RESUMO
We report a detailed theoretical analysis of quadrupolar interactions observed between islands, which are disklike inclusions of extra layers, floating in thin, freely suspended smectic- C liquid crystal films. Strong tangential anchoring at the island boundaries results in a strength +1 chiral defect in each island and a companion -1 defect in the film--these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral-island-defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the interisland potential and the trajectories of the -1 defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.