ELASTIC CONSTANTS OF DENSE CRYSTALLINE PHASES OF TWO-DIMENSIONAL HARD CYCLIC HEPTAMERS
Wojciechowski Krzysztof W., Tretiakov Konstantin V.
Institute of Molecular Physics, Polish Academy of Sciences
Smohichowskiego 17/19, 60-179 Poznań, Poland
kww@man.poznan.pl
DOI: 10.12921/cmst.2000.06.01.101-119
OAI: oai:lib.psnc.pl:505
Abstract:
Two-dimensional system of hard cyclic heptamers is studied by Monte Carlo simulations. Isotherms of various crystalline structures formed by the heptamers are obtained. Melting as well as structural phase transitions between crystalline structures are localized. Above melting a rotational phase is observed of hexagonal lattice and isotropic distribution of molecular orientations. With increasing density the coupling between the orientational and rotational degrees of freedom leads to appearance of clearly anisotropic patterns of the atomic density distribution around the lattice sites. These patterns exhibit 6-fold symmetry. At high densities the heptamers form crystalline structures of rectangular lattice and without molecular rotation. Elastic constants of the dense crystalline structures are computed by using an algorithm based on the strain-fluctuation method. It is shown that the densest known crystalline structures of the heptamers exhibit negative Poisson’s ratios near close packing.
References:
[1] J.-P. Hansen, I. R. McDonald, Theory of Simple Liquids, Academic Press, London, 1986.
[2] M. P. Allen, G. T. Evans, D. Frenkel, B. Mulder, Hard Convex Body Fluids, in Advances in
Chemical Physics, 86, 1-165 (1993). See also references therein.
[3] A. C. Brańka, K. W. Wojciechowski, Phys. Rev. Letters 50, 846-849 (1983).
[4] K. W. Wojciechowski, A. C. Brańka, D. Frenkel, Phys. Rev. Letters 64, 3168-3171 (1991); K. W.
Wojciechowski, Phys. Rev. E46, 26-39 (1992); K. W. Wojciechowski, A. C. Brańka, D. Frenkel,
Physica A196, 519-545 (1993).
[5] Yu. D. Burago, V. A. Zallgaller, Geometric Inequalities, Springer, Berlin 1988.
[6] R. Schneider, Convex bodies: The Brunn-Minkowski Theory, Vol. 44 of Encyclopedia of
Mathematics and its Applications, Ed. G.-C. Rota, Cambridge, 1993.
[7] K. W. Wojciechowski, Physica A232, 723-736 (1996).
[8] K. W. Wojciechowski, J. Chem. Phys. 94, 4099-4100 (1991).
[9] S. Sachdev, D. R. Nelson, Phys. Rev. B32, 1480-1502 (1985).
[10] A. C. Brańka, K. W. Wojciechowski, Phys. Lett. A101, 349-353 (1984).
[11] A. C. Brańka, K. W. Wojciechowski, Mol. Phys. 72,941-953 (1991); A. C. Brańka, K. W. Wojciechowski, Mol. Phys. 78, 1513-1526 (1993).
[12] K. W. Wojciechowski, K. V. Tretiakov, Comput. Phys. Commun. 121-122, 528-530 (1999).
[13] B. L. Holian, O. E. Perçus, T. T. Warnock, P. A. Whitlock, Phys. Rev. E50, 1607-1615 (1994).
[14] M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. 8, 3-30 (1998).
[15] K. V. Tretiakov, K. W. Wojciechowski, Phys. Rev. E60, 7626 (1999); K. W. Wojciechowski,
Comput. Meth. Sci. Technol. 5, 81-85 (1999).
[16] K. W. Wojciechowski, Mol. Phys. 61, 1247-1258 (1987); K. W. Wojciechowski and A. C. Brańka, Phys. Rev. A40, 7222-7225 (1989).
[17] R. Lakes, Science 235, 1038 (1987).
[18] See, e.g., K. E. Evans, Endeavour, New Series 15, 170 (1991); R. Lakes, Adv. Mater. 5, 293 (1993); D. H. Boal, U. Seifert, J. C. Schillcock, Phys. Rev. E48, 4274 (1993); K. W. Wojciechowski, Mol. Phys. Reports 10,129 (1995); E. O. Martz, R. S. Lakes, J. B. Park, Cell. Polym. 15, 349 (1996); K. W. Wojciechowski and K. V. Tretiakov, Comput. Meth. Sci. Technol. 1, 25 (1996); D. Prali, R.
Lakes, Int. J. Mechan. Sci. 39, 305 (1997); U. D. Larsen, O. Sigmund, S. Bouwstra, J. Macromech.
Systems 6, 99 (1997).; P. S. Theocaris, G. E. Stavroulakis, P. D. Panagiotopoulos, Arch. Appl.
Mechan. 67, 274 (1997); R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, and S. Stafstroem,
Nature 392, 362 (1998); K. W. Wojciechowski, Isotropic Systems of Negative Poisson Ratios, in
Proceedings of the 2nd Tohwa International Meeting, Eds. M. Tokuyama and I. Oppenheim (World Scientific, Singapore, 1998); G. Y. Wei and S. F. Edwards, Phys. Rev. E58, 6173 (1998); V. V. Novikov, K. W. Wojciechowski, Phys. Sol. State 41, 1970 (1999); R. H. Baughman, S. O. Dantas,
S. Stafstrom, A. A. Zakhidov, T. B. Michell, D. H. E. Dubin, Science 288, 2018 (2000).
[19] K. W. Wojciechowski, A. C. Brańka, and M. Parrinello, Mol. Phys. 53, 1541-1546 (1984).
[20] M. Parrinello, A. Rahman, J. Chem. Phys. 76, 2662-2666 (1982).
Two-dimensional system of hard cyclic heptamers is studied by Monte Carlo simulations. Isotherms of various crystalline structures formed by the heptamers are obtained. Melting as well as structural phase transitions between crystalline structures are localized. Above melting a rotational phase is observed of hexagonal lattice and isotropic distribution of molecular orientations. With increasing density the coupling between the orientational and rotational degrees of freedom leads to appearance of clearly anisotropic patterns of the atomic density distribution around the lattice sites. These patterns exhibit 6-fold symmetry. At high densities the heptamers form crystalline structures of rectangular lattice and without molecular rotation. Elastic constants of the dense crystalline structures are computed by using an algorithm based on the strain-fluctuation method. It is shown that the densest known crystalline structures of the heptamers exhibit negative Poisson’s ratios near close packing.
[1] J.-P. Hansen, I. R. McDonald, Theory of Simple Liquids, Academic Press, London, 1986.
[2] M. P. Allen, G. T. Evans, D. Frenkel, B. Mulder, Hard Convex Body Fluids, in Advances in
Chemical Physics, 86, 1-165 (1993). See also references therein.
[3] A. C. Brańka, K. W. Wojciechowski, Phys. Rev. Letters 50, 846-849 (1983).
[4] K. W. Wojciechowski, A. C. Brańka, D. Frenkel, Phys. Rev. Letters 64, 3168-3171 (1991); K. W.
Wojciechowski, Phys. Rev. E46, 26-39 (1992); K. W. Wojciechowski, A. C. Brańka, D. Frenkel,
Physica A196, 519-545 (1993).
[5] Yu. D. Burago, V. A. Zallgaller, Geometric Inequalities, Springer, Berlin 1988.
[6] R. Schneider, Convex bodies: The Brunn-Minkowski Theory, Vol. 44 of Encyclopedia of
Mathematics and its Applications, Ed. G.-C. Rota, Cambridge, 1993.
[7] K. W. Wojciechowski, Physica A232, 723-736 (1996).
[8] K. W. Wojciechowski, J. Chem. Phys. 94, 4099-4100 (1991).
[9] S. Sachdev, D. R. Nelson, Phys. Rev. B32, 1480-1502 (1985).
[10] A. C. Brańka, K. W. Wojciechowski, Phys. Lett. A101, 349-353 (1984).
[11] A. C. Brańka, K. W. Wojciechowski, Mol. Phys. 72,941-953 (1991); A. C. Brańka, K. W. Wojciechowski, Mol. Phys. 78, 1513-1526 (1993).
[12] K. W. Wojciechowski, K. V. Tretiakov, Comput. Phys. Commun. 121-122, 528-530 (1999).
[13] B. L. Holian, O. E. Perçus, T. T. Warnock, P. A. Whitlock, Phys. Rev. E50, 1607-1615 (1994).
[14] M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. 8, 3-30 (1998).
[15] K. V. Tretiakov, K. W. Wojciechowski, Phys. Rev. E60, 7626 (1999); K. W. Wojciechowski,
Comput. Meth. Sci. Technol. 5, 81-85 (1999).
[16] K. W. Wojciechowski, Mol. Phys. 61, 1247-1258 (1987); K. W. Wojciechowski and A. C. Brańka, Phys. Rev. A40, 7222-7225 (1989).
[17] R. Lakes, Science 235, 1038 (1987).
[18] See, e.g., K. E. Evans, Endeavour, New Series 15, 170 (1991); R. Lakes, Adv. Mater. 5, 293 (1993); D. H. Boal, U. Seifert, J. C. Schillcock, Phys. Rev. E48, 4274 (1993); K. W. Wojciechowski, Mol. Phys. Reports 10,129 (1995); E. O. Martz, R. S. Lakes, J. B. Park, Cell. Polym. 15, 349 (1996); K. W. Wojciechowski and K. V. Tretiakov, Comput. Meth. Sci. Technol. 1, 25 (1996); D. Prali, R.
Lakes, Int. J. Mechan. Sci. 39, 305 (1997); U. D. Larsen, O. Sigmund, S. Bouwstra, J. Macromech.
Systems 6, 99 (1997).; P. S. Theocaris, G. E. Stavroulakis, P. D. Panagiotopoulos, Arch. Appl.
Mechan. 67, 274 (1997); R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, and S. Stafstroem,
Nature 392, 362 (1998); K. W. Wojciechowski, Isotropic Systems of Negative Poisson Ratios, in
Proceedings of the 2nd Tohwa International Meeting, Eds. M. Tokuyama and I. Oppenheim (World Scientific, Singapore, 1998); G. Y. Wei and S. F. Edwards, Phys. Rev. E58, 6173 (1998); V. V. Novikov, K. W. Wojciechowski, Phys. Sol. State 41, 1970 (1999); R. H. Baughman, S. O. Dantas,
S. Stafstrom, A. A. Zakhidov, T. B. Michell, D. H. E. Dubin, Science 288, 2018 (2000).
[19] K. W. Wojciechowski, A. C. Brańka, and M. Parrinello, Mol. Phys. 53, 1541-1546 (1984).
[20] M. Parrinello, A. Rahman, J. Chem. Phys. 76, 2662-2666 (1982).
