Supporting Information for: A highly elastic, capacitive strain gauge based on percolating nanotube networks 0.2 0.18 0.16 0.14 Force (kgf) 0.12 0.1 0.08 0.06 0.04 0.02 Raw Data Mooney-Rivlin (R 2 =0.996) Linear Elasticity (R 2 =0.997) 0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Stretch (1 + ε) Figure S1. Characterization of silicone mechanical properties. The same test structures used to make the sensors were tested using an Instron and 2mm/sec strain up to 100% strain. The data is characterized with respect to the Stretch parameter (Stretch = 1 + strain), as this is standard for Mooney-Rivlin non-linear elasticity. Curve fitting was performed using an optimization routine within Matlab (fmincon) and manually calculated the residuals and the goodness-of-fit. From the data, it appears that the linear elasticity model seems better suited to the data than the Mooney- Rivlin fit. Mooney-Rivlin underestimates strains below about 30%, while the linear model overestimates strains below 15%. On the higher end, Mooney-Rivlin underestimates the strains once more while the linear model is much more accurate. For these reasons, we opted to use the linear model for all of our subsequent analyses.
Fabrication Methods Nanotube stock solution All experiments were performed using single-walled carbon nanotubes (Cheaptubes, 99 wt%, 2 nm OD, 3-30 microns in length) prepared as follows. We first prepared a stock solution in deionized water with 5 mg/ml of nanotubes and 1 g/ml of surfactant (SDS, Sigma). This solution was bath-sonicated for 180 minutes and then allowed to settle for 12 hours. Vacuum filtration To produce two electrodes for a single capacitive sensor, 30 ml of nanotube stock solution were vacuum filtered through a 220 nm pore-size cellulose filtration membrane (MF class, Millipore). Care was taken to flush residual surfactant out of the network. Once complete the filter was removed and readied for transfer. For consistency, all filters were used for a transfer within 5 minutes of having been removed from the filtration apparatus. Substrate Preparation All devices were produced using silicone elastomer film (Bisco HT-6240 liquid silicone, 275 micron ply). The silicone was laser-cut (VLS2.3, Versa) into the dog-bone test patterns. Once cut, the substrate was masked in preparation for plasma treatment. While we successfully tested the use of traditional positive photoresists (S1818, see SI), we were able to obtain the desired electrode resolution using laser-cut sticker paper. To mask a sample, the laser-cut sticker masks were carefully placed on either side of the sample, with care taken to align them to have the proper overlap. The sample was then mounted in a custom-built 2-point clamp that held the device in a position that allowed plasma full access to all unmasked regions. Once mounted, the sample was placed in an atmospheric plasma chamber (Harrick Plasma) and exposed at 10W for a period of 30s. For higher resolution features (sub-millimeter), a combination of photoresist and oxygen plasma treatment in a reaction ion etcher can provide higher resolution boundaries to features. Plasma patterning characterization While the resolution called for in the Poisson capacitor is fairly coarse (the electrodes are many millimeters in scale), we characterized the performance of the plasma patterning method down to features of 100 microns, as shown in Figure S2. To obtain these features, we used S1818 positive photoresist and traditional photolithography. Briefly, pre-cured silicone sheets (275 microns thick) were reversibly adhered to glass slides and spin-coated with S1818 at 500 rpm (100rps) for 5 seconds followed by 4000 rpm (800rps) for 30 seconds. Following coating, the samples were soft-baked at 115 C for 2.5 min immediately prior to exposure at 65 mj/cm^2 with I-line UV. Post exposure, the samples were developed in CD-30 for 45 sec prior to plasma treatment. While atmospheric plasma is more than sufficient for coarse features (millimeter scale), we found that directional oxygen plasma in a parallel plate reactive ion etcher (RIE) provided much higher resolution, especially in conjunction with photoresist. This is likely because the anisotropic plasma treatment was less likely to infiltrate the resist:silicone interface. The features in Figure 1f were produced using a 10 sec exposure to oxygen plasma at 25 W in a Plasma-Therm PK12. Post-exposure, the resist was stripped in acetone and the substrates were immediately used for transfer experiments with freshly made nanotube percolation network filters.
Transfer and Encapsulation Immediately after exposure, the masks were stripped and the device was reversibly adhered to a cleaned glass slide. This was then placed on top of the nanotube membrane and the two were pressed together. This can be done manually, but we used a hydraulic press set at 0.25 MPa for consistency. Once one side was stamped, the device was carefully removed from the glass, flipped over and the process was repeated for the other side, using the same filtration substrate. For encapsulation, the device was mounted on a new glass slide and carefully taped down to mask the contact pads. Only one side can be done at a time, so the process will be repeated on the other side. Once secured, the sample is transferred to a hotplate with a surface temperature of 110 C. While this is heating, a mixture was made of hexane, PDMS (Sylgard 184, Dow) and PDMS curing agent in a 10:10:1 ratio. The mixture was loaded into in an airbrush and sprayed onto the heated sample. The volatility of hexane means that it was driven off quickly and the remaining PDMS cured within minutes on the heated sample. Thickness of the coating layer varied due to variability in the airbrush process, but no layer exceeded 100 microns as measured by micrometer. Testing Once encapsulated, the device was mounted as shown in Figure 1d. Copper foil was clamped against the exposed contact pads for each electrode using custom clamps. The clamps were then mounted into a modified syringe pump (Cole-Parmer) that allowed cyclic stretching at a rate of 2 mm/s. Alligator leads were used to couple the copper foil electrodes into an electrical impedance spectroscopy system (EIS, Novocontrol). All AC excitation was performed at 10 khz, while all sampling was performed at 3 Hz (the maximum possible with the EIS system). While we opted to use a formal EIS system to characterize the device performance, a much lighter, lower-cost solution for use in the field can be constructed using a simple capacitive Wheatstone bridge design. This approach is analogous to the resistive Wheatstone bridges typically used for piezoresistive strain gauges, except that it incorporates a reference capacitor (see AN990 by Microchip Inc. for a detailed discussion of designing such a bridge). Parallel plate model While the traditional parallel plate model serves to illustrate the functioning of the Poisson capacitor, the way it treats the field between the electrodes is idealized and ignores fringe fields. In order to obtain a better fit to the empirical data, it is necessary to treat the electrodes as finite regions that create fringing fields that lie outside of the dielectric region. This model is much more accurate for situations where the plate gap (g) is large with respect to the width (w) (e.g. use when w >~ w/10). The analytical solution for this, Equation S1, is known as the Palmer model and corrects for fringing fields by introducing a geometric scaling factor. The result is a more accurate model that still exhibits the same linear output in response to strain as was seen in the simple model. "C Palmer =# 0 # PDMS (1+$ z ) wl g & 1+ g & 2%w ))& ( ( 1+ log + + 1+ g & 2%w )) ( ( 1+ log + ' %w ' g **' %L ' L ** + (S1)
Here, ν is Poisson s ratio (typically ~0.5 for silicone elastomers); ε is strain; σ is stress [Pa]; and L, w and g are the initial dimensions of the capacitor (see Figure 1). ϵ 0 is the permittivity of free space [F/m], and ϵ PDMS is the relative permittivity of PDMS. The accuracy of this model can be seen in Figure 2a in the main text. Frequency response Ideal capacitors function independent of the AC excitation frequency. We ran diagnostic frequency sweeps vs. capacitance on the Poisson capacitors to characterize their general performance. Figure S2 presents the frequency sweep data, indicating that the baseline capacitance for this sensor was approximately 16 pf. Higher excitation frequencies are beneficial for improving the signal-to-noise performance, so we used the frequency response data to choose an excitation of 10 khz for all future measurements of strain vs. capacitance. Figure S2. Frequency vs. capacitance. The Poisson capacitor behaves nearly like an ideal capacitor up to an excitation frequency of around 10 5 Hz, so we performed all future measurements at 10 khz. The baseline capacitance in this range was approximately 16 pf. Robotic linkage design and fabrication The four-bar linkage was created using a scaled version of the smart composite microstructure (SCM) process. 1 This process allows flexure mechanisms to be quickly prototyped using cardboard as rigid links and polyethylene terephthalate (PET) film as the flexure material. Simple linkages can be fabricated in under twenty minutes, allowing for a working design to be quickly iterated. Once a working linkage has been validated, the process can be scaled to other materials and sizes, such as the fiberglass process used for MEDIC. 2,3 Video S1. Video of four-bar linkage leg. Please see the separate video file. Here, the four-bar linkage is attached to the stretching apparatus and the strain sensor. The plastic L structure pulls on the top of the linkage and causes it to rotate, simultaneously resulting in the stretching of
the sensor. By coupling the sensor output to the angle, we can use the sensor either for angle transduction or, knowing the dynamics of the linkage, position feedback.