Frustration in smectic layers of polar Gay-Berne systems

The main focus of the present paper is studying dipolar frustration within smectic- A(d) layers as induced by dipole-dipole interactions. Our reference point is the Gay-Berne system with kappa=4, kappa'=5, mu=2 and nu=1, which in the phase diagram shows a stable "island" of smectic- A phase with a short-range hexagonal order within each layer [Phys. Rev. E 57, 6685 (1998)]. We carry out isothermal-isobaric Monte Carlo simulations for a dipolar version of this model, where the Gay-Berne interaction is supplemented by interaction between longitudinal dipole moments. For a fixed off-center position of the dipoles we increase value of the dipole moment and follow evolution of the liquid-crystalline part of the phase diagram focusing on changes of the nematic-smectic- A phase boundaries and on structural response of the smectic- A layers. For weak dipoles only the classical smectic- A phase is stabilized, which then transforms into smectic- A(d) with layers being formed by two ferroelectrically polarized sublayers of opposite polarization. Average positions of dipoles that contribute to the polarization of a sublayer are located in a common plane, referred to as a dipolar plane. For not too strong dipole-dipole interactions increasing magnitude of the dipole moment causes stabilization of nematic at the expense of smectic- A(d). Under the same conditions the layer spacing increases and the distance between the dipolar planes within layers decreases. Each smectic sublayer is characterized by a short-range hexagonal order of the molecular centers of mass. With the dipole moment exceeding the threshold value, the polarization planes that built up the layers start to merge, which sets in the dipolar frustration. This, in turn, forces the system to develop a competition between frustrated hexagonal- and frustration-free tetragonal local order within each layer. When the local hexagonal order is transformed into the tetragonal one the stability range of smectic-A(d) increases with increasing dipole moment at the expense of the nematic phase. Similar competition is observed in crystalline phases. For small dipole moment only crystalline structures with long-range hexagonal order appear stable. They evolve with dipolar strength into monoclinic and tetragonal lattices.