  Liquid crystals are synthetic and biological viscoelastic anisotropic soft
matter materials that combine liquid fluidity with crystal anisotropy and find
use in optical devices, sensor/actuators, lubrication, super-fibers. Frequently
mesogens are mixed with colloidal and nanoparticles, other mesogens, isotropic
solvents, thermoplastic polymers, cross-linkable monomers, among others. This
comprehensive review present recent progress on meso and macro scale
thermodynamic modelling, highlighting the (i) novelties in spinodal and binodal
lines in the various phase diagrams, (ii) the growth laws under phase
transitions and phase separation, (iii) the ubiquitous role of metastability
and its manifestation in complex droplet interfaces, (iv) the various spinodal
decompositions due to composition and order fluctuations, (v) the formation of
novel material architectures such as colloidal crystals, (vi) the particle rich
phase behaviour in liquid crystal nanocomposites, (vii) the use of topological
defects to absorb and organize nanoparticles, and (viii) the ability of faceted
nanoparticles to link into strings and organize into lattices. Emphasis is
given to highlight dominant mechanisms and driving forces, and to link them to
specific terms in the free energies of these complex mixtures. The novelties of
incorporating mesophases into blends, solutions, dispersions and mixtures is
revealed by using theory, modelling, computation, and visualization.
