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Theoretical force curve for a single fiber ESC device acting on a flat surface, consisting of an approach phase and a release phase. 

Theoretical force curve for a single fiber ESC device acting on a flat surface, consisting of an approach phase and a release phase. 

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An electrostatic chuck (ESC) is a type of reversible dry adhesive which clamps objects by means of electrostatic force. Currently an ESC is used only for objects having flat surfaces because the attractive force is reduced for rough surfaces. An ESC that can handle objects with rough surfaces will expand its applications to MEMS (micro electro mech...

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... force is positive in the upward direction from the object's surface. Given the mechanical model of the fiber, we are able to construct a force curve mathematically as shown in figure 5. The force curve signifies the relationship between f att with respect to the displacement of the device base, Z, for a single fiber ESC device when approaching a flat-surfaced object upon applying a voltage. ...
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... the electrostatic force becomes constant once the fiber makes contact with the object, the characteristics of the attractive force are significantly dependent on the elastic force. Therefore, figure 5 shows only the portion with elastic force, from which the behavior of the fiber during the approach and release phases can be analyzed. ...
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... jump-to-contact phenomenon from an energy perspective is discussed thoroughly in Saito et al [21]. The displacement in which contact occurs, Z cont , is indicated in the horizontal axis of figure 5. ...
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... occurs when f k during the release phase is larger than the maximum attractive force, or f k > f kmax . Z det in the horizontal axis of figure 5 indicates the displacement when detachment occurs. When utilizing a fiber with compliance, it can be understood that the maximum attractive force is obtained in the release phase, rather than in the approach phase. ...
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... it was also observed that during the release phase, the fiber maintained contact with the object before detachment, which resulted in the largest attractive pressure in the cycle. These two physically-observed phenomena are consistent with the behavior of the theoretical force curve as shown in figure 5 and are as was discussed by Saito et al [21]. The maximum attractive pressure obtained was −852 Pa during the approach phase and −968 Pa during the release phase. ...
Context 6
... expression for the electrostatic force is obtained by deriving the equation for a model of a capacitor with two different dielectric substrates in series. The force is positive in the upward direction from the object’s surface. Given the mechanical model of the fiber, we are able to construct a force curve mathematically as shown in figure 5. The force curve signifies the relationship between f att with respect to the displacement of the device base, Z , for a single fiber ESC device when approaching a flat-surfaced object upon applying a voltage. Since the electrostatic force becomes constant once the fiber makes contact with the object, the characteristics of the attractive force are significantly dependent on the elastic force. Therefore, figure 5 shows only the portion with elastic force, from which the behavior of the fiber during the approach and release phases can be analyzed. If a voltage is applied when the fiber tip is far enough away from the object, it will approach the surface because of the electrostatic force. In this phase, there is a point where f k + f e = 0, which keeps the fiber at a stable position. If the fiber is brought closer to the object, the fiber will lose its stable energy point [21], and spontaneously make contact with the object’s surface. The contact occurs when f e > − f k . This jump-to-contact phenomenon from an energy perspective is discussed thoroughly in Saito et al [21]. The displacement in which contact occurs, Z cont , is indicated in the horizontal axis of figure 5. After the fiber is already in contact with the object ( d = 0), the base can still be displaced further, i.e. Z can be increased. This means that at this phase the electrostatic force will remain constant at its maximum value, while the elastic force will keep changing until it becomes repulsive when f k > 0. Detachment occurs when f k during the release phase is larger than the maximum attractive force, or f k > f k max . Z det in the horizontal axis of figure 5 indicates the displacement when detachment occurs. When utilizing a fiber with compliance, it can be understood that the maximum attractive force is obtained in the release phase, rather than in the approach phase. The next step in this study is the analysis of an arranged fibers ESC device and its behavior with respect to a rough surface modeled after a sinusoidal curve. Considering an arranged fibers ESC device consisting of eight fibers, we may observe that the attractive force generation becomes more complicated. As opposed to the single fiber model with a flat-surfaced object in which full contact of the spring unit occurs, in the arranged fibers model with an aggregation of spring units, each fiber generates a different attractive force because each has a different d due to the rough surface. In other words, some fibers make full contact while others do not. We could, however, mathematically estimate the total attractive force of the whole ESC device by summing up the attractive force in the individual spring unit. The following equation expresses f device , the force of an arranged fibers ESC ...
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... expression for the electrostatic force is obtained by deriving the equation for a model of a capacitor with two different dielectric substrates in series. The force is positive in the upward direction from the object’s surface. Given the mechanical model of the fiber, we are able to construct a force curve mathematically as shown in figure 5. The force curve signifies the relationship between f att with respect to the displacement of the device base, Z , for a single fiber ESC device when approaching a flat-surfaced object upon applying a voltage. Since the electrostatic force becomes constant once the fiber makes contact with the object, the characteristics of the attractive force are significantly dependent on the elastic force. Therefore, figure 5 shows only the portion with elastic force, from which the behavior of the fiber during the approach and release phases can be analyzed. If a voltage is applied when the fiber tip is far enough away from the object, it will approach the surface because of the electrostatic force. In this phase, there is a point where f k + f e = 0, which keeps the fiber at a stable position. If the fiber is brought closer to the object, the fiber will lose its stable energy point [21], and spontaneously make contact with the object’s surface. The contact occurs when f e > − f k . This jump-to-contact phenomenon from an energy perspective is discussed thoroughly in Saito et al [21]. The displacement in which contact occurs, Z cont , is indicated in the horizontal axis of figure 5. After the fiber is already in contact with the object ( d = 0), the base can still be displaced further, i.e. Z can be increased. This means that at this phase the electrostatic force will remain constant at its maximum value, while the elastic force will keep changing until it becomes repulsive when f k > 0. Detachment occurs when f k during the release phase is larger than the maximum attractive force, or f k > f k max . Z det in the horizontal axis of figure 5 indicates the displacement when detachment occurs. When utilizing a fiber with compliance, it can be understood that the maximum attractive force is obtained in the release phase, rather than in the approach phase. The next step in this study is the analysis of an arranged fibers ESC device and its behavior with respect to a rough surface modeled after a sinusoidal curve. Considering an arranged fibers ESC device consisting of eight fibers, we may observe that the attractive force generation becomes more complicated. As opposed to the single fiber model with a flat-surfaced object in which full contact of the spring unit occurs, in the arranged fibers model with an aggregation of spring units, each fiber generates a different attractive force because each has a different d due to the rough surface. In other words, some fibers make full contact while others do not. We could, however, mathematically estimate the total attractive force of the whole ESC device by summing up the attractive force in the individual spring unit. The following equation expresses f device , the force of an arranged fibers ESC ...
Context 8
... expression for the electrostatic force is obtained by deriving the equation for a model of a capacitor with two different dielectric substrates in series. The force is positive in the upward direction from the object’s surface. Given the mechanical model of the fiber, we are able to construct a force curve mathematically as shown in figure 5. The force curve signifies the relationship between f att with respect to the displacement of the device base, Z , for a single fiber ESC device when approaching a flat-surfaced object upon applying a voltage. Since the electrostatic force becomes constant once the fiber makes contact with the object, the characteristics of the attractive force are significantly dependent on the elastic force. Therefore, figure 5 shows only the portion with elastic force, from which the behavior of the fiber during the approach and release phases can be analyzed. If a voltage is applied when the fiber tip is far enough away from the object, it will approach the surface because of the electrostatic force. In this phase, there is a point where f k + f e = 0, which keeps the fiber at a stable position. If the fiber is brought closer to the object, the fiber will lose its stable energy point [21], and spontaneously make contact with the object’s surface. The contact occurs when f e > − f k . This jump-to-contact phenomenon from an energy perspective is discussed thoroughly in Saito et al [21]. The displacement in which contact occurs, Z cont , is indicated in the horizontal axis of figure 5. After the fiber is already in contact with the object ( d = 0), the base can still be displaced further, i.e. Z can be increased. This means that at this phase the electrostatic force will remain constant at its maximum value, while the elastic force will keep changing until it becomes repulsive when f k > 0. Detachment occurs when f k during the release phase is larger than the maximum attractive force, or f k > f k max . Z det in the horizontal axis of figure 5 indicates the displacement when detachment occurs. When utilizing a fiber with compliance, it can be understood that the maximum attractive force is obtained in the release phase, rather than in the approach phase. The next step in this study is the analysis of an arranged fibers ESC device and its behavior with respect to a rough surface modeled after a sinusoidal curve. Considering an arranged fibers ESC device consisting of eight fibers, we may observe that the attractive force generation becomes more complicated. As opposed to the single fiber model with a flat-surfaced object in which full contact of the spring unit occurs, in the arranged fibers model with an aggregation of spring units, each fiber generates a different attractive force because each has a different d due to the rough surface. In other words, some fibers make full contact while others do not. We could, however, mathematically estimate the total attractive force of the whole ESC device by summing up the attractive force in the individual spring unit. The following equation expresses f device , the force of an arranged fibers ESC ...
Context 9
... expression for the electrostatic force is obtained by deriving the equation for a model of a capacitor with two different dielectric substrates in series. The force is positive in the upward direction from the object’s surface. Given the mechanical model of the fiber, we are able to construct a force curve mathematically as shown in figure 5. The force curve signifies the relationship between f att with respect to the displacement of the device base, Z , for a single fiber ESC device when approaching a flat-surfaced object upon applying a voltage. Since the electrostatic force becomes constant once the fiber makes contact with the object, the characteristics of the attractive force are significantly dependent on the elastic force. Therefore, figure 5 shows only the portion with elastic force, from which the behavior of the fiber during the approach and release phases can be analyzed. If a voltage is applied when the fiber tip is far enough away from the object, it will approach the surface because of the electrostatic force. In this phase, there is a point where f k + f e = 0, which keeps the fiber at a stable position. If the fiber is brought closer to the object, the fiber will lose its stable energy point [21], and spontaneously make contact with the object’s surface. The contact occurs when f e > − f k . This jump-to-contact phenomenon from an energy perspective is discussed thoroughly in Saito et al [21]. The displacement in which contact occurs, Z cont , is indicated in the horizontal axis of figure 5. After the fiber is already in contact with the object ( d = 0), the base can still be displaced further, i.e. Z can be increased. This means that at this phase the electrostatic force will remain constant at its maximum value, while the elastic force will keep changing until it becomes repulsive when f k > 0. Detachment occurs when f k during the release phase is larger than the maximum attractive force, or f k > f k max . Z det in the horizontal axis of figure 5 indicates the displacement when detachment occurs. When utilizing a fiber with compliance, it can be understood that the maximum attractive force is obtained in the release phase, rather than in the approach phase. The next step in this study is the analysis of an arranged fibers ESC device and its behavior with respect to a rough surface modeled after a sinusoidal curve. Considering an arranged fibers ESC device consisting of eight fibers, we may observe that the attractive force generation becomes more complicated. As opposed to the single fiber model with a flat-surfaced object in which full contact of the spring unit occurs, in the arranged fibers model with an aggregation of spring units, each fiber generates a different attractive force because each has a different d due to the rough surface. In other words, some fibers make full contact while others do not. We could, however, mathematically estimate the total attractive force of the whole ESC device by summing up the attractive force in the individual spring unit. The following equation expresses f device , the force of an arranged fibers ESC ...
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... two kinds of fiber ESC device prototypes were developed: one was a prototype with only one fiber and the other one was with ten fibers arranged at an angle of 45 ◦ , with a 1 mm gap in between each fiber (see figure 7(b)). Figure 8 shows a schematic of the fabrication process for the ESC device prototype. The applied voltage was 600 V. The attractive force was measured by an analytical balance on which the object sample was placed and the prototype was moved to approach the object sample. Figure 7(c) shows a schematic of the experimental setup whereas figure 7(d) depicts an image of the fibers’ tips before and after making contact with a neutrally-charged sample object of 200 μ m amplitude. The force exerted by the prototype with respect to the object was then observed. The experiments were conducted in atmospheric pressure and at room temperature with a relative humidity of 23%. The experimental pressure curve for the single fiber ESC device prototype is given in figure 9(a). Through the experiments, with the aid of a video camera, it was observed that upon applying a voltage, when the fiber was within a certain distance, it spontaneously jumped into contact with the object. Additionally, it was also observed that during the release phase, the fiber maintained contact with the object before detachment, which resulted in the largest attractive pressure in the cycle. These two physically-observed phenomena are consistent with the behavior of the theoretical force curve as shown in figure 5 and are as was discussed by Saito et al [21]. The maximum attractive pressure obtained was − 852 Pa during the approach phase and − 968 Pa during the release phase. Similarly, the experimental pressure curve during the release phase for the arranged fibers ESC device prototype was also obtained as shown in figure 9(b). The applied voltage was 600 V and the sinusoidal surface with 100 μ m wave amplitude was employed as the surface sample. In this experiment, a maximum attractive pressure of − 813 Pa was obtained. Comparing to figure 6, a similar phenomenon of ripples which correspond to the detachment of fiber(s) during the release phase could be observed. Furthermore, in order to understand the effect of a fiber’s spring constant in handling rough surfaces, a graph of maximum attractive pressure with respect to surface wave amplitude for different spring constants is presented in figure 9(c). In the graph, the experimental maximum attractive pressures for surface samples of various amplitudes are plotted as circles along with the theoretical curves for the different fiber’s spring constants of k = 0 . 1 N m − 1 , k = 0 . 4 N m − 1 , and larger values of k (no compliance). The value for k of 0 . 4 N m − 1 is of specific interest because it is the same value as the spring constant for the fibers used in this experiment. An important point from figure 9(c) is that the more compliant the fibers, i.e. the smaller the stiffness value, k , the more they are able to adapt to rougher surfaces. The smaller the stiffness value, the more linear the curve becomes without a significant drop in maximum attractive pressure when handling large wave amplitudes. In contrast, a significant drop in maximum attractive pressure is visible for fibers with no compliance, i.e. the pressure drops by about 70% when handling a surface of 100 μ m wave amplitude as compared to the handling of a flat surface. The four measured pressure values correspond to the four different amplitudes of the surface sample fabricated for this study, i.e. 200, 100, 50, and 0 μ m (flat surface). The variations in experimental data were observed to be relatively small and they can be deemed insignificant as far as the maximum attractive pressure is concerned. The range is between 2–4% for surface samples with 0 and 50 μ m amplitude and 6–7% for those with 100 and 200 μ m amplitude. Along with the increase in the sample’s surface amplitude, the attractive pressure decreases, but for those with an amplitude of 50, 100, and 200 μ m, attractive pressures larger than the ones theoretically predicted with non-compliant fibers were observed experimentally. It can be argued that the fiber’s compliance contributes to the performance improvement of the attractive pressure toward a rough surface. Measured attractive pressures for k = 0 . 4 are found to match the theoretical values and are thought to be generally consistent with theory. To assess the capacitor’s fringe effect, a simple finite element simulation for capacitance calculations has been conducted. The simulated value shows a significantly small variation to the theoretical value. The simulation result, in addition to the experimental results which are generally well-matched with the theory, strongly infer that the capacitor’s fringe effect, though important to consider, is of no significant influence in this ESC device prototype. The fringe effect, however, shall be considered more thoroughly in our future work which involves more fibers for a fully-fledged operation. An important observation is also made when the surface amplitude is 0; the measured attractive pressure was only around 65% of the theoretical value. This finding may be the result of irregularities of the fibers’ tips as depicted in figure 10(a). Fiber tips which are longer than the rest exert a repelling pressure during contact with the surface, by which the attractive pressure decreases. In our prototype, a difference of about 50–100 μ m in fiber tip lengths for the device prototype were measured. These length irregularities came about from the fabrication process, which shall be improved in future work. This occurrence brings up a practical implication: 50–100 μ m irregularities in fiber tip lengths for handling a flat surface are generally comparable to an ideal arranged fibers ESC device prototype handling an object with a sinusoidal surface roughness of 50–100 μ m in amplitude. Of course, the latter results in significantly lower attractive pressure than handling of a flat surface. This is believed to be a possible reason to explain the unmatched theoretical and experimental results. Figure 10(b) illustrates this argument by comparing both models. Though it has been shown in the previous sections that the proposed ESC concept successfully produced an attractive force/pressure compared to what has been theoretically predicted, it is still important to show whether with the force it is able to perform the function of an ESC, ...

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