Theoretical analysis of the magnetic Freedericksz transition in the presence of flexoelectricity and ionic contamination

A.A.T. Smith, C.V. Brown, N.J. Mottram

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field H immediately above the critical Fræ#169;edericksz transition H=Hc. The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when H/Hc=1.01. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.
LanguageEnglish
Pages041704-041712
Number of pages8
JournalPhysical Review E
Volume75
Issue number4
DOIs
Publication statusPublished - 18 Apr 2007

Fingerprint

Contamination
Theoretical Analysis
contamination
Polarization
dielectric polarization
Elastic Constants
polarization
Numerical Calculation
Immediately
Analytical Solution
elastic properties
Magnetic Field
Voltage
Charge
electric potential
Coefficient
coefficients
magnetic fields

Keywords

  • flexoelectricity
  • physics
  • numerical mathematics
  • statistics

Cite this

@article{0f9f559feea04a7995b0f90ac0ba50d7,
title = "Theoretical analysis of the magnetic Freedericksz transition in the presence of flexoelectricity and ionic contamination",
abstract = "We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field H immediately above the critical Fr{\ae}#169;edericksz transition H=Hc. The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when H/Hc=1.01. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.",
keywords = "flexoelectricity, physics, numerical mathematics, statistics",
author = "A.A.T. Smith and C.V. Brown and N.J. Mottram",
year = "2007",
month = "4",
day = "18",
doi = "10.1103/PhysRevE.75.041704",
language = "English",
volume = "75",
pages = "041704--041712",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "4",

}

Theoretical analysis of the magnetic Freedericksz transition in the presence of flexoelectricity and ionic contamination. / Smith, A.A.T.; Brown, C.V.; Mottram, N.J.

In: Physical Review E, Vol. 75, No. 4, 18.04.2007, p. 041704-041712.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Theoretical analysis of the magnetic Freedericksz transition in the presence of flexoelectricity and ionic contamination

AU - Smith, A.A.T.

AU - Brown, C.V.

AU - Mottram, N.J.

PY - 2007/4/18

Y1 - 2007/4/18

N2 - We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field H immediately above the critical Fræ#169;edericksz transition H=Hc. The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when H/Hc=1.01. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.

AB - We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field H immediately above the critical Fræ#169;edericksz transition H=Hc. The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when H/Hc=1.01. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.

KW - flexoelectricity

KW - physics

KW - numerical mathematics

KW - statistics

U2 - 10.1103/PhysRevE.75.041704

DO - 10.1103/PhysRevE.75.041704

M3 - Article

VL - 75

SP - 41704

EP - 41712

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 4

ER -