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 less than or equal to e<1. We present an analytical expression for the curvature ene rgy of a FCD that is valid in the entire range 0 less than or equal to e<1. Generally, the curvature energy of an isolated FCD reaches a minimum only at e-l (under the constraint of a fixed major semiaxis of the ellipse); exc eptions include situations with large saddle-splay elastic constant and sma ll domains where the applicability of the elastic theory is limited. In rea listic cases, a value of eccentricity smaller than 1 is stabilized by facto rs other than the curvature energy: by dislocations emerging from the FCD's with e not equal 0, compression of layers and surface anchoring.