Torsional Carbon Nanotube Artificial Muscles

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Science  28 Oct 2011:
Vol. 334, Issue 6055, pp. 494-497
DOI: 10.1126/science.1211220


Rotary motors of conventional design can be rather complex and are therefore difficult to miniaturize; previous carbon nanotube artificial muscles provide contraction and bending, but not rotation. We show that an electrolyte-filled twist-spun carbon nanotube yarn, much thinner than a human hair, functions as a torsional artificial muscle in a simple three-electrode electrochemical system, providing a reversible 15,000° rotation and 590 revolutions per minute. A hydrostatic actuation mechanism, as seen in muscular hydrostats in nature, explains the simultaneous occurrence of lengthwise contraction and torsional rotation during the yarn volume increase caused by electrochemical double-layer charge injection. The use of a torsional yarn muscle as a mixer for a fluidic chip is demonstrated.

Carbon nanotube artificial muscles using linear or bending modes and powered by electricity, fuels, light, or heat are well known (1). Carbon nanotube sheets operated electrochemically by double-layer charge injection typically provide ~0.2% stroke (i.e., percent elongation) and can generate stress 100 times that achievable by natural muscles, whereas electrostatically driven carbon nanotube aerogel muscles can generate more than 220% stroke (1). Torsional and rotational motors that use a single nanotube as the rotation axis have also been demonstrated (2). What is missing is an artificial muscle of any type that provides large torsional rotation per muscle length, especially at high rotation rates.

Our solution exploits strong, highly conducting yarns that are twist-spun from forests of multiwalled carbon nanotubes (MWCNTs) (38). Transmission and scanning electron microscopy (TEM and SEM) images indicate that these MWCNTs, which are drawn from forests ~400 μm high (3), have an outer diameter of ~12 nm, contain ~9 walls, and form large bundles. The nanotubes in the yarn provide an orientation angle α with respect to the yarn direction of approximatelyα=tan1(2πrT)(1)where r is the distance from yarn center and T is the inserted twist in turns per meter of yarn length.

Our torsional artificial muscles operate by electrochemical double-layer charge injection, as seen in carbon nanotube supercapacitors. Immersing a twisted MWCNT yarn and a counterelectrode in an electrolyte and applying a voltage between these electrodes causes the yarn to partially untwist (9). In our first experiments, a vertically suspended actuating yarn was fully immersed in the electrolyte [0.2 M tetrabutylammonium hexafluorophosphate (TBA.PF6) in acetonitrile] and supported a paddle at its lower end (Fig. 1A). This configuration had a problem: Reversible torsional actuation during an actuation cycle was approached only after many cycles, which progressively decreased torsional actuation (fig. S1).

Fig. 1

Illustration of electrochemical cell configurations used for characterizing torsional actuation or the combination of torsional and tensile actuation, where the Ag/Ag+ reference electrode, actuating MWCNT yarn electrode, and Pt mesh counterelectrode are shown from left to right. (A) A one-end-tethered yarn configuration in which a paddle, located at the yarn end, rotates in the electrolyte. (B) A two-end-tethered configuration for simultaneously measuring torsional and tensile actuation, in which the top yarn support is a force/distance transducer that maintains constant tensile force on the yarn and measures the axial length change as the paddle rotates in air (in other cases, the electrolyte level was raised to submerge the paddle). (C) A one-end-tethered configuration in which the paddle rotates in air.

To improve reversibility, we tethered the yarn at both ends to prohibit end rotation (Fig. 1B) and, in most cases, attached a paddle near yarn center; we used only one-half of the yarn as a torsional muscle (for example, by immersing only one-half of the yarn in the electrolyte). Although torsional actuation decreased, reversibility increased because the nonactuating length of the yarn functioned as a torsional spring to return the paddle to its starting angle (fig. S2). A two-end-tethered, uniformly actuated yarn cannot produce torsional rotation unless symmetry breaking arises to provide segments having oppositely directed twist. Also, torsional paddle rotation is maximized by locating the paddle at the junction between the actuating yarn and the torsional spring (figs. S3 and S4), which for our experiments is a nonactuated nanotube yarn.

Although only two electrodes were needed to produce torsional actuation, a reference electrode measuring the potential of the actuating yarn was used for controlling actuation. Potentials (V) are reported with respect to Ag/Ag+, for which 0 V corresponds approximately to the potential of zero charge for sheets of single-walled carbon nanotubes (10) as well as for the present MWCNT yarns. Actuation was measured under constant tensile load so that yarn length change could be measured simultaneously with torsional rotation.

A reversible paddle rotation of more than –41 full turns (–15,000°) was produced (Fig. 2A) by a MWCNT yarn pulsed from 0 V to +5.0 V at 0.1 Hz in an organic electrolyte (0.2 M TBA.PF6 in acetonitrile). The negative sign of rotation indicates that the actuated yarn untwists during charge injection. Because the measured yarn twist inserted during spinning was 20,000 turns/m, and 6 cm of the 12-cm total yarn length was in the electrolyte, the torsional actuation was only 3.4% of the twist inserted in the actuating yarn length. Nonetheless, the observed torsional rotation of 250° per millimeter of actuator length is more than 1000 times the values previously reported for materials that torsionally actuate. For example, hollow-rod torsional actuators based on shape-memory alloy, piezoelectric ceramics, and conducting polymers (with integrated helically wound wire) generated torsional rotations of 0.15°/mm (11), 0.008°/mm (12), and 0.01°/mm (13), respectively. Although the potential applied in this pulse experiment, +5 V, exceeds the stability limit of the electrolyte for continuous operation, our results (Fig. 2C) show that a similarly large, reversible torsional actuation (180°/mm) can be obtained at a potential of only –2 V. These experiments were performed by cyclically ramping the potential between −2 V and +2 V at a slow scan rate of 0.025 V/s.

Fig. 2

Actuation results for two-end-tethered MWCNT yarns. (A) Torsional rotation (black) and axial length actuation (blue) versus time for a MWCNT yarn (length = 120 mm, diameter d = 12 μm, α = 40°) that is half-immersed in 0.2 M TBA.PF6 in acetonitrile and pulsed to +5 V (versus Ag/Ag+ reference) and then to 0 V for about 5 s each. (B and C) Paddle rotation (normalized to the length of actuating yarn) and tensile actuation during a cyclic potential scan at 50 mV/s. Two immersed 18-mm lengths of MWCNT yarn (d = 12 μm and α = 42°) are separated by an insulating fiber at midpoint, where the paddle is located, and only the lower yarn segment is actuated. The electrolytes are 0.1 M BMP.TFSI in propylene carbonate (B) and 0.2 M TBA.PF6 in acetonitrile (C). Arrows indicate scan directions.

Rotation rate measurements for the above voltage-pulsing conditions were obtained by using frame-by-frame analysis to obtain paddle orientation versus time from a movie recorded at 250 frames/s (movie S1). The maximum torsional rotation rate of 590 rotations/min (62 rad/s) was maintained for ~4 s and 30 full rotations. A similar long-sustained high rotation rate was achieved in the opposite direction upon return of the electrode potential to 0 V.

The torque generated in this experiment was sufficient to rotate a rectangular Mylar paddle that was 830 times the diameter of the actuating yarn and 1800 times its mass. The initial paddle acceleration in Fig. 2A was a = 50 rad/s2 (9000°/s2). Because the moment of inertia of the paddle was I ≈ 2 × 10−10 kg·m2 and the mass of actuating yarn was 5.4 μg, the maximum start-up torque (τ) was at least τ = Ia = 10 nN·m, which is 1.85 N·m per kilogram of actuating yarn mass. This specific torque is similar to that achieved by large commercial electric motors, which range from 2.5 to 6 N·m/kg (14). Nature’s bacterial flagellar motors do much better, as a result of elegant complexity that evolved over a billion years, producing about 200 N·m of torque per kilogram of active protein (based on a molecular weight of active proteins of 11 MD and a peak torque of 3700 pN·nm) (15).

The peak power output per kilogram of actuating yarn is also impressive, even for the present case (Fig. 2A) where the mechanical load is not impedance-matched, viscous losses during paddle rotation are ignored, and torsional rotation is reduced by the two-end tethering used to enhance torsional reversibility. The kinetic energy generated in the paddle (½Iω2), normalized by the 1.2 s needed to accelerate the initially stationary paddle to an angular velocity of ω = 62 rad/s and the mass of the actuating yarn, provides a peak power output of 61 W/kg. This power density is less than the 300 W/kg achieved by large, high-power electric motors (16). The nanotube yarn actuator provides an additional peak power contribution of 920 W/kg by contracting against the applied 88-MPa load, which is equivalent to lifting a mass 185,000 times the mass of the actuating nanotube yarn segment in 1.2 s.

These figures of merit for torque generation and power density for nanotube yarns do not incorporate electrolyte, counterelectrode, connector, and packaging masses, which reduce the gravimetric power output of optimized batteries and supercapacitors by typically a factor of 3 to 8 relative to that based on the mass of the working electrode (17). Although use of both the working electrode and counterelectrode for actuation can mitigate this effect, device design optimization will be important for maximizing performance based on total device mass. We anticipate that the advantages of the nanotube torsional actuators in device simplicity (i.e., low cost), miniaturizability, and low-voltage operation will be most important for practical applications.

What is the origin of this fast, giant torsional actuation of twist-spun nanotube yarns? A first insight is obtained by noting that large positive or negative electrochemical charge injection produces length-direction contraction for a heavily twisted MWCNT yarn that is tethered so that it cannot rotate (18). This contraction of total yarn length, normalized to the length of the actuating portion of the yarn, was about –1% for the experiment of Fig. 2A. In contrast, direct measurement of MWCNT length change as a result of charge injection provides an expansion of about 0.2% (19), which is consistent with the expansion obtained from measurements on unoriented MWCNT and single-walled carbon nanotube sheets (20, 21). The opposite sign and much larger tensile actuation for the twist-spun yarns shows that the length changes of individual MWCNTs cannot explain the observed torsional actuation for twist-spun MWCNT yarns.

We provide evidence that the unexpected contraction of twist-spun nanotubes yarns is largely driven by internal pressure associated with ion insertion, which is reminiscent of the hydraulic actuation for McKibben-type artificial muscles (22). The McKibben muscle (whose woven structure is like that used for children’s finger cuff toys) uses a braid of two oppositely handed helices wrapped around a rubber bladder. As the bladder is inflated, the inextensible braid expands in the radial direction and contracts in the length direction if the helix angle with respect to the axial direction is well below 54.73°, which is the helix angle that maximizes helix volume if torsional rotation does not occur. If the helix angle is substantially below this angle, elongation of a finger cuff in an effort to escape traps a child’s fingers by causing a decrease in finger cuff diameter. Nature has applied the generic concept of finger cuffs in muscular hydrostats that provide stiffness, extension, bending, and torsion for an elephant’s trunk, the tentacles of squids and the chambered nautilus, and some lizard tongues (23).

The helix angles of the yarns used for our actuators are much smaller than 54.73°. Hence, stretching these twisted carbon nanotube yarns was expected to decrease yarn volume (figs. S5 and S6) and indeed did so: A single twist-spun yarn tethered on opposite ends to prohibit torsional rotation provided a large lateral contraction when stretched, corresponding to a giant Poisson ratio of 2.2 for the lateral directions (3). In this case, a 1% increase in yarn length produced a 3.2% decrease in yarn volume. Most materials increase volume when stretched (24).

The double-helix structure of the McKibben braid remains torque-balanced if the helices having opposite chirality are otherwise equivalent, so no net rotation occurs. Because the MWCNT yarns consist of helices having only one chirality (Fig. 3, A and B), they resemble unbalanced McKibben muscles (Fig. 3C) that have been driven hydraulically or pneumatically to provide torsional actuation (25). While also being hydrostatically driven, the torsional MWCNT yarn muscles operate at a vastly smaller dimensional scale and a hydraulic pressure is directly generated electrically. Additionally, MWCNT yarns comprise highly distorted chiral scrolls (26), rather than a simple cascade of helices, as well as voids that increase the dependence of yarn volume on axial strain, especially for small yarn bias angles (27). Yarns that are twist-spun symmetrically from nanotube forests for the present study have a distorted Fermat scroll structure (Fig. 3B, left), whereas yarns highly asymmetrically drawn from a forest have a distorted Archimedean scroll structure (Fig. 3B, right). Despite this enormous complexity, the twist insertions predicted from the observed bias angles and yarn diameters according to Eq. 1 are reasonably consistent with direct measurements of twist insertion (9).

Fig. 3

(A) Scanning electron micrograph of a carbon nanotube yarn (d = 3.8 μm, α = 37°) that was symmetrically twist-spun from a MWCNT forest. (B) Schematic illustration of idealized Fermat (left) and Archimedean (right) scroll structures spun symmetrically and highly asymmetrically, respectively, from a carbon nanotube forest. (C) Schematic illustration of the effect of yarn volume expansion during charge injection on yarn length, yarn diameter, and yarn twist, where the pictures on left and right are before and after volume increase, respectively, and the ribbon lengths are approximately constant. The amount of yarn untwist during yarn volume expansion is indicated by the arrow. (D) Photographs of “Springa-Roo” child’s toy showing that spring stretch causes spring twist to increase, which is opposite to the effect of stretch on the carbon nanotube yarns investigated here.

We postulate that hydrostatic (or quasi-hydrostatic) pressure is generated by change in the relative concentrations of ions of opposite signs in the yarn volume to compensate for injected electronic charge on the nanotubes (and associated changes in solvating species). Carbon supercapacitor electrodes with high surface area, such as single-walled carbon nanotube sheets, display an increase in volume upon electrochemical charging; this observation has been related to changes in the volumes of ions and solvating solution contained within the porous electrodes (28).

Support for this torsional and tensile actuation mechanism is found in Fig. 2, B and C, which shows that torsional actuation and yarn tensile actuation are correlated and both depend on the size of the electrolyte ion used to compensate electronic charge. The almost identical oxidative and reductive actuator strokes for 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (BMP.TFSI) electrolyte (Fig. 2B) agree with the similar van der Waals volumes (29) of the anion (147 Å3) and cation (167 Å3). Likewise, the much larger actuation during reduction than for oxidation in Fig. 2C for the TBA.PF6 electrolyte reflects the larger unsolvated van der Waals volume (29) for the TBA cation (293 Å3) than for the PF6 anion (69 Å3). Although torsional actuation has been predicted theoretically for hollow tubes of volume-changing solids reinforced by helically wound fibers (30), such predictions are apparently sensitive to assumed energy functions and structure, and hence they are of limited use in predicting the observed sign of the dependence of torsional actuation on yarn volume change.

The relationship between torsional actuation and tensile actuation is described by the stretch-torsional coefficient CST, which is the ratio of angle change per actuating yarn length (positive for twist and negative for untwist) to the percent tensile strain of the actuating yarn segment. The quasi-equilibrium actuation measurements of Fig. 2, B and C, provide a CST of about 210°/mm% for the cycle region having longest linearity. Results for the same yarn and same yarn configuration, using lithium TFSI salt in propylene carbonate as electrolyte, yield a similar CST (about 170°/mm%). The temporal correlation between torsional and tensile actuation for the slow potential scan measurements of Fig. 2, B and C, contrasts with the occurrence of most of the tensile actuation before large-angle paddle rotation has occurred for the voltage pulse experiment of Fig. 2A. This slower development of torsional actuation than tensile actuation likely results from rate limitations caused by paddle inertia and viscous drag.

The combination of mechanical simplicity, large torsional rotation, high rotation rate, and micrometer-size yarn diameter suggests applications such as microfluidic pumps, valve drives, and mixers. We demonstrated one such application by using a carbon nanotube yarn torsional actuator to mix two laminarly flowing liquids (dyed yellow and blue) that were joined at a T-junction in a fluidic circuit (Fig. 4, fig. S7, and movie S2) (4). By switching between modest interelectrode potentials (0 V and –3 V at 1 Hz), we achieved a reversible paddle rotation of up to 180° with a 65-mm length of actuating yarn 15 μm in diameter. The yarn rotated a paddle that was 100 times the diameter of the yarn, and 80 times its mass, in the flowing liquids at a maximum rotation rate of 360°/s.

Fig. 4

(A) Photograph of prototype mixer that can be downscaled for a microfluidic circuit (9). Channels are 3 mm wide. Mixing of water colored by blue and yellow food dye was by a paddle attached to the middle of a single piece of MWCNT yarn that was half-immersed (cross channel on left) in electrolyte and torsionally actuated in opposite directions by alternately applying 0 V and –3 V between the yarn electrode and a Pt wire counterelectrode at 1 Hz. (B and C) Still images from movie S2 showing unmixed food dye with mixer off (B) and the initial stage of mixing achieved when the mixer was first turned on (C). The electrolyte was 0.2 M TBA.PF6 in acetonitrile.

On the macroscale, the demonstrated torsional actuation is well suited for rotating electrodes used in highly sensitive electrochemical analyte analysis, thereby eliminating the need for an ordinary motor. The torsional muscles can also be driven in reverse for conversion of mechanical energy to electrical energy, such as for sensors that generate electrical signals indicating applied mechanical torque or torsional rotation angle. The built-in linear-to-rotational coupling, voltage control, large and fast rotations, and easily handled yarn configuration suggest ready implementation for applications that require rotational positioning and high torque generation.

Supporting Online Material

Materials and Methods

Figs. S1 to S7

Movies S1 and S2


References and Notes

  1. See supporting material on Science Online.
  2. Acknowledgments: Supported by Air Force Office of Scientific Research grant FA9550-09-1-0537, Air Force grant AOARD-10-4067, Office of Naval Research MURI grant N00014-08-1-0654, and Robert A. Welch Foundation grant AT-0029; the Creative Research Initiative Center for Bio-Artificial Muscle (Korea); the Natural Sciences and Engineering Research Council of Canada through a Discovery Grant and Graduate Scholarship (T.M.); and Centre of Excellence funding from the Australian Research Council. We thank K. E. Smith, G. L. Vanderford, and D. Hastie for technical assistance.
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