Bending and Stretching in a Narrow Ribbon of Nematic Polymer Networks
Source abstract
Abstract
Abstract We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey acomplementarityrelation: one is maximum where the other is minimum. Moreover, we identify ableachingregime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the reference and current configurations), the ribbon’s deformation is essentially independent of its thickness.
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Research context
OpenAlex topics: Advanced Materials and Mechanics · Liquid Crystal Research Advancements · Advanced Sensor and Energy Harvesting Materials
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References (42)
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1. Corbett, D., Modes, C.D., Warner, M.: Photomechanics: bend, curl, topography, and topology. In: White, T.J. (ed.) Photomechanical Materials, Composites, and Systems. Wireless Transduction of Light into Work, pp. 79–116. Wiley, Hoboken (2017)10.1002/9781119123279.ch3 ↗
2. White, T.J.: Photomechanical effects in liquid-crystalline polymer networks and elastomers. In: White, T.J. (ed.) Photomechanical Materials, Composites, and Systems. Wireless Transduction of Light into Work, pp. 153–177. Wiley, Hoboken (2017)10.1002/9781119123279.ch5 ↗
3. Ware, T.H., White, T.J.: Programmed liquid crystal elastomers with tunable actuation strain. Polym. Chem. 6, 4835–4844 (2015). https://doi.org/10.1039/C5PY00640F10.1039/C5PY00640F ↗
4. Sonnet, A.M., Virga, E.G.: Model for photoresponsive nematic elastomers. J. Elast. 2022. https://doi.org/10.1007/s10659-022-09959-410.1007/s10659-022-09959-4 ↗
5. Bladon, P., Terentjev, E.M., Warner, M.: Deformation-induced orientational transitions in liquid crystals elastomer. J. Phys. II France 4(1), 75–91 (1994). https://doi.org/10.1051/jp2:199410010.1051/jp2:1994100 ↗
6. Warner, M., Gelling, K.P., Vilgis, T.A.: Theory of nematic networks. J. Chem. Phys. 88(6), 4008–4013 (1988). https://doi.org/10.1063/1.45385210.1063/1.453852 ↗
7. Warner, M., Wang, X.J.: Elasticity and phase behavior of nematic elastomers. Macromolecules 24(17), 4932–4941 (1991). https://doi.org/10.1021/ma00017a03310.1021/ma00017a033 ↗
8. Warner, M., Mostajeran, C.: Nematic director fields and topographies of solid shells of revolution. Proc. R. Soc. Lond. A 474(2210), 20170566 (2018). https://doi.org/10.1098/rspa.2017.056610.1098/rspa.2017.0566 ↗
9. Warner, M., Terentjev, E.M.: Liquid Crystal Elastomers. International Series of Monographs on Physics, Vol. 120. Oxford University Press, New York (2003)10.1093/oso/9780198527671.001.0001 ↗
10. Warner, M., Bladon, P., Terentjev, E.M.: “Soft elasticity”—deformation without resistance in liquid crystal elastomers. J. Phys. II France 4(1), 93–102 (1994). https://doi.org/10.1051/jp2:199411610.1051/jp2:1994116 ↗
11. Terentjev, E.M., Warner, M., Bladon, P.: Orientation of nematic elastomers and gels by electric fields. J. Phys. II France 4(4), 667–676 (1994). https://doi.org/10.1051/jp2:199415410.1051/jp2:1994154 ↗
12. Verwey, G.C., Warner, M.: Soft rubber elasticity. Macromolecules 28(12), 4303–4306 (1995). https://doi.org/10.1021/ma00116a03610.1021/ma00116a036 ↗
13. Verwey, G.C., Warner, M.: Multistage crosslinking of nematic networks. Macromolecules 28(12), 4299–4302 (1995). https://doi.org/10.1021/MA00116A03510.1021/MA00116A035 ↗
14. Verwey, G.C., Warner, M., Terentjev, E.M.: Elastic instability and stripe domains in liquid crystalline elastomers. J. Phys. II France 6(9), 1273–1290 (1996). https://doi.org/10.1051/jp2:199613010.1051/jp2:1996130 ↗
15. Anderson, D.R., Carlson, D.E., Fried, E.: A continuum-mechanical theory for nematic elastomers. J. Elast. 56, 33–58 (1999). https://doi.org/10.1023/A:100764791336310.1023/A:1007647913363 ↗
16. Zhang, Y., Xuan, C., Jiang, Y., Huo, Y.: Continuum mechanical modeling of liquid crystal elastomers as dissipative ordered solids. J. Mech. Phys. Solids 126, 285–303 (2019). https://doi.org/10.1016/j.jmps.2019.02.01810.1016/j.jmps.2019.02.018 ↗
17. Mihai, L.A., Wang, H., Guilleminot, J., Goriely, A.: Nematic liquid crystalline elastomers are aeolotropic materials. Proc. R. Soc. Lond. A 477(2253), 20210259 (2021). https://doi.org/10.1098/rspa.2021.025910.1098/rspa.2021.0259 ↗
18. White, T.J. (ed.): Photomechanical Materials, Composites, and Systems: Wireless Transduction of Light into Work Wiley, Hoboken, New Jersey (2017)
19. Korley, L.T.J., Ware, T.H.: Introduction to special topic: programmable liquid crystal elastomers. J. Appl. Phys. 130(22), 220401 (2021). https://doi.org/10.1063/5.007845510.1063/5.0078455 ↗
20. Mahimwalla, Z., Yager, K.G., Mamiya, J-i., Shishido, A.: Azobenzene photomechanics: prospects and potential applications. Polym. Bull. 69, 967–1006 (2012). https://doi.org/10.1007/s00289-012-0792-010.1007/s00289-012-0792-0 ↗
21. Ube, T., Ikeda, T.: Photomobile polymer materials with crosslinked liquid-crystalline structures: molecular design, fabrication, and functions. Angew. Chem., Int. Ed. Engl. 53(39), 10290–10299 (2014). https://doi.org/10.1002/anie.20140051310.1002/anie.201400513 ↗
22. White, T.J.: Photomechanical effects in liquid crystalline polymer networks and elastomers. J. Polym. Sci., Part B, Polym. Phys. 56(9), 695–705 (2018). https://doi.org/10.1002/polb.2457610.1002/polb.24576 ↗
23. Ula, S.W., Traugutt, N.A., Volpe, R.H., Patel, R.R., Yu, K., Yakacki, C.M.: Liquid crystal elastomers: an introduction and review of emerging technologies. Liquid Cryst. Rev. 6(1), 78–107 (2018). https://doi.org/10.1080/21680396.2018.153015510.1080/21680396.2018.1530155 ↗
24. Pang, X., Lv, J-a., Zhu, C., Qin, L., Yu, Y.: Photodeformable azobenzene-containing real polymers and soft actuators. Adv. Mater. 31(52), 1904224 (2019). https://doi.org/10.1002/adma.20190422410.1002/adma.201904224 ↗
25. Kuenstler, A.S., Hayward, R.C.: Light-induced shape morphing of thin films. Curr. Opin. Colloid Interface Sci. 40, 70–86 (2019). https://doi.org/10.1016/j.cocis.2019.01.00910.1016/j.cocis.2019.01.009 ↗
26. Warner, M.: Topographic mechanics and applications of liquid crystalline solids. Annu. Rev. Condens. Matter Phys. 11(1), 125–145 (2020). https://doi.org/10.1146/annurev-conmatphys-031119-05073810.1146/annurev-conmatphys-031119-050738 ↗
27. Singh, H., Virga, E.G.: A ribbon model for nematic polymer networks. J. Elast. (2022). https://doi.org/10.1007/s10659-022-09900-910.1007/s10659-022-09900-9 ↗
28. Ozenda, O., Sonnet, A.M., Virga, E.G.: A blend of stretching and bending in nematic polymer networks. Soft Matter 16, 8877–8892 (2020). https://doi.org/10.1039/D0SM00642D10.1039/D0SM00642D ↗
29. Finkelmann, H., Greve, A., Warner, M.: The elastic anisotropy of nematic elastomers. Eur. Phys. J. E 5, 281–293 (2001). https://doi.org/10.1007/s10189017006010.1007/s101890170060 ↗
30. Nguyen, T.-S., Selinger, J.V.: Theory of liquid crystal elastomers and polymer networks. Eur. Phys. J. E 40, 76 (2017). https://doi.org/10.1140/epje/i2017-11569-510.1140/epje/i2017-11569-5 ↗
31. Corbett, D., Warner, M.: Nonlinear photoresponse of disordered elastomers. Phys. Rev. Lett. 96, 237802 (2006). https://doi.org/10.1103/PhysRevLett.96.23780210.1103/PhysRevLett.96.237802 ↗
32. Corbett, D., Warner, M.: Polarization dependence of optically driven polydomain elastomer mechanics. Phys. Rev. E 78, 061701 (2008). https://doi.org/10.1103/PhysRevE.78.06170110.1103/PhysRevE.78.061701 ↗
33. Treloar, L.R.G.: The Physics of Rubber Elasticity, 3rd edn. Oxford Classic Texts in the Physical Sciences. Oxford University Press, Oxford (2005)10.1093/oso/9780198570271.001.0001 ↗
34. Deam, R.T., Edwards, S.F.: The theory of rubber elasticity. Philos. Trans. R. Soc. Lond. A 280, 317–353 (1976). https://doi.org/10.1098/rsta.1976.000110.1098/rsta.1976.0001 ↗
35. Warner, M.: New elastic behaviour arising from the unusual constitutive relation of nematic solids. J. Mech. Phys. Solids 47, 1355–1377 (1999). https://doi.org/10.1016/S0022-5096(98)00100-810.1016/S0022-5096(98)00100-8 ↗
36. White, T.J., Broer, D.J.: Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat. Mater. 14(2210), 1087–1098 (2015). https://doi.org/10.1038/nmat443310.1038/nmat4433 ↗
37. Modes, C.D., Bhattacharya, K., Warner, M.: Disclination-mediated thermo-optical response in nematic glass sheets. Phys. Rev. E 81, 060701 (2010). https://doi.org/10.1103/PhysRevE.81.06070110.1103/PhysRevE.81.060701 ↗
38. Podio-Guidugli, P.: An exact derivation of the thin plate equation. J. Elast. 22, 121–133 (1989). https://doi.org/10.1007/BF0004110710.1007/BF00041107 ↗
39. Ozenda, O., Virga, E.G.: On the Kirchhoff-Love hypothesis (revised and vindicated). J. Elast. 143, 359–384 (2021). https://doi.org/10.1007/s10659-021-09819-710.1007/s10659-021-09819-7 ↗
40. Doedel, E., Keller, H.B., Kernevez, J.P.: Numerical analysis and control of bifurcation problems (II): bifurcation in infinite dimensions. Int. J. Bifurc. Chaos 1, 745–772 (1991). https://doi.org/10.1142/S021812749100055510.1142/S0218127491000555 ↗
41. Doedel, E.J., Fairgrieve, T.F., Sandstede, B., Champneys, A.R., Kuznetsov, Y.A., Wang, X.: AUTO-07P: Continuation and bifurcation software for ordinary differential equations (2007). http://indy.cs.concordia.ca/auto/
42. Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2010)10.1017/CBO9780511762956 ↗