Magnetic field-induced instabilities in liquid crystals

Fang-Hua Lin, Xing Bin Pan

Research output: Contribution to journalArticle

Abstract

We use the Landau-de Gennes model to investigate the magnetic field-induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes' discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields H s and Hsh. The pure smectic states lose their global minimality (strong stability) at Hs and lose their local minimality (weak stability) at Hsh.. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau-de Gennes model for liquid crystals and the Ginzburg-Landau model for superconductivity.

Original languageEnglish (US)
Pages (from-to)1588-1612
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number5
DOIs
StatePublished - 2006

Fingerprint

Liquid Crystal
Liquid crystals
Magnetic Field
Magnetic fields
Strong Stability
Pure State
Minimality
Ginzburg-Landau Model
Superconductivity
Superconductor
Analogy
Superconducting materials
Coefficient
Model

Keywords

  • Critical magnetic field
  • Landau-de Gennes model
  • Liquid crystal
  • Phase transition

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics
  • Numerical Analysis

Cite this

Magnetic field-induced instabilities in liquid crystals. / Lin, Fang-Hua; Pan, Xing Bin.

In: SIAM Journal on Mathematical Analysis, Vol. 38, No. 5, 2006, p. 1588-1612.

Research output: Contribution to journalArticle

@article{9204d06c38514f8dab47e877893c5646,
title = "Magnetic field-induced instabilities in liquid crystals",
abstract = "We use the Landau-de Gennes model to investigate the magnetic field-induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes' discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields H s and Hsh. The pure smectic states lose their global minimality (strong stability) at Hs and lose their local minimality (weak stability) at Hsh.. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau-de Gennes model for liquid crystals and the Ginzburg-Landau model for superconductivity.",
keywords = "Critical magnetic field, Landau-de Gennes model, Liquid crystal, Phase transition",
author = "Fang-Hua Lin and Pan, {Xing Bin}",
year = "2006",
doi = "10.1137/050638643",
language = "English (US)",
volume = "38",
pages = "1588--1612",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",

}

TY - JOUR

T1 - Magnetic field-induced instabilities in liquid crystals

AU - Lin, Fang-Hua

AU - Pan, Xing Bin

PY - 2006

Y1 - 2006

N2 - We use the Landau-de Gennes model to investigate the magnetic field-induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes' discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields H s and Hsh. The pure smectic states lose their global minimality (strong stability) at Hs and lose their local minimality (weak stability) at Hsh.. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau-de Gennes model for liquid crystals and the Ginzburg-Landau model for superconductivity.

AB - We use the Landau-de Gennes model to investigate the magnetic field-induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes' discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields H s and Hsh. The pure smectic states lose their global minimality (strong stability) at Hs and lose their local minimality (weak stability) at Hsh.. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau-de Gennes model for liquid crystals and the Ginzburg-Landau model for superconductivity.

KW - Critical magnetic field

KW - Landau-de Gennes model

KW - Liquid crystal

KW - Phase transition

UR - http://www.scopus.com/inward/record.url?scp=34648831391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34648831391&partnerID=8YFLogxK

U2 - 10.1137/050638643

DO - 10.1137/050638643

M3 - Article

VL - 38

SP - 1588

EP - 1612

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 5

ER -