, or medium values of both approach and retraction angles, contact remained on top surface of the ﬁber. The top of the ﬁber had less available contact area than the ﬂat face of the ﬁber and the adhesion values therefore were less. Small adhesion force regions occurred on either side of the angles leading to top contact when contact with just the edge of the ﬁber was made. Small forces can also occur at large approach and large retraction angles where the curved face of the ﬁber was the contacting surface. The maximum shear adhesion force of 57±1 mN and the minimum shear adhesion force of 6±1 mN were similar to the adhesion values obtained using a vertical test with a preload of 140 mN. The vertical test uses a shear length after preloading the ﬁbers to increase the contact area whereas the angled test bends the ﬁbers during the approach into positions for maximum and minimum forces.

The preloads required for the maximum and minimum shear adhesion values with an angled approach and retraction were 16–51% that needed for the vertical test.

** Chapter 6. Fiber Articulation Figure 6.**

8: The shear adhesion forces without additional shearing using the angled load-drag-pull test with various approach and retraction angles. By changing the articulation and contacting various parts of the ﬁber, very diﬀerent shear adhesion forces were achieved. Small approach and retraction angles resulted in higher shear adhesion forces than other angles due to contact with the ﬂat face of the ﬁber. The maximum shear adhesion force achievable with a shear length of 0 µm was 57±1 mN. Error bars show one standard deviation above and below the mean value based on 5 tests.

** Chapter 6. Fiber Articulation The shear force supported was also highly dependent on approach and retraction angle as shown in Figure 6.**

9. At low approach or low retraction angles, the maximum shear force experienced occurred during the shallow movement engaging the ﬂat face. Maximum shear values without shearing reached 191±6 mN using a small approach and retraction angle and were higher than any shear value across all preloads except 180 mN using a vLDP test. High approach or high retraction angles engaged the ﬁber’s curved face, reducing the maximum shear values in the negative direction. The engagement of the curved face had less surface area with which to make contact and the shear force fell to a maximum negative value of −65±2 mN. This maximum negative value was close to the shear values obtained with a 140 mN preload on a vLDP test. As was the case with the shear adhesion values, the preloads necessary for these maximum and minimum shear forces in each direction were 14–55% of the values needed for the 140 mN vertical test.

The signiﬁcant reduction in preload forces for maximum adhesion and shear forces with an angled approach and retraction prompted investigation into the ratio of adhesion force to preload force, µ′, across all angles. The results, shown in Figure 6.10, highlight that µ′ values can be signiﬁcantly increased, up to 16.4±1.8, by using an aLDP test. This value was approximately 38–55 times greater than the maximum µ′ values obtained with a vLDP test. Unlike the shear adhesion and shear force graphs, the high µ′ values were only possible by using approach angles ** Chapter 6. Fiber Articulation Figure 6.**

9: The shear forces without additional shearing using the angled loaddrag-pull test with various approach and retraction angles. By changing the articulation and contacting various parts of the ﬁber, very diﬀerent shear forces were achieved. Small approach and retraction angles resulted in higher shear forces than other angles due to contact with the ﬂat face of the ﬁber. Large approach and retraction angles resulted in negative maximum shear forces. Shear forces reached a maximum of 191±6 mN and a minimum of −65±2 mN. Error bars show one standard deviation above and below the mean value based on 5 tests.

** Chapter 6. Fiber Articulation less than 10◦ with retraction angles less than 170◦.**

This is in agreement with the simulation results in Figure 6.3 which predicted low preload forces, an important component for high µ′ values, at approach angles less than 10◦. Depending on the approach and retraction angles used, the µ′ values varied greatly, up to a factor of 520 for the data shown in Figure 6.10. The maximum µ′ value here, 16.4, exceeds the range, 8–16, of the gecko’s µ′ value. A µ′ value of this magnitude had not previously been achieved for a vertical side contact, µ′ =2 [31], or angled side contact, µ′ =13 [98], ﬁbers.

The addition of a shear length has been used in many tests to increase the shear adhesion and friction forces of synthetic adhesives. In the vLDP test, Figures 6.6 and 6.7, increases in shear lengths caused higher shear adhesion and shear forces due to increased contact on the ﬂat face of the ﬁber. Here, further testing of the adhesive with additional shearing in both the +Y- and −Y-directions was performed to see if even higher forces, µ′ values, and a larger optimal operating space (high adhesion force, high shear force, and high µ′ value) could be achieved.

Shear lengths of −40, −30, −20, −10, 0, 10, 20, 30, and 40 µm were performed for all approach and retraction angles, a total of 1,521 diﬀerent articulation combinations.

Shearing in the negative direction for shear lengths of −40, −30, or −20 µm resulted in µ′ values less than unity and smaller shear adhesion and shear forces ** Chapter 6. Fiber Articulation Figure 6.**

10: µ′ values without additional shearing using the angled load-dragpull test with various approach and retraction angles. Unlike shear adhesion and shear forces where small approach or retraction angles led to high forces, only small approach angles result in high µ′ values. Small approach angles were shown in the experiments and simulations of Figure 6.3 to reduce the preload forces during attachment, thereby increasing the µ′ values when similar adhesion values are achieved. The maximum µ′ value of 16.4±1.8 represents a minimum of 38 fold increase over a vertical load-drag-pull test and is the highest to date for a side contact ﬁber. Error bars show one standard deviation above and below the mean value based on 5 tests.

** Chapter 6. Fiber Articulation than achieved at other shear lengths.**

A small negative shear length of −10 µm gave a high maximum µ′ value of 13.9±2.5, but shear adhesion and shear forces were lower than those achieved with large positive shear lengths. There was very little diﬀerence between the maximum forces for 20, 30, and 40 µm shear lengths, suggesting that the maximum forces had plateaued. The main diﬀerence between the larger positive shear lengths was the number of approach and retraction angles leading to high shear adhesion and shear forces. This number increased as the shear length became greater. For simplicity, the shear adhesion and shear values with the largest shear length of 40 µm are presented.

The adhesion forces supported by the adhesive with 40 µm of positive shearing are shown in Figure 6.11. The addition of positive shear allowed a greater number of articulations to cause suﬃcient contact between the ﬂat face of the ﬁber and the glass puck for high shear adhesion forces. Instead of only having shear adhesion values above 50 mN at small approach or small retraction angles, as was the case without additional shear, the possible approach and retraction angles with 40 µm of positive shearing only excluded a few approach and retraction angles. The highest shear adhesion forces reached a maximum of 65.8±0.3 mN. This value is higher than the value obtained without additional shearing and is comparable to the maximum shear adhesion value using the vLDP test.

** Chapter 6. Fiber Articulation Figure 6.**

11: The addition of +40 µm of shear displacement increased the range of approach and retraction angles possible for large shear adhesion forces when using the angled load-drag-pull test. The shear adhesion forces were able to reach similar values to those obtained using a vertical load-drag-pull test. The maximum adhesion force increased to 65.8±0.3 mN, close to the vertical load-drag-pull test value of 73.6±0.3 mN. Error bars show one standard deviation above and below the mean value based on 5 tests.

Chapter 6. Fiber Articulation As with the shear adhesion forces, the addition of shear length also increased the shear forces across additional approach and retraction angles as seen in Figure

6.12. With a 40 µm shear length, shear forces above 150 mN were possible with many diﬀerent approach and retraction angles. Most articulations using approach angles up to 70◦ generated shear forces equal to the maximum shear force value without shearing. Signiﬁcant increases in shear forces, up to the maximum shear force value of 225±3 mN, were possible with the 40 µm shear length. This value was comparable to the 237 mN shear force achieved with a 180 mN preload using the vLDP test. In areas with µ′ values greater than unity for the 40 µm shear length, shear values were also high, between 180 and 215 mN.

With increased adhesion and shear values across most approach and retraction angles, the µ′ values for the 40 µm shear length were calculated to determine if they behaved in a similar manner. The µ′ values, shown in Figure 6.13, did not signiﬁcantly change for any approach or retraction angles despite the higher adhesion forces. Again, only the small approach angles with retraction angles less than 170◦ had notable µ′ values. This trend was the same for all shear lengths tested between −10 and 40 µm. The negligible eﬀect of increased adhesion forces on the µ′ values using the additional shear lengths suggests that the µ′ values for the vertical ﬁbers presented here are limited by preload forces. It was found that preload forces for those articulations beneﬁting from the addition of shear ** Chapter 6. Fiber Articulation Figure 6.**

12: The addition of +40 µm of shear displacement increased the range of approach and retraction angles possible for large shear forces when using the angled load-drag-pull test. The shear forces were able to reach similar values to those obtained using a vertical load-drag-pull test. The minimum shear force reaches −59±1 mN in the negative Y-direction and the maximum shear force reaches 225±3 mN in the positive Y-direction, close to the vertical load-drag-pull test value of 237±4 mN. Error bars show one standard deviation above and below the mean value based on 5 tests.

** Chapter 6. Fiber Articulation could be as high as 185 mN, severely limiting the µ′ values possible.**

However, by combining the small approach angles with the correct shear length, an optimal articulation can be implemented to obtain high shear adhesion force, high shear forces, and high µ′ values.

To measure the overall performance of the adhesive for diﬀerent articulations, a ﬁgure of merit (FOM) was calculated for an angled and vertical test. The FOM takes the individual average values of adhesion, shear, and µ′ and normalizes them by their respective maximum values across all 1,521 articulations. The average of the three equally weighted normalized values is then taken to get the FOM. A single articulation scheme with simultaneously high values of µ′, shear, and shear adhesion will have a FOM near one. Figure 6.14 shows the ﬁgure of merit for articulations using a 2.5◦ approach angle. As shown in Figures 6.10 and 6.13, the highest µ′ values were possible with this small approach angle. The FOM results for the angled approach showed that a non-negative shear length, for maximum contact with the ﬂat face of the ﬁber, and a retraction angle close to 90◦, but not perpendicular, resulted in optimal articulation. The maximum FOM was equal to 0.90 and the minimum FOM was equal to 0.45.

The FOM for a vertical approach can be seen in Figure 6.15, with values between 0.06 and 0.64 for all shear lengths and retraction angles tested. Limiting all FOM values for the vertical approach were the high preload forces which reChapter 6. Fiber Articulation Figure 6.13: The addition of +40 µm of shear displacement did not signiﬁcantly change the µ′ values when using the angled load-drag-pull test despite the higher shear adhesion forces across many approach and retraction angles. For those articulations beneﬁting from the addition of shear length, the preload forces during attachment were too large to be able to reach the high µ′ values achieved when using small approach angles. The maximum µ′ value with a 40 µm shear length was

14.0±2.7. The use of an angled load-drag-pull test achieved similar shear adhesion and shear forces while signiﬁcantly increasing the µ′ values possible. Error bars show one standard deviation above and below the mean value based on 5 tests.

Chapter 6. Fiber Articulation

** Figure 6.14: The ﬁgure of merit (FOM) for an approach angle of 2.**

5◦, maximum value equal to 0.90, is calculated as the average of the normalized values (across all tests) of adhesion, shear, and µ′. A score of 1 means that the articulation simultaneously had the highest values of adhesion, shear, and µ′ across all 1,521 articulations. Optimal operation of the adhesive presented here occurs with positive shear lengths and nearly perpendicular, but not 90◦, retractions.

** Chapter 6. Fiber Articulation sulted in low µ′ values and eﬀectively reduced the maximum FOM to 0.**