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

JF - Molecular Crystals and Liquid Crystals

SN - 1542-1406

ER -