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Trade-off effect between the stress and strain range in the soft elasticity of liquid crystalline elastomers


For liquid crystal elastomers (LCEs), crosslinking is a stress reinforcing factor that sufficiently inhibits macroscopic deformation. In this study, coarse-grained molecular simulations were performed to systematically investigate the dependence of the stress–strain curves of LCEs on the crosslink density. For the unidirectionally oriented initial structure of LCEs, uniaxial elongation was performed in perpendicular or parallel directions. The perpendicularly elongated LCEs demonstrated a characteristic plateau region in the stress–strain curve, indicating soft elasticity. This plateau region corresponds to a large change in the orientational order parameter, indicating that the orientation of mesogens is closely related to soft elasticity. The strain region corresponding to the soft elasticity became narrower as the crosslink density increased. The change in the orientation order parameter also became steeper with increasing crosslink density. On the other hand, the stress values in the plateau region increased with increasing crosslink density. These results indicate a systematic trade-off between stress and strain in the soft elasticity of LCEs, which means that it is possible to select the optimal set of values of stress and the strain range through the crosslink density. Furthermore, the presence of optimal solvent and polymer chain densities that can increase the stress while extending the strain range is indicated.

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  1. Kularatne RS, Kim H, Boothby JM, Ware TH. Liquid crystal elastomer actuators: synthesis, alignment, and applications. J Polym Sci B Polym Phys. 2017;55:395–411.

  2. Herbert KM, Fowler HE, McCracken JM, Schlafmann KR, Koch JA, White TJ. Synthesis and alignment of liquid crystalline elastomers. Nat Rev Mater. 2021;1–16.

  3. Warner M, Bladon P, Terentjev E. “soft elasticity”—deformation without resistance in liquid crystal elastomers. J de Phys II. 1994;4:93–102.

    CAS  Google Scholar 

  4. Burke KA, Mather PT. Soft shape memory in main-chain liquid crystalline elastomers. J Mater Chem. 2010;20:3449–57.

    Article  CAS  Google Scholar 

  5. White TJ, Broer DJ. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat Mater. 2015;14:1087–98.

    Article  CAS  PubMed  Google Scholar 

  6. Ware TH, Biggins JS, Shick AF, Warner M, White TJ. Localized soft elasticity in liquid crystal elastomers. Nat Commun. 2016;7:1–7.

    Article  Google Scholar 

  7. Gelebart AH, Mulder DJ, Vantomme G, Schenning APHJ, Broer DJ. A rewritable, reprogrammable, dual light-responsive polymer actuator. Angew Chem (Int ed Engl). 2017;56:13436–9.

    Article  CAS  Google Scholar 

  8. Guo Y, Zhang J, Hu W, Khan MTA, Sitti M. Shape-programmable liquid crystal elastomer structures with arbitrary three-dimensional director fields and geometries. Nat Commun. 2021;12:1–9.

    Article  Google Scholar 

  9. Zhang J, Guo Y, Hu W, Soon RH, Davidson ZS, Sitti M. Liquid crystal elastomer-based magnetic composite films for reconfigurable shape-morphing soft miniature machines. Adv Mater. 2021;33:2006191.

    Article  CAS  Google Scholar 

  10. Thomsen DL, Keller P, Naciri J, Pink R, Jeon H, Shenoy D, et al. Liquid crystal elastomers with mechanical properties of a muscle. Macromolecules. 2001;34:5868–75.

    Article  CAS  Google Scholar 

  11. Wermter H, Finkelmann H. Liquid crystalline elastomers as artificial muscles. e-Polym. 2001;1:013

    Article  Google Scholar 

  12. Buguin A, Li M-H, Silberzan P, Ladoux B, Keller P. Micro-actuators: when artificial muscles made of nematic liquid crystal elastomers meet soft lithography. J Am Chem Soc. 2006;128:1088–9.

    Article  CAS  PubMed  Google Scholar 

  13. Li M-H, Keller P. Artificial muscles based on liquid crystal elastomers. Philos Trans A Math Phys Eng Sci. 2006;364:2763–77.

  14. Urayama K, Honda S, Takigawa T. Deformation coupled to director rotation in swollen nematic elastomers under electric fields. Macromolecules. 2006;39:1943–9.

    Article  CAS  Google Scholar 

  15. Corbett D, Warner M. Changing liquid crystal elastomer ordering with light – a route to opto-mechanically responsive materials. Liq Cryst. 2009;36:1263–80.

    Article  CAS  Google Scholar 

  16. Kato T, Tanabe K. Electro- and photoactive molecular assemblies of liquid crystals and physical gels. Chem Lett. 2009;38:634–9.

    Article  CAS  Google Scholar 

  17. Ohm C, Brehmer M, Zentel R. Liquid crystalline elastomers as actuators and sensors. Adv Mater. 2010;22:3366–87.

  18. Winkler M, Kaiser A, Krause S, Finkelmann H, Schmidt AM. Liquid crystal elastomers with magnetic actuation. Macromol Symp. 2010;291–292:186–92.

  19. White TJ. Photomechanical effects in liquid crystalline polymer networks and elastomers. J Polym Sci B Polym Phys. 2018;56:695–705.

  20. Shenoy DK, Laurence Thomsen D III, Srinivasan A, Keller P, Ratna BR. Carbon coated liquid crystal elastomer film for artificial muscle applications. Sens Actuators A: Phys. 2002;96:184–8.

    Article  CAS  Google Scholar 

  21. Bispo M, Guillon D, Donnio B, Finkelmann H. Main-chain liquid crystalline elastomers: monomer and cross-linker molecular control of the thermotropic and elastic properties. Macromolecules. 2008;41:3098–108.

    Article  CAS  Google Scholar 

  22. Urayama K, Kohmon E, Kojima M, Takigawa T. Polydomain−monodomain transition of randomly disordered nematic elastomers with different cross-linking histories. Macromolecules. 2009;42:4084–9.

    Article  CAS  Google Scholar 

  23. White TJ, Serak SV, Tabiryan NV, Vaia RA, Bunning TJ. Polarization-controlled, photodriven bending in monodomain liquid crystal elastomer cantilevers. J Mater Chem 2009;19:1080–5.

    Article  CAS  Google Scholar 

  24. Lee KM, Smith ML, Koerner H, Tabiryan N, Vaia RA, Bunning TJ, et al. Photodriven, flexural–torsional oscillation of glassy azobenzene liquid crystal polymer networks. Adv Funct Mater. 2011;21:2913–8.

  25. Ohm C, Haberkorn N, Theato P, Zentel R. Template-based fabrication of nanometer-scaled actuators from liquid-crystalline elastomers. Small. 2011;7:194–8.

  26. Okamoto T, Urayama K, Takigawa T. Large electromechanical effect of isotropic-genesis polydomain nematic elastomers. Soft Matter. 2011;7:10585–9.

    Article  CAS  Google Scholar 

  27. Fleischmann E-K, Ohm C, Serra C, Zentel R. Preparation of soft microactuators in a continuous flow synthesis using a liquid-crystalline polymer crosslinker. Macromol Chem Phys. 2012;213:1871–8.

  28. Tsuchitani A, Ashida H, Urayama K. Pronounced effects of cross-linker geometries on the orientation coupling between dangling mesogens and network backbones in side-chain type liquid crystal elastomers. Polymer. 2015;61:29–35.

    Article  CAS  Google Scholar 

  29. Guin T, Settle MJ, Kowalski BA, Auguste AD, Beblo RV, Reich GW, et al. Layered liquid crystal elastomer actuators. Nat Commun. 2018;9:2531

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Rešetič A, Milavec J, Domenici V, Zupančič B, Bubnov A, Zalar B. Stress-strain and thermomechanical characterization of nematic to smectic a transition in a strongly-crosslinked bimesogenic liquid crystal elastomer. Polymer. 2018;158:96–102.

    Article  CAS  Google Scholar 

  31. He Q, Wang Z, Wang Y, Wang Z, Li C, Annapooranan R, et al. Electrospun liquid crystal elastomer microfiber actuator. Sci Robot. 2021;6:9704.

    Article  Google Scholar 

  32. Mistry D, Traugutt NA, Sanborn B, Volpe RH, Chatham L, Zhou R, et al. Soft-elasticity optimises dissipation in 3D-printed liquid crystal elastomers. Nat Commun. 2021;12:6677.

  33. Mbanga BL, Ye F, Selinger JV, Selinger RL. Modeling elastic instabilities in nematic elastomers. Phys Rev E. 2010;82:051701.

    Article  Google Scholar 

  34. Skačej G, Zannoni C. Main-chain swollen liquid crystal elastomers: a molecular simulation study. Soft Matter. 2011;7:9983–91.

    Article  Google Scholar 

  35. Skačej G, Zannoni C. Molecular simulations shed light on supersoft elasticity in polydomain liquid crystal elastomers. Macromolecules. 2014;47:8824–32.

    Article  CAS  Google Scholar 

  36. Whitmer JK, Roberts TF, Shekhar R, Abbott NL, de Pablo JJ. Modeling the polydomain-monodomain transition of liquid crystal elastomers. Phys Rev E. 2013;87:020502

    Article  CAS  Google Scholar 

  37. Tagashira K, Takahashi K, Fukuda J, Aoyagi T. Development of coarse-grained liquid-crystal polymer model with efficient electrostatic interaction: toward molecular dynamics simulations of electroactive materials. Materials. 2018;11:83.

  38. Yasuoka H, Takahashi KZ, Fukuda J-I, Aoyagi T. Molecular architecture dependence of mesogen rotation during uniaxial elongation of liquid crystal elastomers. Polymer. 2021;229:123970.

    Article  CAS  Google Scholar 

  39. Brannum MT, Auguste AD, Donovan BR, Godman NP, Matavulj VM, Steele AM, et al. Deformation and elastic recovery of acrylate-based liquid crystalline elastomers. Macromolecules. 2019;52:8248–55.

    Article  CAS  Google Scholar 

  40. Doi H, Takahashi KZ, Tagashira K, Fukuda J-I, Aoyagi T. Machine learning-aided analysis for complex local structure of liquid crystal polymers. Sci Rep. 2019;9:16370

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Takahashi KZ, Aoyagi T, Fukuda J-I. Multistep nucleation of anisotropic molecules. Nat Commun. 2021;12:5278.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Yakacki C, Saed M, Nair D, Gong T, Reed S, Bowman C. Tailorable and programmable liquid-crystalline elastomers using a two-stage thiol–acrylate reaction. Rsc Adv. 2015;5:18997–9001.

    Article  CAS  Google Scholar 

  43. Aoyagi T, Sawa F, Shoji T, Fukunaga H, Takimoto J, Doi M. A general-purpose coarse-grained molecular dynamics program. Computer Phys Commun. 2002;145:267–79.

    Article  CAS  Google Scholar 

  44. Swope WC, Andersen HC, Berens PH, Wilson KR. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters. J Chem Phys. 1982;76:637–49.

    Article  CAS  Google Scholar 

  45. Mistry D, Gleeson HF. Mechanical deformations of a liquid crystal elastomer at director angles between 0° and 90°: deducing an empirical model encompassing anisotropic nonlinearity. J Polym Sci Part B: Polym Phys. 2019;57:1367–77.

    Article  CAS  Google Scholar 

  46. Oh S-W, Guo T, Kuenstler AS, Hayward R, Palffy-Muhoray P, Zheng X. Measuring the five elastic constants of a nematic liquid crystal elastomer. Liq Cryst. 2021;48:511–20.

    Article  CAS  Google Scholar 

  47. Okamoto S, Sakurai S, Urayama K. Effect of stretching angle on the stress plateau behavior of main-chain liquid crystal elastomers. Soft Matter. 2021;17:3128–36.

    Article  CAS  Google Scholar 

  48. Warner M, Terentjev EM. Liquid crystal elastomers. London, United Kingdom: Oxford University Press; 2007.

  49. Xiao Y-Y, Jiang Z-C, Hou J-B, Zhao Y. Desynchronized liquid crystalline network actuators with deformation reversal capability. Nat Commun. 2021;12:624.

    Article  CAS  Google Scholar 

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This paper is based on results obtained from a project (JPNP16010) commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

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Correspondence to Kazuaki Z. Takahashi.

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Yasuoka, H., Takahashi, K.Z. & Aoyagi, T. Trade-off effect between the stress and strain range in the soft elasticity of liquid crystalline elastomers. Polym J 54, 1017–1027 (2022).

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