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Liquid Crystals Volume 36, 2009 - Issue 10-11: Pierre-Gilles de Gennes Commemoration
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Invited Articles

Landau–de Gennes modelling of nematic liquid crystal colloids

Miha Ravnik Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
&
Slobodan Žumer Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia; J. Stefan Institute, Jamova 39, 1000, Ljubljana, SloveniaCorrespondence[email protected]
Pages 1201-1214 | Received 16 Apr 2009, Accepted 11 May 2009, Published online: 08 Oct 2009
 
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Abstract

Phenomenological Landau–de Gennes modelling based on the free energy of nematic liquid crystal colloids is reviewed. Nematic phase, gradient of order, and surface anchoring contributions to the total free energy are used. The numerical finite difference relaxation technique is explained as an efficient tool for the minimisation of the free energy. Effects of the mesh and mesh allocation are discussed. Various conceptually different colloidal structures are calculated to show the universality of the model. Single particles, dipolar–quadrupolar dimers, entangled dimers, dimers bound by escaped hyperbolic rings, and hierarchically patterned Saturn-ring colloidal superstructures are presented.

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