Abstract
A theoretical model is proposed that describes the experimentally observed phase diagram of colloidal dispersions of disk-shaped polydisperse particles. In the framework of the phenomenological theory of phase transitions, it is shown that if disk-shaped particles have polydispersity comparable in thickness and disk diameter, then the following sequence of phase transitions should be expected with increasing volume fraction of ϕ particles: an isotropic liquid (I); a nematic liquid crystal (N), in which the director n sets the preferred orientation of the disk normal; and the discotic (columnar) phase (C), in which the disklike molecules aggregate into liquid columns, and the latter form a two-dimensional hexagonal crystal consisting of liquid columns. However, when the particles forming the colloidal dispersion do not have any polydispersity in thickness (but the polydispersity in the particle diameter is preserved), another sequence of phase transitions takes place, in which the columnar phase is replaced by a smectic liquid crystal (S); that is, particles form a system of equidistant liquid layers. This work proposes and discusses the mechanisms of this behavior and new predictions that follow from this consideration.
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REFERENCES
D. Sun, Hung-Jue Sue, Zh. Cheng, Yu. Martinez-Raton, and E. Velasco, Phys. Rev. E 80, 041704 (2009).
M. Dijkstra, Curr. Opin. Colloid Interface Sci. 6, 372 (2001).
D. Frenkel and B. Smit, in Algorithms to Applications (Academic, New York, 2001).
D. Frenkel, Phys. A (Amsterdam, Neth.) 313, 1 (2002).
H. N. W. Lekkerkerker and R. Tuiner, Colloids and the Depletion Interaction (Springer, Berlin, 2011).
A. Mertelj, D. Lisjak, M. Drofenik, and M. Copic, Nature (London, U.K.) 504, 237 (2013).
Q. Liu, P. J. Ackerman, T. C. Lubensky, and I. I. Smalyukh, Proc. Natl. Acad. Sci. (U.S.A.) 113, 1601235 (2016).
F. Brochard and P. G. de Gennes, J. Phys. 31, 691 (1970).
E. I. Kats and V. V. Lebedev, Sov. Phys. JETP 69, 1155 (1989).
A. B. D. Brown, C. Ferrero, T. Narayanan, and A. R. Rennie, Eur. Phys. J. B 11, 481 (1999).
F. M. var der Kooij, K. Kassapidon, and M. N. W. Lekkerker, Nature (London, U.K.) 406, 868 (2000).
M. Bates and D. Frenkel, J. Chem. Phys. 110, 6553 (1999).
P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993).
P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 2000).
T. Odagaki and K. Okazuki, J. Phys.: Condens. Matter 17, 4531 (2005).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1995; Pergamon, Oxford, 1980).
L. G. Fel, Phys. Rev. E 52, 702 (1995).
E. V. Gurovich, E. I. Kats, and V. V. Lebedev, Sov. Phys. JETP 73, 473 (1991).
P. G. Bolhuis and H. N. W. Lekkerkerer, Phys. A (Amsterdam, Neth.) 196, 375 (1993).
P. Woolston and J. S. van Duijneveldt, J. Chem. Phys. 142, 184901 (2015).
S. A. Brazovskii, Sov. Phys. JETP 41, 85 (1975).
E. I. Kats and A. R. Muratov, Sov. Phys. JETP 67, 89 (1988).
E. I. Kats, V. V. Lebedev, and A. R. Muratov, Phys. Rep. 228, 1 (1993).
V. V. Brazhkin, A. G. Lyapin, V. N. Ryzhov, K. Trachenko, Yu. D. Fomin, and E. N. Tsiok, Phys. Usp. 55, 1061 (2012).
ACKNOWLEDGMENTS
I am grateful to Zhengdong Cheng for discussing the current state of the problem of phase diagrams of polydisperse colloidal dispersions. The work was started during the author’s stay at Tohoku University (Sendai, Japan), and I am grateful to T. Nakanishi and N. Yoshinaga for their hospitality and useful questions when I reported this topic.
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Contribution for the JETP special issue in honor of L.P. Pitaevskii’s 85th birthday
Translated by Andrey Zeigarnik
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Kats, E.I. Effect of Polydispersity on the Phase Diagram of Colloid Systems. J. Exp. Theor. Phys. 127, 939–944 (2018). https://doi.org/10.1134/S1063776118110055
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DOI: https://doi.org/10.1134/S1063776118110055