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<~eeisolated FCD reaches a minimum only at e⃗1 (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≠0, compression of layers and surface anchoring.
Physical Review E
Copyright 2000 American Physical Society. Available on publisher's site at http://dx.doi.org/10.1103/PhysRevE.61.1574.
Kleman, Maurice; Lavrentovich, Oleg (2000). Curvature Energy of a Focal Conic Domain with Arbitrary Eccentricity. Physical Review E 61(2) 1574-1578. doi: 10.1103/PhysRevE.61.1574. Retrieved from https://oaks.kent.edu/cpippubs/80