www.sciencemag.org/cgi/content/full/338/6109/928/DC1

Supplementary Materials for

Electrically, Chemically, and Photonically Powered Torsional and

Tensile Actuation of Hybrid Carbon Nanotube Yarn Muscles

Márcio D. Lima, Na Li, Mônica Jung de Andrade, Shaoli Fang, Jiyoung Oh, Geoffrey

M. Spinks, Mikhail E. Kozlov, Carter S. Haines, Dongseok Suh, Javad Foroughi, Seon

Jeong Kim, Yongsheng Chen, Taylor Ware, Min Kyoon Shin, Leonardo D. Machado,

Alexandre F. Fonseca, John D. W. Madden, Walter E. Voit, Douglas S. Galvão, Ray H.

Baughman*

*To whom correspondence should be addressed: E-mail: ray.baughman@utdallas.edu

Published 16 November 2012, Science 338, 928 (2012)

DOI: 10.1126/science.1226762

This PDF file includes:

Materials and Methods

Supplementary Text

Figs. S1 to S11

References (33–37)

Other Supplementary Material for this manuscript includes the following:

(available at www.sciencemag.org/cgi/content/full/338/6109/928/DC1)

Movies S1 to S5

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MATERIALS AND METHODS

1. Fabrication and Structure of Twist-Spun Nanotube Yarns

Drawable carbon multiwalled nanotube (MWNT) forests for producing twist-spun yarns were grown by chemical vapor deposition (CVD) on silicon wafers coated by iron catalyst using acetylene (C2H2) gas as the carbon precursor (9). Transmission and scanning electron microscope (SEM) images of the ~350 µm high forests indicate that the MWNTs have an outer diameter of ~9 nm, contain ~6 walls, and form large bundles. Thermogravimetric analysis indicates that the amount of non-combustible material in the drawn nanotubes is below 1 wt%, which places an upper limit on the amount of residual catalyst.

Small and large diameter yarns were fabricated in which twist insertion resulted in two different scroll geometries, Fermat and dual-Archimedean (17). Small diameter yarns were made by symmetrical twist insertion during sheet draw from a forest or into a pre-drawn nanotube sheet suspended between either a forest and one rigid end support or two rigid end supports. Symmetric twist insertion means that opposite sides of the sheet wedge formed during spinning are equivalently stressed during spinning. Because of differences in end constraints, these methods provide Fermat scrolls (Fig 1H) for the former cases of sheets connected to a forest and dual-Archimedean scrolls (Fig 1I) for the latter case, where two rigid rod supports are used. The yarn diameter could be conveniently varied from ~10 µm to ~30 µm by changing the drawn forest width from ~0.5 cm to ~5 cm. Much larger diameter dual-Archimedean yarns were typically fabricated by stacking 20 to 40 MWNT sheets (1.0 cm to 2.5 cm wide and 5 to 17 cm long) between rigid rods and inserting twist using an electric motor, while one end of the sheet stack supported a 5 g weight that was tethered to prohibit rotation. Approximately 150 turns were necessary to collapse a 5 cm long sheet stack into a 4.5 cm long yarn having dual-Archimedean structure. Fermat yarns directly spun during sheet draw from a forest were used for immersion-driven torsional actuation; polydiacetylene hybrid yarn muscles; two-ply yarn muscles; and non-plied, wax-filled torsional muscles. The Fermat yarns of Fig. 2A inset; Fig. 3, A and B; Fig. 4, A and B; Figs. S1 and S2; and Movies S1 and S2 were fabricated by drawing a length of nanotube sheet from a forest, and then inserting twist into one end of the sheet via a motor and a rigid support, while allowing the other end to freely draw from the MWNT forest. Unless otherwise noted, inserted twist is normalized with respect to the final yarn length. For these other instances, where in most cases twist was inserted in a sheet stack to form a dual-Archimedean yarn, twist was normalized to the length of the sheet stack.

The amount of inserted twist per final yarn length (T) and the final yarn diameter (d) are important parameters, which for Fermat yarns determine the bias angle () between the nanotube orientation on the yarn surface and the yarn direction. Unless otherwise indicated, both d and were measured by SEM microscopy on yarns that were two-end-tethered under tension to prohibit untwist. For Fermat yarns, the theoretical relationship = tan-1(dT) is consistent with observations, despite the complex nature of the realized yarn structure, which contains stochastic elements due to such processes as sheet pleating during twist insertion (15). In contrast, since the number of turns inserted by plying two Archimedean scrolls into a dual-Archimedean scroll (versus the initial number of turns that provide twist in each Archimedean scroll) is a consequence of yarn energetics, a strictly topological equation to predict from only d and T does not exist. For the same reason, such a simple topological relationship, involving no added parameters, cannot be obtained for coiled yarns of any type.

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According to the direction of twist insertion, yarns are classified as S or Z yarns (for clockwise and anticlockwise twist insertion, respectively). If all segments in a yarn have the same chirality at corresponding structural levels, the yarn is called homochiral. This means, for instance, that a SZ two ply yarn (with S twist due to plying and Z twist within each ply) is homochiral. If the yarn has segments having different chirality at the same structural level, then the yarn is called heterochiral. For the heterochiral yarns presently described, different chirality yarn segments are essentially mirror image of each other (Fig. 4C and Movie S3).

Coiled yarns (Figs. 1E, 2, A and B, 3 and Movie S4) were typically fabricated under constant load from non-coiled, twist-spun yarns by inserting additional twist until the yarn contracted to 30-40% of its original length. For a dual-Archimedean yarn made under 4 g load by twist insertion in a stack of 40 co-oriented, 9 mm wide, 15 cm long sheets, coiling started at ~580 turns and the yarn was completely coiled after ~620 turns. Twist insertion until complete coiling occurred (except in the vicinity of the yarn ends) produced a 60% contraction in yarn length.

Four-ply yarns (Figs. 1, G and J) were fabricated by inserting S twist of plying into four identical, parallel-aligned, S-twisted, single-ply Fermat yarns. Two-ply yarns (Fig. 1F, Section 7, and Movie S5) were fabricated as follows: A SZ yarn was obtained by inserting about 30% extra twist into a 11 µm diameter, Fermat Z yarn having an initial twist of 20,000 turns per meter. This highly twisted yarn was then folded upon itself, so that part of the Z twist was converted to S twist due to plying. A ZS yarn was made analogously. 2. Hybrid Yarn Muscle Fabrication

2.1 Yarn muscles containing paraffin wax guest Though we obtained similar results for other commercially obtained waxes (like those used

for canning and candles), the described results are for a wax more likely to be readily available to future researchers (Sigma-Aldrich 411671 wax), which comprises a mixture of alkanes. Results in Section 3 show that this wax fully melts at 83C, expands by 20% between 30 and 90C during solid-state transitions and melting, and provides 10% additional volume expansion between 90 and 210C.

MWNT yarns were typically infiltrated with paraffin wax using the “hot wire method”, wherein a two-end-tethered, twist-spun yarn, under constant tensile load was electrically heated to above the melting point of the paraffin wax and then contacted with a small amount of solid paraffin. Upon touching the heated yarn with flakes of solid paraffin or droplets of molten paraffin, the paraffin quickly spread through the yarn. For a 100 µm diameter MWNT yarn, an applied voltage of ~3V/cm was sufficient to enable infiltration of the Aldrich paraffin wax. Since excess paraffin on the yarn surface degraded actuation, the yarn was electrically heated to above the evaporation temperature of the paraffin (233C) until no excess paraffin was observed on the yarn surface. The need for this second step can be avoided by multiple applications of molten droplets to the heated yarn, and stoping this process before excess paraffin accumulates on the yarn surface. Another wax infiltration method, which was used for all Fermat yarns that were directly twist spun during forest draw, is to slowly immerse a two-end-tethered, as-spun yarn into melted paraffin (~0.1 cm/s) under constant tensile load (10% of the failure stress).

The extent of paraffin wax infiltration was determined by SEM microscopy of the yarn cross-section (Fig. S3). Neat and hybrid MWNT yarns were cut along their diameters using Ga ions (5 nA beam current) in a Focused Ion Beam (FIB, Nova 2000) operated at 30 kV. The obtained cross-sections were cleaned (via ion-polishing) by etching several micrometers of yarn

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length with consecutively decreasing ion-currents ranging 3.0 to 0.3 nA. These cut yarns were next transferred to a Zeiss Supra 40 SEM in order to perform microscopy (at 15 kV). The SEM micrographs of Fig. S3 show that the porosity of the neat yarn has been largely eliminated by wax infiltration using the above slow immersion method. In fact, the few small pores observed for the wax infiltrated yarn might have been introduced during preparation of the yarn cross-section.

2.2 Yarn muscles containing polydiacetylene guest The utilized diacetylene (DA) was 10,12-pentacosadiynoic acid [CH3(CH2)11CC-

CC(CH2)8COOH], which was purchased from Alfa Aesar Co., Ltd and used as received. An as-spun, two-end-tethered, Fermat yarn (9 m in diameter, with 20,000 turns/m of inserted twist) was first immersed in 8 M DA tetrahydrofuran solution for an hour, and then the DA infiltrated yarn was removed from the solution and dried overnight at room temperature while maintaining tethering. UV light (254 nm from a 30W UV lamp) was used to in situ polymerize the DA into a polydiacetylene (PDA). The polymerization time was typically around 3 minutes, which caused the yarn to develop a dark blue color. However, polymerization was incomplete, in part because nanotube and diacetylene absorption prevents deep penetration of the UV light inside the yarn.

2.3 Yarn muscles containing polyethylene glycol guest Polyethylene glycol (PEG), H(OCH2CH2)nOH, with an average molecular weight of 6000

and a melting temperature range of 60 to 63oC, was obtained as flakes from Sigma Aldrich (Bio-Ultra 6000) and used as received. The PEG was infiltrated into the lower half of a 13 µm diameter Fermat yarn (containing 15,000 turns/m of inserted twist) by immersion of this yarn segment in a molten bath of PEG for 30 minutes at 100C. Then the two-end-tethered yarn was removed from the PEG bath and allowed to cool to room temperature. The diameter of the PEG-filled yarn segment was 17 µm and the bias angle was = 31.

2.4 Yarn muscles containing palladium guest Using e-beam deposition (CHA-50 e-beam evaporator), individual nanotubes and nanotube

bundles within a stack of two co-oriented MWNT sheets, supported by rigid rods, were coated first with a 5 nm thick Ti buffer layer (to ensure uniform Pd deposition) and then with a 60, 80, 120, or 140 nm thick Pd layer, where the layer thicknesses are nominal values that correspond to the layer thickness of depositions on a planar substrate that is in the same environment. Then, the sheets stack (Fig. S4A) was twist spun (0.1 to 0.2 turns/mm) to obtain a 144 m diameter yarn (Fig S4B) having dual-Archimedean structure. A 60 nm Pd layer was sufficient to obtain reversible actuation of the yarn and a thicker coating undesirably increased the difficulty of inserting yarn twist.

3. Characterization of Temperature Dependent Properties

3.1 The thermal properties of paraffin wax yarn guest Differential Scanning Calorimetry (DSC) was performed in nitrogen atmosphere on a

Mettler Toledo DSC 1, which has an accessory that enables sample cooling to -35°C. Measurements were performed at atmospheric pressure in an aluminium crucible with a perforated lid, using heating and cooling rates of 10°C/min. During DSC measurements the samples were heated from room temperature to 120°C, cooled to -20°C, and then this heating and cooling process was repeated. The data shown are for the second heating and cooling ramps. Thermogravimetric analysis (TGA) was performed on a Mettler Toledo TGA/DSC 1 in dry air. Samples were heated from 30 to 500°C in an open alumina crucible at 10°C/min.

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The volume expansion of paraffin wax (Sigma-Aldrich 411671) was measured using the MPA100 OptiMelt Automated Melting Point System. The paraffin was loaded into a melting point capillary tube, and then subjected to several heat/cool cycles to ensure that the wax was void-free. The sample height was between 2.0 and 3.0 mm, as recommended for optimum results in the OptiMelt. Three samples were tested by heating from 30 to 210°C (at 10°C/min) and cooling down at the same rate. The volume expansion of paraffin was determined from sample images obtained from the internal camera and a calibrated digital image processor.

Figure S5 shows DSC, volume change, and TGA (inset) curves for Sigma-Aldrich 411671 paraffin wax. This wax, which is a mixture of alkanes, has a main endothermic peak during heating at 55°C, with shoulder at 43°C. While this main peak is most likely associated with the melting of a wax component, and the shoulder at 43°C might be due to a solid-state transition, the minor peak in the DSC data between 73 and 83°C shows that complete melting does not occur until about 83°C. This interpretation of the final melting temperature is consistent with optical characterization using the above OptiMelt Automated Melting Point System, as well as the abrupt decrease in the temperature dependence of volume change at close to 83°C. Dilatometer data shows that wax expands by 20% between 30 and 90C, and provides 10% additional volume expansion between 90 and 210C. Weight loss due to evaporation starts at 233°C for the used 10°C/min scan rate.

3.2 Torsional modulus of neat and wax-filled yarns Since changes in the torsional modulus of a yarn can affect both torsional and tensile

actuation, we here characterize this parameter for both neat and wax-infiltrated yarns using a torsional pendulum method (1, 33, 34). This torsional modulus is the product of yarn length and the ratio of the torque applied to one yarn end to the resultant rotational angle change in radians (with respect to a clamped yarn end). A dual-Archimedean yarn with ~3,000 turns/m inserted twist (corresponding to 1,360 turns per initial stack length) was characterized, which was trained by thermal cycling prior to use in both experiments. The yarn was initially 200 µm diameter and increased to 210 µm after wax infiltration.

Heating the neat yarn in air from ambient to 190°C caused little change in torsional modulus. For an applied stress of 4.8 MPa, a torsional modulus of 3 x 10-9 N·m2 was maintained over this temperature range (Fig. S6). Heating this neat, dual-Archimedean yarns to 1500°C in vacuum confirmed that the temperature dependence of torsional modulus was small. However, the ~11 x 10-9 N·m2 torsional force constant of wax-infiltrated yarn (under 4.4 MPa stress) decreased by a factor of 3.5 upon heating to 130°C, thereby approaching that of the neat yarn (Fig. S6). These stress values are normalized with respect to yarn diameter measured in the SEM. 4. Method and Apparatus for Actuator Testing

The investigated tensile and torsional actuators were subjected to at least 30 initial training cycles in order to stabilize the structure of the hybrid yarn, and thereby enable highly reversible operation during subsequent evaluation for sometimes over 2 million reversible actuation cycles. With the exception of described use of actuating yarns as catapults (and related characterization of maximum generated torque) all actuator measurements were isotonic, meaning that a constant mechanical force was applied to the yarn during actuation. Reported gravimetric work and power capabilities are normalized with respect to the total weight of the actuated yarn.

Actuation to above the melting point of guest material in hybrid single-ply nanotube yarn used the two-end tethered configurations shown in Fig. 1A and B (or horizontal analogues), since

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only such configurations provided reversible actuation when the guest is completely melted during actuation, the yarn is single ply, and the applied tensile load is large. However, a modified Fig. 1D type configuration (with fixed separation between tethers and artificially restricted paddle rotation) was used to provide reversible torsional rotation to above the wax melting point for the miniature catapult of Fig. 4C (inset). Also, all tether types in Fig. 1A-D were used to provide reversible actuation (tensile and/or torsional) when the temperature during actuation did not exceed the melting point of the guest.

The methods deployed for measuring tensile and torsional actuation evolved during this investigation. In initial studies we deployed movie cameras (recording at up to 1,000 frames/s) to capture torsional and tensile actuation, and then obtained quantitative data by analysis of the movie frames. We later measured the distance that the actuating yarn lifted an attached metal weight by using a contactless inductive proximity sensor (Omega LD701 5/10) with data acquisition (Omega module OM-USB-1408Fs), which simplified and improved the accuracy of ultrafast tensile strain measurements. Measurements of high-speed torsional actuation used a small, reflective paddle (typically Al foil) attached to the actuating yarn to deflect the beam of a 532 nm laser (Fig. S7). The reflections were measured using an oscilloscope (Agilent MSO6032A) by placing the paddle/actuator within a ring of photodiodes.

Tethering a vertical yarn against rotation at the bottom end, while still allowing tensile actuation stroke (configuration Fig. 1A), was accomplished by attaching a plate-shaped end weight that was restrained from rotating by contact with an adjacent vertical surface. Electrical contact to the yarn end that undergoes displacement during actuation was made through a metal end weight that is electrically connected to the yarn by either (1) attaching a mechanically loose electrical wire (Cu wire AWG40) to the metal weight or (2) electrically contacting a horizontal metal plate to a flexible metal pin that is attached to the weight.

For the horizontal torsional motor of Fig. S8A, a half-infiltrated yarn (with paddle attached at the junction between infiltrated and non-infiltrated segments) passed between an end support and a metal hook (between which the actuation voltage was applied). The opposite end of the yarn was tethered using an attached weight, whose rotation was prohibited by contact with a vertical surface. This two-end-tethered arrangement is analogous to the vertical configuration of Fig. 1B. The Fig. S8B configuration for a fully infiltrated yarn is similar to the one-end tethered configuration of Fig. 1C, since the attached weight was free to rotate.

The static torque of the heterochiral yarn investigated in Fig. 4C was determined using a digital microbalance to measure the force exerted by a metal paddle (23 mm long) attached to the central junction point of the heterochiral yarn. The paddle was in the horizontal position, pressing against the plate of the microbalance during force measurement. So that no force was applied to the microbalance when the actuating voltage was zero, at the beginning of the experiment the wax in the yarn was melted (by electrical heating) and resolidified while the metal paddle was in contact with the plate of the microbalance. This same yarn was used to build the miniature Greco-Roman style catapult (Movie S3).

For characterization of actuation as a function of temperature within a home-built temperature control chamber, an optical microscope (Moticam 1000) was used to measure tensile displacement and torsional actuation was recorded using a high speed camera that captured paddle rotation. Comparison of the known thermal expansion of a 0.2 mm diameter platinum wire with that measured in the chamber was used to correct tensile actuation measurements.

For actuation measurements (as well as torsional modulus measurements) in vacuum for neat yarns to incandescent temperature, yarn temperature (T) was estimated from input electrical

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power by using Stefan-Boltzmann law for black body radiation and an emissivity of 1. The effective radiant surface area of the coil was calculated for a cylinder with the outer diameter of the coiled yarn. Correction for heat transport by conductance was made by using the measured thermal actuation of the coiled yarn as function of temperature (Fig. 2A) to deduce the correspondence between temperature and input power in the low temperature region. Approximating the heat loss due to thermal conductance as being linearly proportional to (T - 300 K) and equating total input energy to the sum of radiated and conducted thermal energy, we calculated the energy loss at all input power levels that was due to radiation and thereby derived the temperature using the Stefan-Boltzmann law. 5. The Effects of Actuating Yarn Configuration on Torsional and Tensile Actuation

So that the advantages and disadvantages of different actuating yarn configurations in Fig. 1A-D can be compared, we consider the case where all infiltrated yarn segments are equivalent (ignoring chirality differences), non-plied, and exposed to the same actuating conditions. To avoid any unnecessary complexity for the discussion, all actuators have the same total yarn length L, torsionally actuated paddles are located either at yarn midpoint or end, and paddle weight is negligible compared with the applied tensile force.

We first discuss torsional actuation. Consider that the actuating homochiral yarn in Fig. 1C generates a rotation per yarn length of (degrees/mm) when heated from the initial temperature to the final actuation temperature. The rotation at any distance x from the tethered end to the free yarn end is simply (x) = x, which is (L) = L at yarn end, where the paddle is located. Paddle rotation at yarn midpoint for the heterochiral yarn with segment lengths L/2 in Fig. 1D will be one-half that for the paddle suspended at the end of the homochiral yarn of Fig. 1C. However, since both S and Z yarns provide equal torque on the paddle of Fig. 1D, the initial torque that accelerates paddle rotation in this configuration will be double that of the homochiral configuration of Fig. 1C. Nevertheless, since this torque disappears after L/2 rotations for the heterochiral yarn of Fig. 1D and Lrotations for the homochiral yarn of Fig. 1C, the ability to accomplish torsional work is the same in both cases.

From a view point of combined torsional stroke and torsional work capability, the half-infiltrated homochiral yarn structure of Fig. 1B provides the poorest performance. One-half of the torsional rotation generated by untwisting of the actuating yarn segment must be used to up-twist the non-actuating yarn segment, so the paddle rotation produced by the L/2 actuating length during actuation is only L/4, and net torque vanishes when this rotation occurs. Even though this half-infiltrated Fig. 1B configuration does not optimize torsional actuation below the guest melting point, this and similar configurations having a torsional return spring (which need not be a nanotube yarn) are the only configurations for a single ply yarn that can provide both highly reversible torsional and tensile actuation when the temperature for complete melting of the guest is exceeded.

However, the combination of highly reversible torsional and tensile actuation can be obtained for the Fig. 1, C and D configurations even when the guest fully melts if the yarn is two ply (where S twist in the yarn is accompanied by Z twist due to plying for a ZS yarn and the opposite is true for ZS yarn). The origin of this reversibility is that when a yarn actuates to provide increased twist due to plying, it simultaneously decreases twist in each of the plied yarns, thereby providing the returning force that acts to maintain reversibility.

Since present observations show that single-ply actuating yarn segments untwist as they contract during actuation, the yarn configurations that maximizes tensile contraction are not

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those that maximize torsional actuation. Consider a two-end tethered actuating yarn of Fig. 1A that provides a tensile contraction of L/L. When untethered, as in Fig. 1C, the untwist of a homochiral yarn during actuation provides an elongation that partially cancels tensile contraction. This undesirable elongation can be largely avoided by using the two-end tethered, one-half infiltrated yarn of Fig. 1B, since expansion during untwist of the actuating yarn segment is compensated by contraction during up-twist of the unactuated yarn segment. The heterochiral yarn configuration of Fig. 1D for non-plied yarn has decreased tensile performance for a volume expanding guest, especially when yarn diameter and torsional rotation are large, since both yarn segments untwist during actuation, and thereby provide elongations that partially cancel the desired contraction during thermal actuation.

This undesirable partial cancellation of tensile contraction can be significant: experiments on non-plied Fermat yarn contraction during twist insertion under constant load show that the ratio of percent tensile strain to inserted twist (degrees per mm of length) near the end of twist insertion to produce a non-coiled yarn is -0.231 d %/mm, where d is yarn diameter. These measurements, which are for yarn bias angle between 22 and 32 and yarn diameters between 9.6 and 15 µm, predict that actuating 10 and 100 µm diameter single-ply, Fermat yarn undergoing 100/mm torsional rotation (in either the Fig. 1C or 1D configurations) would provide a degradative tensile expansion component due to untwist of 0.23 and 2.3%, respectively. Like the case for torsional actuation, for a single-ply, twist-spun yarn only the Fig. 1, A and B configurations can maintain fully reversible tensile actuation when the guest becomes completely fluid during actuation. 6. Comparison of Torsional Actuation for Non-Plied Neat and Paraffin-Infiltrated Yarn

This experiment characterizes the effect of wax infiltration on torsional actuation for a two-end tethered homochiral yarn, where one-half of the yarn is actuated and the other half largely functions as a torsional return spring. The utilized 16 m diameter Fermat yarn had 15,000 turns/m of inserted twist and a bias angle of 35. The configuration for the wax containing yarn was exactly the same as for Fig. 1B, and that for the non-infiltrated yarn differs only in that the two yarn segments were equivalent except that electrical power was applied to only one-half of the yarn length. In these comparative examples the same mechanical load was applied and the voltage used to achieve actuation was identical (11.6 V/cm). Although some torsional actuation rotation was observed for the neat yarn (4.9°/mm), which may be due to small difference in torsional and tensile moduli between the low and high temperature yarn segments, this rotation was low compared to the 71.2°/mm torsional actuation observed when one of the yarn segments was subsequently infiltrated with paraffin wax. 7. Torsional Actuation of a Neat, Two-Ply, Heterochiral Yarn

This experiment demonstrates that use of two-ply heterochiral yarn (instead of an non-plied heterochiral yarn) enables reversible torsional actuation for the Fig. 1D configuration. Two-ply SZ and ZS yarns were made as described in Section 1. Then these yarns were knotted together, and a paddle was attached at the position of the knot. The resulting two-ply SZ-ZS yarn structure was 20 µm in diameter.

Steady-state measurements of torsional actuation as a function of input electrical power measurements (Fig. S9) show that reversible torsional rotation results in the Fig. 1D configuration for heterochiral, two-ply Fermat yarn that is either (1) wax-filled and actuated to above the melting point of the wax or (2) neat and actuated to incandescent temperature in

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vacuum. The applied stresses for these experiments were 3.2 MPa for the neat yarn and 5.8 MPa for the wax-filled yarn. While the maximum torsional actuation achieved here for wax-filled SZ-ZS yarn (68°/mm) is about the same as for the half-infiltrated homochiral yarn of Section 6 in the Fig. 1B configuration (71.2°/mm), the neat SZ-ZS yarn in vacuum provided 30°/mm torsional actuation (versus the 4.9°/mm for the half-actuated, neat, homochiral yarn of Section 6 in air). This latter difference shows, at least in part, the actuation enhancement for neat yarn that results from actuation to high temperatures (which are presently enabled at the same power as for wax-filled yarn by using vacuum to eliminate convective energy loss for the porous neat yarn). Although low for nanotube torsional actuators, this 30°/mm of torsional actuation for the neat yarn is 200 times the maximum previously reported for shape memory alloys (2), ferroelectric ceramics (3), or conducting polymers (4). Movie S5 shows torsional actuation for this neat two-ply yarn when driven in vacuum to incandescent temperatures using 9.7 V/cm voltage pulses with 1 Hz frequency and 20% duty cycle. A 27/mm rotation was observed with an average speed of 510 revolutions per minute.

This reversible behavior contrasts with the lack of reversibility of actuation of heterochiral, single-ply yarn in the Fig. 1D configuration when the yarn does not contain solid guest at all points in the actuation cycle. In the latter case, permanent cancellation of the opposite twist in the two yarn segments occurs during actuation, thereby resulting in permanent elongation and reduction of torsional rotation during cycling. 8. The Effect of Inserted Twist on the Tensile Contraction of Neat Yarn

Experimental data on tensile actuation versus twist insertion for a neat Fermat yarn in the Fig. 1A configuration shows the importance of twist and resulting bias angle increase on thermal contraction (Fig. S1). With increase of inserted twist from ~9,650 turns/m to ~28,130 turns/m, tensile actuation at constant applied power increased ~2.8 times (from ~0.03% to ~0.086%). However, when the start of coiling was first observed (at 33,800 turns/m) there was ~4.5% decrease in thermal contraction, which might be due to the predominance of non-coiled yarn segments in providing contraction when there is little coiling and the effect of introduced coiling on decreasing modulus. 9. Yarn Tensile Modulus and the Effects of Tensile Load and Yarn Modulus on Tensile Stroke

All tensile actuation measurements were isotonic, meaning that a constant mechanical force was applied to the yarn during actuation. Consequently, the generated tensile strain will be the sum of the tensile strain for zero applied force (0) and a term that is the difference in elastic strain of final actuator state and initial actuator state under the applied tensile force (f). If K and K’ are the yarn tensile stiffness in the initial and final states, respectively, the overall strain (f) at a constant tensile force f is:

))()'((

1

'

1 1100

EEEf YY

KKf . (1)

The stiffnesses are the product of the yarn cross-sectional area and Young’s modulus for the non-coiled yarn or the spring constant of the coiled yarn. YE and Y’E are corresponding engineering Young’s modulus for the initial and final actuation states, respectively, and E is the engineering applied stress, where engineering here means that normalization is with respect to yarn area in the initial unactuated state at zero f. From these equations, the actuation strain is expected to be linearly related to applied force unless these elastic moduli depend on applied load (35).

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Figure S2 shows tensile actuation strain and non-actuated length at room temperature as a function of applied stress for neat and wax-infiltrated Fermat (A) and dual-Archimedean (B) yarns having similar inserted twist (20,000 turns/m) and similar diameters (17.5 0.5 μm and 18.1 0.9 μm, respectively, for the Fermat yarns and 16.4 0.9 μm and 16.2 1.1 μm, respectively, for the dual-Archimedean yarns). The same electrical power (35 2 mW/cm) was provided for all yarns to go from the non-actuated state to the actuated state. This applied power was selected so that the yarn temperature for the wax-infiltrated yarns was far above the temperature of complete wax melting (83C), but below the temperature at which significant wax evaporation is observed (233C).

From the data in Fig. S2A, wax infiltration increases the engineering Young’s modulus of the Fermat yarn by a factor of 2.46 (from 1.51 0.15 GPa to 3.72 0.52 GPa), where the indicated uncertainty is plus or minus one standard deviation. The Young’s modulus for the dual-Archimedean yarn increases by a factor of 3.45 upon wax infiltration (from 0.53 0.03 GPa to 1.83 0.16 GPa). Using these room temperature moduli, the slope of the dependence of tensile actuation on stress (Fig. S2B) and Eqn. 1, there is a 9.60 1.14% decrease in the Young’s modulus of the wax-infiltrated, dual-Archimedean yarn in going from room temperature to the actuated state. The possible non-linear dependence of tensile contraction on load prohibits a similar calculation for the wax-infiltrated Fermat yarn (Fig. S2A). Calculations for the neat Fermat and dual-Archimedean yarns provide approximate values for the percent change in Young’s modulus upon heating (-2.62 1.07% and -0.94 0.14%, respectively).

Since precise temperatures were not known for the above electrically driven actuation study, companion measurements of the temperature dependence of the Young’s modulus were made in nitrogen atmosphere using Dynamic Mechanical Analysis (DMA) equipment (a Mettler Toledo DMA 861e/SDTA). As the above <20 µm diameter yarns could not support the mechanical load needed for using this DMA, 140-190 µm diameter, dual-Archimedean yarn was prepared by inserting twist in a 2.5 cm wide, 12.5 cm long stack of 20 parallel-oriented nanotube sheets. The inserted twist was 3,000 turns/m when normalized to the final yarn length (5.7 cm) and 1,360 turns/m when normalized to the initial sheet stack length. Though this amount of twist insertion caused the start of coiling for low applied tensile load (4 g), the coiling disappeared when a small amount of twist was released when the yarn was cut from the spinning support. Yarn prepared identically was used for all measurements; wax infiltration was accomplished by touching the electrically heated yarn with flakes of paraffin wax.

Each yarn was knotted to steel supports and the supports were subsequently clamped to prevent damage to the yarn, thereby providing a 9 mm gauge length. The mode of deformation was tension and dynamic strain was limited to a maximum of 0.3%. An offset of 20 MPa was used to maintain the yarn in a state of tension and simulate conditions where actuation was characterized. Samples were tested at a heating rate of 2°C/min, using a deformation frequency of 1 Hz. Tests at higher deformation frequencies of up to 100 Hz for the neat yarn showed that results are insensitive to frequency in this range.

During initial heating and cooling cycles in nitrogen gas the initial Young’s modulus for the neat yarn of 4.8 GPa at 30C decreased to about 4.1 GPa at 150C. Since on subsequent cycles from 30 to 300C the modulus was maintained at 4.0 GPa, the progressive irreversible modulus change during initial cycles is apparently due to thermal modification of inter-nanotube interactions, including possible removal of trace impurities at these interconnections. The first heating cycle for the as-wax-infiltrated yarn provided a major drop in modulus from ~7 GPa to

11

~2.5 GPa at 150C, which is likely due to reorganization of the wax within the yarn. Subsequently obtained reversible behavior provided a Young’s modulus decrease from 3.3 GPa at 40C to 2.0 GPa at 110C, with 77% of this decrease occurring below the temperature where the wax is completely molten (80C). Note that this 1.65 ratio between the modulus of a 155 µm diameter, wax-filled, dual-Archimedean yarn at 40C to that for the same yarn at 110C is comparable to (but smaller than) the above determined modulus ratio of 3.45 for a much smaller diameter (16 µm) dual-Archimedean before and after wax filling. However, the modulus ratio derived using Eqn. 1 from the dependence of actuation strain on applied stress between room temperature and the actuated molten state for the above described 16 µm diameter, wax-filled, dual-Archimedean yarn is much smaller (1.11). Though the reason for this discrepancy is presently unknown, it may originate from the dependence of the Young’s modulus and Poisson’s ratio on tensile stress for twist-spun nanotube yarns (8), which is neglected in Eqn. (1). Additionally note that all Young’s modulus results in this section for the molten state ignore expansion in yarn diameter in going from low temperature to the molten wax state, which has the effect of decreasing the ratio of the Young’s modulus of the solid-wax yarn state to that for the liquid-wax yarn state.

Though systematic investigations have not been conducted, preliminary results show that wax infiltration into nanotube yarns little effects yarn breaking force and produces about a 6% increase in yarn resistance. 10. Structural Changes During Isotonic Tensile Actuation of Wax-Filled Carbon Nanotube Yarns

Movies recorded by optical microscopy were used to characterize yarn structure changes as overall yarn length change was measured during isotonic electrothermal tensile actuation. A wax-filled, non-coiled, dual-Archimedean yarn was two-end-tethered in the Fig. 1A configuration. This 150 µm diameter yarn had a bias angle of 35 and contained 2,500 turns/m of inserted twist per stack length. The applied load was 13.4 MPa and 123 mW/cm of electrical power was applied to cycle between actuated and non-actuated steady states. We observed that yarn diameter increased by 4.06 ± 1.87% as total yarn length contracted by 0.585 ± 0.003%, thereby indicating that the yarn volume increased by 7.7 ± 2.6% during actuation. As expected because of nanotube volume, this percent yarn volume change from ambient temperature to 210 C was much smaller than the percent volume change of the wax, which is about 30% (Fig. S5).

For comparison with the above result, the percent volume change for the yarn during actuation (Vy/Vy) was calculated from the density of bundled nanotubes (b), the initial density of the wax before actuation (w), the fraction of yarn weight that is wax (Fw), and the fractional change in wax volume during actuation (Vw/Vw). The result is:

Vy/Vy = (Vw/Vw)(1 + (w/b)((1-Fw)/Fw))-1. A nanotube bundle density of b = 1.65 g/cm3 was calculated by approximating that a typical bundle contains hexagonally close-packed, 9 nm diameter nanotubes having six walls. Using 0.9 g/cm3 for the density of the solid wax, w/b = 0.54. For the measured weight fraction of wax in a 180 µm diameter, dual-Archimedean yarn (0.28) and the measured Vw/Vw between 30 and 210C (30%), the calculated yarn volume change is 12.6%, which is within two standard deviations of the above measured value (7.7 2.6%).

12

Again using the Fig. 1A configuration, photographs before and after actuation were made of the entire length of a highly coiled, wax-filled, dual-Archimedean yarn. This 107.9 ± 3.4 μm yarn was made similarly to the above uncoiled yarn except that it contained higher inserted twist (4,000 turns/m). The applied stress was 4.3 ± 0.3 MPa and 306 mW/cm of input power was applied to cycle between non-actuated and actuated steady states. Other than for non-coiled yarn very close to the end tethers, the entire yarn was coiled. Precise measurements of geometry changes during actuation were not possible because of irregularities in coil structure and deviation of the yarn cross-section from circular. Importantly, no change in number of coils was observed as a result of actuation of this coiled yarn having an initial length of 1.38 cm: direct count showed that the yarn contained 72 coils both before and after actuation. These results show that the observed 2.15 ± 0.22% yarn contraction is principally due to decrease in the separation between neighbouring coils, and not to a change in the number of coils in the yarn.

In order to do the same study for a lightly coiled yarn (which is 57.4% coiled), twist was partially released from the above 1.38 cm long, heavily-coiled yarn to obtain a 1.74 cm long, wax-filled yarn that contained separated coiled and non-coiled regions and 3,400 turns/m of inserted twist. Before and after similar electrothermal actuation as used above, the numbers of coils in the non-actuated and actuated states were counted. The number of coils in the yarn appeared to decrease from 55 coils before actuation to 54 coils after steady-state actuation. Such a decrease in coil number would contribute to expansion, rather than to the 0.95 ± 0.36% contraction observed during actuation. These results again support the conclusion that decrease in the separation between adjacent coils is predominately the origin of enhanced actuation for the coiled yarns. While we do sometimes observe insertion of a fraction of a coil near the upper tether (Fig. 1A configuration) for 99% coiled yarn, this effect is not highly reproducible for different yarns and is apparently due to the proximity of the tether.

Since stretch of a coiled yarn can convert writhe (i.e., coiling) to twist, isometric actuation is likely to provide different results. We have focused the above measurements on isotonic actuation because isometric actuation does no mechanical work. 11. Thermal Actuation Using Guests Other Than Paraffin Wax

11.1 Torsional actuation of yarn containing a polydiacetylene guest Using horizontal yarn configurations (Fig. S8, A and B) and either fully infiltrated or one-

half infiltrated yarns, torsional actuation was investigated for a 9 μm diameter Fermat yarn having a bias angle of 26°. The process of Section 2.2 was used for solution-based infiltration of the yarn or a yarn segment with 10,12-pentacosadiynoic acid, and subsequent partial UV polymerization of this guest by 1,4-addition polymerization. This guest was chosen since this polydiacetylene (PDA) is known to undergo a solid-state blue-red color transition at about 57C, which is reversible unless too high a temperature is reached. However, the partial degree of polymerization is a complication, since the unpolymerized monomer melts at 63C, and produces additional yarn expansion.

For the first investigated horizontal configuration (Fig. S8A, which is analogous to the Fig. 1B configuration) the two-end-tethered homochiral Fermat yarn supported a constant load (2 MPa, when normalized to the cross-section of the unactuated yarn). The PDA-containing yarn segment used for torsional actuation was 3 cm long and the total yarn length was 7 cm, of which 6 cm was located before the wire eye hole support and the rest of the yarn length vertically supported a slotted weight, which was not free to rotate (but was free to move vertically as the actuating yarn segment contracted and expanded). Hence, the non-infiltrated yarn length acts as a

13

torsional return spring. Both for this and the second described configuration, Joule heating was by applying a voltage between the yarn end and the metal eye hole support. When 2 mA DC current was applied to the yarn (corresponding to 13 mW/cm input power), reversible paddle rotation of 100/mm was produced as the actuated yarn untwisted during Joule heating. Highly reversible actuation was demonstrated for over 5,000 on-off cycles, which were the maximum investigated.

Even when in a one-end tethered configuration (Fig. S7B, which is analogous to the Fig. 1C configuration), the fully infiltrated, PDA-hybrid yarn can provide reversible torsional rotation even when heated to above the melting point of unpolymerized monomer. When 2 mA DC current was applied to the 3 cm long diacetylene-infiltrated yarn segment, the paddle rotated in the direction that corresponds to untwist of the actuating yarn, and this rotation was then reversed when electrical heating was stopped. This indicates that the polydiacetylene inside the yarn functions as an internal torsional spring to enable torsional actuation to reverse when yarn volume decreases during cooling. Since the corresponding neat yarn does not have a return spring, it does not provide reversible torsional actuation.

11.2 Torsional actuation for yarn infiltrated with polyethylene glycol guest Torsional actuation was characterized for a two-end-tethered, homochiral, non-coiled

Fermat yarn that was partially infiltrated with PEG, which was chosen as guest since it expands volume by 10% during melting (36). The yarn diameter, amount of inserted twist, and bias angle were 17 µm, 15,000 turns/m, and 31, respectively. The total yarn length was 5.2 cm, a 2.6 cm long section at one yarn end was infiltrated with PEG, and the paddle was at the junction between infiltrated and non-infiltrated yarn segments, like in Fig. 1B. This paddle, which is 92 times heavier than the infiltrated yarn segment, was a rectangular strip (3.7 mm long, 1.1 mm wide, and 130 µm thick) that was cut from Kapton tape. Torsional actuation was recorded using a high speed movie camera (240 frames/s), and data was obtained by frame-by-frame analysis of the time dependence of paddle rotation angle.

Using the Fig. 1B configuration, actuation to above the melting temperature of the PEG was produced by applying a 2.4 mA square wave current pulse (3.4 Hz frequency and 25% duty cycle) along the entire yarn length. The corresponding power during actuation was 16 mW/cm and the tensile stress applied during actuation was 23 MPa (when normalized to the cross-section of the non-actuated yarn). Using this pulsed electrical power input, a maximum rotation speed of 1,040 revolutions per minute and a torsional rotation of 37o/mm were obtained (during an actuation cycle where the infiltrated yarn segment first untwists during heating and then retwists during unaided cooling). No degradation in actuation was observed up to the maximum number of observed cycles (100,000 cycles). 12. Non-Electrical Actuation

12.1 Photo-thermal actuation Instead of using electrical heating, torsional and tensile actuation of paraffin-containing

carbon nanotube hybrid yarns was produced by incandescent heating from a 100 W white-light lamp that was manually switched on (1.6-2s) and off (0.3-0.5s). Movie S1 shows the resulting torsional actuation of 12.6°/mm for a two-end tethered homochiral Fermat yarn (15 m diameter with 20,000 turns/m of inserted twist) that is half-infiltrated with paraffin wax (Fig.1B).

14

12.2 Immersion driven torsional actuation This study demonstrates that largely reversible torsional rotation can be obtained by

varying the immersion depth of a two-end-tethered homochiral yarn in a wetting liquid. The actuator test configuration of Fig. S10A was deployed, where the total yarn length was 80 mm, the paddle used for recording actuation was approximately at yarn midpoint, the top end of the yarn was attached to a flexible rod support and the bottom yarn end was rigidly attached to the bottom of a stationary 20 mm diameter glass vial. The investigated Fermat yarn contained ~25,000 turns/m of inserted twist and the initial yarn diameter and bias angle were 8 µm and 32, respectively. The Mylar paddle was 3.5 mm wide, 2 mm tall and 0.1 µm thick and weighed 1.0 mg, which is 100 times heavier that the total yarn.

The actuator response was trained by first injecting ~4 cm3 of test liquid into the glass, which provided a yarn immersion depth of ~12 mm. After the paddle rotation stopped, indicating torque balance, the liquid was removed at about 0.1 ml/s, which corresponded to a 0.3 mm/s decrease in yarn immersion depth. The liquid filling/removal procedure was repeated 3 times to ensure a degree of reversibility for the dependence of paddle rotation angle on yarn immersion. After this training period, the data in Fig. S10B shows that the paddle rotation angle () is a function of yarn immersion depth, with approximate slopes of 49.6 3.4 and 35.3 1.7 degree/mm for acetonitrile and hexane, respectively.

These results suggest that the immersion liquids are acting to swell yarn volume, just like absorbed liquids swell the volume of ordinary polymers. However, since the twist spun nanofiber yarn has a chiral structure, this swelling induces yarn rotation. The higher slope of the dependence on paddle rotation angle on yarn immersion depth for acetonitrile than for hexane is consistent with the lower interfacial energy between the nanotubes in the yarn and the acetonitrile (37). Nevertheless, even this type of actuation is complex, and changes in the torsional modulus of infiltrated yarn segments versus non-infiltrated segments might be providing the torque unbalance that provides paddle rotation.

12.3 Torsional actuation powered by hydrogen absorption The preparation of the Pd-hybrid yarn used for this experiment is described in Section 2.4.

This dual-Archimedean yarn was 144 µm in diameter, 1.6 cm long, contained 100 to 200 turns/m of inserted twist, had a linear density of 20 g/cm, and contained 90 wt% palladium (corresponding to a 60 nm thick palladium layer on nanotubes bundles). The configuration of Fig. 1D was deployed for characterization of torsional actuation using 0.022 MPa tensile stress. Injection of 0.05 atm of H2 into a vacuum chamber containing the one-end-tethered actuating yarn caused 1.5 rotations of a 1,100 heavier paddle within 6 s, which was fully reversed on a similar time scale during repeated cycling between hydrogen exposure and vacuum. 13. Theoretical Analyses of Tensile Actuation for Non-Coiled Nanotube Yarns

We here describe the conflict between the tensile dimension changes of interconnected inner and outer radius nanotube helices, which reduce tensile contraction in twist-spun, non-coiled yarn. In this analysis a non-coiled twist-spun yarn is approximated by nested helices. A helix at yarn radius r is obtained by winding a thin string (representing nanotube bundle lengths) at a bias angle of = tan-1(2rT), where T is the twist inserted per yarn length. For each individual helix the relationship between the helix volume (V), helix length (L), string length (Ls), number of turns (n), and bias angle () is:

15

0

2

20

20

20,

220

20

2

0 αsin

αsin

n

n

LL

LL

n

n

r

r

V

V

s

s

, (2)

where parameters with a zero subscript define the initial helix and is the extension ratio (L/L0) of the helix such that the tensile actuation strain is 100 x (-1)%.

In using this equation to predict the dependence of tensile actuation on helix volume change for different helix bias angles, we keep string length constant (since nanotube thermal expansion in the length direction is small) and set n=n0 (since the yarn is two-end tethered). The results (Fig. S11) show that a contraction in helix length occurs when the helix volume increases and the starting bias angle is above zero and below 54.73o. Moreover, they show that helix length change, for a given percent helix volume change, strongly depends on helix bias angle. Since this bias angle varies from = tan-1(2rT) on the yarn surface to 0 at yarn center there is a fundamental conflict (which we call frustration) between volume change produced tensile contractions for different radius helices within the yarn. While this frustration can be reduced by concentration of wax towards the yarn core during actuation, it cannot be eliminated. Consequently, yarn tensile contraction of non-coiled yarns is greatly reduced compared to values that would be predicted for a helix with the outer helical geometry and a given percent volume change of the yarn.

In contrast, although pore volume (and therefore wax concentration and associated expansion during actuation) can vary radially, torsional actuation of twist spun yarns is not subject to the above singularity problem at the core of a helical scroll. In the context of the simple helix model, the yarns are twist spun by inserting the same twist in yarn layers having different radii and this twist insertion results in the same tensile contraction for all radial layers. Volume expansion can just reverse this twist insertion, thereby providing torsional rotation, although some redistribution of wax concentration can occur during actuator training and during subsequent transitions between unactuated and actuated states.

16

Figures and Figure Captions

10 15 20 25 30 350.00

-0.02

-0.04

-0.06

-0.08

-0.10

Twist (thousand turns/m)

Ten

sile

act

uatio

n (%

)

5.2

5.6

6.0

6.4

6.8

Leng

th (

cm)

Fig. S1. Tensile actuation strain (left axis) and unactuated yarn length (right axis) as a function of inserted twist for a neat, homochiral, Fermat yarn in the Fig. 1A configuration. The steady-state electrical power applied to obtain yarn contraction was constant (85 ± 2.6 mW/cm) when normalized to the measured yarn length for each degree of twist, so the input power per yarn weight was also constant. Mechanical load was constant and corresponded to 72 MPa stress for the 13.5 µm yarn diameter measured by SEM microscopy for the untethered yarn. The lines are guides for the eyes.

17

20 30 40 50 600.0

-0.1

-0.2

-0.3

-0.4

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n (%

)

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72

73

74

75

76 Neat Fermat yarn Wax-filled Fermat yarn

L o (m

m)

20 30 40 50 60 70 80 900.0

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Tensile stress (MPa)

Ten

sile

act

uatio

n (%

)

70

72

74

76

78

80

L 0 (m

m)

Neat dual-Archimedean yarn Wax-filled dual-Archimedean yarn

Fig. S2. Tensile actuation (left axis) and non-actuated length (right axis) versus applied stress for homochiral, non-coiled Fermat (A) and dual-Archimedean yarns (B) having 20,000 ± 500 turns/m of inserted twist and about the same diameter before (17.5 0.5 μm and 16.4 0.9 μm, respectively) and after wax infiltration (18.1 0.9 μm and 16.2 1.1 μm, respectively). The Fig.1A configuration was used and the electric power per length was adjusted to be 35 ± 2 mW/cm for each load. The lines are guides for the eyes.

B 

A 

18

Fig. S3. SEM micrographs of the cross-section of a non-coiled Fermat carbon nanotube yarn before (A, C) and after (B, D) wax infiltration. Pores shown in the high magnification image of the neat yarn (C) are not visible in the corresponding image for the wax hybrid yarn (D). The diameter of the wax hybrid yarn (8.2 ± 0.3 μm) was less than that of the neat yarn (10.4 ± 0.3 μm) because additional twist was inserted in the yarn before wax solidification.

Fig. S4. SEM micrographs of (A) a sheet stack which contained 90 wt% palladium and (B) an untethered 144 µm diameter, dual-Archimedean yarn obtained by twist -based spinning the sheet stack of (A) between rigid supports.

19

20 40 60 80 100 120 140 160 180 200 2200

5

10

15

20

25

30

Temperature (oC)

Vol

ume

chan

ge (

%)

3

2

1

0

-1

-2

-3

Hea

t flo

w (

W/g

)

Fig. S5. DSC for increasing and decreasing temperature (blue solid and dashed lines, respectively), the temperature dependence of volume change during heating (solid small circles) and cooling (open large circles), and TGA (inset) for Sigma-Aldrich 411671 wax. The lines for the volume change data are guides for the eyes.

30 60 90 120 150 1800.0

0.2

0.4

0.6

0.8

1.0

1.2

Temperature (oC)

To

rsio

nal M

odu

lus

(10

-8 N

·m2 )

Neat dual-Archimedean yarn 1st 2nd 3rd

Wax-filled dual-Archimedean yarn 1st 2nd

Fig. S6. The temperature dependence of torsional modulus of neat (open symbols) and wax-filled (closed symbols), non-coiled, dual-Archimedean yarns. The yarn diameter and applied stress were 200 m and 4.8 MPa for the neat yarn and 210 m and 4.4 MPa for the wax filled yarn. The lines for the data are guides for the eyes and the symbols in the insets denote different runs.

100 200 300 400 5000

20

40

60

80

100

Temperature (oC)

Mas

s (%

)

20

Fig. S7. Measurement configuration for characterizing high-rate torsional actuation for a two-end-tethered, half-wax-filled yarn using a 532 nm wavelength laser. An aluminium paddle attached to the yarn reflects the laser beam to a ring of photodiodes.

Fig. S8. Horizontal configurations deployed for torsional actuators. (A) Variant of a two-end-tethered, partially infiltrated yarn motor in which contact with a lateral surface prohibits rotation of an attached end weight, but still enables vertical movement of this mechanical load. (B) Torsional motor based on a fully infiltrated yarn that is one-end tethered. In this case the attached mechanical weight can both rotate and translate vertically.

21

0 10 20 30 40 50 60 70

0

10

20

30

40

50

60

70

Electrical power (mW/cm)

Rot

atio

n (o /m

m)

Fig. S9. Steady-state torsional rotation as a function of electrical power for a neat, heterochiral, two-ply, Fermat yarn in vacuum (blue triangles) and the same yarn type in air after wax filling (black circles) on increasing and decreasing temperature (filled and open symbols, respectively). The insets are SEM micrographs showing the structure of SZ and ZS segments, which were knotted together to make the heterochiral SZ-ZS yarn. The paddle was located between the SZ and ZS segments for the used two-end tethered configuration of Fig. 1D. The lines are guides for the eyes.

22

0 2 4 6 8 10 12 14 16 18

0

200

400

600

800

1000

Acetonitrile

Hexane

Liquid level (mm)

Rot

atio

n (o )

Fig. S10. (A) Measurement apparatus and (B) the observed dependence of paddle rotation angle on yarn immersion depth in acetonitrile and in hexane for an 8 µm diameter, homochiral, Fermat, carbon nanotube yarn having 25,000 turns/m of inserted twist. Closed and open symbols are for liquid filling and removal, respectively. The lines are guides for the eyes.

B 

A  camera

syringe

23

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-8

-6

-4

-2

0

2

4

6

8

10

Volume change (%)

90o

68o

60o54.73o

50o

45o

35o

Ten

sile

act

uatio

n (%

)

25o

Fig. S11. Calculated tensile strain as a function of volume change for single helices having various initial bias angles. The string length is constant and torsional rotation is prohibited.

Supplemental Movies

Movie S1. Photothermal torsional actuation of a half-wax-filled, two-end-tethered, homochiral, Fermat yarn.

Movie S2. Electrothermal torsional actuation of a half-wax-filled, two-end-tethered, homochiral, Fermat yarn to produce an average speed of 5,500 revolutions per minute.

Movie S3. A miniature Greco-Roman style catapult driven by a wax-filled, two-end-tethered, heterochiral, dual-Archimedean yarn hurls a projectile.

Movie S4. Tensile actuation of a neat, two-end-tethered, coiled, dual-Archimedean yarn during electrothermal heating in vacuum to incandescent temperature, during which it lifts a 50,200 times heavier weight by 7.3% of yarn length.

Movie S5. Electrothermal torsional actuation of a neat, two-end-tethered, two-ply, heterochiral, Fermat yarn.

References and Notes:

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