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Electrohydrodynamic convection due to the Carr-Helfrich (CH) effect has been extensively investigated in nematics. It has been predicted also for freely suspended smectic C and C* films. On the other hand, in smectic A films another type of electroconvection (vortex flow) has been described (Morris S. W., De Bruyn J. R. and May A., Phys. Rev. Lett. 65 (1990) 2378) but is not sufficiently understood by theory so far. We report experiments on freestanding smectic C films in lateral AC electric fields. A convective instability bifurcating continuously from the homogeneous ground state is found. Evidently the mechanism of the instability is of a similar type as in SA. The director field in the convection vortices is directly visualized in the optical texture.

a Frederiks transition and any non-zero external eld, even in nitesimally small, leads to a ferroelectric torque and to a distortion of the ground state. The reason for this di erence to the planar case is that P ? E is no equilibrium state, while P k E (parallel or antiparallel) is either a stable or an unstable equilibrium state. The dielectric torques behave di erently, since both cases, c k E and c ? E are (stable or unstable) equilibrium states (depending on the sign of " a). Therefore, in systems without a polarization, the planar and homeotropic cases are similar to each other and both show a nite threshold for Frederiks transitions in contrast to SmC lms. For external AC voltages the ferroelectric torque, being linear in the eld strength, is almost averaged to zero during a full cycle. Thus, for AC frequencies larger than the reciprocal reorientation time of the director the ferroelectric torque is small, while for lower frequencies a statistical description is necessary. Of course, the dielectric torque, which is quadratic in the eld strength is not averaged out in an AC eld. Thus, for AC elds the Frederiks transition in SmC lms is qualitatively similar to that in SmC lms or nematics and does not carry new features. For a nite wavelength electroconvective instability, which is the preferred instability type for strong negative values of F, the situation is di erent for AC-driving elds, where the existence of the polarization leads to a qualitatively new subharmonic bifurcation 10]. The experimental detection of the very special e ects of the polarization in the Frederiks transition of a planar ground state and external DC eld, discussed in the previous sections, should be no problem using substances of su ciently high purity.

Novel static hybrid instabilities in smectic C liquid (SmC) crystal films are described. The Frederiks transition, well known for nematic liquid crystals, also takes place in smectic C layers, but here it is spatially periodic and coupled to undulations of the smectic layer. The Helfrich-Hurault undulational instability, typical for smectic A liquid crystals, occurs in SmC liquid crystals too, but the wave vector of the undulation of the layers is oblique to the applied external field. In addition, this modified Helfrich-Hurault instability not only involves layer undulations, but also contains deformations of the director field, which are typical for the Frederiks transition. The coupled deformations depend on all three coordinate axis, thus characterizing 3-dimensional patterns. There are parameter ranges, where both types of static instabilities, which differ by the spatial wavenumber, compete with each other near codimension-2 bifurcations.

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