Volume 27, 2021
|Number of page(s)||58|
|Published online||06 October 2021|
Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study
BCAM, Basque Center for Applied Mathematics,
2 UPV/EHU, Universidad del País Vasco/Euskal Herriko Unibertsitatea, Barrio Sarriena s/n, 48940 Leioa, Bizkaia, Spain.
3 UAIC, Alexandru Ioan Cuza University of Iasi, Bulevardul Carol I, Nr. 11, 700506 Iasi, Romania.
* Corresponding author: firstname.lastname@example.org
Accepted: 22 September 2021
We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.
Mathematics Subject Classification: 35J50 / 35B27 / 76M50 / 76A15
Key words: Liquid crystals / Landau-de Gennes / Gamma-convergence / Cubic microlattices
© The authors. Published by EDP Sciences, SMAI 2021
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