Linear dielectric response of antiferroelectric liquid crystals

We use a phenomenological model to find theoretically the linear dielectric response at the direct smectic A* to smectic CA* transition in antiferroelectric liquid crystals. The ferroelectric soft mode is the only collective mode present in the SmA* phase. However, according to the results of theory the SmCA* phase exhibits three collective modes: the ferroelectric soft mode, antiferroelectric soft mode and antiferroelectric Goldstone mode. The temperature dependence of the linear dielectric permittivity is presented for the SmA* and SmCA* phases.