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

Giacomo Canevari

Dipartimento di Informatica, Università Degli Studi di Verona, Strada le Grazie 15, Verona 37134, Italy

E-mail Address: [email protected]

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and

Arghir Zarnescu

IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, Bilbao 48013, Bizkaia, Spain

BCAM, Basque Center for Applied Mathematics, Mazarredo 14, Bilbao 48009, Bizkaia, Spain

“Simion Stoilow” Institute of the Romanian Academy, 21 Calea Griviţei, Bucharest 010702, Romania

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0218202520500086Cited by:8

Abstract

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 also any coefficient of the quartic Landau–de Gennes bulk potential can be tuned, by suitably choosing the surface anchoring energy density.

Communicated by G. Allaire

Keywords:

AMSC: 35J50, 35B27, 76M50, 76A15

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Vol. 30, No. 02

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History

Received 14 March 2019

Revised 16 October 2019

Accepted 29 October 2019

Published: 30 December 2019

Keywords

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

Abstract

References

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