Undulation Instability of the Interface Between a Smectic-C Liquid Crystal and its Isotropic or Nematic Melt

The spontaneous undulation instability of phase boundaries of smectics C is investigated both theoretically and experimentally. The driving mechanism is more efficient than that of Herring's instability of crystal surfaces, due to the coupling of a periodic distortion of the c-director with the interfacial undulation. The instability is studied experimentally in various geometries: free drops, capillaries and sandwiched cells. In the presence of a thermal gradient $G$, the undulation period is shown to scale as $G^{-1/3}$, as predicted theoretically. The existence of a threshold reflattening the interface in the presence of strong thermal gradients is investigated. Upon varying the thickness of the smectic, a sequence of instabilities occurs which produces first the interfacial undulations, then focal conic defects as in the textural instability of the smectic-A–isotropic interface. In free drops, the undulation instability yields a richer phenomenology: arborescent patterns, splayed islands, spirals, trefoils, and eventually rows and triangular networks of focal conics