Energy considerations for parabolic cyclides in SmA liquid crystals

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

For Dupin cyclides in the SmA liquid crystal phase, Kleman and Lavrentovich [1] found that increasing the saddle-splay constant K¯ caused the minimum of the total elastic energy to occur at a decreased value of the eccentricity e, close to unity. We extend this work to the parabolic cyclides and present an analytical expression for the total elastic energy that is finite over a suitable range of values for the latus rectum, conventionally denoted in this context by −4- (>0). The length of the latus rectum characterises the parabolic focal conic structure analogously to the eccentricity of the Dupin cyclide focal conics. We demonstrate that the total energy is minimised at a particular value of -. It is further observed that the usual saddle-splay elastic term acts independently of - and that varying the value of K¯ does not affect the actual value of - at which the minimum of the elastic energy occurs.
LanguageEnglish
Pages1827-1833
Number of pages6
JournalMolecular Crystals and Liquid Crystals
Volume438
DOIs
Publication statusPublished - 2005

Fingerprint

Liquid Crystals
Liquid crystals
liquid crystals
rectum
saddles
eccentricity
energy
unity

Keywords

  • parabolic cyclides
  • smectic a liquid crystals
  • smectics
  • molecular physics

Cite this

@article{2665987ff1a5421482adc1e591c9b75c,
title = "Energy considerations for parabolic cyclides in SmA liquid crystals",
abstract = "For Dupin cyclides in the SmA liquid crystal phase, Kleman and Lavrentovich [1] found that increasing the saddle-splay constant K¯ caused the minimum of the total elastic energy to occur at a decreased value of the eccentricity e, close to unity. We extend this work to the parabolic cyclides and present an analytical expression for the total elastic energy that is finite over a suitable range of values for the latus rectum, conventionally denoted in this context by −4- (>0). The length of the latus rectum characterises the parabolic focal conic structure analogously to the eccentricity of the Dupin cyclide focal conics. We demonstrate that the total energy is minimised at a particular value of -. It is further observed that the usual saddle-splay elastic term acts independently of - and that varying the value of K¯ does not affect the actual value of - at which the minimum of the elastic energy occurs.",
keywords = "parabolic cyclides, smectic a liquid crystals, smectics, molecular physics",
author = "KIDNEY, {Kevin John} and Geoffrey McKay and Stewart, {Iain William}",
year = "2005",
doi = "10.1080/15421400590955497",
language = "English",
volume = "438",
pages = "1827--1833",
journal = "Molecular Crystals and Liquid Crystals",
issn = "1542-1406",

}

Energy considerations for parabolic cyclides in SmA liquid crystals. / KIDNEY, Kevin John; McKay, Geoffrey; Stewart, Iain William.

In: Molecular Crystals and Liquid Crystals, Vol. 438, 2005, p. 1827-1833.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Energy considerations for parabolic cyclides in SmA liquid crystals

AU - KIDNEY, Kevin John

AU - McKay, Geoffrey

AU - Stewart, Iain William

PY - 2005

Y1 - 2005

N2 - For Dupin cyclides in the SmA liquid crystal phase, Kleman and Lavrentovich [1] found that increasing the saddle-splay constant K¯ caused the minimum of the total elastic energy to occur at a decreased value of the eccentricity e, close to unity. We extend this work to the parabolic cyclides and present an analytical expression for the total elastic energy that is finite over a suitable range of values for the latus rectum, conventionally denoted in this context by −4- (>0). The length of the latus rectum characterises the parabolic focal conic structure analogously to the eccentricity of the Dupin cyclide focal conics. We demonstrate that the total energy is minimised at a particular value of -. It is further observed that the usual saddle-splay elastic term acts independently of - and that varying the value of K¯ does not affect the actual value of - at which the minimum of the elastic energy occurs.

AB - For Dupin cyclides in the SmA liquid crystal phase, Kleman and Lavrentovich [1] found that increasing the saddle-splay constant K¯ caused the minimum of the total elastic energy to occur at a decreased value of the eccentricity e, close to unity. We extend this work to the parabolic cyclides and present an analytical expression for the total elastic energy that is finite over a suitable range of values for the latus rectum, conventionally denoted in this context by −4- (>0). The length of the latus rectum characterises the parabolic focal conic structure analogously to the eccentricity of the Dupin cyclide focal conics. We demonstrate that the total energy is minimised at a particular value of -. It is further observed that the usual saddle-splay elastic term acts independently of - and that varying the value of K¯ does not affect the actual value of - at which the minimum of the elastic energy occurs.

KW - parabolic cyclides

KW - smectic a liquid crystals

KW - smectics

KW - molecular physics

UR - http://taylorandfrancis.metapress.com/openurl.asp?genre=article&eissn=1563-5287&volume=438&spage=263/[1827]

U2 - 10.1080/15421400590955497

DO - 10.1080/15421400590955497

M3 - Article

VL - 438

SP - 1827

EP - 1833

JO - Molecular Crystals and Liquid Crystals

T2 - Molecular Crystals and Liquid Crystals

JF - Molecular Crystals and Liquid Crystals

SN - 1542-1406

ER -