  We present a simplified molecular model of mesogenic dimers consisting of two
identical uniaxial mesogenic cores separated by a fixed-length spacer and
allowed to assume only two, statistically equivalent, conformations which are
non-planar and of opposite handedness. In the mean-field approximation, with
additive interactions among the mesogenic cores, the model yields up to three
positionally disordered phases, one isotropic and two nematic. The low
temperature nematic phase ($\mathrm{N_X}$) has a local two-fold symmetry axis
which is also a direction of molecular polar ordering and is tightly twisted
about a macroscopic phase axis. The onset of polar ordering generates
spontaneous chiral symmetry breaking, manifested primarily by the twisting of
the polar director and the formation of chiral domains of opposite handedness.
Within these domains the statistical balance between the two enantiomer
conformations is shifted and the principal axes of the ordering tensors of the
molecular segments twist at constant tilt angles with the helix axis. Key
experimental results on the $\mathrm{N_X}$ phase of liquid crystalline dimers
are discussed in the light of the theoretical predictions of the model, which
are also contrasted with the predictions of the twist-bend nematic model.
