Polydispersity and surface energy strength in nematic colloids

Giacomo Canevari; Arghir Zarnescu; Giacomo Canevari; Arghir Zarnescu

doi:10.3934/mine.2020015

Mathematics in Engineering

2020, Volume 2, Issue 2: 290-312. doi: 10.3934/mine.2020015

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Polydispersity and surface energy strength in nematic colloids

Giacomo Canevari ^{1
,
,},
Arghir Zarnescu ^2,3,4

1.
Dipartimento di Informatica, Università degli Studi di Verona, Strada le Grazie 15, 37134 Verona, Italy
2.
IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Bizkaia, Spain
3.
BCAM, Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Bizkaia, Spain
4.
“Simion Stoilow” Institute of the Romanian Academy, 21 Calea Griviţei, 010702 Bucharest, Romania

Received: 02 October 2019 Accepted: 02 January 2020 Published: 13 February 2020

We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit and compute the effective free energy of the composite material. By suitably choosing the shape of the inclusions and imposing a quadratic, Rapini-Papoular type surface anchoring energy density, we obtain an effective free energy functional with an additional linear term, which may be interpreted as an "effective field" induced by the inclusions. Moreover, we compute the effective free energy in a regime of "very strong anchoring", that is, when the surface energy effects dominate over the volume free energy.
- liquid crystals,
- nematic colloids,
- Landau-de Gennes,
- effective field,
- strong anchoring
Citation: Giacomo Canevari, Arghir Zarnescu. Polydispersity and surface energy strength in nematic colloids[J]. Mathematics in Engineering, 2020, 2(2): 290-312. doi: 10.3934/mine.2020015

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Abstract

We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit and compute the effective free energy of the composite material. By suitably choosing the shape of the inclusions and imposing a quadratic, Rapini-Papoular type surface anchoring energy density, we obtain an effective free energy functional with an additional linear term, which may be interpreted as an "effective field" induced by the inclusions. Moreover, we compute the effective free energy in a regime of "very strong anchoring", that is, when the surface energy effects dominate over the volume free energy.

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