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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2019029100
pages 339-359


Adam Mrozek
AGH University of Science and Technology, Cracow, Poland


So-called two-dimensional (2D) materials play important roles in recent research and industrial applications due to their interesting mechanical, electronic, and optoelectronic properties. The single-layer MoS2 (SLMoS2) is one of them. The basic properties such as elastic constants, Young's moduli, and the stress–strain relations of the 2H and 1T SLMoS2 phases were obtained using energy minimization and molecular dynamics with Stillinger-Weber, REBO, and ReaxFF potentials. Comparison and discussion of the achieved results is presented.


  1. Bertolazzi, S., Brivio, J., and Kis, A., Stretching and Breaking of Ultrathin MoS2, ACSNano, vol. 5, no. 12, pp. 9703-9709,2011.

  2. Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni, B., and Sinnott, S.B., A Second-Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression for Hydrocarbons, J. Phys.: Condensed Matter, vol. 14, pp. 783-802, 2002.

  3. Burczynski, T., Mrozek, A., Gorski, R., and Kus, W., Molecular Statics Coupled with the Subregion Boundary Element Method in Multiscale Analysis, Int. J. Multiscale Comput. Eng., vol. 8, no 3, pp. 319-330,2010.

  4. Chenoweth, K., van Duin, A.C.T., and Goddard, W.A., ReaxFF Reactive Force Field for Molecular Dynamics Simulations of Hydrocarbon Oxidation, J. Phys. Chem. A, vol. 112, pp. 1040-1053,2008.

  5. Cooper, R.C., Lee, C., Marianetti, C.A., Wei, X., Hone, J., and Kysar, J.W., Nonlinear Elastic Behavior of Two-Dimensional Molybdenum Disulfide, Phys. Rev. B, vol. 87, p. 035423,2013.

  6. Cranford, S.W. andBuehler, M.J., Mechanical Properties of Graphyne, Carbon, vol. 49, pp. 4111-4121,2011.

  7. Enyashin, A.N. and Ivanovskii, A.L., Graphene Allotropes, Physica Status Solidi, vol. 248, no. 8, pp. 1879-1883,2011.

  8. Henck, H., Pierucci, D., Chaste, J., Naylor, C.H., Avila, J., Balan, A., Silly, M.G., Asensio, M.C., Sirotti, F., Johnson, A.T.C, Lhuillier, E., and Ouerghi, A., Electrolytic Phototransistor based on Graphene-MoS2 van der Waals P-N Heterojunction with Tunable Photoresponse, Appl. Phys. Lett, vol. 109, pp. 113103-1-5,2016.

  9. Hoover, W.G., Canonical Dynamics: Equilibrium Phase-Space Distributions, Phys. Rev. A, vol. 31, no. 3, pp. 1695-1697,1985.

  10. Jiang, J.-W., Graphene versus MoS2: A Mini Review, Front. Phys., vol. 10, p. 106801,2015.

  11. Jiang, J.-W., Park, H.S., and Rabczuk, T., Molecular Dynamics Simulations of Single-Layer Molybdenum Disulphide (MoS2): Stillinger-WeberParametrization, Mechanical Properties, and Thermal Conductivity, J. Appl. Phys., vol. 114, p. 064307,2013.

  12. Kandemir, A., Yapicioglu, H., Kinaci, A., Cagin, T., and Sevik, C., Thermal Transport Properties of MoS2 and MoSe2 Monolayers, Nanotechnology, vol. 27, p. 055703,2016.

  13. Kus, W. and Burczynski, T., Parallel Bioinspired Algorithms in Optimization of Structures, Lecture Notes Comp. Sci., vol. 4967, pp. 1285-1292,2008.

  14. Kus, W. and Mrozek, A., Optimization of Carbon-Based Flat Structures Topologies by Using Parallel Computing, Comp. Methods Mat. Sci., vol. 16, no. 3, pp. 163-168,2016.

  15. Kus, W., Mrozek, A., and Burczynski, T., Memetic Optimization of Graphene-Like Materials on Intel PHI Coprocessor, Artificial Intelligence and Soft Computing, 15th International Conference, ICAISC 2016, Zakopane, Poland, Lecture Notes in Computer Science, vol. 9692, pp. 401-110,2016. DOI: 10.1007/978-3-319-39378-035.

  16. LAMMPS, LAMMPS Molecular Dynamics Simulator, accessed Sept. 24, 2018, from, 2018.

  17. Li, H., Contryman, A.W., Qian, X., Ardakani, S.M., Gong, Y., Wang, X., Weisse, J.M., Lee, C.H., Zhao, J., Ajayan, P.M., Li, J., Manoharan, H.C., and Zheng, X., Optoelectronic Crystal of Artificial Atoms in Strain-Textured Molybdenum Disulphide, Nature Commun., vol. 6, pp. 1-6,2015.

  18. Liang, T., Phillpot, S.R., and Sinnot, S.R., Parametrization of a Reactive Many-Body Potential for Mo-S Systems, Phys. Rev. B, vol. 79, p. 245110,2009.

  19. Liang, T., Phillpot, S.R., and Sinnot, S.R., Erratum: Parametrization of a Reactive Many-Body Potential for Mo-S Systems, Phys. Rev. B, vol. 85, p. 199903(E), 2012.

  20. Lin, Y.-C., Dumcenco, D.O., Huang, Y.-S., and Suenaga, K., Atomic Mechanism of the Semiconducting-to-Metallic Phase Transition in Single-Layered MoS2, Nature Nanotechnol., vol. 9, pp. 391-396,2014. DOI: 10.1038/nnano.2014.64.

  21. Liu, W.K, Jun, S., and Qian, D., Computational Nanomechanics of Materials, in Handbook of Theoretical and Computational Nanotechnology, M. Rieth and W. Schommers, Eds., Stevenson Ranch, CA: American Scientific Publishers, 2005.

  22. Liu, F., Ming, P., and Li, J., Ab Initio Calculation of Ideal Strength and Phonon Instability of Graphene under Tension, Phys. Rev. B, vol. 86, p. 064120, 2007.

  23. Mazdziarz, M., Mrozek, A., Kus, W., and Burczynski, T., Anisotropic-Cyclicgraphene: A New Two-Dimensional Semiconducting Carbon Allotrope, Materials, vol. 11, no. 432, pp. 1-12,2018.

  24. Mortazavi, B., Ostadhossein, A., Rabczuk, T., and van Duin, A.C.T., Mechanical Response of All-MoS2 Single-Layer Heterostructures: A ReaxFF Investigation, Phys. Chem. Chem. Phys, vol. 18, no. 34, pp. 23695-23701,2016.

  25. Mrozek, A. and Burczynski, T., Examination of Mechanical Properties of Graphene Allotropes by Means of Computer Simulation, Comp. Assisted Methods Eng. Sci., vol. 20, no. 4, pp. 309-323,2013.

  26. Mrozek, A., Kus, W., and Burczynski, T., Searching of Stable Configurations of Nanostructures Using Computational Intelligence Methods, Tech. Sci, vol. 20, no. 107, pp. 85-97,2010.

  27. Mrozek, A., Kus, W., and Burczynski, T., Nano Level Optimization of Graphene Allotropes by Means of a Hybrid Parallel Evolu-tionary Algorithm, Comput. Mat. Sci., vol. 106, pp. 161-169,2015.

  28. Mrozek, A., Kus, W., and Burczynski, T., Method for Determining Structures ofNew Carbon-Based 2D Materials with Predefined Mechanical Properties, Int. J. Muliscale Comput. Eng., vol. 15, no. 5, pp. 379-394,2017a.

  29. Mrozek, A., Kus, W., and Burczynski, T., Modelling of Molybdenum-based 2D Materials, Computer Methods in Mechanics, in Proc. of the 22nd International Conference on Computer Methods in Mechanics, J. Podgorski, Ed., Lublin, Poland, 2017b.

  30. Nakano, A., Parallel Multilevel Preconditioned Conjugate-Gradient Approach to Variable-Charge Molecular Dynamics, Comp. Phys. Commun, vol. 104, pp. 59-69, 1997.

  31. Naylor, C.H., Kybert, N.J., Schneier, C., Xi, J., Romero, G., Jeffery, G., Saven, J.G., LiuR., and Johnson, C., Scalable Production of Molybdenum Disulfide based Biosensors, ACS Nano, vol. 10, no. 6, pp. 6173-6179,2016.

  32. Nose, S., A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys., vol. 81, no. 1, pp. 511-519,1984.

  33. Ostadhossein, A., Rahnamoun, A., Wang, Y., Zhao, P., Zhang, S., Crespi, V.H., and van Duin, A.C.T., ReaxFF Reactive Force-Field Study of Molybdenum Disulfide (MoS2), J. Phys. Chem. Lett., vol. 8, no. 3, pp. 631-640,2017.

  34. Park, H., Fellinger, M.R., Lenosky, T.J., Tipton, W.W., Trinkle, D.R., Rudin, S.P., Woodward, Ch., Wilkins, J.W., and Hennig, R.G., Ab Initio-Based Empirical Potential Used to Study the Mechanical Properties of Molybdenum, Phys. Rev. B, vol. 85, p. 214121, 2012.

  35. Peng, Q., Ji, W., and De, S., Mechanical Properties of Graphyne Monolayers: A First-Principles Study, Phys. Chem. Chem. Phys, vol. 14, no. 38, pp. 13385-13391,2012.

  36. Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V., and Kis, A., Single-Layer MoS2 Transistors, Nature Nanotechnol., vol. 6, pp. 147-150,2011.

  37. Rapaport, D., The Art of Molecular Dynamics Simulation, Cambridge: Cambridge University Press, 2004.

  38. Rappe, A.K. and Goddard, W.A., Charge Equilibration for Molecular Dynamics Simulations, J. Chem. Phys., vol. 95, no. 8, pp. 3358-3363,1991.

  39. Shengping, S. and Atluri, S.N., Atomic-Level Stress Calculation and Continuum-Molecular System Equivalence, Comp. Model. Eng. Sci, vol. 6, no. 1, pp. 91-104,2004.

  40. Sinha, A., Dhanjai, Tan, B., Huang, Y., Zhao, H., Dang, X., Chen, J., and Jain, R., MoS2 Nanostructures for Electrochemical Sensing ofMultidisciplinary Targets: A Review, TrAC Trends Anafyt. Chem, vol. 102,2018. DOI: 10.1016/j.trac.2018.01.008.

  41. Sinley, H.E., Solid Lubricant Materials for High Temperatures-A Review, Tribol. Int., vol. 15, pp. 303-315,1982.

  42. Stillinger, F.H. and Weber, T.A., Computer Simulation of Local Order in Condensed Phases of Silicon, Phys. Rev. B, vol. 31, p. 5262,1985.

  43. Stuart, S.J., Tutein, A.B., and Harrison, J.A., A Reactive Potential for Hydrocarbons with Intermolecular Interactions, J. Chem. Phys, vol. 112, no. 14, pp. 6472-6486,2000.

  44. Tuckerman, M.E., Mundy, Ch.J., Balasubramanian, S., and Klein, M.L., Modified Nonequilibrium Molecular Dynamics for Fluid Flows with Energy Conservation, J. Chem. Phys, vol. 106, no. 13, pp. 5615-5621,1997.

  45. van Duin, A.C.T.,Dasgupta, S.,Lorant, F., and Goddard, W.A., ReaxFF: A Reactive Force Field for Hydrocarbons, J. Phys. Chem. A, vol. 105, no. 41, pp. 9396-9409,2001.

  46. Voiry, D., Mohiteb, A., and Chhowalla, M., Phase Engineering of Transition Metal Dichalcogenides, Chem. Soc. Rev, vol. 44, p. 2702,2015.

  47. Wakabayashi, N., Smith, H.G., and Nicklow, R.M., Lattice Dynamics of Hexagonal MoS2 Studied by Neutron Scattering, Phys. Rev. B, vol. 12, p. 659,1975.

  48. Wang, Y., Lv, J., Zhu, L., and Ma, Y., Crystal Structure Prediction via Particle-Swarm Optimization, Phys. Rev. B, vol. 82, no. 9, pp. 09411-6-23,2010.

  49. Weismiller, M.R., van Duin, A.C.T., Lee, J., and Yetter, R.A., ReaxFF Reactive Force Field Development and Applications for Molecular Dynamics Simulations of Ammonia Borane Dehydrogenation and Combustion, J. Phys. Chem., vol. 114, pp. 5485-5492,2010.

  50. Xiong, S. and Cao, G., Molecular Dynamics Simulations of Mnechanical Properties of Monolayer MoS2, Nanotechnology, vol. 10, pp. 1857-1865,2015.

  51. Yin, Z., Li, H., Li, H., Jiang, L., Shi, Y., Sun, Y., Lu, G., Zhang, Q., Chen, X., and Zhang, H., Single-Layer MoS2 Phototransistors, ACSNano, vol. 6, no. 1, pp. 74-80,2012.

  52. Zhao, W., Pan, J., Fang, Y., Che, X., Wang, D., Bu, K., and Huang, F., Metastable MoS2: Crystal Structure, Electronic Band Structure, Synthetic Approach and Intriguing Physical Properties, Chemistry, vol. 24, pp. 15942-15954, 2018. DOI: 10.1002/chem.201801018.

  53. Zhou, M., A New Look at the Atomic Level Virial Stress: On Continuum-Molecular System Equivalence, in Proc. Royal Soc. London Series A-Math. Phys.Engin. Sci., vol. 459, pp. 2347-2392,2003.