Poisson’s Ratio of Yukawa Systems with Nanoinclusions: Nanochannel vs. Nanolayer
Tretiakov Konstantin V. 1,2*, Wojciechowski Krzysztof W. 1,2, Narojczyk Jakub W. 1, Pigłowski Paweł M. 1
1 Polish Academy of Sciences
Institute of Molecular Physics
Smoluchowskiego 17, 60-179 Poznań, Poland2 Calisia University – Kalisz
Nowy Świat 4, 62-800 Kalisz, Poland∗E-mail: tretiakov@ifmpan.poznan.pl
Received:
Received: 5 May 2022; revised: 25 June 2022; accepted: 27 June 2022; published online: 9 August 2022
DOI: 10.12921/cmst.2022.0000011
Abstract:
The influence of periodically distributed inclusions on elastic properties of crystals in which particles interact through Yukawa potential is discussed briefly. The inclusions in the form of channels oriented along the [001]-direction and layers orthogonal to the [010]-direction are considered. Monte Carlo simulations have shown that, depending on the type of inclusion and the concentration of inclusion particles in Yukawa crystal, qualitative changes in elastic properties occur. In selected directions, one observes appearance of auxetic properties for systems with nanolayers and enhancement of auxeticity for systems with nanochannels.
Key words:
auxetics, crystals with nanoinclusions, elastic properties of solids, mechanical metamaterials, Monte Carlo simulations, negative Poisson’s ratio
References:
[1] A. van Blaaderen, R. Ruel, P. Wiltzius, Template-directed colloidal crystallization, Nature 385, 321–324 (1997).
[2] D.V. Talapin, J.S. Lee, M.V. Kovalenko, E.V. Shevchenko, Prospects of colloidal nanocrystals for electronic and optoelectronic applications, Chem. Rev. 110, 389–458 (2010).
[3] J. Galisteo-López, M. Ibisate, R. Sapienza, L. Froufe-Peérez, A. Blanco, López, Self-assembled photonic structures, Adv. Mater. 23, 30–69 (2011).
[4] S. Sacanna, L. Rossi, D.J. Pine, Magnetic click colloidal assembly, J. Am. Chem. Soc. 134, 6112–6115 (2012).
[5] A.F. Demirors, P.P. Pillai, B. Kowalczyk, B.A. Grzybowski, Colloidal assembly directed by virtual magnetic moulds, Nature 503, 99–103 (2013).
[6] A.-P. Hynninen, M. Dijkstra, Phase diagrams of hard-core repulsive Yukawa particles, Phys. Rev. E 68, 021407 (2003).
[7] K.E. Evans, M.A. Nkansah, I.J. Hutchinson, S.C. Rogers, Molecular network design, Nature 353, 124 (1991).
[8] R.S. Lakes, Foam structures with a negative Poisson’s ratio, Science 235, 1038–1040 (1987).
[9] K.W. Wojciechowski, Two-dimensional isotropic model with a negative Poisson ratio, Phys. Lett. A 137, 60–64 (1989).
[10] T.C. Lim, Auxetic Materials and Structures, Springer (2015). [11] K.V. Tretiakov, K.W. Wojciechowski, Partially auxetic behavior in fcc crystals of hard-core repulsive Yukawa particles, Phys. Status Solidi B 251, 383–387 (2014).
[12] P.M. Piglowski, J.W. Narojczyk, K.W. Wojciechowski, K.V. Tretiakov, Auxeticity enhancement due to size polydispersity in fcc crystals of hard-core repulsive Yukawa particles, Soft Matter 13, 7916–7921 (2017).
[13] J. Smardzewski, R. Klos, B. Fabisiak, Design of small auxetic springs for furniture, Materials & Design 51, 723–728 (2013).
[14] T. Allen, T. Hewage, C. Newton-Mann, W. Wang, O. Duncan, A. Alderson, Fabrication of auxetic foam sheets for sports applications, Phys. Status Solidi B 254, 1700596 (2017).
[15] X. Ren, R. Das, J.P. Tran, T. Ngo, Auxetic metamaterials and structures: A review, Smart Mater. Struct. 27, 023001 (2018).
[16] K.V. Tretiakov, P.M. Piglowski, K. Hyzorek, K.W. Wojciechowski, Enhanced auxeticity in Yukawa systems due to introduction of nanochannels in [001]-direction, Smart Mater. Struct. 25, 054007 (2016).
[17] P.M. Piglowski, K.W. Wojciechowski, K.V. Tretiakov, Partial auxeticity induced by nanoslits in the Yukawa crystal, Phys. Status Solidi RRL 10, 566–569 (2016).
[18] K.V. Tretiakov, P.M. Piglowski, J.W. Narojczyk, K.W. Wojciechowski, Selective enhancement of auxeticity through changing a diameter of nanochannels in Yukawa systems, Smart Mater. Struct. 27, 115021 (2018).
[19] M. Parrinello, A. Rahman, Strain fluctuations and elastic constants, J. Chem. Phys. 76, 2662–2666 (1982).
[20] S.P. Tokmakova, Stereographic projections of Poisson’s ratio in auxetic crystals, Phys. Status Solidi B 242, 721–729 (2005).
The influence of periodically distributed inclusions on elastic properties of crystals in which particles interact through Yukawa potential is discussed briefly. The inclusions in the form of channels oriented along the [001]-direction and layers orthogonal to the [010]-direction are considered. Monte Carlo simulations have shown that, depending on the type of inclusion and the concentration of inclusion particles in Yukawa crystal, qualitative changes in elastic properties occur. In selected directions, one observes appearance of auxetic properties for systems with nanolayers and enhancement of auxeticity for systems with nanochannels.
Key words:
auxetics, crystals with nanoinclusions, elastic properties of solids, mechanical metamaterials, Monte Carlo simulations, negative Poisson’s ratio
References:
[1] A. van Blaaderen, R. Ruel, P. Wiltzius, Template-directed colloidal crystallization, Nature 385, 321–324 (1997).
[2] D.V. Talapin, J.S. Lee, M.V. Kovalenko, E.V. Shevchenko, Prospects of colloidal nanocrystals for electronic and optoelectronic applications, Chem. Rev. 110, 389–458 (2010).
[3] J. Galisteo-López, M. Ibisate, R. Sapienza, L. Froufe-Peérez, A. Blanco, López, Self-assembled photonic structures, Adv. Mater. 23, 30–69 (2011).
[4] S. Sacanna, L. Rossi, D.J. Pine, Magnetic click colloidal assembly, J. Am. Chem. Soc. 134, 6112–6115 (2012).
[5] A.F. Demirors, P.P. Pillai, B. Kowalczyk, B.A. Grzybowski, Colloidal assembly directed by virtual magnetic moulds, Nature 503, 99–103 (2013).
[6] A.-P. Hynninen, M. Dijkstra, Phase diagrams of hard-core repulsive Yukawa particles, Phys. Rev. E 68, 021407 (2003).
[7] K.E. Evans, M.A. Nkansah, I.J. Hutchinson, S.C. Rogers, Molecular network design, Nature 353, 124 (1991).
[8] R.S. Lakes, Foam structures with a negative Poisson’s ratio, Science 235, 1038–1040 (1987).
[9] K.W. Wojciechowski, Two-dimensional isotropic model with a negative Poisson ratio, Phys. Lett. A 137, 60–64 (1989).
[10] T.C. Lim, Auxetic Materials and Structures, Springer (2015). [11] K.V. Tretiakov, K.W. Wojciechowski, Partially auxetic behavior in fcc crystals of hard-core repulsive Yukawa particles, Phys. Status Solidi B 251, 383–387 (2014).
[12] P.M. Piglowski, J.W. Narojczyk, K.W. Wojciechowski, K.V. Tretiakov, Auxeticity enhancement due to size polydispersity in fcc crystals of hard-core repulsive Yukawa particles, Soft Matter 13, 7916–7921 (2017).
[13] J. Smardzewski, R. Klos, B. Fabisiak, Design of small auxetic springs for furniture, Materials & Design 51, 723–728 (2013).
[14] T. Allen, T. Hewage, C. Newton-Mann, W. Wang, O. Duncan, A. Alderson, Fabrication of auxetic foam sheets for sports applications, Phys. Status Solidi B 254, 1700596 (2017).
[15] X. Ren, R. Das, J.P. Tran, T. Ngo, Auxetic metamaterials and structures: A review, Smart Mater. Struct. 27, 023001 (2018).
[16] K.V. Tretiakov, P.M. Piglowski, K. Hyzorek, K.W. Wojciechowski, Enhanced auxeticity in Yukawa systems due to introduction of nanochannels in [001]-direction, Smart Mater. Struct. 25, 054007 (2016).
[17] P.M. Piglowski, K.W. Wojciechowski, K.V. Tretiakov, Partial auxeticity induced by nanoslits in the Yukawa crystal, Phys. Status Solidi RRL 10, 566–569 (2016).
[18] K.V. Tretiakov, P.M. Piglowski, J.W. Narojczyk, K.W. Wojciechowski, Selective enhancement of auxeticity through changing a diameter of nanochannels in Yukawa systems, Smart Mater. Struct. 27, 115021 (2018).
[19] M. Parrinello, A. Rahman, Strain fluctuations and elastic constants, J. Chem. Phys. 76, 2662–2666 (1982).
[20] S.P. Tokmakova, Stereographic projections of Poisson’s ratio in auxetic crystals, Phys. Status Solidi B 242, 721–729 (2005).
