Macroscopic dynamics of the ferroelectric smectic C_{F} phase with C_{1h} symmetry

We present the macroscopic dynamics of ferroelectric smectic C, smectic C_{F}, liquid crystals reported recently experimentally by two groups. In this fluid and tilted smectic phase, the macroscopic polarization, P, is tilted with respect to the layer normal, thus giving rise to C_{1h} overall symmetry for this phase in the spatially homogeneous limit. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and sufficiently long wavelengths. Compared to nonpolar smectic C phases, we find two static cross-coupling terms between compression of the layering and bending of the layers, which do not lead to elastic forces but to elastic stresses. In addition, a number of static cross-coupling terms is elucidated, which can exist in smectic C_{F} but not in the ferroelectric A_{F} phase because of the polar in-plane preferred direction in smectic C_{F}. Due to the fact that the magnitude of the polarization is a slowly relaxing variable, the velocities of the first and second sound both reflect the monoclinic symmetry of the ground state, thus rendering all sound velocities to be biaxial. We also analyze reversible cross-coupling terms between elongational flow and electric fields as well as temperature and concentration gradients, which lend themselves to experimental detection. Such cross-coupling terms have apparently never been considered before for monoclinic symmetry since they are absent without the presence of a polar direction and thus do not exist in nonpolar smectic C phases. Among the dissipative cross-coupling terms characteristic of smectic C_{F}, we find that bending of the layers can couple to temperature gradients. We also address the question how the linear P·E coupling in the energy alters the macroscopic response behavior when compared to usual nonpolar smectic C phases.