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.
Keywords: Liquid crystals, Landau-de Gennes, Gamma-convergence, Cubic microlattices
@article{COCV_2021__27_1_A97_0,
author = {Ceuca, Razvan-Dumitru},
title = {Cubic microlattices embedded in nematic liquid crystals: a {Landau-de} {Gennes} study},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021093},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021093/}
}
TY - JOUR AU - Ceuca, Razvan-Dumitru TI - Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021093/ DO - 10.1051/cocv/2021093 LA - en ID - COCV_2021__27_1_A97_0 ER -
%0 Journal Article %A Ceuca, Razvan-Dumitru %T Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021093/ %R 10.1051/cocv/2021093 %G en %F COCV_2021__27_1_A97_0
Ceuca, Razvan-Dumitru. Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 95. doi: 10.1051/cocv/2021093
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