Two-state model for the SmAP_{R} phase with randomized layer polarization exhibited by some compounds with bent-core...

One of the unusual liquid crystalline phases exhibited by some compounds with bent-core (BC) molecules is designated as SmAP_{R}, in which transverse polarization (P) of smectic layers with upright molecules has a random orientational distribution. Most of such compounds undergo a transition to the SmAP_{A} phase with antiferroelectric order of adjacent layers as the temperature is lowered. Second harmonic studies have shown that the medium consists of polarized domains with only a few hundred molecules, the number increasing at lower temperatures. This is in contrast to the random orientations of entire layers predicted by a few phenomenological models which have been proposed for the SmAP_{R} phase. In this paper we show that the two-state model, developed earlier by us to describe modulated phases found in compounds with BC molecules, can successfully account for all the experimental results on the SmAP_{R} phase. It is proposed that polarized domains which are made of ground state conformers, with a large bend of the aromatic cores, nucleate as circular disks in a first order transition from the isotropic phase. Excited state conformers (with a smaller bend) freely rotate about their long axes and surround the disks. The polarization in the disk has a spontaneous splay distortion which generates a texture with an expelled center of a partial disclination. The interdisk electrostatic energy is lower than the thermal energy and the disks are subject to significant rotational fluctuations, resulting in the uniaxial symmetry of the medium. Calculated equilibrium properties of the medium as functions of temperature and electric field reflect the trends seen in experiments. The model overestimates properties such as the radius of the disks as the transition to a lower temperature uniform phase is approached, and physical arguments are given to show that interlayer interactions ignored in the model become important in that regime, and should be included for an improved description of the medium.