Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces

Recent research on interfacial instabilities of smectic films has shown unexpected morphologies that are not fully explained by classical local equilibrium thermodynamics. Annealing focal conic domains can lead to conical pyramids, changing the sign of the Gaussian curvature and exposing smectic layers at the interface. In order to explore the role of the Gaussian curvature on the stability and evolution of the film-vapor interface, we introduce a phase-field model of a smectic-isotropic system as a first step in the study. Through asymptotic analysis of the model, we generalize the classical condition of local equilibrium, the Gibbs-Thomson equation, to include contributions from surface bending and torsion and a dependence on the layer orientation at the interface. A full numerical solution of the phase-field model is then used to study the evolution of focal conic structures in smectic domains in contact with the isotropic phase via local evaporation and condensation of smectic layers. As in experiments, numerical solutions show that pyramidal structures emerge near the center of the focal conic owing to evaporation of adjacent smectic planes and to their orientation relative to the interface. Near the center of the focal conic domain, a correct description of the motion of the interface requires the additional curvature terms obtained in the asymptotic analysis, thus clarifying the limitations in modeling motion of hyperbolic surfaces solely driven by mean curvature.