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An empirical description for the hinge-like mechanism in single-layer black phosphorus: The angle—angle cross interaction

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Abstract

The single-layer black phosphorus is characterized by its puckered configuration that possesses the hinge-like behavior, which leads to the highly anisotropic in-plane Poisson’s ratios and the negative out-of-plane Poisson’s ratio. We demonstrate that the hinge-like mechanism can be described by the angle—angle cross interaction, which, combined with the bond stretching and angle bending interactions, is able to provide a good description for the mechanical properties of single-layer black phosphorus. We also propose a nonlinear angle—angle cross interaction, which follows the form of Stillinger—Weber potential and can be advantageous for molecular dynamics simulations of single-layer black phosphorus under large deformation.

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References

  1. J.-W. Jiang, H.S. Park, Mechanical properties of single-layer black phosphorus, J. Phys. D: Appl. Phys. 47 (2014) 385304.

    Article  Google Scholar 

  2. J. Qiao, X. Kong, Z.-X. Hu, F. Yang, W. Ji, High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus, Nat. Commun. 5 (2014) 4475.

    Google Scholar 

  3. G. Qin, Z. Qin, S.-Y. Yue, H.-J. Cui, Q.-R. Zheng, Q.-B. Yan, G. Su, Hinge-like structure induced unusual properties of black phosphorus and new strategies to improve the thermoelectric performance, Sci. Rep. 4 (2014) 6946.

    Article  Google Scholar 

  4. Q. Wei, X. Peng, Superior mechanical flexibility of phosphorene and few-layer black phosphorus, Appl. Phys. Lett. 104 (2014) 251915.

    Article  Google Scholar 

  5. J.-W. Jiang, H.S. Park, Negative Poisson’s ratio in single-layer black phosphorus, Nat. Commun. 5 (2014) 4727.

    Google Scholar 

  6. M. Elahi, K. Khaliji, S.M. Tabatabaei, M. Pourfath, R. Asgari, Modulation of electronic and mechanical properties of phosphorene through strain, Phys. Rev. B 91 (2014) 115412.

    Article  Google Scholar 

  7. Y. Du, J. Maassen, W. Wu, Z. Luo, X. Xu, P.D. Ye, Auxetic black phosphorus: a 2d material with negative Poisson’s ratio, Nano Lett. 16 (2016) 6701–6708.

    Article  Google Scholar 

  8. F. Scarpa, Auxetic materials for bioprostheses, IEEE Signal Process. Mag. 25 (2008) 126–128.

    Article  Google Scholar 

  9. J.B. Choi, R.S. Lakes, Design of a fastener based on negative Poisson’s ratio foam, Cell Polym. 10 (1991) 205–212.

    Google Scholar 

  10. Y. Sun, N. Pugno, Hierarchical fibers with a negative Poisson’s ratio for tougher composites, Materials 6 (2013) 699–712.

    Article  Google Scholar 

  11. Y.J. Park, J.K. Kim, The effect of negative Poisson’s ratio polyurethane scaffolds for articular cartilage tissue engineering applications, Adv. Mater. Sci. Eng. 2013 (2013) 853289.

    Google Scholar 

  12. Q. Liu, Literature Review: Material with Negative Poisson’s Ratios and Potential Applications to Aerospace and Defence, DSTO Defence Science and Technology Organisation, Australia, 2006.

    Google Scholar 

  13. C. Kaneta, H. Katayama-Yoshida, A. Morita, Lattice dynamics of black phosphorus, Solid State Commun. 44 (1982) 613–617.

    Article  Google Scholar 

  14. J.-W. Jiang, Parameterization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus, Nanotechnology 26 (2015) 315706.

    Article  Google Scholar 

  15. D. Midtvedt, A. Croy, Comment on „parameterization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus’, Nanotechnology 27 (2016) 238001.

    Article  Google Scholar 

  16. Y. Takao, Electronic structure of black phosphorus: tight binding approach, Physica (Amsterdam) 105B (1981) 580.

    Google Scholar 

  17. J.D. Gale, Gulp: a computer program for the symmetry-adapted simulation of solids, J. Chem. Soc. Faraday Trans. 93 (1997) 629. Code available from https://projects.ivec.org/gulp/.

    Article  Google Scholar 

  18. LAMMPS, http://www.cs.sandia.gov/~sjplimp/lammps.html.

  19. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81 (1984) 511.

    Article  Google Scholar 

  20. W.G. Hoover, Canonical dynamics: equilibrium phase-space distributions, Phys. Rev. A 31 (1985) 1695.

    Article  Google Scholar 

  21. W. Ji. Private communication, 2015.

  22. N. Karasawa, S. Dasgupta, W.A Goddard III, Mechanical properties and force field parameters for polyethylene crystal, J. Phys. Chem. 95 (1991) 2261.

    Article  Google Scholar 

  23. N. Karasawa, W.A Goddard III, Force fields, structures, and properties of poly(viny1idene fluoride) crystals, Macromolcules 25 (1992) 7268–7281.

    Article  Google Scholar 

  24. J.A. Wendel, W.A. Goddard III, The Hessian biased force field for silicon nitride ceramics: predictions of thermodynamic and mechanical properties for α- and β-Si3N4, J. Comput. Phys. 97 (1992) 5048.

    Google Scholar 

  25. R.J. Meier, J.R. Maple, M.-J. Hwang, A.T. Hagler, Molecular modeling urea- and melamine-formaldehyde resins. 1. A force field for urea and melamine, J. Phys. Chem. 99 (1995) 5445–5456.

    Article  Google Scholar 

  26. B. Ma, R. Nussinov, Stabilities and conformations of Alzheimer’s p-amyloid peptide oligomers: sequence effects, Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 14126–14131.

    Article  Google Scholar 

  27. K. Kuwata, T. Matumoto, H. Cheng, K. Nagayama, T.L. James, H. Roder, NMR-detected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment 106–126, Proc. Natl. Acad. Sci. U.S.A. 100 (2003) 14790–14795.

    Article  Google Scholar 

  28. Z. Zhu, D. Tomanek, Semiconducting layered blue phosphorus: a computational study, Phys. Rev. Lett. 112 (2014) 176802.

    Article  Google Scholar 

  29. L. Kou, Y. Ma, S.C. Smith, C. Chen, Anisotropic ripple deformation in phosphorene, J. Phys. Chem. Lett. 6 (2015) 1509–1513.

    Article  Google Scholar 

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Jiang, JW. An empirical description for the hinge-like mechanism in single-layer black phosphorus: The angle—angle cross interaction. Acta Mech. Solida Sin. 30, 227–233 (2017). https://doi.org/10.1016/j.camss.2017.04.002

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  • DOI: https://doi.org/10.1016/j.camss.2017.04.002

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