No Access Submitted: 17 December 2020 Accepted: 19 February 2021 Published Online: 09 March 2021
J. Chem. Phys. 154, 104902 (2021); https://doi.org/10.1063/5.0040942
Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length (L) and diameter (D) using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate L/D > 1 and the oblate L/D < 1 phase diagrams are reported with no solution of continuity. In the prolate L/D > 1 case, we find intermediate nematic N and smectic SmA phases in addition to a low density isotropic I and a high density crystal X phase with I–N-SmA and I-SmA-X triple points. An apparent columnar phase C is shown to be metastable, as in the case of spherocylinders. In the oblate L/D < 1 case, we find stable intermediate cubatic (Cub), nematic (N), and columnar (C) phases with I–N-Cub, N-Cub-C, and I-Cub-C triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.
We are indebted to Cristiano De Michele and Maria Barbi for useful discussions. The use of the SCSCF multiprocessor cluster at the Università Ca’ Foscari Venezia and of the LESC cluster at the University of Campinas is gratefully acknowledged. This work was supported by MIUR PRIN-COFIN2017 Soft Adaptive Networks Grant No. 2017Z55KCW and Galileo Project No. 2018-39566PG (A.G.), São Paulo Research Foundation (FAPESP) Grant No. 2018/02713-8, and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) –Finance Code 001. F.R. acknowledges IdEx Bordeaux (France) for financial support. J.T.L. gratefully acknowledges the hospitality of the Ca’ Foscari University of Venice where part of this work was carried out. The authors would like to acknowledge the contribution of the Eutopia COST Action Grant No. CA17139.
  1. 1. L. Onsager, “The effects of shape on the interaction of colloidal particles,” Ann. N. Y. Acad. Sci. 51, 627–659 (1949). https://doi.org/10.1111/j.1749-6632.1949.tb27296.x, Google ScholarCrossref
  2. 2. T. Gibaud, E. Barry, M. J. Zakhary, M. Henglin, A. Ward, Y. Yang, C. Berciu, R. Oldenbourg, M. F. Hagan, D. Nicastro, R. B. Meyer, and Z. Dogic, “Reconfigurable self-assembly through chiral control of interfacial tension,” Nature 481, 348 (2012). https://doi.org/10.1038/nature10769, Google ScholarCrossref
  3. 3. E. Grelet, “Hard-rod behavior in dense mesophases of semiflexible and rigid charged viruses,” Phys. Rev. X 4, 021053 (2014). https://doi.org/10.1103/physrevx.4.021053, Google ScholarCrossref
  4. 4. Y. Liang, Y. Xie, D. Chen, C. Guo, S. Hou, T. Wen, F. Yang, K. Deng, X. Wu, I. I. Smalyukh, and Q. Liu, “Symmetry control of nanorod superlattice driven by a governing force,” Nat. Commun. 8, 1410 (2017). https://doi.org/10.1038/s41467-017-01111-4, Google ScholarCrossref
  5. 5. B. Sung, A. de la Cotte, and E. Grelet, “Chirality-controlled crystallization via screw dislocations,” Nat. Commun. 9, 1405 (2018). https://doi.org/10.1038/s41467-018-03745-4, Google ScholarCrossref
  6. 6. M. P. Allen, G. T. Evans, D. Frenkel, and B. M. Mulder, “Hard convex body fluids,” Adv. Chem. Phys. 86, 1–166 (1993). https://doi.org/10.1002/9780470141458.ch1, Google ScholarCrossref
  7. 7. C. Vega and S. Lago, “A fast algorithm to evaluate the shortest distance between rods,” Comput. Chem. 18, 55–59 (1994). https://doi.org/10.1016/0097-8485(94)80023-5, Google ScholarCrossref
  8. 8. P. Bolhuis and D. Frenkel, “Tracing the phase boundaries of hard spherocylinders,” J. Chem. Phys. 106, 666–687 (1997). https://doi.org/10.1063/1.473404, Google ScholarScitation, ISI
  9. 9. D. Frenkel and B. M. Mulder, “The hard ellipsoid-of-revolution fluid,” Mol. Phys. 55, 1171–1192 (1985). https://doi.org/10.1080/00268978500101971, Google ScholarCrossref
  10. 10. E. Frezza, A. Ferrarini, H. B. Kolli, A. Giacometti, and G. Cinacchi, “The isotropic-to-nematic phase transition in hard helices: Theory and simulation,” J. Chem. Phys. 138, 164906 (2013). https://doi.org/10.1063/1.4802005, Google ScholarScitation, ISI
  11. 11. K. Milinković, M. Dennison, and M. Dijkstra, “Phase diagram of hard asymmetric dumbbell particles,” Phys. Rev. E 87, 032128 (2013). https://doi.org/10.1103/PhysRevE.87.032128, Google ScholarCrossref
  12. 12. J. D. Bernal and I. Fankuchen, “X-ray and crystallographic studies of plant virus preparations,” J. Gen. Physiol. 25, 111–165 (1941). https://doi.org/10.1085/jgp.25.1.111, Google ScholarCrossref
  13. 13. X. Wen, R. B. Meyer, and D. L. D. Caspar, “Observation of smectic-A ordering in a solution of rigid-rod-like particles,” Phys. Rev. Lett. 63, 2760–2763 (1989). https://doi.org/10.1103/physrevlett.63.2760, Google ScholarCrossref
  14. 14. A. Leforestier, A. Bertin, J. Dubochet, K. Richter, N. Sartori Blanc, and F. Livolant, “Expression of chirality in columnar hexagonal phases or DNA and nucleosomes,” C. R. Chim. 11, 229–244 (2008). https://doi.org/10.1016/j.crci.2007.09.008, Google ScholarCrossref
  15. 15. F. Livolant, S. Mangenot, A. Leforestier, A. Bertin, M. de Frutos, E. Raspaud, and D. Durand, “Are liquid crystalline properties of nucleosomes involved in chromosome structure and dynamics?,” Philos. Trans. R. Soc., A 364, 2615–2633 (2006). https://doi.org/10.1098/rsta.2006.1843, Google ScholarCrossref
  16. 16. G. Odriozola, “Revisiting the phase diagram of hard ellipsoids,” J. Chem. Phys. 136, 134505 (2012). https://doi.org/10.1063/1.3699331, Google ScholarScitation, ISI
  17. 17. E. Grelet, “Hexagonal order in crystalline and columnar phases of hard rods,” Phys. Rev. Lett. 100, 168301 (2008). https://doi.org/10.1103/physrevlett.100.168301, Google ScholarCrossref
  18. 18. E. Grelet and R. Rana, “From soft to hard rod behavior in liquid crystalline suspensions of sterically stabilized colloidal filamentous particles,” Soft Matter 12, 4621 (2016). https://doi.org/10.1039/c6sm00527f, Google ScholarCrossref
  19. 19. S. Dussi, M. Chiappini, and M. Dijkstra, “On the stability and finite-size effects of a columnar phase in single-component systems of hard-rod-like particles,” Mol. Phys. 116, 2792–2805 (2018). https://doi.org/10.1080/00268976.2018.1471231, Google ScholarCrossref
  20. 20. H. H. Wensink and H. N. W. Lekkerkerker, “Phase diagram of hard colloidal platelets: A theoretical account,” Mol. Phys. 107, 2111–2118 (2009). https://doi.org/10.1080/00268970903160605, Google ScholarCrossref
  21. 21. R. Blaak, D. Frenkel, and B. M. Mulder, “Do cylinders exhibit a cubatic phase?,” J. Chem. Phys. 110, 11652–11659 (1999). https://doi.org/10.1063/1.479104, Google ScholarScitation, ISI
  22. 22. A. G. Orellana, E. Romani, and C. De Michele, “Speeding up Monte Carlo simulation of patchy hard cylinders,” Eur. Phys. J. E 41, 51 (2018). https://doi.org/10.1140/epje/i2018-11657-0, Google ScholarCrossref
  23. 23. A. Stukowski, “Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool,” Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010). https://doi.org/10.1088/0965-0393/18/1/015012, Google ScholarCrossref
  24. 24. H. B. Kolli, G. Cinacchi, A. Ferrarini, and A. Giacometti, “Chiral self-assembly of helical particles,” Faraday Discuss. 186, 171–186 (2016). https://doi.org/10.1039/c5fd00132c, Google ScholarCrossref
  25. 25. P. D. Duncan, M. Dennison, A. J. Masters, and M. R. Wilson, “Theory and computer simulation for the cubatic phase of cut spheres,” Phys. Rev. E 79, 031702 (2009). https://doi.org/10.1103/physreve.79.031702, Google ScholarCrossref
  26. 26. Y. Liu and A. Widmer-Cooper, “A versatile simulation method for studying phase behavior and dynamics in colloidal rod and rod-polymer suspensions,” J. Chem. Phys. 150, 244508 (2019). https://doi.org/10.1063/1.5096193, Google ScholarScitation, ISI
  27. 27. S. C. McGrother, D. C. Williamson, and G. Jackson, “A re-examination of the phase diagram of hard spherocylinders,” J. Chem. Phys. 104, 6755–6771 (1996). https://doi.org/10.1063/1.471343, Google ScholarScitation, ISI
  28. 28. J. M. Polson and D. Frenkel, “First-order nematic-smectic phase transition for hard spherocylinders in the limit of infinite aspect ratio,” Phys. Rev. E 56, R6260 (1997). https://doi.org/10.1103/physreve.56.r6260, Google ScholarCrossref
  29. 29. M. Marechal, S. Dussi, and M. Dijkstra, “Density functional theory and simulations of colloidal triangular prisms,” J. Chem. Phys. 146, 124905 (2017). https://doi.org/10.1063/1.4978502, Google ScholarScitation, ISI
  30. 30. J. A. C. Veerman and D. Frenkel, “Phase behavior of disklike hard-core mesogens,” Phys. Rev. A 45, 5632–5648 (1992). https://doi.org/10.1103/physreva.45.5632, Google ScholarCrossref
  31. 31. A. Repula, M. Oshima Menegon, C. Wu, P. van der Schoot, and E. Grelet, “Directing liquid crystalline self-organization of rodlike particles through tunable attractive single tips,” Phys. Rev. Lett. 122, 128008 (2019). https://doi.org/10.1103/physrevlett.122.128008, Google ScholarCrossref
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