Hierarchically buckled sheath-core fibers for superelastic electronics, sensors, and muscles

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Science  24 Jul 2015:
Vol. 349, Issue 6246, pp. 400-404
DOI: 10.1126/science.aaa7952

Composite stretchable conducting wires

Think how useful a stretchable electronic “skin” could be. For example you could place it over an aircraft fuselage or a body to create a network of sensors, processors, energy stores, or artificial muscles. But it is difficult to make electronic interconnects and strain sensors that can stretch over such surfaces. Liu et al. created superelastic conducting fibers by depositing carbon nanotube sheets onto a prestretched rubber core (see the Perspective by Ghosh). The nanotubes buckled on relaxation of the core, but continued to coat it fully and could stretch enormously, with relatively little change in resistance.

Science, this issue p. 400; see also p. 382


Superelastic conducting fibers with improved properties and functionalities are needed for diverse applications. Here we report the fabrication of highly stretchable (up to 1320%) sheath-core conducting fibers created by wrapping carbon nanotube sheets oriented in the fiber direction on stretched rubber fiber cores. The resulting structure exhibited distinct short- and long-period sheath buckling that occurred reversibly out of phase in the axial and belt directions, enabling a resistance change of less than 5% for a 1000% stretch. By including other rubber and carbon nanotube sheath layers, we demonstrated strain sensors generating an 860% capacitance change and electrically powered torsional muscles operating reversibly by a coupled tension-to-torsion actuation mechanism. Using theory, we quantitatively explain the complementary effects of an increase in muscle length and a large positive Poisson’s ratio on torsional actuation and electronic properties.

Highly elastic electrical conductors are needed for stretchable electronic circuits, pacemaker leads, light-emitting displays, batteries, supercapacitors, and strain sensors (1). For such purposes, conducting elastomers have been fabricated by incorporating conducting particles in rubber (25) or by attaching sheets of conducting nanofibers (69), graphene sheets (10, 11), or coiled or serpentine conductors to a rubber sheet or fiber (1217). Although reversible strains exceeding 500% have been demonstrated, the quality factor (Q, the percent strain divided by the percent resistance change) has been below three for such large strains (1720). Elastomeric conductors with very low quality factors are useful as strain sensors, but the other applications noted above would benefit from the realization of very high quality factors. The availability of conducting fibers that can be stretched to great extents without significantly changing conductivity could enable the deployment of superelastic fibers as artificial muscles, electronic interconnects, supercapacitors, or light-emitting elements.

We replaced the frequently used laminate of a carbon nanotube (CNT) sheet wrapped on a stretched rubber sheet with a multilayer CNT sheath wrapped on a rubber fiber core (21, 22). We enabled additional functions by including other rubber and CNT sheath layers. The conducting sheaths were derived from highly oriented multiwalled CNT aerogel sheets, which were drawn from CNT forests (21). Three basic configurations were deployed: NTSm@fiber, rubber@NTSm@fiber, and NTSn@rubber@NTSm@fiber. NTSm@fiber denotes m carbon nanotube sheet (NTS) layers deposited on top of a rubber fiber core, rubber@NTSm@fiber is a rubber-coated NTSm@fiber, and NTSn@rubber@NTSm@fiber indicates an NTSn sheath (where n is the number of NTS layers) on a rubber@NTSm@fiber core.

The rubber fiber core was highly stretched (typically to 1400% strain) during the wrapping of NTS layers, and the CNT orientation was parallel to the rubber fiber direction (Fig. 1A). For the preparation of rubber@NTSm@fibers, the outermost rubber coating was applied while the rubber core was fully stretched, whereas for the preparation of NTSn@rubber@NTSm@fibers, the thicker rubber layer used as a dielectric was deposited on an NTSm@fiber that was not stretched (22). The parallel orientations of CNT fibers and the rubber core, the substantial strain applied during sheath wrapping, and the use of a large m resulted in the observed hierarchical two-dimensional buckling and corresponding high performance. The rubber core and rubber layers separating nanotube sheets were a styrene-(ethylene-butylene)-styrene (SEBS) copolymer containing a plasticizer (Marcol 82, Exxon Mobil) (22). The diameter of the nonstrained rubber fiber was typically 2 mm, which decreased to 0.52 mm at 1400% strain (22).

Fig. 1 Two-dimensional, hierarchically buckled sheath-core fibers.

(A) Steps in the fabrication of an NTSm@fiber. The circular arrow indicates the belt direction. (B) Illustration of the structure of a longitudinal section of an NTSm sheath, showing two-dimensional hierarchical buckling. The fiber direction is horizontal. The yellow color in (A) and (B) represents SEBS rubber; the gray shells are NTS layers. (C and D) Low- and high-resolution SEM images showing long- and short-period buckles for an NTS180@fiber at 100% applied strain. The fiber direction, which is the direction of the applied strain, is horizontal and the belt direction is vertical. The fabrication strain was 1400%.

Because the rubber fiber core must increase in diameter (and circumference) as it relaxes from the maximum fiber stretch, we observed that the realizable elastic deformation range decreased with increasing m for the NTSm@fibers. Even though the CNT sheets were highly anisotropic, with a lower modulus in the belt direction of the CNT sheath, this low modulus and the bending modulus of the nanofibers were sufficient to limit the elastic range for the sheath-core fiber when m was large. The elastic range dramatically decreased when the nanotube orientation had a nonzero bias angle with respect to the fiber axis (fig. S4B).

We observed periodic hierarchical buckling in two dimensions for NTSm@fibers when m was larger than 10 and the fabrication strain, εfab (i.e., the strain applied to the rubber fiber core during the wrapping of CNT sheaths), was large (typically 1400%). The scanning electron microscope (SEM) images (Fig. 1, C and D) show an elongation (100%) for which short and long buckling periods were simultaneously observed in the fiber axial direction (at ~8 and ~35 μm, respectively) and the fiber belt direction (at ~8.5 and ~51 μm, respectively). Unless otherwise indicated (for instance, with the term “fabrication strain”), mentioned strains are associated with the relaxed state of the sheath-core structure, rather than with the relaxed state of the sheath-free core. Also, characterizations of structure and properties refer to conducting elastomer fibers that have been conditioned by applying about five stretch-release cycles to the maximum strain that does not plastically stretch the NTSs in the sheet alignment direction. This conditioning was needed because the two-dimensionally buckled structure appeared during the first cycle and thereafter evolved slightly over the next few cycles, as indicated by a permanent increase of about 10% or less in the resistance of the strain-released state.

The reversible buckling in the fiber axial and belt directions was out of phase, as illustrated by the SEM images of an NTS92@fiber (fig. S12), which can be reversibly elongated by 1000%. Long-period buckling along the fiber axis was seen at 0% strain (where short-period axial buckles exist but are squeezed together); at 200% strain, the axial short-period buckles were pulled apart. The long-period axial buckles disappeared at 400% strain and the short-period axial buckles disappeared near 1000% strain. There was no buckling in the belt direction at 0% strain, and long-period buckling in the belt direction appeared between 200 and 400% strain, becoming more pronounced at higher strains. During strain release (from 1000% strain), these out-of-phase buckling processes in the axial and belt directions reversed without noticeable hysteresis.

Although the emergence of these different types of buckling and their corresponding periods for NTSm@fibers depended on m and the fabrication strain, the out-of-phase behavior for axial and belt buckling and the order in which short- and long-period axial buckling occurred were general phenomena for our sheath-core elastomeric fibers. As the fabrication strain or m decreased, the long-period buckling in the axial and belt directions disappeared, and subsequently all out-of-plane buckling disappeared (figs. S9 and S13). For about five NTS layers and a 1200% fabrication strain, only short-period axial buckles were observed. Long-period axial buckling appeared when m and the fabrication strain were large. Using a single sheet layer for the sheath resulted in only in-plane buckling for fabrication strains up to the maximum investigated, 1400% (fig. S8).

The explanation for this out-of-phase behavior in the axial and belt directions lies in the out-of-phase relationship between rubber fiber elongations in these directions, which resulted from the large positive Poisson’s ratio of the rubber. Consequently, the relaxation of tensile strain from the fabrication strain quasi-plastically elongated the CNT sheath in the belt direction during the first contraction, causing periodic necking (Fig. 1D). Subsequent stretching of the rubber fiber caused the elongated sheath to buckle in the belt direction at the necking locations. During subsequent stretch-release cycles, this dependence of structure on strain was reversibly retained.

The dependence of R(ε)/Lmax on tensile strain (ε) for sheath-core NTSm@fibers is shown in Fig. 2A, where R(ε) is the resistance of a fiber with a maximum stretched length (Lmax) of Lfab, and Lfab is the stretched length (corresponding to the fabrication strain) used for sheath wrapping. Reflecting the constraint on fiber belt expansion provided by the NTSm sheath during fiber contraction, the length of the unloaded sheath-core fiber (Lmin) was longer than the starting sheath-free rubber fiber. Hence, the available strain range (εmax) was smaller than the fabrication strain and decreased with increasing m (Fig. 2B, inset).

Fig. 2 The strain dependence of electrical properties for sheath-core fibers.

(A) Measured data points and predicted curves for the dependence of resistance on strain for NTSm@fibers (black circles), rubber@NTS50@fibers (red diamonds), and seven-ply rubber@NTS90@fibers (red squares). σC and σD are conductivities in the axial direction and in the inter-buckle contact region, respectively. (B) Resistance change versus strain for NTSm@fibers under increasing strain (open circles) and decreasing strain (solid circles). The inset shows the dependence of the available strain range and the maximum percent resistance change on m. (C) Comparison of Q and the maximum reversible tensile strain for the sheath-core fibers in our study and previous elastomeric conductors with a strain range ≥200%. Red squares (open for rubber@NTSm@fibers, solid for NTSm@fibers) represent our results; blue symbols represent results previously published in the literature, which are described in the table on the right. The arrow indicates the direction of property changes (improvements) compared with previous results.

The strain dependence of [R(ε) − R0]/R0, where R0 is R(0), is shown in Fig. 2B. Although applying an m of 1 resulted in reversible performance up to a very high strain (1320%), the maximum percent resistance change over this strain range, ΔRmax/R0 = [Rmax) − R0]/R0, decreased with increasing m (from 53% for m = 1 to 18% for m = 200) (Fig. 2B, inset). The corresponding values of R0/Lmax decreased monotonically from 2.1 kiloohm/cm for m = 1 to 26.1 ohm/cm for m = 200.

The increased ΔRmax/R0 for low m values is explained by the effect of sheath thickness on the period of axial short-period buckling. For low m values, the period of short-range buckling decreased with decreasing strain until adjacent buckles came into contact laterally. This contact provided a new transport path for the electric current, which was orthogonal to the local CNT orientation (which largely followed the buckles). Hence, when m was low, this pathway resulted in decreased fiber resistance relative to higher strain states where buckles were not in contact. To validate this hypothesis, a resistor network model was developed that agreed with the measured data (Fig. 2A), despite the limited experimental information on structural evolution during buckle contact (22). Correlation of transport data and SEM images as a function of strain (figs. S3A and S12) indicates that the strain below which R(ε) deviates from Rfab) corresponds to the strain at which buckles come into contact.

The measured increase in conductance caused by buckles coming into contact, which occurred abruptly at small strains, was appreciable (37% for the sheath-core fiber with m = 19, which contracted by 1200%). Despite the fact that the ratio of sheet conductivity in the nanotube direction to that in the orthogonal direction is about 10 to 20 for densified as-drawn sheets and 50 to 70 for nondensified sheets (21), this sizeable effect arose because the contacting area of buckle sidewalls was large compared with the cross-sectional area of the conducting pathway before the buckles came into contact. The conductivity ratios derived theoretically from R(ε) for the sheath-core fibers (29 for m = 19 to 58 for m = 200) are consistent with the electrical anisotropy of the CNT sheets (22).

To avoid resistance changes resulting from buckle contact at low strains, we overcoated a fully stretched NTSm@fiber conductor with a layer of SEBS ∼6 μm thick, thereby reducing the resistance change to 4.5% for the application of 1000% strain to a rubber@NTS50@fiber (Fig. 2A). For comparison, an NTS50@fiber provided a 28% change in resistance over the same strain range.

The elastic range for reversible performance of a straight conducting fiber that we have demonstrated is much higher than previously realized for noncoiled elastomeric conducting fibers and continuous conducting coatings on elastomeric sheets and fibers (Fig. 2C). The Q that we demonstrated for a noncoiled sheath-core fiber was 75 times the value previously obtained for any of the above types of elastomeric conductors with a strain range above 450%. For NTSm@fiber conductors (Fig. 2C), Q monotonically increased from 25 to 50 as the number of NTS layers increased from 1 to 100; Q then remained essentially constant for up to 200 NTS layers. Adding a thin outer layer of rubber to an NTS100@fiber to prohibit inter-buckle electrical contact during contraction increased Q from 50 to 421 (corresponding to a 2.15% resistance change for a 905% elongation).

We can further increase the strain range of nearly strain-invariant electrical conductance by coiling a nonstretched rubber@NTSm@fiber on a rigid mandrel of similar diameter. The resistance of a coiled rubber@NTS19@fiber reversibly changed by only 5.01% when stretched up to 3000% strain, providing a Q of 598 (Fig. 3A). In this experiment, the mandrel (which was 1/29th the length of the stretched elastomeric conductor) was retained inside the coiled rubber@NTSm@fiber to prevent the conducting fiber from relaxing to an inner coil diameter smaller than that of the mandrel fiber. Without this constraint, the strain range and Q value (2470% and 526, respectively) slightly decreased, but highly reversible behavior was still realized (Fig. 3A and fig. S6D).

Fig. 3 Electromechanical response of coiled sheath-core fibers.

(A) Resistance change versus strain for coiled rubber@NTS19@fibers made by mandrel-free coiling (black circles) and by coiling a fiber on a rigid mandrel of similar diameter (red diamonds). (B) The strain dependence of capacitance and linear capacitance (per instantaneous length) of NTS4@rubber@NTS3@fibers. The upper inset shows the capacitance change during selected cycles to 950% strain. The lower inset illustrates the fiber’s structure and uses the symbol for a variable capacitor to indicate the fiber’s tunable capacitance. In (A) and (B), open and solid symbols indicate increasing and decreasing strains, respectively.

This near invariance of conductance during extreme elongations was complemented by highly reversible retention of nearly constant conductance over thousands of high strain cycles, extremely small changes in conductance during small radius coiling, and no degradation in conductance during fiber twisting, which is important for electrically driven torsional actuation. For example, the resistance change over a 500% strain range varied little during 2000 cycles for rubber@NTS15@fibers (from 0.22 to 0.36%) (fig. S6A). Similarly, completely coiling a 1.5-mm-diameter rubber@NTS200@fiber around a 0.5-mm-diameter mandrel decreased resistance by only 0.7% (fig. S6C). Finally, inserting 37 turns/cm of twist into a 1.7-mm-diameter rubber@NTS50@fiber at a constant load (37.1 kPa, normalized to the original diameter) caused a 0.76% decrease in resistance (fig. S6B), probably because of increased inter-nanotube electronic connectivity produced by twist-induced NTS densification. A tightly knotted rubber@NTS116@fiber underwent a <3% resistance change when elongated to 600% strain (fig. S3C). Additionally, the resistance of a 1.7-mm-diameter rubber@NTS92@fiber changed less than 2.8% when it was cyclically bent to a radius of 2 mm for 200,000 cycles (fig. S6E).

The large strain range (and the small dependence of fiber resistance on strain) of the NTSm@fiber encouraged our fabrication of the NTSn@rubber@NTSm@fiber for use as a fiber capacitor, tensile strain sensor, and artificial muscle that combines torsional and tensile actuation. Because the choice of small n and m values enabled especially large strain ranges where electronic properties were reversible, we used n = 10 and m = 20 for these studies unless otherwise indicated.

Relevant for its application as a capacitive strain sensor, a 950% stretch of an NTS4@rubber@NTS3@fiber provided a 860% increase in capacitance (C), and this capacitance change was largely nonhysteretic and reversible (Fig. 3B). This percent of capacitance change was substantially higher than that obtained for an elastomeric fiber dielectric capacitor [230% for a maximum 300% strain, using carbon black–elastomer composite as electrodes (23)] and for an electrochemical fiber supercapacitor [7.5% for a maximum strain of 400%, using NTS electrodes wrapped helically around a rubber core (17)].

Capacitance measurements for the stretched fiber provide a convenient means to determine strain, and our results show that both high linearity and high sensitivity can be obtained over an immense strain range (Fig. 3B). In agreement with the theoretical prediction that ΔC/C0 = ΔL/L0 (22), the data show that the change in capacitance is linearly proportional to the change in length and that the proportionality constant (0.91) is close to unity. This end-to-end capacitance could be used to control muscle stroke for artificial muscles.

Artificial muscles based on the electrostatic attraction between electrodes of dielectric rubber capacitors are well known and commercially exploited (2428). High-stroke torsional fiber muscles have been made by inserting twist into sheath-core NTSn@rubber@NTSm@fibers while maintaining a constant fiber length (22). The amount of inserted twist was far below the amount needed to provide coiling (22). The twisted fiber geometry in our fabrication provides torsional actuators with a torsional stroke per muscle length up to 104 times the value previously demonstrated for electrically driven, nonthermal, nonelectrochemical muscle fibers (29, 30). It avoids the Carnot efficiency limit of thermally powered artificial muscles and the use of liquids or vapors for electrochemically or absorption-powered muscles (3133).

The first actuator that we fabricated comprised a twist-inserted dielectric muscle that was mechanically in series with a nonactuating rubber fiber, which served as a torsional return spring (Fig. 4A, inset). Our theoretical analysis shows that to maximize torsional stroke, the torsional return spring should serve as a reservoir of twist at constant torque (22). Therefore, it should have low torsional stiffness, so that the inserted twist is large compared to the torsional stroke. This muscle operated isobarically (i.e., under a constant applied tensile load), such that it provided both tensile and torsional actuation. The applied load during isobaric actuation prohibited coiling. The maximum applied electric field was between 10.3 and 11.7 million volts (MV)/m.

Fig. 4 Maximum equilibrium muscle strokes and maximum rotation speeds obtained using a single voltage step for single-ply and two-ply NTS10@rubber@NTS20@fibers.

(A) Theoretical (dashed curves) and experimental data points showing the dependence of the rotation angle and tensile stroke on the electric field for an isobarically operated single-ply muscle, plied using 3.20 turns/cm of twist. The inset shows the relationship between the maximum rotation speed and the torsional stroke. (B) The dependence of the rotation angle, rotation speed, and tensile stroke on the inserted twist for the single-ply muscle in (A), operated isobarically at a field of 10.3 MV/m. (C) The dependence of the rotation angle and tensile stroke on the electric field for an isobarically operated two-ply muscle, plied using 3.47 turns/cm of twist. The inset shows the relationship between the maximum rotation speed and the torsional stroke. (D) The dependence of the rotation angle, rotation speed, and tensile stroke on the inserted twist for the two-ply muscle in (B), operated isobarically at a field of 11.7 MV/m. The fabrication strain for the single- and two-ply muscles was 900%. The applied stress was 15.6 kPa for the single-ply muscle and 10.0 kPa for the two-ply muscle.

One might expect that the torsional stroke for a noncoiled NTSn@rubber@NTSm@fiber would linearly increase with inserted twist. This is not the case because of the nonlinear elastic behavior of the rubber at high strains, which is apparent in the measured tensile stress-strain curve (fig. S5B) and the dependence of torsional stiffness on the stretch ratio (fig. S11). For an intermediate degree of twist insertion, the torsional stiffness of the rubber is low, which enables the torque of torsional actuation to act as an enhanced torsional stroke. Torsional stroke for isobaric actuation was maximized for a 0.9-mm-diameter NTS10@rubber@NTS20@fiber by inserting 3.20 turns/cm of twist (Fig. 4B).

The dependencies of maximum equilibrium rotation angle, rotation speed, and tensile stroke on the applied field and inserted twist for an isobarically operated NTS10@rubber@NTS20@fiber muscle are shown in Fig. 4, A and B. The torsional stroke reached a maximum value of 21.8°/cm for this 0.9-mm-diameter muscle. When applying a square-wave voltage pulse (fig. S14), tensile and torsional strokes simultaneously reached peak values for a 2-mm-diameter fiber of this type (4.1% and 7.8°/cm, respectively); they then simultaneously decayed to steady-state tensile and torsional strokes of 2.9% and 6.1°/cm, respectively (fig. S14).

Theory can be used to quantitatively explain these results for the low-twist region and to show that the drive mechanism for torsional actuation is fundamentally different from that for previously fabricated torsional muscles (22). For earlier electrochemically or thermally driven hybrid nanofiber muscles, the volume change of guest material in the twisted nanofiber yarns has driven both tensile and torsional actuation (32). On the other hand, tensile actuation of coiled, thermally driven polymer fiber muscles has been shown experimentally and theoretically to be driven by torsional rotation of the twisted fiber (31).

Similar to planar dielectric muscles, the electrostatic attraction between cylindrical capacitor electrodes in the twisted rubber muscle generates a stress that reduces the thickness of the rubber dielectric in the muscle (25). Because the rubber in the muscle core and surrounding capacitor has a Poisson’s ratio of ∼0.5, the muscle increases in length to conserve volume. The resulting reduced torsional stiffness of the actuating segment causes a transfer of twist to the actuating segment, such that the paddle rotates to maintain torque balance. Consequently, torsional actuation arises from two complementary effects on torsional stiffness: the increase in muscle length and the decrease of muscle diameter caused by the large positive Poisson’s ratio.

Using a neo-Hookean hyperelastic model shows that the coupling of tensile to torsional actuation is realized through an equivalent axial force, which effectively reduces the torsional stiffness of the muscle fiber and causes it to uptwist. Theory and experiment show that torsional actuation is quadratic with the electric field and linear with the initial inserted twist (22). Because the same torsional actuation energy is responsible for the maximum kinetic energy of the paddle, the maximum torsional stroke is proportional to maximum rotation speed, as we observed experimentally (Fig. 4A, inset). Theory accurately predicts the measured field dependence of torsional and tensile stroke (Fig. 4A). A more sophisticated nonlinear model (22), which considers the nonlinear stress-strain relationship of rubber, explains the observed plateau in torsional stroke when the inserted twist is high (Fig. 4B).

Other configurations were explored as alternatives to the isobaric single-ply torsional muscle described above. An isometric (constant length), single-ply, dual-segment torsional muscle provided a slightly smaller equilibrium torsional stroke than did the isobaric (constant load) configuration shown in Fig. 4, because tensile stroke (which drives torsional actuation) was partially absorbed by the contraction of the torsional return spring. Instead of inserting twist in a single-ply NTSn@rubber@NTSm@fiber, we made a torsional muscle by plying together (with 3.47 turns/cm of twist) two 0.9-mm-diameter, non-twisted NTS10@rubber@NTS20@fibers. When this two-ply muscle was operated isobarically in the muscle–return-spring configuration used for the single-ply muscles, an unusually large torsional stroke was observed (44.4°/cm) with a tensile stroke of 3.7% (Fig. 4, C and D). The torsional actuation of the two-ply muscle is shown in movie S1.

Similar to thermally driven torsional muscles, theory predicts that the product of muscle diameter and stroke is scale-invariant for dielectric torsional muscles (22). Hence, torsional stroke per muscle length for a given electric field can be dramatically increased (while the voltage is decreased) by proportionally decreasing core and sheath thicknesses, as long as the bias angle α is kept constant, where tanα = πDTw (D is the muscle diameter; Tw is the inserted twist in turns per muscle length). This inverse dependence of torsional stroke on muscle diameter must be considered when comparing the torsional strokes of muscles with different diameters. Electrothermally or electrochemically driven fiber-based muscles with smaller diameters provide much higher torsional strokes per muscle length (32, 34). Nevertheless, when this length-normalized torsional stroke is scaled by multiplying by the fiber diameter, the dielectric fiber torsional muscles that are advantageously liquid-free and unlimited in Carnot efficiency provide length- and diameter-corrected torsional strokes of 1.50° for single-ply muscles and 4.71° for the two-ply muscle. These values are comparable to those measured for the highest performing electrically driven torsional muscles [0.71° for electrothermally driven wax-filled CNT yarn muscles (32), 4.30° for electrothermally driven nylon muscles (31), and 2.16° for electrochemically driven CNT muscles (34)].

Various potential applications for the sheath-core conducting fibers are suggested by our results. The capacitance-based torsional actuation could be exploited for rotating optical elements, such as mirrors, in optical circuits. For applications in which increased electrical conductance or capacitance is needed (9, 15), we have shown that a fundamentally unlimited number of individual small-diameter NTSm@fibers or NTSn@rubber@NTSm@fibers can be plied together (using a small plying angle) or interconnected by infiltrated rubber (applied in the zero-stress state) without a loss of per-fiber performance (22). Additionally, we can increase the conductivity of an fiber stretched to 870% by a factor of 13 (realizing a conductivity of 360 S/m) by reducing the diameter of the rubber core from 2 mm to 150 μm while maintaining constant sheath thickness (fig. S15). The elastomeric fibers of our design might be deployable for such applications as pacemaker leads (movie S2) (35). Other possibilities include cables that are extendable up to 31 times their initial length without significant resistance change, which could be applied for morphing structures in space, robotic arms or exoskeletons capable of extreme reach, or interconnects for highly elastic electronic circuits.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S15

References (3843)

Movies S1 and S2


  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: We thank A. Ruhparwar, S. F. Cogan, and X. Li for discussions of pacemaker applications; X. Zhang, B. Lin, X. Zhou, Y. Hou, and F. Jia for sample preparations; H. Luo for mechanical properties characterizations; A. Needleman for discussions on periodic necking and buckling; T. Xu, L. Tong, H. Zhang, and Y. Du for discussions on modeling and measurement techniques; and D. Wang for drawings. Support in the United States was from Air Force Office of Scientific Research grants FA9550-12-1-0211, FA9550-15-1-0089, and FA9550-14-1-0227; Robert A. Welch Foundation grant AT-0029; U.S. Army grants W91CRB-14-C-0019 and W91CRB-13-C-0037; Department of Defense grant W81XWH-14-1-0228; NIH grant 1R01DC011585-01; NSF grants CMMI-1031829, CMMI-1120382, CMMI-1335204, and ECCS-1307997; Office of Naval Research Multidisciplinary University Research Initiative grant NOOD14-11-1-0691; and the Louis A. Beecherl Jr. Chair. Support in China was from the Priority Academic Program Development of Jiangsu Higher Education Institutions on Renewable Energy Materials Science and Engineering, Jiangsu Key Laboratory for Photovoltaic Engineering Science, Jiangsu Specially-Appointed Professor Program Sujiaoshi-2012-34, National Natural Science Foundation of China grant 31200637, Jiangsu Basic Research Program grant BK2012148, Science and Technology Support Program of Changzhou grants CC20140016 and CZ20140013, Chinese Ministry of Science and Technology grant 2013AA014201, and State Scholarship Fund grant 201406290125. Brazilian support was from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Scholarship 12264/13-0 and Fundação de Amparo à Pesquisa do Estado de São Paulo-Centros de Pesquisa, Inovação e Difusão grant 2013/08293-7. A provisional patent application has been filed.
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