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Auxetic metamaterials inspired from wine-racks

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Abstract

‘Wine-rack’ motifs are formally shown to exhibit the unexpected property of a negative Poisson’s ratio (auxetic behaviour) for loading in particular directions. This property is confirmed through the analysis of analytical expressions for the in-plane off-axis mechanical properties derived for an idealised hinging wine-rack model as well as through molecular simulations of nanoscale molecular systems. It is also shown that auxeticity for loading off-axis complements the more well-known property of negative compressibility demonstrated in other directions which results from the very high positive Poisson’s ratio exhibited on-axis.

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References

  1. Baughman RH, Stafstrom S, Cui C, Dantas SO (1998) Materials with negative compressibilities in one or more dimensions. Science 279:1522–1524. https://doi.org/10.1126/science.279.5356.1522

    Article  Google Scholar 

  2. Goodwin AL, Keen DA, Tucker MG (2008) Large negative linear compressibility of Ag3[Co(CN)6]. Proc Natl Acad Sci USA 105:18708–18713. https://doi.org/10.1073/pnas.0804789105

    Article  Google Scholar 

  3. Fortes AD, Suard E, Knight KS (2011) Negative linear compressibility and massive anisotropic thermal expansion in methanol monohydrate. Science 331:742–746. https://doi.org/10.1126/science.1198640

    Article  Google Scholar 

  4. Cairns AB, Catafesta J, Levelut C et al (2013) Giant negative linear compressibility in zinc dicyanoaurate. Nat Mater 12:212–216. https://doi.org/10.1038/nmat3551

    Article  Google Scholar 

  5. Cairns AB, Thompson AL, Tucker MG et al (2012) Rational design of materials with extreme negative compressibility: selective soft-mode frustration in KMn[Ag(CN)2]3. J Am Chem Soc 134:4454–4456. https://doi.org/10.1021/ja204908m

    Article  Google Scholar 

  6. Ortiz AU, Boutin A, Fuchs AH, Coudert F-X (2013) Metal-organic frameworks with wine-rack motif: what determines their flexibility and elastic properties? J Chem Phys 138:174703. https://doi.org/10.1063/1.4802770

    Article  Google Scholar 

  7. Coudert F-X (2013) Systematic investigation of the mechanical properties of pure silica zeolites: stiffness, anisotropy, and negative linear compressibility. Phys Chem Chem Phys 15:16012. https://doi.org/10.1039/c3cp51817e

    Article  Google Scholar 

  8. Grima JN, Attard D, Caruana-Gauci R, Gatt R (2011) Negative linear compressibility of hexagonal honeycombs and related systems. Scr Mater 65:565–568. https://doi.org/10.1016/j.scriptamat.2011.06.011

    Article  Google Scholar 

  9. Gatt R, Caruana-Gauci R, Grima JN (2013) Negative linear compressibility: giant response. Nat Mater 12:182–183. https://doi.org/10.1038/nmat3584

    Article  Google Scholar 

  10. Zhou X, Zhang L, Zhang H et al (2016) 3D cellular models with negative compressibility through the wine-rack-type mechanism. Phys Status Solidi B 253:1977–1993. https://doi.org/10.1002/pssb.201600128

    Article  Google Scholar 

  11. Qiao Y, Wang K, Yuan H et al (2015) Negative linear compressibility in organic mineral ammonium oxalate monohydrate with hydrogen bonding wine-rack motifs. J Phys Chem Lett 6:2755–2760. https://doi.org/10.1021/acs.jpclett.5b01129

    Article  Google Scholar 

  12. Barnes DL, Miller W, Evans KE, Marmier A (2012) Modelling negative linear compressibility in tetragonal beam structures. Mech Mater 46:123–128. https://doi.org/10.1016/j.mechmat.2011.12.007

    Article  Google Scholar 

  13. Li W, Probert MR, Kosa M et al (2012) Negative linear compressibility of a metal-organic framework. J Am Chem Soc 134:11940–11943. https://doi.org/10.1021/ja305196u

    Article  Google Scholar 

  14. Yeung HH-M, Kilmurray R, Hobday CL et al (2017) Hidden negative linear compressibility in lithium l-tartrate. Phys Chem Chem Phys 19:3544–3549. https://doi.org/10.1039/C6CP08690J

    Article  Google Scholar 

  15. Harty EL, Ha AR, Warren MR et al (2015) Reversible piezochromism in a molecular wine-rack. Chem Commun (Camb) 51:10608–10611. https://doi.org/10.1039/c5cc02916c

    Article  Google Scholar 

  16. Goodwin AL, Calleja M, Conterio MJ et al (2008) Colossal positive and negative thermal expansion in the framework material Ag3[Co(CN)6]. Science 319:794–797. https://doi.org/10.1126/science.1151442

    Article  Google Scholar 

  17. Calleja M, Goodwin AL, Dove MT (2008) Origin of the colossal positive and negative thermal expansion in Ag3[Co(CN)6]: an ab initio density functional theory study. J Phys: Condens Matter 20:255226. https://doi.org/10.1088/0953-8984/20/25/255226

    Google Scholar 

  18. Wang L, Wang C, Luo H, Sun Y (2017) Correlation between uniaxial negative thermal expansion and negative linear compressibility in Ag3[Co(CN)6]. J Phys Chem C 121:333–341. https://doi.org/10.1021/acs.jpcc.6b09944

    Article  Google Scholar 

  19. Smith CW, Grima JN, Evans KE (2000) A novel mechanism for generating auxetic behaviour in reticulated foams: missing rib foam model. Acta Mater 48:4349–4356. https://doi.org/10.1016/S1359-6454(00)00269-X

    Article  Google Scholar 

  20. Masters IG, Evans KE (1996) Models for the elastic deformation of honeycombs. Compos Struct 35:403–422. https://doi.org/10.1016/S0263-8223(96)00054-2

    Article  Google Scholar 

  21. Lakes RS (1987) Foam structures with a negative Poisson’s ratio. Science 235:1038–1040. https://doi.org/10.1126/science.235.4792.1038

    Article  Google Scholar 

  22. Friis EA, Lakes RS, Park JB (1988) Negative Poisson’s ratio polymeric and metallic foams. J Mater Sci 23:4406–4414. https://doi.org/10.1007/BF00551939

    Article  Google Scholar 

  23. Wojciechowski KW (1987) Constant thermodynamic tension Monte Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers. Mol Phys 61:1247–1258. https://doi.org/10.1080/00268978700101761

    Article  Google Scholar 

  24. Evans KE (1991) Auxetic polymers: a new range of materials. Endeavour 15:170–174. https://doi.org/10.1016/0160-9327(91)90123-S

    Article  Google Scholar 

  25. Lakes RS (1991) Deformation mechanisms in negative Poisson’s ratio materials: structural aspects. J Mater Sci 26:2287–2292. https://doi.org/10.1007/BF01130170

    Article  Google Scholar 

  26. Evans KE, Alderson A (2000) Auxetic materials: functional materials and structures from lateral thinking! Adv Mater 12:617–628. https://doi.org/10.1002/(SICI)1521-4095(200005)12:9<617:AID-ADMA617>3.0.CO;2-3

    Article  Google Scholar 

  27. Prall D, Lakes RS (1997) Properties of a chiral honeycomb with a Poisson’s ratio of -1. Int J Mech Sci 39:305–314. https://doi.org/10.1016/S0020-7403(96)00025-2

    Article  Google Scholar 

  28. Sigmund O, Torquato S, Aksay IA (1998) On the design of 1–3 piezocomposites using topology optimization. J Mater Res 13:1038–1048. https://doi.org/10.1557/JMR.1998.0145

    Article  Google Scholar 

  29. Grima JN, Evans KE (2000) Auxetic behavior from rotating squares. J Mater Sci Lett 19:1563–1565. https://doi.org/10.1023/A:1006781224002

    Article  Google Scholar 

  30. Yeganeh-Haeri A, Weidner DJ, Parise JB (1992) Elasticity of α-cristobalite: a silicon dioxide with a negative Poisson’s ratio. Science 257:650–652. https://doi.org/10.1126/science.257.5070.650

    Article  Google Scholar 

  31. Alderson KL, Evans KE (1993) Strain-dependent behaviour of microporous polyethylene with a negative Poisson’s ratio. J Mater Sci 28:4092–4098. https://doi.org/10.1007/BF00351238

    Article  Google Scholar 

  32. Baughman RH, Shacklette JM, Zakhidov AA, Stafstrom S (1998) Negative Poisson’s ratios as a common feature of cubic metals. Nature 392:362–365. https://doi.org/10.1038/32842

    Article  Google Scholar 

  33. He C, Liu P, Griffin AC (1998) Toward negative Poisson ratio polymers through molecular design. Macromolecules 31:3145–3147. https://doi.org/10.1021/ma970787m

    Article  Google Scholar 

  34. Hine PJ, Duckett RA, Ward IM (1997) Negative Poisson’s ratios in angle-ply laminates. J Mater Sci Lett 16:541–544

    Article  Google Scholar 

  35. Gaspar N, Smith CW, Alderson A et al (2011) A generalised three-dimensional tethered-nodule model for auxetic materials. J Mater Sci 46:372–384. https://doi.org/10.1007/s10853-010-4846-0

    Article  Google Scholar 

  36. Attard D, Grima JN (2008) Auxetic behaviour from rotating rhombi. Phys Status Solidi B 245:2395–2404. https://doi.org/10.1002/pssb.200880269

    Article  Google Scholar 

  37. Wojciechowski KW (1989) Two-dimensional isotropic system with a negative Poisson ratio. Phys Lett A 137:60–64. https://doi.org/10.1016/0375-9601(89)90971-7

    Article  Google Scholar 

  38. Wojciechowski KW (2003) Non-chiral, molecular model of negative Poisson ratio in two dimensions. J Phys A: Math Gen 36:11765–11778

    Article  Google Scholar 

  39. Babaee S, Shim J, Weaver JC et al (2013) 3D soft metamaterials with negative Poisson’s ratio. Adv Mater 25:5044–5049. https://doi.org/10.1002/adma.201301986

    Article  Google Scholar 

  40. Alderson A (1999) A triumph of lateral thought. Chem Ind 10:384–391

    Google Scholar 

  41. Lakes RS (1993) Advances in negative Poisson’s ratio materials. Adv Mater 5:293–296. https://doi.org/10.1002/adma.19930050416

    Article  Google Scholar 

  42. Hassan MR, Scarpa F, Mohamed NA (2004) Shape memory alloys honeycomb: design and properties. In: Proc. SPIE 5387, Smart Structures and Materials 2004: Active Materials: Behavior and Mechanics, pp 557–564. https://doi.org/10.1117/12.555597

  43. Strek T, Kedziora P, Maruszewski BT et al (2009) Finite element analysis of auxetic obstacle deformation and fluid flow in a channel. J Non Cryst Solids 355:1387–1392. https://doi.org/10.1016/j.jnoncrysol.2009.05.032

    Article  Google Scholar 

  44. Scarpa F, Pastorino P, Garelli A et al (2005) Auxetic compliant flexible PU foams: static and dynamic properties. Phys Status Solidi B 242:681–694. https://doi.org/10.1002/pssb.200460386

    Article  Google Scholar 

  45. Jacobs MJN, Van Dingenen JLJ (2001) Ballistic protection mechanisms in personal armour. J Mater Sci 36:3137–3142. https://doi.org/10.1023/A:1017922000090

    Article  Google Scholar 

  46. Yang W, Li Z-M, Shi W et al (2004) Review on auxetic materials. J Mater Sci 39:3269–3279. https://doi.org/10.1023/B:JMSC.0000026928.93231.e0

    Article  Google Scholar 

  47. Bianchi M, Scarpa F, Smith CW (2008) Stiffness and energy dissipation in polyurethane auxetic foams. J Mater Sci 43:5851–5860. https://doi.org/10.1007/s10853-008-2841-5

    Article  Google Scholar 

  48. Ali MN, Busfield JJC, Rehman IU (2013) Auxetic oesophageal stents: structure and mechanical properties. J Mater Sci Mater Med 25:527–553. https://doi.org/10.1007/s10856-013-5067-2

    Article  Google Scholar 

  49. Grima JN, Williams JJ, Evans KE (2005) Networked calix[4]arene polymers with unusual mechanical properties. Chem Commun 1:4065–4067. https://doi.org/10.1039/b505839b

    Article  Google Scholar 

  50. Sanami M, Ravirala N, Alderson KL, Alderson A (2014) Auxetic materials for sports applications. Procedia Eng 72:453–458. https://doi.org/10.1016/j.proeng.2014.06.079

    Article  Google Scholar 

  51. Grima JN, Gatt R (2010) Perforated sheets exhibiting negative Poisson’s ratios. Adv Eng Mater 12:460–464. https://doi.org/10.1002/adem.201000005

    Article  Google Scholar 

  52. Milton GW, Cherkaev AV (1995) Which elasticity tensors are realizable? J Eng Mater Technol 117:483–493. https://doi.org/10.1115/1.2804743

    Article  Google Scholar 

  53. Grima JN, Alderson A, Evans KE (2005) Auxetic behaviour from rotating rigid units. Phys Status Solidi B 242:561–575. https://doi.org/10.1002/pssb.200460376

    Article  Google Scholar 

  54. Nye JF (1964) Physical properties of crystals: Their representation by tensors and matrices. Oxford University Press, Oxford

    Google Scholar 

  55. Evans KE, Nkansah MA, Hutchinson IJ, Rogers S (1991) Molecular network design. Nature 353:124. https://doi.org/10.1038/353124a0

    Article  Google Scholar 

  56. Grima JN, Zerafa C, Brincat J-P (2014) Development of novel poly(phenylacetylene) network polymers and their mechanical behaviour. Phys Status Solidi B 251:375–382. https://doi.org/10.1002/pssb.201384254

    Article  Google Scholar 

  57. Grima JN, Degabriele EP, Attard D (2016) Nano networks exhibiting negative linear compressibility. Phys Status Solidi B 253:1419–1427. https://doi.org/10.1002/pssb.201600276

    Article  Google Scholar 

  58. Formosa JP, Cauchi R, Grima JN (2015) Carbon allotropes exhibiting negative linear compressibility. Phys Status Solidi B 252:1656–1663. https://doi.org/10.1002/pssb.201552234

    Article  Google Scholar 

  59. Mayo SL, Olafson BD, Goddard WA (1990) DREIDING: a generic force field for molecular simulations. J Phys Chem 94:8897–8909. https://doi.org/10.1021/j100389a010

    Article  Google Scholar 

  60. Rappe AK, Goddard WA (1991) Charge equilibration for molecular dynamics simulations. J Phys Chem 95:3358–3363. https://doi.org/10.1021/j100161a070

    Article  Google Scholar 

  61. Hautman J, Klein ML (1992) An Ewald summation method for planar surfaces and interfaces. Mol Phys 75:379–395. https://doi.org/10.1080/00268979200100301

    Article  Google Scholar 

  62. Rappe AK, Casewit CJ, Colwell KS et al (1992) UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J Am Chem Soc 114:10024–10035. https://doi.org/10.1021/ja00051a040

    Article  Google Scholar 

  63. Walker PL (1990) Carbon: an old but new material revisited. Carbon 28:261–279. https://doi.org/10.1016/0008-6223(90)90001-F

    Article  Google Scholar 

  64. Hunter CA, Sanders JKM (1990) The nature of Pi-Pi interactions. J Am Chem Soc 112:5525–5534. https://doi.org/10.1021/ja00170a016

    Article  Google Scholar 

  65. Huang C, Chen L (2016) Negative Poisson’s ratio in modern functional materials. Adv Mater 28:8079–8096. https://doi.org/10.1002/adma.201601363

    Article  Google Scholar 

  66. Ortiz AU, Boutin A, Fuchs AH, Coudert F-X (2012) Anisotropic elastic properties of flexible metal-organic frameworks: how soft are soft porous crystals? Phys Rev Lett 109:195502. https://doi.org/10.1103/PhysRevLett.109.195502

    Article  Google Scholar 

  67. Ortiz AU, Boutin A, Coudert F-X (2014) Prediction of flexibility of metal-organic frameworks CAU-13 and NOTT-300 by first principles molecular simulations. Chem Commun 50:5867–5870. https://doi.org/10.1039/c4cc00734d

    Article  Google Scholar 

  68. Huang CW, Ren W, Nguyen VC et al (2012) Abnormal Poisson’s ratio and linear compressibility in perovskite materials. Adv Mater 24:4170–4174. https://doi.org/10.1002/adma.201104676

    Article  Google Scholar 

  69. Ogborn JM, Collings IE, Moggach SA et al (2012) Supramolecular mechanics in a metal–organic framework. Chem Sci 3:3011–3017. https://doi.org/10.1039/c2sc20596c

    Article  Google Scholar 

  70. Serra-Crespo P, Dikhtiarenko A, Stavitski E et al (2014) Experimental evidence of negative linear compressibility in the MIL-53 metal–organic framework family. CrystEngComm 17:276–280. https://doi.org/10.1039/c4ce00436a

    Article  Google Scholar 

  71. Bennett TD, Cheetham AK (2014) Amorphous metal-organic frameworks. Acc Chem Res 47:1555–1562. https://doi.org/10.1021/ar5000314

    Article  Google Scholar 

  72. Coudert F-X (2015) Responsive metal–organic frameworks and framework materials: under pressure, taking the heat, in the spotlight, with friends. Chem Mater 27:1905–1916. https://doi.org/10.1021/acs.chemmater.5b00046

    Article  Google Scholar 

  73. Furukawa H, Cordova KE, O’Keeffe M, Yaghi OM (2013) The chemistry and applications of metal-organic frameworks. Science 341:1230444. https://doi.org/10.1126/science.1230444

    Article  Google Scholar 

  74. Grima JN, Gatt R, Alderson A, Evans KE (2006) An alternative explanation for the negative Poisson’s ratios in alpha-cristobalite. Mater Sci Eng A 423:219–224. https://doi.org/10.1016/j.msea.2005.08.230

    Article  Google Scholar 

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Acknowledgements

This work was funded by the University of Malta.

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Authors and Affiliations

  1. Metamaterials Unit, Faculty of Science, University of Malta, Msida, MSD, 2080, Malta

    Roberto Caruana-Gauci, Edera P. Degabriele, Daphne Attard & Joseph N. Grima

  2. Department of Chemistry, Faculty of Science, University of Malta, Msida, MSD, 2080, Malta

    Joseph N. Grima

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  1. Roberto Caruana-Gauci
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Caruana-Gauci, R., Degabriele, E.P., Attard, D. et al. Auxetic metamaterials inspired from wine-racks. J Mater Sci 53, 5079–5091 (2018). https://doi.org/10.1007/s10853-017-1875-y

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