One-particle description of antiferroelectric smectic-Aphases

A theoretical description is proposed for recently observed smectic-$A$ phases which possess antiferroelectric character. Order parameters are introduced that retain information on the head-tail asymmetry of the constituent molecules. Minimum ingredients are given for a mean-field model potential, with the additional use of the approximation of ideal orientational order. With reasonable estimates for the various types of interaction (dispersion, dipole—induced-dipole, and dipole-dipole) no ferroelectric smectic phase is found. Polarized layers can couple, however, to double layers, which leads to the antiferroelectric smectic-$A_2$ phase. In addition, an antiferroelectric smectic-$A_1$ phase is found, which has a single-layer periodicity. In that case there is a bilayer structure as in smectic-$A_2$, which is now not long ranged. For high orientational order the antiferroelectricity of these phases is shown to be the best compromise between the repulsion of the permanent dipole moments and the attractive induced interactions. The relative stability of the various phases is considered in detail. The predictions agree well with present experimental observations.