Calculus of Variations and Geometric Measure Theory

G. Canevari - A. Zarnescu

Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation

created by canevari on 29 Jan 2021


Accepted Paper

Inserted: 29 jan 2021
Last Updated: 29 jan 2021

Journal: Mathematical Models and Methods in Applied Sciences
Volume: 30
Number: 2
Pages: 309-342
Year: 2020
Doi: 10.1142/S0218202520500086

ArXiv: 1901.03541 PDF


We consider a Landau-de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime - i.e., the size of the inclusions is much smaller than the typical separation distance between them, so that the total volume occupied by the inclusions is small. By studying the homogenised limit, and proving rigorous convergence results for local minimisers, we compute the effective free energy for the doped material. In particular, we show that not only the phase transition temperature, but any coefficient of the quartic Landau-de Gennes bulk potential can be tuned, by suitably choosing the surface anchoring energy density.