Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Polydispersity and surface energy strength in nematic colloids

1 Dipartimento di Informatica, Università degli Studi di Verona, Strada le Grazie 15, 37134 Verona, Italy
2 IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Bizkaia, Spain
3 BCAM, Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Bizkaia, Spain
4 “Simion Stoilow” Institute of the Romanian Academy, 21 Calea Griviţei, 010702 Bucharest, Romania

This contribution is part of the Special Issue: Variational Models in Elasticity
Guest Editors: Lucia De Luca; Marcello Ponsiglione
Link: https://www.aimspress.com/newsinfo/1369.html

Special Issues: Variational Models in Elasticity

We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit and compute the effective free energy of the composite material. By suitably choosing the shape of the inclusions and imposing a quadratic, Rapini-Papoular type surface anchoring energy density, we obtain an effective free energy functional with an additional linear term, which may be interpreted as an “effective field” induced by the inclusions. Moreover, we compute the effective free energy in a regime of “very strong anchoring”, that is, when the surface energy effects dominate over the volume free energy.
  Article Metrics

Keywords liquid crystals; nematic colloids; Landau-de Gennes; effective field; strong anchoring

Citation: Giacomo Canevari, Arghir Zarnescu. Polydispersity and surface energy strength in nematic colloids. Mathematics in Engineering, 2020, 2(2): 290-312. doi: 10.3934/mine.2020015


  • 1. Alama S, Bronsard L, Lamy X (2016) Minimizers of the Landau-de Gennes energy around a spherical colloid particle. Arch Ration Mech An 222: 427-450.    
  • 2. Alama S, Bronsard L, Lamy X (2018) Spherical particle in nematic liquid crystal under an external field: The Saturn ring regime. J Nonlinear Sci 28: 1443-1465.    
  • 3. Alexe-Ionescu AL, Barberi R, Barbero G, et al. (1992) Surface energy for nematic liquid crystals: A new point of view. Z Naturforsch A 47: 1235-1240.    
  • 4. Ball JM, Zarnescu A (2011) Orientability and energy minimization in liquid crystal models. Arch Ration Mech An 202: 493-535.    
  • 5. Bennett TP, D'Alessandro G, Daly KR (2014) Multiscale models of colloidal dispersion of particles in nematic liquid crystals. Phys Rev E 90: 062505.
  • 6. Berlyand L, Cioranescu D, Golovaty D (2005) Homogenization of a Ginzburg-Landau model for a nematic liquid crystal with inclusions. J Math pure Appl 84: 97-136.    
  • 7. Calderer MC, DeSimone A, Golovaty D, et al. (2014) An effective model for nematic liquid crystal composites with ferromagnetic inclusions. SIAM J Appl Math 74: 237-262.    
  • 8. Canevari G, Ramaswamy M, Majumdar A (2016) Radial symmetry on three-dimensional shells in the Landau-de Gennes theory. Physica D 314: 18-34.    
  • 9. Canevari G, Segatti A, Veneroni M (2015) Morse's index formula in VMO on compact manifold with boundary. J Funct Anal 269: 3043-3082.    
  • 10. Canevari G, Segatti A (2018) Defects in Nematic Shells: A Γ-convergence discrete-to-continuum approach. Arch Ration Mech An 229: 125-186.    
  • 11. Canevari G, Segatti A (2018) Variational analysis of nematic shells. In: Trends in Applications of Mathematics to Mechanics, Cham: Springer, 81-102.
  • 12. Canevari G, Zarnescu AD (2019) Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation. Math Mod Meth Appl Sci doi: 10.1142/S0218202520500086
  • 13. De Gennes PG, Prost J (1993) The Physics of Liquid Crystals, Oxford university press.
  • 14. Gartland Jr EC (2018) Scalings and Limits of Landau-de Gennes Models for Liquid Crystals: A Comment on Some Recent Analytical Papers. Math Model Anal 23: 414-432.    
  • 15. Goossens JW (1985) Bulk, Interfacial and Anchoring Energies of Liquid Crystals. Mol Cryst Liq Cryst 124: 305-331.    
  • 16. Kurochkin O, Atkuri H, Buchnev O, et al. (2010) Nano-colloids of sn2P2S6 in nematic liquid crystal pentyl-cianobiphenile. Condens Matter Phys 13: 33701.    
  • 17. Lavrentovich O, Lev B, Trokhymchuk A (2010) Liquid crystal colloids. Condens Matter Phys 13: 30101.
  • 18. Lax PD (2002) Functional Analysis, Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts, Wiley.
  • 19. Li F, Buchnev O, Cheon CI, et al. (2006) Orientational coupling amplification in ferroelectric nematic colloids. Phys Rev letter 97: 147801.    
  • 20. Longa L, Montelesan D, Trebin HR (1987) An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals. Liq Cryst 2: 769-796.    
  • 21. Mottram NJ, Newton CJP (2014) Introduction to Q-tensor theory. arXiv:1409.3542.
  • 22. Nguyen L, Zarnescu A (2013) Refined approximation for minimizers of a Landau-de Gennes energy functional. Calc Var Partial Dif 47: 383-432.    
  • 23. Ravnik M, Žumer S (2009) Landau-de Gennes modelling of nematic liquid crystal colloids. Liq Cryst 36: 1201-1214.    
  • 24. Rey A (2001) Generalized nematostatics. Liq Cryst 28: 549-556.    
  • 25. Reznikov Y, Buchnev O, Tereshchenko O, et al. (2003). Ferroelectric nematic suspension. Appl Phys Lett 82: 1917-1919.    
  • 26. Sluckin TJ, Poniewierski A (1984) Fluid and Interfacial Phenomena, Chichester: John Wiley.
  • 27. Smalyukh II (2018) Liquid crystal colloids. Annu Rev Condens Matter Phys 9: 207-226.    
  • 28. Wang Y, Canevari G, Majumdar A (2019) Order reconstruction for nematics on squares with isotropic inclusions: A Landau-de Gennes study. SIAM J Appl Math 79: 1314-1340.    
  • 29. Wang Y, Zhang P, Chen JZY (2017) Topological defects in an unconfined nematic fluid induced by single and double spherical colloidal particles. Phys Rev E 96: 042702.


Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved