Artificial muscles made of chiral two-way shape memory polymer fibers

Structural chirality can be found in many natural materials, such as climbing plant tendrils,¹ DNA,² snail shells³ and even the nanostructure of butterfly wings.⁴ One of the merits of chirality is to endow the materials with unusual mechanical, optical, and magnetic properties. Inspired by our mother nature, the researchers have introduced chirality to many man-made materials and have fabricated materials and devices with outstanding features, such as helical nanowires,⁵ chiral carbon nanotubes (CNTs),⁶ etc. Recently, Haines et al.⁷ have created artificial muscles (AM) with hierarchical chiral structure made of polymer fibers that can offer up to 49% tensile actuation. The giant tensile stroke, robustness, low cost and easy tuning procedure of this polymeric artificial muscle have confirmed the significance of this innovative discovery and have opened up new horizons toward the development of effective devices, for instance, morphing airplanes and vehicles,⁸ self-healing composite,⁹ robotics,¹⁰ etc.

Recently, Sharafi and Li¹¹ have developed a bottom-up multiscale modeling framework to explain the remarkable actuation response of this type of artificial muscles. However, their model is very complex and needs significant curve fitting effort. Most recently, Yang and Li¹² have developed a top-down multi-scale model and elucidated the physical origin behind the remarkable tensile actuation behavior of the twisted-then-coiled artificial muscles. They have demonstrated that the anisotropic dimensional changes at the meso-scale level, i.e., reversible thermal contraction in axial direction and expansion in radial direction in the precursor (untwisted) fiber, result in an intrinsic torsion in the chiral (twisted) fiber upon heating and eventually lead to the giant tensile actuation of the helical coil in the macro-scale level. This underlying mechanism shares the same essence with the climbing tendrils,¹³ where the intrinsic torque is provided by the change in helical angle in the cellulose fibrils at the subcellular level. Additionally, the model suggested that the intrinsic torque of the chiral fiber, hence the tensile actuation of the helical artificial muscle, can be enhanced by increasing the thermal anisotropy of the fiber while keeping other properties unchanged. The axial thermal actuations of the precursor fibers previously used in Haines' work are driven by the intrinsic axial thermal contraction (negative coefficient of thermal expansion (NCTE)) of the polymer components.⁷ The NCTE of the precursor fibers are limited to about 5%, which limits the maximum tensile actuation of the twisted-then-coiled artificial muscles to 49%. Therefore, in order to further improve the thermal actuation of the precursor fiber, a different driving force should be adopted. We believe that precursor fibers made of two-way shape memory polymer (2W-SMP) (contraction upon heating and expansion upon cooling, similar to polymers with NCTE) can be a promising candidate, since the reported thermal actuation of the 2W-SMPs in the existing literature is sometimes an order higher than that of the precursor fibers used previously.

Regardless of compositions, architectures and designs, the necessary condition for two-way shape memory effect (2W-SME) is the co-existence of a stable network and a switching domain that can respond to the external stimuli.¹⁴ The stable network, mostly constructed from chemical cross-links, can endure load and retain permanent shape upon heating. The switching domain, consisting of oriented and crystallizable molecular chains, is responsible for the reversible shape change of the SMP, driven by the non-isothermal stress-induced crystallization. 2W-SME has been demonstrated in several polymer systems, in the form of film or bulky materials.^15–21 However, fabrication of chemically cross-linked 2W-SMP fiber is still challenging due to the thermosetting nature in chemical cross-linked polymers. Nevertheless, our group has recently fabricated the chemically cross-linked poly(ethylene-co-vinyl acetate) (PEVA) based 2W-SMP fibers that can offer reversible actuation up to ∼15%. The fabrication details can be found in the supplementary material. In this paper, the thermomechanical properties of the precursor and chiral 2W-SMP fibers are investigated, and then the tensile actuation performances of both fibers are presented. The polymeric chiral fibers are subsequently fabricated into coiled muscles, and the unusual improvement in the tensile actuation is finally demonstrated both experimentally and theoretically.

The fabrication of the artificial muscles follows the same procedure as in the work of Haines et al.,⁷ which takes two consecutive steps: twist insertion and coiling (See Fig. 1 for the optical images).

To characterize the thermomechanical properties of the fibers and provide input information for our mechanical model, we measured the temperature dependence of the axial Young's moduli $E1$ of both precursor and chiral fibers using a TA Instrument Dynamic Mechanical Analyzer (DMA Q800). In the test, the samples were heated from $Tlow$(20 °C) to $Thigh$(67 °C). The choices of the temperature are based on the crystallization and melting behavior of the fiber. $Tlow$ should be lower than the onset of the crystallization temperature, and $Thigh$ should be within the broad melting range of the fiber. For the shear moduli $G12$⁠, a torsional pendulum apparatus, together with a temperature controlled coil heater, was used (See Fig. 2 for the experiment setup). In the test, one end of the fiber sample was clamped in a fixed grip and the other end was carefully centered in a slotted disk shaped pendulum and secured using a set of screws. Following the experimental and analysis procedure presented by Deteresa et al.,²² the shear modulus $G12$ of a circular cross-sectioned fiber can be expressed in terms of the fiber gauge length $Lf$⁠, the fiber radius $rf$⁠, the moment of inertia of the disc $I$ and the oscillation period $τ$ using Eq. (1)

A summary of the thermomechanical properties of both the precursor and chiral fibers at different thermal conditions is given in Table I.

Notice that a decrease in axial Young's modulus $E1$ can be observed after the twisting procedure. Interestingly, the fiber experiences almost the same level of degradation at low and high temperatures. In other words, the ratios of the precursor fiber modulus to the twisted fiber modulus at $Tlow$ and $Thigh$ are very close (8.30 and 8.65, respectively). The shear modulus $G12$⁠, on the other hand, increases after the twisting procedure. The changes in the thermomechanical properties between the precursor and twisted fibers can be understood and reproduced by the coordinate transformation in a transversely isotropic material.¹² It is worth mentioning that, for a twisted fiber, it tends to rewind or untwist upon heating. Therefore, the shear modulus of the twisted fiber at an elevated temperature cannot be obtained using the current experimental apparatus. In our work, for the sake of simplicity, we estimated the value of $G12$ at $Thigh$ for the twisted fiber by assuming that the levels of enhancement in shear modulus at the high temperature are the same as that at the low temperature.

The DMA Q800 under force controlled mode was used to explore the two-way shape memory effect of the fibers, and the results for the precursor fiber are presented in Fig. 3(a). In the test, the samples were heated and cooled at the rate of 10 °C/min, under a constant load $σact$ between $Tlow$(20 °C) and $Thigh$ (67 °C). The actuation strain (ε_act) of the 2W-SMP fiber is defined as

where $Lhigh$ is the length of the sample at high-temperature $Thigh$ and $Llow$ is the length at low temperature $Tlow$⁠, both with stress, $σact$⁠, applied. The 2W-SME is quantified using the average negative coefficient of thermal expansion (NCTE), defined as

In Fig. 3(b), the average NCTEs of the precursor and chiral fibers are presented in terms of the applied load. Fig. 3(b) reveals that the 2W-SME increases linearly with the applied load, mostly due to the fact that higher stress can promote extended chain crystallite growth toward a direction parallel to the stretching direction.¹⁵ Twisting the fiber will disturb the alignment of the molecular chains. As a result, a degradation in 2W-SME can be observed in the chiral fiber. In Fig. 3(b), we also presented the average NCTEs of the polyethylene (PE) fibers that we previously used to make artificial muscles.¹² Our 2W-SMP fibers possess an average NCTE that is at least one order higher than that of the PE fiber. Indeed, the PE fiber has a higher melting temperature. However, in the situation where high operating temperature is not necessary or not allowed, our 2W-SMP fiber can serve as a more efficient light-weight actuator.

As pointed out previously, the chiral fiber can generate intrinsic torque upon heating. In this work, we used a torque sensor (Mark-10 MR50-50Z Plug and Test Universal Torque Sensor) together with the coil heater to measure the torque generated by the twisted fiber fixed at both ends. The torque generated at $Thigh$ is as high as $4.4 Nmm$ (tests were repeated for three times and the results were stable), which is about an order higher than the recovered torque (⁠$0.6 Nmm$⁠) generated at 80 °C in the twisted PE fiber we used previously.¹² This unusual improvement in the recovered torque is attributed to the improvement in the tensile actuation of the precursor fiber and will contribute to the tensile actuation of the artificial muscle. As can be seen from Fig. 4, the coiled muscle can generate up to $67.81±1.82%$ actuation strain, which corresponds to an outstanding average NCTE of (⁠$144.27±3.87)×10−4 °C−1$⁠. We thus have reason to believe that if we could fabricate a precursor fiber with even stronger 2W-SME, the tensile stroke of the artificial muscle made of such fiber can be further increased. It is reported that cross-linked poly(ε-caprolactone) 2W-SMP can generate reversible actuation stroke up to $70%$ and thus can be a promising candidate.²³ 

As an actuator, the specific work for this artificial muscle during contraction was $81J/kg$⁠, which is about twice that of the natural muscle,²⁴ but much lower than that of the PE fiber we used previously (⁠$520J/kg$⁠).¹² The output work is mainly limited by the maximum force that can be sustained by our 2W-SMP. As can be seen from Table I, the fabricated 2W-SMP fibers have relatively lower tensile moduli, as compared to PE fibers (about $2000 MPa$⁠).¹² Therefore, the coiled spring cannot resist much bending moment and may deform into a spring with a large pitch angle. Under this circumstance, the torsional actuation of the chiral fiber cannot be converted into the tensile actuation of the coiled muscle effectively. In addition, since melting is involved in each working cycle of the muscle actuation, the actuation force must be limited, which reduces the specific work; otherwise, viscoplastic behavior may reduce the reversibility of the muscle. Another limitation of this new type of artificial muscle is the energy conversion efficiency, which is defined as the ratio of the output mechanical energy to the input thermal energy (calculated via differential scanning calorimetry (DSC) curve). During contraction, only $0.05%$ of the input thermal energy was converted into mechanical work, which is lower than the PE fiber we used previously (⁠$0.3%$⁠) and those used in the work of Haines et al.⁷ The reason for this is again due to the low stiffness of the 2W-SMP, which leads to reduced mechanical work. With similar specific heat between PEVA and PE, the reduced work translates to reduced energy conversion efficiency. A possible approach to improve these performances is to add conductive reinforcement, such as carbon nanotubes (CNTs), which may increase the actuation stress and energy conversion efficiency. This will be a topic for our future studies.

To further understand the working mechanism behind the hierarchical chiral structured artificial muscle, a simple mechanical model based on a consistent application of Castigliano's second theorem (CST)²⁵ is developed. Throughout the working cycle, a constant load $F=FZc$ is applied to the coil. In addition, since both ends of the twisted fiber are tethered, a recovered torque $Mrec=Mreczf$ is acting along the axial direction in the twisted fiber (see detailed derivation in the supplementary material). During the thermal cycle, the dimensional change in the axial direction of the fiber also contributes to the overall actuation of the coiled spring and cannot be neglected. In other words, the coiled artificial muscle is driven simultaneously by the externally applied load $F$ and the recovered torque $Mrec$⁠, along with the 2W-SME of the twisted fiber.

By assuming that, at each step of temperature increment, the deformations along the fiber caused by the external loads are infinitesimal, the complementary energy can be expressed as²⁶ 

in which

The displacement can also be expressed in terms of the pitch angle $αc$ using the kinematic relationship

By using Eqs. (5) and (6), together with the temperature dependence of the thermomechanical properties, such as moduli, CTEs and recovered torque, of the chiral fiber, we are able to reproduce the unusual tensile actuation of the coiled 2W-SMP based artificial muscle. Here, in this work, we only focus on the actuation strain $εact$ within one cycle for the artificial muscle (AM).

The model was coded and implemented into the MATLAB program. The theoretical value for $εact$ is 64.17%, which is in good agreement with the experimental value (67.81%). A parametric study in the inset of Fig. 4 indicates the sensitivity to both the recovered torque and the NCTE. The study indicates that both parameters have a positive impact on the tensile actuation of the muscle. From the above analysis, it is seen that the mechanical model captures the fundamental mechanisms and can help researchers understand the working principles of the artificial muscle and can facilitate the future material design.

In conclusion, a hierarchical chiral structured artificial muscle has been fabricated using two-way shape memory polymer fiber. Experimentally, we have presented the two-way shape memory effect of the precursor and twisted (chiral) fibers that eventually leads to the improvement in the axial actuation of the coiled artificial muscle at lower actuation temperatures. Theoretically, a mechanical model based on Castigliano's second theorem (CST) has been proposed and the calculated result is consistent with the experimental result. The model proves the significance of the 2W-SME and the recovered torque on tensile actuation and can be used as a guidance for the future study.

It is noted that the artificial muscles still have some limitations in terms of energy efficiency, such as specific work and energy conversion efficiency. It is envisioned that, by adding conductive reinforcement such as carbon nanotubes (CNTs) into 2W-SMPs, for example, grafting PEVA or poly(ε-caprolatone) (PCL, which has much higher 2W-SME than that of PEVA) chains onto the CNTs, the specific work and energy conversion efficiency may be enhanced, without the penalty of low actuation strain. This will be the topic for future studies.

See supplementary material for detailed experiment and derivation procedures.

The authors gratefully acknowledge the financial support by the National Science Foundation under Grant No. CMMI 1333997, Army Research Office under Grant No. W911NF-13-1-0145, and NASA cooperative agreement NNX16AQ93A under contract number NASA/LEQSF(2016-19)-Phase3-10.