Conformational degrees of freedom and stability of splay-bend ordering in the limit of a very strong planar anchoring

We study the self-organization in a monolayer (a two-dimensional system) of flexible planar trimer particles. The molecules are made up of two mesogenic units linked by a spacer, all of which are modeled as hard needles of the same length. Each molecule can dynamically adopt two conformational states: an achiral bent-shaped (cis-) and a chiral zigzag (trans-) one. Using constant pressure Monte Carlo simulations and Onsager-type density functional theory (DFT), we show that the system consisting of these molecules exhibits a rich spectrum of liquid crystalline phases. The most interesting observation is the identification of stable smectic splay-bend (SSB) and chiral smectic-A (SA*) phases. The SSB phase is also stable in the limit, where only cis- conformers are allowed. The second phase that occupies a considerable portion of the phase diagram is SA* with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cisconformers in various phases shows that while in the isotropic phase all fractions are equally populated, the SA* phase is dominated by chiral conformers (zigzag), but the achiral conformers win in the smectic splay-bend phase. To clarify the possibility of stabilization of the nematic splay-bend (NSB) phase for trimers, the free energy of the NSB and SSB phases is calculated within DFT for the cis- conformers, for densities where simulations show stable SSB. It turns out that the NSB phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of SSB, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition.