Supporting Information for

1

Supporting Information for

Limiting Mechanisms and Scaling of Electrostatically Controlled

Adhesion of Soft Nanocomposite Surfaces for Robotic Gripping

Michael S. H. Boutilier,1,2 Changhong Cao,1 Nigamaa Nayakanti,1 Sanha Kim,1,3 Seyedeh Mohadeseh Taheri-Mousavi,1,4 A. John Hart1,*

1_{Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.} 2_{Department of Chemical and Biochemical Engineering, Western University, London, ON, Canada.}

3_{Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.} 4_{Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.} *_{Corresponding author: [email protected]}

Flexure mechanism design

Multi-axis load cells capable of accurately measuring the <0.1 N forces in these experiments were not available commercially. In order to simultaneously measure two components of force, we instead selected a pair of single axis load cells (Futek, LRM200, 100 g range) accurate for the range of forces to be measured and designed a flexure mechanism to decouple the forces on each. This mechanism is responsible for transmitting most of the axial force to the corresponding load cell while preventing lateral loads from being transmitted. In this way, most of the horizontal force exerted on the tip is recorded by one load cell while most of the vertical force exerted is recorded by the other. This improves the accuracy of the force measurement while also preventing damage to the load cells due to off-axis forces.

Double parallelogram flexure elements were selected to provide low angular deflections and similar stiffness in tension and compression.1,2 The design is illustrated in Fig. 2b, S1. Based on the design optimization in Refs. [1,2], we selected parameters 𝑤₁ = 0.3882𝐿 and 𝑤₂ = 0.2697𝐿 . The design iterations for dimensions and material selection employed the analysis tools developed in Refs. [1,2_{]. Based} on the force diagrams in Fig. S1b, when forces 𝑓_𝑥 and 𝑓_𝑦 are exerted on the tip, the forces on the load cells are related by the following equilibrium conditions:

Horizontal force: −𝑓̃₂+ 𝑓̃_𝑥+ 𝑔̃₁ = 0 (S1) Vertical force: 𝑓̃𝑦+ 𝑔̃2+ 𝑓̃1 = 0 (S2) Moment: −𝑚̃2− 𝑚̃1 + 𝑓̃1𝑠̃ + 𝑓̃2𝑠̃ + 𝑓̃𝑥𝑞̃ = 0 (S3) where the Young’s modulus of the flexure material (𝐸), the area moment of inertia (𝐼_𝑦𝑦 = 1

12𝐵𝑇

3_{, 𝐵 is} beam depth into the page in Fig. S1, and 𝑇 is beam thickness), and the length of the beam (𝐿) are used in normalization as 𝑓̃_𝑖 = 𝑓_𝑖𝐿2 _𝐸𝐼

𝑦𝑦

⁄ , 𝑔̃_𝑖 = 𝑔_𝑖𝐿2 _𝐸𝐼 𝑦𝑦

⁄ , 𝑚̃_𝑖 = 𝑚_𝑖𝐿 𝐸𝐼⁄ _𝑦𝑦, 𝑠̃ = 𝑠 𝐿⁄ , and 𝑞̃ = 𝑞 𝐿⁄ . The two load cells act as springs with elastic constant, 𝑘 = 4905 N/m. The spring force relation gives two more equations,

Horizontal load cell: 𝑔̃₁ = 𝑘̃𝑥̃_𝐴 (S4) Vertical load cell: 𝑔̃2 = 𝑘̃𝑦̃𝐵 (S5)

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with normalization, 𝑥̃_𝑖 = 𝑥_𝑖⁄ , 𝑦̃𝐿 _𝑖 = 𝑦_𝑖⁄ , and 𝐿 𝑘̃ = 𝑘𝐿3⁄𝐸𝐼_𝑦𝑦. We then use relations between the forces exerted on double parallelogram flexures and the resulting deformations developed in Ref 1,2. For the double parallelogram flexure attached to the horizontal load cell,

Lateral deflection: −(𝑦̃𝐶+ 𝑠̃𝜃𝑐) = 4𝑎̃𝑓̃1 (2𝑎̃)2_{−(𝑒̃𝑔̃} 1)2 (S6) Axial deflection: (𝑥̃𝐴− 𝑥̃𝐶) = 𝑔̃1( 1 𝑑̃+ [−(𝑦̃𝐶+𝑠𝜃̃𝑐)] 2 2 [ 𝑠̃ 2− 𝑒̃𝑖̃ 𝑎̃]) (S7) Angular deflection: 𝜃_𝐶 = 1 2𝑤̃₁2[ 1 𝑑̃+ 𝑓̃₁2 (2𝑎̃ − 𝑔̃₁𝑒̃)2𝑠̃] {𝑚̃1− 𝑓̃₁ 2𝑎̃ − 𝑔̃₁𝑒̃[1 − 𝑔̃₁ 2𝑎̃ + 𝑔̃₁𝑒̃+ (2𝑐̃ − 𝑔̃1ℎ̃)]} + 1 2𝑤̃₂2[ 1 𝑑̃+ 𝑓̃₁2 (2𝑎̃ + 𝑔̃₁𝑒̃)2𝑠̃] [𝑚̃1 − 𝑓̃₁ 2𝑎̃ + 𝑔̃₁𝑒̃(2𝑐̃ + 𝑔̃1ℎ̃)] (S8)

Similarly, for the double parallelogram flexure attached to the vertical load cell, Lateral deflection: (𝑥̃_𝐶− 𝑠̃𝜃_𝑐) = 4𝑎̃𝑓̃2 (2𝑎̃)2_{−(𝑒̃𝑔̃} 2)2 (S9) Axial deflection: (𝑦̃𝐵− 𝑦̃𝐶) = 𝑔̃2( 1 𝑑̃+ [𝑥̃𝐶−𝑠̃𝜃𝑐]2 2 [ 𝑠̃ 2− 𝑒̃𝑖̃ 𝑎̃]) (S10) Angular deflection: 𝜃_𝐶 = 1 2𝑤̃₁2[ 1 𝑑̃+ 𝑓̃₂2 (2𝑎̃ − 𝑔̃₂𝑒̃)2𝑠̃] {𝑚̃2− 𝑓̃₂ 2𝑎̃ − 𝑔̃₂𝑒̃[1 − 𝑔̃₂ 2𝑎̃ + 𝑔̃₂𝑒̃+ (2𝑐̃ − 𝑔̃2ℎ̃)]} + 1 2𝑤̃₂2[ 1 𝑑+ 𝑓̃₂2 (2𝑎̃ + 𝑔̃₂𝑒̃)2𝑠̃] [𝑚̃2− 𝑓̃₂ 2𝑎̃ + 𝑔̃₂𝑒̃(2𝑐̃ + 𝑔̃2ℎ̃)] (S11)

where for these simple beams the constants are, 𝑎̃ = 12, 𝑐̃ = −6, 𝑒̃ = 1.2, ℎ̃ = −0.1, 𝑖̃ = −0.6, 𝑟̃ = 1 700⁄ , and 𝑑̃ = 12𝐿2_⁄𝑇2 _[Refs. 1,2_].

Design parameters were selected to transmit >95% of applied forces to the correct load cells while ensuring that the beams were rigid enough to withstand buckling as determined from Euler’s buckling criterion at the maximum design load (𝐹𝑚𝑎𝑥 = 1 N),

𝐹𝑚𝑎𝑥 =

4𝜋2_𝐸𝐼 𝑦𝑦

𝐿2 (S12)

The remaining difference between applied forces and those measured by the load cells are accounted for through the calibration procedure described in the Calibration section. Longer (greater 𝐿), shallower (smaller 𝐵) beams provide greater force decoupling but buckle at lower loads. Furthermore, the weight of the flexure increases rapidly with larger values of 𝐿. This weight is carried by the vertical load cell and must therefore be much less than the sensor’s force range so as not to compromise the measurement range. After iterating on the parameters, we selected a beam length of 𝐿 = 25 mm, depth of 𝐵 = 9.5 mm, thickness 𝑇 = 0.52 mm, and polycarbonate material. The flexure mechanism was machined on a water jet capable of accurately cutting the thin beam sections.

The predicted response of the flexure mechanism to applied forces computed by solving Eq. S1-S11 is presented in Fig. S2.

Force-displacement measurement system photos

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Force-displacement measurement system calibration

Remaining off-axis forces on the horizontal and vertical load cells that were not eliminated by the flexure mechanism were removed through calibration of the system. A calibration probe was attached to the flexure mechanism that had a thread connected at the location where the tip would otherwise be. The thread was strung over a pin with a calibration weight hanging on the other end (Fig. S4). The precision motion system was used to position the probe along an arc, 10 cm from the pin. The forces on both load cells were recorded. Calibration points were taken at 15° increments along the arc and for five different weights covering the sensor range.

From the known weights and thread angles, the measured forces on the horizontal (𝐹𝑥) and vertical (𝐹𝑧) load cells could be mapped to the actual horizontal (𝑓_𝑥) and vertical (𝑓_𝑧) forces on the tip. Planar calibration curves were employed with the form,

𝑓_𝑥 = 𝑎_𝑥𝐹_𝑥+ 𝑏_𝑥𝐹_𝑧+ 𝑐_𝑥 (S13)

𝑓𝑧 = 𝑎𝑧𝐹𝑥+ 𝑏𝑧𝐹𝑧+ 𝑐𝑧 (S14)

The calibration coefficients (𝑎𝑥, 𝑏𝑥, 𝑐𝑥, 𝑎𝑧, 𝑏𝑧, 𝑐𝑧) were determined by numerical least squares fitting to the measured calibration data.

Alumina ALD breakdown measurement

The results of a DC probe station measurement of dielectric breakdown of 300 cycles of alumina ALD coating over gold are shown in Fig. S5. This is more than 10 times the number of cycles applied during CNT coating and the film no longer acts as an insulator above 22 V, less than the lowest applied voltage in this study.

Description of passive dry adhesives in Fig. 7

Below, we describe the reversible dry adhesives presented in Fig. 7. The data in Fig. 7 and the descriptions below are based on the compilation of results presented in Ref. 3_.

Fibrillar polymer adhesives consist of an array of slender pillars made of soft polymers such as

polyurethane or polydimethylsiloxane. These pillars are tilted from the base to which they are attached, such that contacting the target object and subsequently shearing in one direction will bring the sides of the pillars into contact with the surface. The high contact area produces normal adhesion through van der Waals forces. When sheared in the opposite direction, side contact is not created due to the fiber tilt. After shearing to engage the adhesive, shearing in the opposite direction eliminates contact with the sides of the fibers, releasing the surface.

CNT passive dry adhesives can be reversible, but they are not usually used in this way. CNT forests have

a similar structure to fibrillar polymer adhesives, except that the slender fibers are vertically aligned CNTs and they are not “tilted” from the base substrate. When used as a reversible dry adhesive, the disordered crust layer on the surface of the CNT forest is left intact. The adhesive is pressed into the target surface and then sheared. This shearing pulls on the tangled crust, increasing CNT sidewall contact with the surface. The shearing causes the CNTs to contact the surface in nearly parallel lines. To release the adhesive, the forest is sheared in the opposite direction, causing the CNTs to peel away from the surface, reducing adhesion.

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Flat polymer adhesives consist of continuous, non-patterned soft polymer, commonly

polydimethylsiloxane. The surface compliance of the polymer creates high effective contact areas with the target when preloaded. One design uses a woven fabric within the polymer pad to create direction dependent compliance.4 _{In this design, adhesion is high when loaded in one direction but low when loaded} in another direction, allowing for controlled release. Other designs use changes in the polymer surface contacting the target during shearing for object release.5

Magnetic release adhesives incorporate a magnetic powder in a polymer material. Exposing the material

to a magnetic field will strain the polymer and can change the compliance of the material. Strong adhesion can be created when the material is highly compliant and creates high contact areas with the target on contact. Inducing a lower compliance state reduces the contact as well as the adhesion strength.

Shape memory polymer adhesives are set and released by heating and cooling through their glass

transition temperature. They are commonly made of epoxies. By heating above the glass transition temperature, the material becomes compliant, allowing it to conform to the target object surface. Cooling the adhesive below the glass transition temperature makes the polymer rigid, fixing its strained shape to maintain adhesion. When the adhesive is once again heated above the glass transition temperature, its compliance is restored, relaxing strain and releasing the object.

Other reusable heat release adhesives refers to those developed in Ref. 6 consisting of a two phase polymer material. By heating above the melting temperature of one phase, liquid can fill voids at the contact interface with the target object to create effective contact. The solid phase maintains the shape and rigidity of the adhesive during this process. Cooling solidifies the material and creates strong adhesion. When reheated, the adhesive releases.

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Figure S1. Flexure mechanism design. a Overall force diagram. b Component diagrams showing forces

(blue) and displacement (red) on the load cells (yellow), double parallelogram flexures, and probe. Component labels are provided in Fig. 2b.

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Figure S2. Calculated flexure performance. a,b Percentage difference in measured horizontal force on

horizontal load cell (a) and vertical force on vertical load cell (b) as the forces exerted on the tip (𝑓_𝑥, 𝑓_𝑦) vary over the design range. 𝑔 is the gravitational acceleration (9.81 m/s2_{). c Angular deflection of tip over} the designed applied force range.

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Figure S5. 300 cycle alumina ALD coating dielectric breakdown measurement. Inset shows the

measurement setup in which voltage was gradually increased and current measured. After breakdown, the current rises abruptly to the 1 mA limit setting.

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Figure S6. Force drift measurement on conductive probe. a Diagram of applied voltage profile.

Voltage steps from 0 V up to 100 V and later steps back to 0 V. b Resulting vertical force time-trace measured on conductive probe positioned 4 µm above the SNE. The plot shows a fast step response of the force when voltage is switched on, a stable force while voltage is held constant, and a fast step back down to zero force when voltage is switched off. The force on the conductive probe does not drift over time, in contrast to the non-conductive probe (Fig. S7).

b

a

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Figure S7. Force drift measurement on acrylic probe. a Diagram of applied voltage profile. Voltage

steps up to 2800 V at time zero, then further steps up to 3000 V approximately 650 s later. b Resulting vertical force time-trace measured on acrylic probe positioned 2 µm above the SNE. Both times that voltage is stepped up, the force steps up immediately, then continues to drift higher as a result of charge accumulation on the non-conductive probe. Unlike the conductive probe (Fig. S6), charge buildup on the non-conductive probe causes the force to change over time. The initial force when voltage is stepped on is most relevant to rapid manufacturing operations. For this reason, during adhesion measurements, the time between switching on voltage and beginning to retract the probe was kept short (< 2 s). Furthermore, between measurements, voltage was turned off for a longer time than it had been on during the previous measurement to allow for charge to dissipate.

b

a

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Figure. S8. Repeatability of SNE adhesive performance. A series of 19 pull-off force measurements

were taken at the same location on the SNE sample, with the same preload but various applied voltages between 0 and 240 V. Voltages were not measured in any particular order. The markers show the measurements of normalized pull-off force at 220 V, 230 V, and 235 V vs. the number of measurements taken at the location. Measurements are presented normalized by the maximum pull-off force measured over the 19 samples. The data illustrate the repeatable adhesion of SNEs.

13 References

(1) Awtar, S.; Slocum, A. H. Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms.

J. Mech. Des. 2007, 129 (8), 816. https://doi.org/10.1115/1.2735342.

(2) Awtar, S.; Slocum, A. H. Closed-Form Nonlinear Analysis of Beam-Based Flexure Modules. In

ASME International Design Engineering Technical Conference & Computers and Information in Engineering Conference (DETC2005-85440); Long Beach, California, USA, 2005; pp 1–10.

(3) Eisenhaure, J.; Kim, S. A Review of the State of Dry Adhesives: Biomimetic Structures and the Alternative Designs They Inspire. Micromachines 2017, 8 (4), 125. https://doi.org/10.3390/mi8040125.

(4) Bartlett, M. D.; Croll, A. B.; King, D. R.; Paret, B. M.; Irschick, D. J.; Crosby, A. J. Looking Beyond Fibrillar Features to Scale Gecko-Like Adhesion. Adv. Mater. 2012, 24 (8), 1078–1083. https://doi.org/10.1002/adma.201104191.

(5) Carlson, A.; Kim-Lee, H.-J.; Wu, J.; Elvikis, P.; Cheng, H.; Kovalsky, A.; Elgan, S.; Yu, Q.; Ferreira, P. M.; Huang, Y.; Turner, K. T.; Rogers, J. A. Shear-Enhanced Adhesiveless Transfer Printing for Use in Deterministic Materials Assembly. Appl. Phys. Lett. 2011, 98 (26), 264104. https://doi.org/10.1063/1.3605558.

(6) Luo, X.; Lauber, K. E.; Mather, P. T. A Thermally Responsive, Rigid, and Reversible Adhesive.