We investigate the onset of electroconvection in freely suspended smectic-${\mathit{C}}^{\mathrm{*}}$ (Sm-${\mathit{C}}^{\mathrm{*}}$) liquid crystal films. Compared to nematic liquid crystals the Sm-${\mathit{C}}^{\mathrm{*}}$ phase shows in addition a macroscopic electric polarization within the smectic planes. Describing the Sm-${\mathit{C}}^{\mathrm{*}}$ film by a two-dimensional theory we find for low and high frequencies of the applied electric ac field, respectively, a conductive and a dielectric instability regime, similar to the case of electroconvection in nematic liquid crystals. Because of the polarization in the Sm-${\mathit{C}}^{\mathrm{*}}$ phase an additional, ‘‘subharmonic regime’’ appears at intermediate frequencies, where all the hydrodynamic and electric variables are moving with half the frequency of the applied ac voltage at the onset of convection. For some special but experimentally accessible values of material parameters, geometric dimensions, and ac voltage frequency also a codimension-three point is found, where the threshold voltages of all three possible regimes coincide. For dc voltages the generalized Frederiks transition is presented and discussed as far as it restricts the observation of pattern forming convective instabilities. Both types of instabilities are investigated for dc voltages to get a fundamental insight into the mechanisms involved as well as for ac voltages to stimulate experiments. © 1996 The American Physical Society.

• Received 7 December 1995

DOI:https://doi.org/10.1103/PhysRevE.53.6101