  We report a novel multi-scale simulation methodology to quantitatively
predict the thermodynamic behaviour of polymer mixtures, that exhibit phases
with broken orientational symmetry. Our system consists of a binary mixture of
oligomers and rod-like mesogens. Using coarse-grained molecular dynamics (CGMD)
simulations we infer the topology of the temperature-dependent free energy
landscape from the probability distributions of excess volume fraction of the
components. The mixture exhibits nematic and smectic phases as a function of
two temperature scales, the nematic-isotropic temperature $T_{NI}$ and the
$T_c$, the transition that governs the polymer demixing. Using a mean-field
free energy of polymer-dispersed liquid crystals (PDLCs), with suitably chosen
parameter values, we construct a mean-field phase diagram that
semi-quantitatively match those obtained from CGMD simulations. Our results are
applicable to mixtures of synthetic and biological macromolecules that undergo
phase separation and are orientable, thereby giving rise to the liquid
crystalline phases.
