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.
Graphical abstract
Similar content being viewed by others
References
A.P. Gast, W.B. Russel, Phys. Today 51, 24 (1998)
T.C. Lubensky, D. Pettey, N. Currier, H. Stark, Phys. Rev. E 57, 610 (1998)
B.I. Lev, P.M. Tomchuk, Phys. Rev. E 59, 591 (1999)
B.I. Lev, S.B. Chernyshuk, P.M. Tomchuk, H. Yokoyama, Phys. Rev. E 65, 021709 (2002)
V.M. Pergamenshchik, V.A. Uzunova, Phys. Rev. E 83, 021701 (2011)
S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 81, 041701 (2010)
S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 84, 011707 (2011)
S.B. Chernyshuk, O.M. Tovkach, B.I. Lev, Phys. Rev. E 85, 011706 (2012)
O.M. Tovkach, S.B. Chernyshuk, B.I. Lev, Phys. Rev. E 86, 061703 (2012)
S.B. Chernyshuk, Eur. Phys. J. E 37, 6 (2014)
S.B. Chernyshuk, O.M. Tovkach, B.I. Lev, Phys. Rev. E 89, 032505 (2014)
P. Poulin, Holger Stark, T.C. Tubensky, D.A. Weitz, Science 275, 1770 (1997)
C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids, Vol. I (Oxford University Press, 1984)
P. Linse, G. Karlstrm, J. Stat. Phys. 145, 418 (2011)
S. Ramaswamy, R. Nityananda, V.A. Gaghunathan, J. Prost, Mol. Cryst. Liq. Cryst. 288, 175 (1996)
Shri Singh, Liquid Crystals, Fundamentals, 1st ed. (World Scientific Publishing, Singapore, 2002)
S.L. Lopatnikov, V.A. Namiot, J. Exp. Theor. Phys. 75, 3691 (1978)
H. Stark, Phys. Rep. 351, 387 (2001)
J.C. Loudet, P. Barois, P. Poulin, Nature (London) 407, 611 (2000)
M. Yada, J. Yamamoto, H. Yokoyama, Phys. Rev. Lett. 92, 185501 (2004)
I.I. Smalyukh, A.N. Kuzmin, A.V. Kachynski, P.N. Prasad, O.D. Lavrentovich, Appl. Phys. Lett. 86, 021913 (2005)
I.I. Smalyukh, O.D. Lavrentovich, A.N. Kuzmin, A.V. Kachynski, P.N. Prasad, Phys. Rev. Lett. 95, 157801 (2005)
J. Kotar, M. Vilfan, N. Osterman, D. Babic, M. Copic, I. Poberaj, Phys. Rev. Lett. 96, 207801 (2006)
I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, S. Zumer, Science 313, 954 (2006)
V.G. Nazarenko, A.B. Nych, B.I. Lev, Phys. Rev. Lett. 87, 075504 (2001)
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)
A.B. Nych et al., Phys. Rev. Lett. 98, 057801 (2007)
D.K. Yoon et al., Nat. Mater. 6, 866 (2007)
A. Nych, U. Ognysta, M. Skarabot, M. Ravnik, S. Zumer, I. Musevic, Nat. Commun. 4, 1489 (2013)
I.G. Kaplan, Intermolecular Interactions: Physical Picture, Computational Methods, and Model Potentials (Wiley, New York, 2006)
A. Kumar, Biplab Kumar Mandal, Pankaj Mishra, J. Phys.: Conf. Ser. 765, 012022 (2016)
T.V. Ramakrishnan, M. Yussouff, Phys. Rev. B 19, 2775 (1979)
W.G. Hoover, S.G. Gray, K.W. Johnson, J. Chem. Phys. 55, 1128 (1971)
J.P. Hansen, I. McDonald, Theory of Simple Liquids, 3rd ed. (Academic Press, London, 2005)
F.J. Rogers, D.A. Young, Phys. Rev. A 30, 999 (1984)
S. Kumar, M. Mukherjee, P. Mishra, J. Mol. Liq. 197, 84 (2014)
J.M. Caillol, D. Levesque, J.-J. Weiss, Mol. Phys. 44, 733 (1981)
J.D. Talman, J. Comput. Phys. 29, 35 (1978)
Y. Singh, Phys. Rep. 207, 351 (1991)
M. Mukherjee, P. Mishra, H. Löwen, J. Phys.: Condens. Matter 26, 465101 (2014)
K. Zahn, R. Lenke, G. Maret, Phys. Rev. Lett. 82, 2721 (1999)
N.D. Mermin, Phys. Lett. A 109, 289 (1985)
K. Zahn, G. Maret, Phys. Rev. Lett. 85, 3656 (2000)
A.R. Denton, N.W. Ashcroft, Phys. Rev. A 39, 4701 (1989)
P. Mishra, Y. Singh, Phys. Rev. Lett. 97, 177801 (2006)
P. Mishra, S.L. Singh, J. Ram, Y. Singh, J. Chem. Phys. 127, 044905 (2007)
S.L. Singh, Y. Singh, EPL 88, 16005 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2017-11572-x