Self-Organized Ordered Arrays of Core-Shell Columns in Viscous Bilayers Formed by Spatially Varying Electric Fields

A nonlinear analysis is presented to identify the conditions for the formation of ordered patterns consisting of arrays of core-shell columnar structures in thin viscous bilayers by applying a spatially varying electric field. The influence of the electric field strength, film thickness, and topography of the electrode patterns on the order and morphology of the mesostructures is thus investigated. The material with the higher permittivity in the bilayer forms the core, the other one forming the shell. Bilayers under a uniform electric field show only a hexagonal order, whereas a patterned electrode can impose other more complex ordered arrangements, which upon etching of one of the phases produces three-dimensional imbedded hollow structures. Simulations also capture the onset of a phase-inversion phenomenon where the upper layer descends into the lower layer and the latter rises upward to form simple columns without the core-shell structure. When the permittivity of the lower layer is higher (or lower), the columns formed are spatially synchronized with the electrode protrusions (or depressions).