Curvature energy of a focal conic domain with arbitrary eccentricity
The most frequently observed focal conic domains (FCD's) in lamellar phases are those based on confocal paris of ellipse and hyperbola. Experimentally, the eccentricity of the ellipse takes a broad range of values 0</=e<1. We present an analytical expression for the curvature energy of a FCD that is valid in the entire range 0</=e<1. Generally, the curvature energy of an isolated FCD reaches a minimum only at e-->1 (under the constraint of a fixed major semiaxis of the ellipse); exceptions include situations with large saddle-splay elastic constant and small domains where the applicability of the elastic theory is limited. In realistic cases, a value of eccentricity smaller than 1 is stabilized by factors other than the curvature energy: by dislocations emerging from the FCD's with e not equal0, compression of layers and surface anchoring.
Kleman
M
Laboratoire de Mineralogie-Cristallographie, UMR 7590, Universite de Paris-VI and Universite de Paris-VII, Case 115, 4 place Jussieu, 75252 Paris Cedex 05, France.
Lavrentovich
OD