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

Abstract

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 (S_{SB}) and chiral smectic-A (S_{A}^{*}) phases. The S_{SB} 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 S_{A}^{*} with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cis- conformers in various phases shows that while in the isotropic phase all fractions are equally populated, the S_{A}^{*} 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 (N_{SB}) phase for trimers, the free energy of the N_{SB} and S_{SB} phases is calculated within DFT for the cis- conformers, for densities where simulations show stable S_{SB}. It turns out that the N_{SB} phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of S_{SB}, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition.