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

Eduardo Vitral, Perry H. Leo, Jorge Viñals

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2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number032805
JournalPhysical Review E
Volume100
Issue number3
DOIs
StatePublished - Sep 25 2019

Bibliographical note

Funding Information:
We are indebted to Oleg Lavrentovich for many stimulating discussions. This research has been supported by the Minnesota Supercomputing Institute and by the Extreme Science and Engineering Discovery Environment (XSEDE) [63] , which is supported by the National Science Foundation Grant No. ACI-1548562. E.V. thanks the continuous support from the Aerospace Engineering and Mechanics Department, University of Minnesota, during the entire length of this work. J.V. is supported by the National Science Foundation, Contract No. DMR-1838977.

Funding Information:
This research has been supported by the Minnesota Supercomputing Institute and by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation Grant No. ACI-1548562. E.V. thanks the continuous support from the Aerospace Engineering and Mechanics Department, University of Minnesota, during the entire length of this work. J.V. is supported by the National Science Foundation, Contract No. DMR-1838977.

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