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Freezing transitions in a system of two-dimensional octupolar multipoles

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Abstract.

We have investigated the fluid-solid freezing transitions in a system of axially symmetric particles confined to a two-dimensional plane and interacting via purely repulsive octupolar interaction potential varying as the seventh power of the inverse interparticle separation. Both the one-component and two-component cases have been considered. The classical density functional theory of freezing has been employed to study the relative stability of the triangular solid phase of the system with respect to the fluid phase of the system using the structural inputs calculated by solving the Rogers-Young integral equation theory. Considering the freezing of the fluid into substitutionally disordered solid, in the case of binary mixtures, we observe that the temperature-composition phase diagram is a spindle for moderate particle asymmetries in the range 0.90-0.75. Further increasing the asymmetry to 0.70 results in the coexistence of the fluid phases of two different compositions.

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References

  1. A.P. Gast, W.B. Russel, Phys. Today 51, 24 (1998)

    Article  ADS  Google Scholar 

  2. T.C. Lubensky, D. Pettey, N. Currier, H. Stark, Phys. Rev. E 57, 610 (1998)

    Article  ADS  Google Scholar 

  3. B.I. Lev, P.M. Tomchuk, Phys. Rev. E 59, 591 (1999)

    Article  ADS  Google Scholar 

  4. B.I. Lev, S.B. Chernyshuk, P.M. Tomchuk, H. Yokoyama, Phys. Rev. E 65, 021709 (2002)

    Article  ADS  Google Scholar 

  5. V.M. Pergamenshchik, V.A. Uzunova, Phys. Rev. E 83, 021701 (2011)

    Article  ADS  Google Scholar 

  6. S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 81, 041701 (2010)

    Article  ADS  Google Scholar 

  7. S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 84, 011707 (2011)

    Article  ADS  Google Scholar 

  8. S.B. Chernyshuk, O.M. Tovkach, B.I. Lev, Phys. Rev. E 85, 011706 (2012)

    Article  ADS  Google Scholar 

  9. O.M. Tovkach, S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 86, 061703 (2012)

    Article  ADS  Google Scholar 

  10. S.B. Chernyshuk, Eur. Phys. J. E 37, 6 (2014)

    Article  Google Scholar 

  11. S.B. Chernyshuk, O.M. Tovkach, B.I. Lev, Phys. Rev. E 89, 032505 (2014)

    Article  ADS  Google Scholar 

  12. P. Poulin, Holger Stark, T.C. Tubensky, D.A. Weitz, Science 275, 1770 (1997)

    Article  Google Scholar 

  13. C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids, Vol. I (Oxford University Press, 1984)

  14. P. Linse, G. Karlstrm, J. Stat. Phys. 145, 418 (2011)

    Article  ADS  Google Scholar 

  15. S. Ramaswamy, R. Nityananda, V.A. Gaghunathan, J. Prost, Mol. Cryst. Liq. Cryst. 288, 175 (1996)

    Article  Google Scholar 

  16. Shri Singh, Liquid Crystals, Fundamentals, 1st ed. (World Scientific Publishing, Singapore, 2002)

  17. S.L. Lopatnikov, V.A. Namiot, J. Exp. Theor. Phys. 75, 3691 (1978)

    Google Scholar 

  18. H. Stark, Phys. Rep. 351, 387 (2001)

    Article  ADS  Google Scholar 

  19. J.C. Loudet, P. Barois, P. Poulin, Nature (London) 407, 611 (2000)

    Article  ADS  Google Scholar 

  20. M. Yada, J. Yamamoto, H. Yokoyama, Phys. Rev. Lett. 92, 185501 (2004)

    Article  ADS  Google Scholar 

  21. I.I. Smalyukh, A.N. Kuzmin, A.V. Kachynski, P.N. Prasad, O.D. Lavrentovich, Appl. Phys. Lett. 86, 021913 (2005)

    Article  ADS  Google Scholar 

  22. I.I. Smalyukh, O.D. Lavrentovich, A.N. Kuzmin, A.V. Kachynski, P.N. Prasad, Phys. Rev. Lett. 95, 157801 (2005)

    Article  ADS  Google Scholar 

  23. J. Kotar, M. Vilfan, N. Osterman, D. Babic, M. Copic, I. Poberaj, Phys. Rev. Lett. 96, 207801 (2006)

    Article  ADS  Google Scholar 

  24. I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, S. Zumer, Science 313, 954 (2006)

    Article  ADS  Google Scholar 

  25. V.G. Nazarenko, A.B. Nych, B.I. Lev, Phys. Rev. Lett. 87, 075504 (2001)

    Article  ADS  Google Scholar 

  26. I.I. Smalyukh, S.B. Chernyshuk, B.I. Lev, A.B. Nych, U.M. Ognista, V.G. Nazarenko, O.D. Lavrentovich, Phys. Rev. Lett. 93, 117801 (2004)

    Article  ADS  Google Scholar 

  27. A.B. Nych et al., Phys. Rev. Lett. 98, 057801 (2007)

    Article  ADS  Google Scholar 

  28. D.K. Yoon et al., Nat. Mater. 6, 866 (2007)

    Article  ADS  Google Scholar 

  29. A. Nych, U. Ognysta, M. Skarabot, M. Ravnik, S. Zumer, I. Musevic, Nat. Commun. 4, 1489 (2013)

    Article  ADS  Google Scholar 

  30. I.G. Kaplan, Intermolecular Interactions: Physical Picture, Computational Methods, and Model Potentials (Wiley, New York, 2006)

  31. A. Kumar, Biplab Kumar Mandal, Pankaj Mishra, J. Phys.: Conf. Ser. 765, 012022 (2016)

    Google Scholar 

  32. T.V. Ramakrishnan, M. Yussouff, Phys. Rev. B 19, 2775 (1979)

    Article  ADS  Google Scholar 

  33. W.G. Hoover, S.G. Gray, K.W. Johnson, J. Chem. Phys. 55, 1128 (1971)

    Article  ADS  Google Scholar 

  34. J.P. Hansen, I. McDonald, Theory of Simple Liquids, 3rd ed. (Academic Press, London, 2005)

  35. F.J. Rogers, D.A. Young, Phys. Rev. A 30, 999 (1984)

    Article  ADS  Google Scholar 

  36. S. Kumar, M. Mukherjee, P. Mishra, J. Mol. Liq. 197, 84 (2014)

    Article  Google Scholar 

  37. J.M. Caillol, D. Levesque, J.-J. Weiss, Mol. Phys. 44, 733 (1981)

    Article  ADS  Google Scholar 

  38. J.D. Talman, J. Comput. Phys. 29, 35 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  39. Y. Singh, Phys. Rep. 207, 351 (1991)

    Article  ADS  Google Scholar 

  40. M. Mukherjee, P. Mishra, H. Löwen, J. Phys.: Condens. Matter 26, 465101 (2014)

    ADS  Google Scholar 

  41. K. Zahn, R. Lenke, G. Maret, Phys. Rev. Lett. 82, 2721 (1999)

    Article  ADS  Google Scholar 

  42. N.D. Mermin, Phys. Lett. A 109, 289 (1985)

    Article  ADS  Google Scholar 

  43. K. Zahn, G. Maret, Phys. Rev. Lett. 85, 3656 (2000)

    Article  ADS  Google Scholar 

  44. A.R. Denton, N.W. Ashcroft, Phys. Rev. A 39, 4701 (1989)

    Article  ADS  Google Scholar 

  45. P. Mishra, Y. Singh, Phys. Rev. Lett. 97, 177801 (2006)

    Article  ADS  Google Scholar 

  46. P. Mishra, S.L. Singh, J. Ram, Y. Singh, J. Chem. Phys. 127, 044905 (2007)

    Article  ADS  Google Scholar 

  47. S.L. Singh, Y. Singh, EPL 88, 16005 (2009)

    Article  ADS  Google Scholar 

Download references

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Kumar, A., Kumar Mandal, B., Kumar, S. et al. Freezing transitions in a system of two-dimensional octupolar multipoles. Eur. Phys. J. E 40, 80 (2017). https://doi.org/10.1140/epje/i2017-11572-x

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