### Abstract

We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the "thermodynamic-transition" field strength H _{1} at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H _{2} at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H _{1} is non-monotonically dependent on the particle radius R _{0}, H _{2} monotonically increases with R _{0} and the dependence of H _{2} is weak for large R _{0}. The non-monotonic dependence of H _{1} on R _{0} can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R _{0} the critical field strength is independent of R _{0}, which agrees with our numerical finding.

Original language | English |
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Pages (from-to) | 341-347 |

Number of pages | 7 |

Journal | European Physical Journal E |

Volume | 21 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2006 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Biotechnology
- Biophysics
- Chemistry(all)
- Materials Science(all)
- Surfaces and Interfaces

### Cite this

**Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field.** / Fukuda, J.; Yokoyama, H.

Research output: Contribution to journal › Article

*European Physical Journal E*, vol. 21, no. 4, pp. 341-347. https://doi.org/10.1140/epje/i2006-10072-6

}

TY - JOUR

T1 - Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field

AU - Fukuda, J.

AU - Yokoyama, H.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the "thermodynamic-transition" field strength H 1 at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H 2 at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H 1 is non-monotonically dependent on the particle radius R 0, H 2 monotonically increases with R 0 and the dependence of H 2 is weak for large R 0. The non-monotonic dependence of H 1 on R 0 can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R 0 the critical field strength is independent of R 0, which agrees with our numerical finding.

AB - We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the "thermodynamic-transition" field strength H 1 at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H 2 at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H 1 is non-monotonically dependent on the particle radius R 0, H 2 monotonically increases with R 0 and the dependence of H 2 is weak for large R 0. The non-monotonic dependence of H 1 on R 0 can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R 0 the critical field strength is independent of R 0, which agrees with our numerical finding.

UR - http://www.scopus.com/inward/record.url?scp=33847282458&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847282458&partnerID=8YFLogxK

U2 - 10.1140/epje/i2006-10072-6

DO - 10.1140/epje/i2006-10072-6

M3 - Article

C2 - 17294085

AN - SCOPUS:33847282458

VL - 21

SP - 341

EP - 347

JO - European Physical Journal E

JF - European Physical Journal E

SN - 1292-8941

IS - 4

ER -