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such as transistor, [ 5 ] triboelectric, [ 6 ] capaci-tive, [ 7,8 ] piezoelectric, [ 9–11 ] and piezoresis-tive [ 12–35 ] properties.

Piezoresistive pressure sensors, which transform an input force into an electrical signal caused by the change in the resist-ance, have attracted considerable atten-tions by virtue of its simplicity and low cost in design and implementation. Most fl exible piezoresistive sensors are pre-pared by loading conductive nanomate-rials (e.g., carbon nanotubes (CNTs), [ 12–28 ] graphene, [ 29–32 ] nanowires, [ 33–35 ] nan-oparticles) onto fl exible substrates (e.g., fi bers, [ 12,13 ] fi lms, [ 14–17 ] open-cell foams [ 29 ] ) via a number of pro-cessing methods, such as blending, [ 19,20 ] coating, [ 21,29 ] and printing. [ 17 ] Among the different conductive nanomaterials, carbon nanotubes have attracted a con-siderable amount of attention due to their remarkably high piezoresistive sensitivity. [ 36,37 ] In addition to the nano-materials, which are the active sensing elements, the properties of the substrates

also play a key role in determining the overall sensor per-formance. [ 27,28 ] Most studies on the effects of the substrates focus on the modulus, and it has been suggested that porous substrates with reduced elastic modulus result in increased sensing properties. [ 19 ] Yet from the classical mechanics point of view, the other most fundamental property that dictates the elastic properties is the Poisson ratio, which is defi ned as the ratio of the lateral contractile strain to the longitudinal tensile strain for a material undergoing tension in the longitudinal direction. Collectively, they defi ne the elastic properties and deformation characteristics of the materials in a 3D space. Conceivably, the Poisson ratio would impact the sensing per-formance of piezoresistive sensors; however, this effect has not been studied.

Classical mechanics predicts that for isotropic materials, the Poisson ratio lies between –1 and 0.5, a fairly small range. [ 38 ] With a few exceptions such as α-cristobalite, [ 39 ] certain cubic metal, [ 40 ] and few biological tissues, [ 41 ] the range of Poisson ratio of almost all natural or synthetic materials is even smaller, typically 0.3–0.5. [ 42 ] Research on fabrication of auxetic mate-rials or materials with negative Poisson ratios has progressed steadily since the initial report by Lakes [ 43 ] on the possibility of such materials. [ 44,45 ]

Poisson Ratio and Piezoresistive Sensing: A New Route to High-Performance 3D Flexible and Stretchable Sensors of Multimodal Sensing Capability

Yan Li , Sida Luo , Ming-Chia Yang , Richard Liang , * and Changchun Zeng *

The performance of fl exible and stretchable sensors relies on the optimization of both the fl exible substrate and the sensing element, and their synergistic interactions. Herein, a novel strategy is reported for cost-effective and scalable manufacturing of a new class of porous materials as 3D fl exible and stretchable piezoresistive sensors, by assembling carbon nanotubes onto porous substrates of tunable Poisson ratios. It is shown that the piezoresistive sensitivity of the sensors increases as the substrate’s Poisson’s ratio decreases. Substrates with negative Poisson ratios (auxetic foams) exhibit signifi cantly higher piezoresistive sensitivity, resulting from the coherent mode of deformation of the auxetic foam and enhanced changes of tunneling resistance of the carbon nanotube networks. Compared with conventional foam sensors, the auxetic foam sensor (AFS) with a Poisson’s ratio of –0.5 demonstrates a 300% improvement in piezoresistive sensitivity and the gauge factor increases as much as 500%. The AFS has high sensing capability, is extremely robust, and capable of multimodal sensing, such as large deformation sensing, pressure sensing, shear/torsion sensing, and underwater sensing. AFS shows great potential for a broad range of wearable and portable devices applications, which are described by reporting on a series of demonstrations.

DOI: 10.1002/adfm.201505070

Dr. Y. Li, Dr. S. Luo, M.-C. Yang, Prof. R. Liang, Prof. C. Zeng High Performance Materials Institute Florida State University Tallahassee , FL 32310 , USA E-mail: zliang@fsu.edu; czeng@fsu.edu Dr. Y. Li, Dr. S. Luo, M.-C. Yang, Prof. R. Liang, Prof. C. Zeng Department of Industrial and Manufacturing Engineering FAMU-FSU College of Engineering Tallahassee , FL 32310 , USA

1. Introduction

Flexible, stretchable, highly sensitive, and low-cost pressure sensors are key elements in advancing wearable or implant-able measuring devices. [ 1–4 ] Since the last decade, [ 1,2 ] the pur-suit of such sensors has become a rapidly expanded area of research that covers electronics, chemistry, physics, mechanics, and materials science, and has enabled a wide variety of new ideas in sensor design based on different sensing mechanisms,

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Recently, we developed a technology for large scale manu-facturing of auxetic foams with tunable Poisson ratio. [ 46 ] In the present study, we report on a novel strategy to fabricate piezore-sistive sensors using the auxetic foam with tunable Poisson ratio as the substrate, and the investigation of their effects on the piezoresistive properties. To the best of our knowledge, this is the fi rst study of its kind, considering all foams employed in previous studies had positive Poisson ratios. The auxetic foam sensor (AFS) was fabricated by assembling a thin layer of carbon nanotubes onto the surface of the porous micro-structures via a facile and scalable dip-coating process. The piezoresistive sensing performance of the AFS was studied in response to a variety of deformation modes and environmental conditions. The results show that AFS is a new class of piezore-sistive materials that is intrinsically stretchable and fl exible. We further demonstrated that the AFS has board sensing capa-bilities for potential applications in smart wearables, protective equipment, point-of-care diagnostics devices, human–machine, and pressure mapping interfaces.

2. Results and Discussions

2.1. Preparation and Characterization of Auxetic Foam Sensor

The auxetic foams with different ν (including ν = 0) were prepared using the technology we developed previously. [ 46 ] Figure 1 a shows the schematics of the process, which involved the triaxial compression of a conventional pristine PU foam (control sample) to generate the re-entrant structure. Figure 1 b shows a comparison of the shapes of a typical fabricated auxetic foam. The expansion of the foam in the transverse direction under tension is evident (Video S1, Supporting Information). The scanning electron microscopy (SEM) images, also shown in Figure 1 b, revealed the deformation mechanism of the aux-etic foam originates from their unique re-entrant morphology. Under applied tensile stress, the re-entrant cell struts appear to rotate and unravel, and the foam cells are seen to expand longi-tudinally (Video S2, Supporting Information).

Subsequently, both the conventional foam and the auxetic foams with different Poisson ratios were dip-coated using a CNT suspension (Figure 1 c). Note that to achieve uniform CNT deposition for high sensing performance, it is critically important to use a suspension with high-quality CNT disper-sion, which has been verifi ed qualitatively by direct atomic force microscopy (AFM) observations (Figure 1 d), and quanti-tative analysis using the preparative ultracentrifuge method. [ 47 ] (Details are described in Figure S1, Supporting Information.) The CNT-coated foams were immersed in deionized water for 2 h to remove the residual surfactant, after which they were dried overnight in vacuum at 70 °C. The CNT contents were determined by thermogravimetric analysis (TGA), which were ≈1 wt% of the total sample weight for all foams. The struc-ture of CNT-coated auxetic foam was inspected using SEM. The low-magnifi cation SEM image shows the typical re-entrant wall structure in the CNT-coated auxetic foam (Figure 1 e). An enlarged view shows a very homogenous CNT layer on the surface of the cell wall (Figure 1 f). This simple manufacturing process can easily be scaled. In our lab, we are able to fabricate

the auxetic foam sensors with different geometries and sizes as large as 900 cm 2 . Figure 1 g shows some AFS we fabricated.

2.2. Poisson’s Ratio and Sensing Performance

We fi rst studied the effects of ν on the piezoresistive sensitivity of the foam sensors. In the experimental setup ( Figure 2 a), the loading machine controlled the stretch/compression profi le, the video system measured the displacements of foam sensors, and the two electrometers simultaneously measured the changes in electrical resistance in both the longitudinal ( L ) and transverse ( T ) directions. Figure 2 b shows the relative resistance change (Δ R ) in longitudinal-direction ( RRC L ) under 10% tension strain, calculated by the relation RRC L = Δ R L / R 0L , where Δ R L denotes the axial-directional resistance change and R 0L denotes the axial-directional resistance at the initial state. The sen-sitivity of the sensors increased considerably as the Poisson’s ratio decreased. For example, the AFS with a negative Poisson’s ratio of –0.5 ( ν = –0.5) showed an increase of the piezoresis-tive sensitivity by 300% compared with the conventional foam sensor (CFS) with a positive Poisson’s ratio of 0.4 ( ν = 0.4). Analyses were also performed for the relative resistance change in the transverse-direction ( RRC T ). As expected, the sign of RRC T (positive or negative) differed between AFS (with nega-tive ν ) and CFS (with positive ν ). By calculating the negative ratio of lateral relative resistance change to axial relative resist-ance change (− RRC T / RRC L ), we were able to estimate the value of ν for each sample. Figure 2 c shows the plotted results, which were in excellent agreement with the values obtained by image analysis (see Figure S3, Supporting Information).

To further investigate the effects of ν on sensing perfor-mance, we plotted the relative resistance change in axial direction against the applied strain for both CFS and AFS (Figure 2 d). Unless otherwise noted, the discussions below are for AFS with a ν of –0.5. The behavior of the CFS can be adequately described by a linear response ( R 2 = 0.98) under the entire strain range with a constant gauge factor (GF) of 0.49. By comparison, the AFS showed distinct behaviors in three strain regimes (one in compression and two in tension), and exhibited a signifi cantly better sensing response over a broad range of strains. The compressive GF was 1.45, almost three times (300%) that of the GF for CFS. The performance was even better for tensile GF (2.63), which was more than fi ve times (500%) greater, albeit within a moderate strain of 30%. The sensing performance went through an abrupt change at the tensile strain of ≈30%, beyond which the GF of the AFS decreased to ≈0.464, comparable to that of CFS.

The signifi cantly higher piezoresistive sensitivity of the AFS can be understood from the standpoint of enhanced strain sen-sitivity of the tunneling-effect caused by the unique deforma-tion characteristics of auxetic foams in the 3D space. Previous studies have shown that the tunneling effect has a dominant role in the piezoresistive response of various CNT-enabled sen-sors. [ 27,48 ] When the sensor is under tension (compression), its resistance would increase (decrease) due to the enlarged (reduced) separation and the correspondingly increased (decreased) tunneling resistance between the neighboring CNTs. In AFS, the same type (or mode) of deformation always

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occurred in all three dimensions (both the applied stress direc-tion and the transverse direction). This coherent deformation leads to superimposed and amplifi ed increase (decrease) of the tunneling resistance under tension (compression). In contrast, for CFS with a positive Poisson’s ratio, the mode of deforma-tion of the transverse direction is always the opposite of that of the imposed stress direction. Consequently, when the tunnel resistance increases (decreases) under tension (compression) in the applied stress direction, it decreases (increase) in the transverse direction. This destructive effect diminishes the

overall change of tunneling resistance and results in inferior piezoresistive sensitivity. The insets in Figure 2 d schematically illustrate the different behavior between AFS and CFS. The mechanism is also supported by the experimentally measured change of resistance (under tension) in the longitudinal and transverse directions for AFS and CFS as shown in Figure 2 b. For AFS the resistances in both directions increased, whereas for CFS the resistance in the transverse direction decreased along with the increase of the resistance in the stress direction. The different sensitivity of the AFS in compression and tension

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Figure 1. Design concept, preparation, and microstructures of the CNT-coated auxetic foams. a) Schematic illustration of the structure conversion from conventional foams to auxetic foams. b) The digital photographs and corresponding SEM images of auxetic foam before (left) and after (right) stretching force were applied in the transverse direction (40% of strain). For the digital photographs (top), a ruler was placed in the background to help visualizing the foam dimension change in the longitudinal direction. c) Schematic illustration of the fabrication procedure of the CNT-coated foams as piezoresistive sensors. d) Atomic force microscopy image of dispersed CNTs and the representative height profi le across the nanotube. Representative scanning electron micrographs of CNT-coated auxetic foam ( ν = –0.5) at low e) and high f) magnifi cation (marked with a white rectangle in (e)), the inset shows an enlarged view of CNT network (marked with a red rectangle in (f)). g) Photograph of CNT-coated auxetic foams with different shapes and sizes.

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modes may be related to the difference in the microscopic deformation of the cellular structure under the same nominal strain, which depends on the initial re-entrant structure and the modes of deformation they may experience. [ 49,50 ] Under a large tensile strain the re-entrant structure may deteriorate (fl atten) and eventually disappear, and the morphology will resume to that of the conventional foam. This may be the reason that the GF of the AFS under large tensile strain approaches to that of CFS. Nevertheless, the AFS demonstrated superior sensing performance over broad range of strain under both tension and compression. Aside from the Poisson’s ratio discussed herein, slight difference in the cell morphology, e.g., pore size and overall porosity of the sensing foams, may also play a role in the sensing performance. Higher porosity and larger pore size would presumably result in larger deformation under the same stress. In addition, the size of pores can also infl u-ence the deformation of CNT pathways because CNT layers were coated on the surface of the foams. Further studies on these effects may be necessary.

To reassure the superior sensitivity, we did a series of static pressure sensing tests to validate the high sensitivity and relia-bility of AFS for capturing a wide range of pressures. As shown in Figure 2 e, a series of standard weights from 100 mg to 2 kg were individually placed on top of a cuboid-shaped AFS sample (length: 15 mm, width: 14.5 mm, height: 8.5 mm). Each time

a greater weight was added, the signal instantly jumped to a higher level (response time < 100 ms) and remained stable. As soon as the weight was removed the signal returned to the baseline. As a consequence, the amplitude of the sensing signal consistently registered with the level of the pressure applied on the sensor. Moreover, the sensed pressure covered an extremely wide range (more than four orders of magnitude) from subtle-pressure regime (1 Pa–1 kPa), low-pressure regime (1–10 kPa), medium-pressure regime (10–100 kPa) to high-pressure regime (>100 kPa). Such a wide range of sensing capabilities made the auxetic foam sensors excellent for applications such as struc-ture health monitoring of aircraft and automobile structures, which usually undergoes a large range of load spectrums during service.

2.3. Multimodal Sensing Capability of AFS

This section reports on the multimodal sensing capabilities of the AFS, including tension, compression, and shear/torsion sensing, which are enabled by its fl exible and stretchable nature and the unique auxetic characteristics. We fi rst performed cou-pled electrical-cyclic tension/compression tests to evaluate the piezoresistive response of the AFS when they were subjected to a wide range of mechanical strains. As representative examples,

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Figure 2. a) Left panel: Schematic of the measuring technique. Right panel: Schematic of the foam sensor in its original state. b) The effect of Poisson’s ratio on the resistive pressure response of foams over both transverse and longitudinal directions under 10% tensile strain. The dash lines are meant to guide the eye. Inset: SEM images taken for foam samples with various Poisson’s ratio (–0.5, 0, 0.4, from left to right, respectively). c) The negative ratio of relative resistance changes in transverse direction and longitudinal direction (– RRC T / RRC L ) versus the measured Poisson’s ratio. d) Variation of relative resistance change with respect to both tensile and compressive strain for conventional foam sensor ( ν = 0.4) and auxetic foam sensor ν = –0.5). The four straight lines correspond to the plotted data fi tted by linear equation. Slopes of the fi tted lines are shown ( R 2 > 0.98). e) Static pres-sure sensing test. The inset photograph shows that a 100 g weight is placed on an auxetic foam sensor.

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Figure 3 a,b, respectively, show the resistance responses when the sensors were deformed by different levels of tensile or com-pressive strains. For all sensors, the resistance change was in phase with the cyclic deformation stimulations –, i.e., when the strain increased/decreased, the sensor resistance accordingly increased/decreased. We then performed dynamic shear tests to examine the resistance response of the AFS under various dynamic shear loading. Time sweep measurements at 0.16 Hz frequency confi rmed the stability of the output signal under various shear strains (Figure 3 c). The strain sweep at 0.16 Hz frequency demonstrated a clear dependence of sensing perfor-mance of the AFS on shear strain from 1% to 70% (Figure 3 d). Also, the resistance response of AFS was tested under various frequencies ranges from 0.02 to 3 Hz under 30% shear strain

(Figure 3 e). The output signal remained approximately con-stant during the frequency sweep, indicating a wide dynamic sensing range of AFS.

To investigate the effects of environment on the sensor per-formance, the measurements of resistance under cyclic com-pression loading were conducted in various environments (air, water, air, as shown in Figure 3 f). The sample was tested in air and then 20 °C de-ionized water was fi lled in the test chamber. Interestingly, the sensitivity in water was found to be approxi-mately twofold higher than that in air. This observation can be understood by considering how the adsorbed water moves with strain. Initially, adsorbed water in the AFS acts as spacer that keeps the adjacent cell walls apart. When the AFS is com-pressed, the adsorbed water is squeezed out, resulting in a

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Figure 3. Multimodal sensing performance of auxetic foam sensors. a) The resistance response of the AFS to tensile strain. b) The resistance response of the AFS to compressive strain. c) The resistance response of the AFS during time sweep test at 0.16 Hz frequency when deformed by different levels of shear strain (see also Video S3, Supporting Information). d) The resistance response of the AFS during shear strain sweep test at 0.16 Hz frequency. e) The resistance response of the AFS during shear frequency sweep test between 0.02 and 3 Hz under 30% strain. f) The resistance response of the AFS to cyclic compression loading under various environment conditions (following a sequence: air, water, air). g) The resistance response of the AFS to ultrasound acoustic wave in artifi cial seawater (an aqueous 3.5 wt% sodium chloride solution). h) The underwater durability test during tube sonication in an ice bath on pulse model (10 s on/10 s off) for up to 7000 s. The upper inset shows a detailed of view of sample set-up. The lower inset shows the zoomed in performance over 12 cycles. i) The durability of the AFS by comparing the resistance response for the fi rst 20 cycles and last 50 cycles is a 10 000-cycle test.

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massive increase in the contact area and a larger decrease in resistance. After removing the water, the sensor recovered to its original sensitivity. The performance of the AFS was also exam-ined in saline water (an aqueous solution with 3.5 wt% sodium chloride). Figure 3 g shows the measured resistance response of the AFS to a pulsed-ultrasound acoustic wave (10 s on/10 s off) generated at different powers. These plots showed a very good signal-to-noise (S/N) ratio in contrast to that in water (see inset of Figure 3 h).

In addition to the multimodal and wide range of sensing capability, high stability, and environmental responsiveness, durability of the sensor is another key parameter for assessing the sensor quality. We performed durability tests by applying a 10 000 cycle compression test with the maximum loading pres-sure of 2 kPa (Figure 3 i). The cyclic frequency was 0.07 Hz. The difference was indiscernible in the real-time resistance response from the fi rst 20 cycle and the last 50 cycles. The sensor maintained its initial performance property after 10 000 cycle test.

Because of its multimodal capability, stretchability, water repellence, lightweight, and high sensitivity, AFS could be well suited for wearable applications. This section reports on the potential applications of AFS through a series of demon-strations to illustrate potential areas on the body where the AFS can be worn. Figure 4 a illustrates our effort to develop a smart helmet with intrinsic sensing capabilities, by replacing the foam pads in the current helmet design with auxetic sensing foams to capture the impact event. Such sensing foam pads are capable of multizone, multipoint measure-ments for typical impacts occurring to different parts of the head (front, back, top, and sides, inset in Figure 4 a, left inset), detecting their precise location, magnitude, duration, and fre-quency. The right inset in Figure 4 a shows the experimental setup for the testing of the foam sensing performance (inset in Figure 4 a, right). An impact tester was used to repeatedly strike the top of the helmet at increasingly higher forces at a frequency of 0.5 Hz. As Figure 4 a shows, the foam sen-sors performed well by dependably detecting the timing, fre-quency, and magnitude of the impact event and outputting signals in sharp spikes corresponding to the impact events. Such a system would be invaluable in detection of harmful impacts for prevention of injuries and indicating when timely treatment is required to prevent chronical, cumulative brain damage. Moreover, compared with existing foam pads, the auxetic sensing foam has signifi cantly better energy absorbing capabilities to provide substantially better protection to the players from both direct impacts and rotational blows (Sup-porting Information, Figure S4). Such a two-pronged solution is superior to any other existing solution to address this issue in terms of accuracy, versatility, simplicity, cost, and ease of implementation and use.

The auxetic foam sensors were also demonstrated in wear-able biosignal-measuring devices. As shown in Figure 4 b, a foam sensor was attached onto a person’s neck to monitor the muscle movement during speech. When the simple words “go” were repeated, signals were produced which timing and pattern corresponded well with the vocal events. As a further example, the AFS was successfully used to monitor the wrist pulse (Figure 4 c). A typical pulse waveform was detected and

the pulse frequency of 76 beats min –1 was obtained. The AFS can be used for many additional body-monitoring applications, such as monitoring the rehabilitation progress of a patient, wound healing, respiratory condition, and heart rate detec-tion. It can also be used for monitoring the muscle, breath, and fatigue condition of an athlete during training to reduce inju-ries and boost performance.

These foam sensors can potentially be used in the fi eld of human–machine interfaces. For example, attaching the AFS directly to the fi ngertip can serve as a means to transfer the human intentions of pressing buttons and switches (Figure 4 d). Figure 4 e demonstrates that the AFS is wearable on the fi nger joint as a gesture control interface for human–machine inter-action applications. The signal of the foam sensor dependably registered the fi nger motion to recognize different gestures. The gestures can be converted to different commands to con-trol various electronic devices or robots. For example, a user wearing the sensor can make phone calls, write emails, play games, and adjust music volume using only a fi nger or body movement. [ 49,50 ] For mechanical engineers, this invention has a potential for remotely controlling robots working in harsh and dangerous situations, such as bomb disposal and deep sea exploration.

Finally, to demonstrate its ability in measuring the pressure distribution, we fabricated a 25 × 25 sensor array over a total area of 30 × 30 cm 2 . Figure 4 f,g shows the schematic and a pho-tograph of the sensor matrix, respectively. Figure 4 h illustrates the sensing system and a simplifi ed electrical schematic that scan the intersecting points of the sensor’s rows and columns and measure the resistance at each crossing point. The experi-mental results reported here illustrate the application of the AFS matrix in plantar pressure distribution analysis, which is an essential evaluation tool widely used in many fi elds ranging from sports performance and injury prevention to prosthetics and orthotics design. As shown in Figure 4 j–n, the colored con-tour maps clearly display the various barefoot pressure distribu-tion applied by a human right foot (Figure 4 o) at fi ve various gait phases (neutral position, pronation, supination, plantar-fl exion, and dorsifl exion). By additional shaping, this AFS matrix can also be inserted into shoes for in-shoe plantar pres-sure measurement. We anticipate that the presented technical platform may fi nd a wide range of application in measuring body pressure distribution, adjusting sitting posture, or moni-toring muscle movements.

3. Conclusion

In summary, we herein demonstrated a new class of auxetic foams-based piezoresistive sensors and their potential applica-tions. The results show that the negative Poisson ratio of the substrate led to signifi cant improvement of the piezoresistive sensitivity and gauge factor of the sensor. This is the result of the coherent deformation in all three dimensions resulting from the re-entrant cellular structure of the auxetic foams, which in turn resulted in the amplifi cation of the change of pie-zoresistive properties of CNT conductive network coated on the auxetic foam cell surface. The AFS possesses multimodal and wide range of sensing capabilities.

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Figure 4. Potential applications of CNT-coated auxetic foam sensors in various daily life situations. a) The application of the AFS in a helmet for measuring impact pressure in real time (see also Video S4, Supporting Information). The measured sensor performances under different forces in a span of ≈120 s. The left inset shows a simple prototype helmet used for preliminary testing. The sensing foams are attached to the inner side of the helmet. In this particular prototype impact forces at fi ve locations (gold colored spots, front, back, left, and right side, and top) can be measured. The right inset shows the experimental setup for the testing of foam sensor performance. An impact simulator is used repeatedly hitting the top of the helmet with increasingly higher forces. b) Real-time signal pattern of resistance change ratio as a function of time for monitoring the muscle movement during speech. The inset shows the sensor directly attached to a tester’s neck. c) Measurement of the physical force of a heartbeat under normal (76 beats min –1 ). The inset photograph showing the skin-attachable sensor directly above the artery of the wrist. d) The signal of the foam sensor when monitoring the fi nger motion to recognize different gestures (see also Video S5, Supporting Information). The smart foam is wearable on human body as a gesture control interface for man–machine interaction applications. e) Example of the fi nger touch with pressure. f) Schematic diagram of sensor array (25 × 25). g) Magnifi ed view of the sensor array corresponding to a region highlighted with the red dash box in (f). h) Optical photograph of a fabricated sensor array containing 25 × 25 pixels with a size of 30 × 30 cm 2 . i) Circuit Schematic of the sensor matrix. j–n) Measured right foot pressure pattern at different gait phases: j) normal standing, k) shifting weight to the inside of the foot, l) shifting weight to the outside of the foot, m) lifting heel off from ground, n) shifting weight onto the heel. The insets show the schematic of different gait phases: neutral position (back view, in (j)) pronation (back view, in (k)), supination (back view, in (l)), plantarfl exion (side view, in (m)), and dorsifl exion (side view, in (n)), respectively. Here, small pressure is shown in blue and larger pressure is shown in red. o) Photograph showing that the static pressure is applied to the AFS matrix using human right foot.

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Compared with conventional sensors, the auxetic behavior of the AFS, i.e., expansion in the transverse direction when stretched, provides a unique advantage and is particularly ben-efi cial in stretchable sensors and devices. In addition, due to the negative Poisson ratio, when bent, the auxetic foam form doubly curved or domed shapes due to their synclastic curva-ture properties, as shown in Figure S5 (Supporting Informa-tion). This unique shape conforming capability, which is not possible in any other materials, is particularly advantageous and benefi cial in wide application in wearable sensing equip-ment, considering the complexity of the human body contours, which often include various double curvature surfaces (e.g., head and shoulder). Also, such equipment can more comfort-ably fi t the shape change of a body’s fl exible zones (e.g., elbow and knee) to satisfy the dynamic needs of humans and provide a more accurate means for motion monitoring. Moreover, the combination of protecting and sensing function in such sensor foams should fi nd important applications in the smart protec-tive equipment, such as helmet, bulletproof vests, or kneepads.

We also successfully demonstrated potential underwater applications of the auxetic foam sensors. Excellent sensitivity of auxetic foam sensors were presented in both deionized water and salt water. Considering its open-cell structure, which could permit a pressure equilibration to the external pressure refer-ence, such sensors can theoretically be operated at an arbitrary water depth.

Furthermore, from the classic mechanics point of view, the elastic properties of isotropic materials are defi ned by the quartet of elastic constants: Young’s modulus ( E ), shear mod-ulus ( G ), and bulk modulus ( K ), and the Poisson ratio ( ν ). The three moduli are the measures of stiffness, rigidity, and com-pressibility of a material. They are related through Poisson’ ratio via the following equations

ν

=+2(1 )

GE

(1)

ν

=−3(1 2 )

KE

(2)

Therefore by gaining the capability to tune the Poisson’s ratio, it is possible to further expand the range of mechanical charac-teristics that can be realized in the substrates. This may offer opportunity to the development of new fl exible and stretchable sensors with unique electromechanical performance that is not possible today.

4. Experimental Section Preparation and Characterization of Aqueous Dispersion of MWCNT :

Typically, 200 mg MWCNT (General Nano LLC.) was suspended in 200 mL of deionized water with 5 mL of nonionic surfactant triton X-100 (Sigma-Aldrich). Then the suspension was sonicated in an ice bath using a Misonix 3000 (45 W, 20 KHz) on pulse model (10 s on/10 s off) for up to 30 min. The length and diameter of dispersed CNTs in the resulting dispersion were characterized (the dispersed CNTs are 5 nm in diameter and 2 µm in length) with the ultracentrifuge method with the Optima MAX-XP ultracentrifuge (TLA-100.3, 30 o fi xed angle rotor,

13 000 g-force, Beckman Coulter Inc.) and Delsa Nano C particle Size Analyzer (Beckman Coulter Inc.). AFM observation was performed using a NanoScope MultiMode AFM (Veeco Instruments Inc.) operating in tapping mode for directly examining the size of dispensed CNT. The AFM samples were prepared by spin coating cleaned Si wafers with 25 µL CNT dispersion at 1000 rpm using a spin coater (Spin Coat G3P, Specialty Coating Systems, Inc.).

Preparation of CNT Foam Sensors and Structure Characterization : Auxetic foams were prepared from commercial open-cell, fl exible PU foams using our recently developed CO 2 -assisted method. [ 46 ] CNT-coated foams were achieved by a simple dipping-drying process. Foams were fi rst dipped into the CNT dispersion for 30 min, removed, and dried in vacuum at 70 °C. Then, the resulting foam was immersed in deionized water for 2 h to remove the residual Triton X-100 molecules. Finally, the CNT-coated foam was dried in vacuum at 70 °C overnight.

The large size auxetic foam sheet (30 cm × 30 cm × 0.7 cm) was prepared via vacuum-bagging method. For the CNT coating of the large size auxetic foam sheet, the above-described dipping-drying approach works very well and no additional process steps was required.

Morphologies of the CNT-coated foams were examined by scanning electron microscopy (JEOL 7401F). The Raman spectra were collected on a Raman microscope (inVia microscope, Renishaw) using 785 nm excitation at a laser power of 0.5 mW with a 50× objective lens. To measure the mass uptake of CNT, TGA were tested on TA 100 by heating from 30 to 900 °C in nitrogen at 10 °C min –1 (Supporting fi gure). In the present investigation, the CNT coating weight was constant at ≈1%.

Sensing Performance Evaluation of Smart Auxetic Foam : The real-time electrical properties of the sensor under various mechanical deformation were measured by a two-point probe method using a Keithley 2401 SourceMeter controlled by a custom LabVIEW program. Two thin copper-wires were attached to the two end-sides of CNT-coated foam sensors with silver paste to connect the sensor to the electrometer. After testing samples were inspected to ensure no sliding of the wire or cracking of the paste occurred during the test. The stretching and compression tests were performed using Shimadzu AGS-J micro test frame with a 500N load cell. The shear tests were carried out on an ARES-LS3 rheometer with 25 mm parallel plate fi xture (TA instruments).

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements Y.L. and S.L. contributed equally to this work.

Received: November 25, 2015 Revised: December 26, 2015

Published online: February 19, 2016

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