  We study the self-organization of flexible planar trimer particles on a
structureless surface. 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 (quasi-)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
occupying 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.
