Sci. Bull. DOI 10.1007/s11434-016-1149-0
www.scibull.com www.springer.com/scp
Article
Materials Science
Soft piezoresistive pressure sensing matrix from copper nanowires composite aerogel Lim Wei Yap • Shu Gong • Yue Tang Yonggang Zhu • Wenlong Cheng
•
Received: 21 April 2016 / Revised: 14 June 2016 / Accepted: 30 June 2016 Ó Science China Press and Springer-Verlag Berlin Heidelberg 2016
Abstract We report on a simple yet efficient approach to fabricate soft piezoresistive pressure sensors using copper nanowires-based aerogels. The sensors exhibit excellent sensitivity and durability and can be easily scalable to form large-area sensing matrix for pressure mapping. This opens a low-cost strategy to wearable biomedical sensors. Keywords Copper nanowires Aerogel Piezoresistive Pressure sensing matrix
1 Introduction Soft flexible pressure sensing devices can have a plethora of technical applications in future, ranging from electronic skins [1–3], energy harvesting from motions [4, 5], flexible touch display [6], implantable and wearable electronics [7–10]. The key requirement is to integrate compliant mechanics with outstanding optoelectronic properties into one single multifunctional system, which
Electronic supplementary material The online version of this article (doi:10.1007/s11434-016-1149-0) contains supplementary material, which is available to authorized users. L. W. Yap S. Gong Y. Tang W. Cheng (&) Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia e-mail:
[email protected] L. W. Yap S. Gong Y. Tang Y. Zhu W. Cheng Melbourne Centre for Nanofabrication, Clayton, VIC 3168, Australia L. W. Yap Y. Zhu CSIRO Manufacturing Flagship, Clayton, VIC 3168, Australia
is often challenging to realize with traditional rigid inorganic bulk materials. Recently, various nanomaterials, including metallic and nonmetallic nanowires [8, 11–13], ionic liquids [14, 15], carbon nanotubes [16–18], graphene [7, 19–21], polymer based materials [22, 23] had been reported as promising candidates in terms of fabrication of flexible pressure sensors. Despite the abundance of material choices, some of the material mentioned above involves tedious fabrication processes or scarcity of the material which results in higher production cost and depletion of materials [24–26]. In this context, copper nanomaterial is recently gaining popularity due to its low price and more abundance compared to indium tin oxide, yet possesses comparable conductivity to silver [25, 26]. Recently, we have demonstrated ultralight aerogel monoliths from copper nanowires (CuNWs) [27] and CuNWs-poly(vinyl alcohol) (PVA) composite aerogel monolith [11] using freeze drying techniques. The resulting aerogels could be used as waste oil clean up and stretchable conductors [11, 27]. Nevertheless, it has to be noted that the hydrazine-reduced CuNWs used in these demonstration have small aspect ratios [25, 27], hence limiting the elasticity of resulting aerogels. Highly stretchable sensors were not possible unless embedding them into polydimethylsiloxane (PDMS) [11]. Recently, a CuNWs synthesis approach had been reported producing CuNWs with aspect ratio higher than 4,000 without involving the use of highly hazardous hydrazine [28, 29]. These CuNWs are mechanically robust and highly electrical conductive, which emerge as a candidate in fabrication of transparent conducting film [29]. By combining these materials with rubbery polymer composites, this design would offer superior elasticity and mechanical robustness while remain electrically conductive.
123
Sci. Bull.
The composite aerogel has to be sealed to retard the oxidation of CuNWs and mechanically assisted by Ecoflex support to improve the life cycle due to cyclic loading. The presence of this support also helps to improve the sensitivity at higher pressure range. More importantly, this pressure sensor design could be scaled up to any number of pixels required as most of the fabrication processes are wet chemistry based and does not incur complicated processes. We believe that this pressure sensor has the capability of being used for medical purposes such as examine force exerted by a person’s foot by orthopedist in order to diagnose foot pathologies such as diabetic foot and Plantar Fasciitis.
2 Materials and methods 2.1 Materials Copper(II) chloride dihydrate (CuCl22H2O, reagent grade), hexadecylamine (HDA, 90 % technical grade), and polyvinyl alcohol (PVA, Mw = 85,000–124,000) were purchased from Sigma-Aldrich. D(?)-Glucose (anhydrous for biochemistry Reag. Ph Eur) was obtained from Merck. DuPontTM SolametÒ PV412 silver based polymer conductive paste was purchased from DuPont Microcircuit Materials. EcoflexÒ supersoft 0030 platinum cure silicone rubber set were obtained from Smooth-On, Inc. SYLGARDÒ 184 Silicon Elastomer Curing Agent and SYLGARDÒ 184 Silicon Elastomer Base were obtained from Dow Corning. All of these chemicals were used as received. Stainless thin conductive yarn/thick conductive thread was obtained from Adafruit Industries. 2.2 Synthesis of CuNWs 1.8 g HDA (capping agent), 210 mg CuCl22H2O (precursor) and 100 mL water were mixed in a 250 mL Schott bottle, capped, heated and stirred at 100 °C and 600 r/min for 30 min. After the mixture turned into light blue in colour, 1 g D(?)-glucose was added into the mixture. The stirring speed was reduced to 350 r/min and allowed to react for 6 h. The mixture was allowed to cool for 15 min before purification. For purification, mixture was centrifuged at 6,000 r/min for 15 min. Then, the precipitated CuNWs were re-dispersed in 5 mg/mL PVA solution and sonicated for 15 min. 2.3 Fabrication of CuNWs-PVA-Ecoflex In the first step, Ecoflex template was fabricated using three-dimensional (3D) printed pole structure. Briefly, precured Ecoflex, the mixture of the ‘‘Ecoflex part A’’ and the
123
‘‘Ecoflex part B’’ with a ratio of 1:1, was poured into a petri dish. The 3D printed poles structure was then inverted so that the poles were being embed into the Ecoflex mixture in order to create holes when the mixture was cured. The mixture of CuNWs and PVA poured into Ecoflex template and left in a freezer at -80 °C for 2 h. Then, the frozen sample was freeze-dried at a sublimation temperature of -85 °C and a pressure of 0.01 mbar (1 mbar = 100 Pa). 2.4 Sensor fabrication The Cr/Au electrode (thickness at 5 nm/40 nm) were deposited onto PDMS substrates (40 mm 9 40 mm) using a designed shadow mask by electric beam evaporator. The spacing between adjacent electrodes was 2 mm with the width of electrodes at 3 mm. Six contact pads of size 1 mm 9 3 mm were deposited at the ends of the electrodes to establish external contact. The electrodes were coated with silver conductive paste to ensure a conformal contact between the electrode and CuNWs-PVA aerogel. The electrode coated PDMS and the bottom of the CuNWsPVA-Ecoflex were treated by thin oxygen plasma (Harrick Plasma Cleaner PDC-001) followed by an irreversible bonding. The top electrode coated PDMS was oriented 90°, oxygen plasma treated and sealed to the top of the CuNWsPVA-Ecoflex. 2.5 Instruments CuNW-PVA aqueous solutions were frozen by a SANYO ultra-low temperature freezer at -80 °C, and the freeze drying process was performed with FreeZone 2.5 L Benchtop Freeze Dry system. The dimensions of pressure sensors were measured by a Stamvick caliper with an accuracy of 0.01 mm, and the weight of the samples were checked through a Mettler Toledo balance (MS 105DU) with an accuracy of 0.01 mg. Scanning electron microscope (SEM) images of CuNW-PVA composite aerogels were taken with FEI Nova NanoSEMTM 430 field emission gun SEM operated at an acceleration voltage of 3 kV and a working distance of 4–5 mm. Transmission electron microscope (TEM) images of CuNWs were taken with FEI TecnaiTM T20 operated at an accelerating voltage of 200 kV. The Cr/Au electrodes were deposited onto 40 mm 9 40 mm PDMS substrates using a designed shadow mask by an electric beam evaporator (Intlvac Nanochrome II, 10 kV). The designed shadow mask and the template which used to fabricate Ecoflex template for aerogel were printed using 3D printer (Objet Eden260V). The mechanical properties measurements were done using SmarAct stepping positioner (SLC-1730) controlled by custom LabView program and force data measured by a GSO series load cell with capacity of 25 g (GSO-25)
Sci. Bull.
connected to Keithley 2604B SourceMeterÒ. The electrical properties were measured simultaneously using two probe method with Keithley 2604B SourceMeterÒ with a computer based user interface.
3 Results and discussion Figure 1a illustrates the fabrication process of CuNWs composite aerogel pressure sensor. We synthesized CuNWs by the published protocol [24]. Firstly, CuCl2, HDA and D(?)-glucose were allowed to react at high temperature for 6 h. The aspect ratio of the nanowire produced was around 700 (50 nm 9 35 lm). The CuNWs was then purified by centrifugation and re-dispersed in aqueous PVA solutions. Ecoflex rubber polymer was made by mixing two different part of Ecoflex liquid in a petri dish. Before the Ecoflex rubber started to cure, a glass rod was dip into the Ecoflex liquid. When the Ecoflex rubber was cured, the glass rod was removed, forming a hole as a template for
CuNWs-PVA composite aerogel in the middle of Ecoflex rubber sheet. Freeze drying was done after filling hole in the Ecoflex template with CuNWs-PVA solution. After freeze-drying, the CuNWs-PVA-Ecoflex was sandwiched between two sheets of aluminium foil which acts as a large contacting pad connected with conducting wire. Lastly Kapton tape was used to hold the sandwiched pressure sensor in place. Figure 1b shows the photographic image of the CuNWsPVA composite aerogel in the Ecoflex support. SEM was used to further characterize the surface morphology of the composite aerogel and it demonstrated well distributed and interconnected CuNWs and PVA structure. By varying the concentration of CuNWs from 0.14 % to 0.82 % (v/v), the electrical conductivity increased by more than double from 0.12 to 0.26 S/cm (Fig. S1 online). These phenomena can be explained via the conductor–insulator mixture percolation theory, as CuNWs-PVA composite aerogel is a mixture of insulator (air and PVA) and metallic component (CuNWs). In a continuum percolation theory, the equation can be expressed as
Fig. 1 (Color online) Fabrication of CuNW–PVA composite aerogel monoliths with Ecoflex template. a Schematic illustration of the synthesis process. b Photographic image. c, d SEM images at different magnifications
123
Sci. Bull.
r ¼ r0 ðU Uc Þt ;
ð1Þ
where, r and r0 represents the electrical conductivity of CuNWs-PVA composite aerogel and the bulk copper respectively. U and Uc are the volume fraction and critical volume fraction of the CuNWs [30]. This CuNWs composite aerogel obeys the continuum percolation theory with a conductivity exponent of 0.4272. However, the conductivity exponent for this system is much less than the predicted t = 2 for 3D system [31, 32]. The apparent discrepancy in conductivity exponents could be understood since composite aerogel is not a bulk 3D system which makes it different from the literature value. The effect of CuNWs concentration in the CuNWs-PVA aerogel on the resistance-strain sensitivity is shown in Fig. S2 (online). Figure S2a (online) shows that the composite aerogel with 2 % (v/v) of CuNWs is able to quantify compression up to 14 kPa with a sensitivity of 0.032 kPa-1. At lower compression pressure of 0–1 kPa, the sensitivity is determined to be 0.581 kPa-1. As compared to the composite aerogel with 4 % (v/v) (Fig. S2b online) and 8 % (v/ v) (Fig. S2c online), the higher CuNWs content in the composite aerogel is unable to quantify compression above 5 and 4 kPa, respectively. At low concentration of CuNWs, the conductivity of the composite aerogel is low. The connection between the CuNWs in the aerogel were not completely established. Hence the external loading could further increase the number of connection points and increase percolation conductivity. However, composite aerogel with high concentration of CuNWs is densely packed, therefore the compressive strain would not have much effect on the connection network of CuNWs. The sensing mechanism behind CuNWs-PVA composite aerogel is by pressure-driven percolation conductivity. As the composite aerogel was compressed, the air gap in the composite aerogel was forced out, leaving a higher concentration of CuNWs to the volume of deformed aerogel [11]. This enables more CuNWs in contact with each other, creating more conductive pathway in the composite aerogel [8]. When released, the CuNWs recovered to their original position, reducing the concentration of CuNWs per unit volume of aerogel and leading to reduce in conductive pathway in the composite aerogel. In order to determine the benefit support on the pressure sensor, we investigated the sensitivity of the pressure sensor over different Ecoflex height. Ecoflex, in general is more flexible and deformable as compared to PDMS [16]. The sensitivity of this CuNWs-PVA-Ecoflex pressure sensor is defined as S = (DR/Roff)/DP, where DR is the relative change in resistance, Roff is the resistance of the sensor without load and DP is the pressure being applied onto the pressure sensor. By varying the thickness of the CuNWs-PVA-Ecoflex pressure sensor from 2 to 4 mm, the
123
current change increased from 1.25 to 3.35 mA. However, the sensitivity of the pressure sensor at low region decreases from 6.685 to 0.129 kPa-1 (Fig. S3 online). Interestingly, the pressure sensor with thickness of 3 mm has a sensitivity of 0.159 kPa-1 that is able to sustain from 0 to 6 kPa, which shows outstanding consistency. However, at compressive stress beyond 6 kPa, the sensitivity sustained at 0.004 kPa-1 as the Ecoflex had already been highly compressed and require larger force to deform the Ecoflex further. At low pressure region (0–2 kPa), this pressure sensor is less sensitive as compared to carbon nanotube (CNT)-based, graphene-based, organic-based and our previously reported gold nanowire-based pressure sensors [19, 33, 34], but this device do not require costly materials and tedious processing steps as compared to reported devices. Besides, the ability of this device to be able to maintain sensitivity of 0.159 kPa-1 up to 6 kPa-1 is unique. As mentioned before, the CuNWs-PVA aerogel holds on to the Ecoflex support during compression and relaxation. By inputting same amount of pressure, CuNWsPVA composite aerogel will deform more than this device as Ecoflex requires higher force to deform due to higher Young’s modulus. This improves the ability of this device to operate from low to medium pressure range. A comparison has been done on mechanical strength of the CuNWs-PVA-Ecoflex system and the CuNWs-PVA composite aerogel (Fig. 2). The compressive stress–strain curve for CuNW-PVA composite aerogel with Ecoflex support reflects a viscoelastic hysteresis curve. The curve started with a plateau region followed by a steep region while loading. In the plateau region, compressive stress increased gradually with strain, indicating elastic deformation whereas in the steep regions. The compressive stress increased rapidly with the strain due to densification process of Ecoflex polymer. When unloading, the stress– strain curve did not follow the loading curve, and the stress was lower than the loading curve. This is because Ecoflex support is a viscoelastic material, which absorbs energy in the deformation process. The energy absorbed is indicated by the area between the loading and unloading curve. The Young’s modulus of composite aerogel was 329 Pa whereas the presence of Ecoflex support increased the Young’s modulus to 86.9 kPa, which is an increment of *265-folds. The surge in mechanical strength of the system is due to the presence of the Ecoflex support which holds the composite aerogel when it is compressed and released. Hence, the mechanical strength of the pressure sensor is mostly contributed by the Ecoflex support while the electrical conductivity and the sensitivity are contributed by CuNWs-PVA composite aerogel. Force-induced current change of our pressure sensor towards various dynamic forces applied were tested by using the piezoelectric stepping positioner and an electrical source
Sci. Bull.
meter. As shown in Fig. 3a, the minimum pressure of 800 Pa could be detected by our device with very slight change in current. At higher pressure range from 2 to 5.5 kPa, the pressure sensor gives continuous and sharp response.
Fig. 2 (Color online) Compressive stress–strain curves of CuNWPVA composite aerogels with Ecoflex support and CuNW-PVA composite aerogels at the compressive strain of 20 %
The response time of our pressure sensor towards external force was examined by comparing the output current of the pressure sensor with the dynamic pressure input by the stepping positioner at a frequency of 1.5 Hz. The current wave response was at the similar timeframe as the induced force wave. Looking closely into the difference, the response time was as quick as 0.01 s during the loading and unloading process, which is almost negligible. This hysteresis may be caused by elastic deformation of composite aerogel and Ecoflex support which takes time to recover to its original state [8]. In addition, the durability of the pressure sensor was also demonstrated under a pressure of 10.5 kPa at frequency of 10 Hz for 10,000 loading and unloading cycles and the pressure sensing performance of the sensor after durability test was also examined. The signal to noise ratio of the sensor was fairly repeatable (Fig. 3c) and the sensing performance of the sensor did not show drastic changes after continuously compressed for 10,000 cycles (Fig. 3d). The fabrication process of CuNWs-PVA-Ecoflex pressure sensors are mostly based on wet chemistry technique and readily to be scaled up to flexible large-scale pressure sensors. In order to demonstrate the scalability, we fabricated
Fig. 3 (Color online) Pressure sensing characteristic of CuNWs-PVA composite aerogels with Ecoflex support. a Dynamic pressure response at loading and unloading pressure ranging from 0.8 to 10.5 kPa. b Time resolved response with applied pressure of 10.5 kPa at frequency of 1.5 Hz. c Durability test of pressure sensor under repeated pressure of 10.5 kPa at frequency of 10 Hz for 10,000 cycles. d Current response signal curve after 10,000 cycles
123
Sci. Bull.
Fig. 4 (Color online) Schematic illustration of the fabrication process. Large-area manufacturability of CuNWs-PVA composite aerogel pressure sensor with Ecoflex support
an Ecoflex templated CuNWs–PVA pressure sensor with six pixels by six pixels array as shown in Fig. 4. This is done by fabricating the Ecoflex template for composite aerogel with 3D printed 6 9 6 poles. After that, CuNWs-PVA mixture was used to fill up the holes in the Ecoflex template and freeze dried. Two electrode layers were deposited on PDMS sheet via e-beam evaporator and used to sandwich the CuNWs-PVA-Ecoflex layer. Each contact pad of the electrode was extended and connected by a conducting thread. As shown in Fig. 5a, a finger with unknown force was placed lightly onto the pressure sensor to test its response to external pressure. The resistive signal of each pixel was recorded in order to map the pressure distribution on the pressure sensor. Grayscale colour contrast was used to map the recorded result and the pressure distribution was in consistency with the shape of the finger even with light force exerted. If the pressure sensor could be properly calibrated, the force exerted onto each pixel of the pressure sensor could be determined. After that, two fingers were pressure hardly onto the pressure sensor and the grayscale colour mapping also shows consistent result as the shape of the fingers. In future, the pressure sensor could be further scaled up for more applications.
Fig. 5 (Color online) Large-area pressure sensor mapping. a Top view of a finger lays on the (6 9 6) pixels pressure sensor. b Resistive signal mapping of pressure distribution for (a). c Top view of two fingers pressed hardly on the (6 9 6) pixels pressure sensor. d Resistive signal mapping of pressure distribution of (c)
123
Sci. Bull.
4 Conclusions In summary, we report a piezoresistive pressure sensor design and the fabrication method which involves previously reported CuNWs-PVA composite aerogel as the main sensing platform with Ecoflex polymer as support. The benefit of this design is the good and unique sensitivity of the pressure sensor which can range from low range pressure to high range. Besides from good sensitivity, the sensor also is able to sustain 10,000 cycles cyclic loading test and produces repeatable result after the test. Lastly we also show the ability to scale up the sensors to 36 pixels large area pressure sensing device. With these outstanding characteristics, this pressure sensor shows itself as a promising candidate for medical applications especially by orthopedist. Acknowledgments This work was supported by ARC discovery Project (DP150103750). We also acknowledge Bin Su, Zheng Ma, Jiarong Li and Kean Aik Tan. This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). Conflict of interest The authors declare that they have no conflict of interest.
References 1. Tien N, Jeon S, Kim D et al (2014) A flexible bimodal sensor array for simultaneous sensing of pressure and temperature. Adv Mater 26:796–804 2. Sekitani T, Someya T (2010) Stretchable, large-area organic electronics. Adv Mater 22:2228–2246 3. Wang C, Hwang D, Yu Z et al (2013) User-interactive electronic skin for instantaneous pressure visualization. Nat Mater 12:899–904 4. Park KI, Son JH, Hwang GT et al (2014) Nanogenerators: highlyefficient, flexible piezoelectric PZT thin film nanogenerator on plastic substrates. Adv Mater 26:2514–2520 5. Pan C, Dong L, Zhu G et al (2013) High-resolution electroluminescent imaging of pressure distribution using a piezoelectric nanowire LED array. Nat Photon 7:752–758 6. Fan FRR, Lin L, Zhu G et al (2012) Transparent triboelectric nanogenerators and self-powered pressure sensors based on micropatterned plastic films. Nano Lett 12:3109–3114 7. Kim DH, Lu NL, Ma R et al (2011) Epidermal electronics. Science 333:838–843 8. Gong S, Schwalb W, Wang Y et al (2014) A wearable and highly sensitive pressure sensor with ultrathin gold nanowires. Nat Commun 5:3132 9. Gong S, Lai DTH, Su B et al (2015) Highly stretchy black gold e-skin nanopatchs as highly sensitive wearable biomedical sensors. Adv Electron Mater 1:1400063 10. Gong S, Lai DTH, Wang Y et al (2015) Tatoo-like polyaniline microparticle-doped gold nanowire patches as highly durable wearable sensors. ACS Appl Mater Interfaces 7:19700–19708 11. Tang Y, Gong S, Chen Y et al (2014) Manufacturable conducting rubber ambers and stretchable conductors from copper nanowire aerogel monoliths. ACS Nano 8:5707–5714 12. Takei K, Takahashi T, Ho JC et al (2010) Nanowire active-matrix circuitry for low-voltage macroscale artificial skin. Nat Mater 9:821–826
13. Zhu B, Wang H, Liu Y et al (2016) Skin-inspired haptic memory arrays with an electrically reconfigurable architecture. Adv Mater 28:1559–1566 14. Wang Y, Gong S, Wang SJ et al (2016) Volume-invariant ionic liquid microbands as highly durable wearable biomedical sensors. Mater Horizon 3:208–213 15. Ma Z, Su B, Gong S et al (2016) Liquid-wetting-solid strategy to fabricate stretchable sensors for human–motion detection. ACS Sensor 1:303–311 16. Lipomi DJ, Vosgueritchian M, Tee BCK et al (2011) Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes. Nat Nanotechnol 6:788–792 17. So HM, Sim JW, Kwon J et al (2013) Carbon nanotube based pressure sensor for flexible electronics. Mater Res Bull 48:5036–5039 18. Cohen DJ, Mitra D, Peterson K et al (2012) A highly elastic, capacitive strain gauge based on percolating nanotube networks. Nano Lett 12:1821–1825 19. Yao HB, Ge J, Wang CF et al (2013) A flexible and highly pressure-sensitive graphene–polyurethane sponge based on fractured microstructure design. Adv Mater 25:6692–6698 20. Smith AD, Niklaus F, Paussa A et al (2013) Electromechanical piezoresistive sensing in suspended graphene membranes. Nano Lett 13:3237–3242 21. Qiu L, Coskun MB, Tang Y et al (2016) Ultrafast dynamic piezoresistive response of graphene-based cellular elastomers. Adv Mater 28:194–200 22. Park M, Im J, Park JJ et al (2013) Micropatterned stretchable circuit and strain sensor fabricated by lithography on an electrospun nanofiber mat. ACS Appl Mater Interfaces 5:8766–8771 23. Gao Q, Meguro H, Okamoto S et al (2012) Flexible tactile sensor using the reversible deformation of poly(3-hexylthiophene) nanofiber assemblies. Langmuir 28:17593–17596 24. Ye S, Rathmell AR, Stewart IE et al (2014) A rapid synthesis of high aspect ratio copper nanowires for high-performance transparent conducting films. Chem Commun 50:2562 25. Rathmell AR, Wiley BJ (2011) The synthesis and coating of long, thin copper nanowires to make flexible, transparent conducting films on plastic substrates. Adv Mater 23:4798–4803 26. Bhanushali S, Ghosh P, Ganesh A et al (2015) 1D copper nanostructures: progress, challenges and opportunities. Small 11:1232–1252 27. Tang Y, Yeo KL, Chen Y et al (2013) Ultralow-density copper nanowire aerogel monoliths with tunable mechanical and electrical properties. J Mater Chem A 1:6723–6726 28. Jin M, He G, Zhang H et al (2011) Shape-controlled synthesis of copper nanocrystals in an aqueous solution with glucose as a reducing agent and hexadecylamine as a capping agent. Angew Chem Int Ed 50:10560–10564 29. Sachse C, Weiß N, Gaponik N et al (2014) ITO-free, smallmolecule organic solar cells on spray-coated copper-nanowirebased transparent electrodes. Adv Energy Mater 4:1300737 30. Yang QQ, Liang JZ (2008) A percolation model for insulator– metal transition in polymer–conductor composites. Appl Phys Lett 93:131918 31. Bergma DJ, Stroud DG (1992) Physical properties of macroscopically inhomogeneous media. In: Mingzhong W, Hoffmann A (eds) Solid state physics. Elsevier, Amsterdam, pp 147–269 32. Clern JP, Giraud G, Laugier JM et al (1990) The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models. Adv Phys 39:191–309 33. Schwartz G, Tee BCK, Mei J et al (2013) Flexible polymer transistors with high pressure sensitivity for application in electronic skin and health monitoring. Nat Commun 4:1859 34. Park S, Kim H, Vosgueritchian M et al (2014) Stretchable energyharvesting tactile electronic skin capable of differentiating multiple mechanical stimuli modes. Adv Mater 26:7324–7332
123