Effect of a bias electric field on the structure and dielectric response of the ferroelectric smectic-A liquid crystal in thin planar cells

The phenomenological continuum model is used to study the director structure and dielectric response of the ferroelectric smectic-A phase in thin planar cells. The frequency of the phase mode and the dielectric permittivity are calculated numerically as a function of the bias external DC electric field, cell thickness, the strength of polar surface anchoring, and the ratio between the bend and splay elastic constants. The theoretically obtained dependencies are in agreement with the recently reported experimental measurements, which show that in thin planar cells both the phase mode frequency and the dielectric permittivity decrease with increasing external bias electric field.