Modelling complex liquid crystal mixtures: from polymer dispersed mesophase to nematic nanocolloids

Liquid crystals (LCs) are synthetic and biological viscoelastic anisotropic soft matter materials that have a combination of fluidity of liquids and anisotropy of solids and find use in optical devices, sensor/actuators, lubrication and super-fibres. Mesogens are frequently mixed with colloidal and nanoparticles (NPs), other mesogens, isotropic solvents, thermoplastic polymers, cross-linkable monomers, among others. This comprehensive review presents recent progress in meso-and macro-scale thermodynamic modelling, highlighting (i) the novelties in spinodal and binodal lines in 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 LC nanocomposites, (vii) the use of topological defects to absorb and organise NPs and (viii) the ability of faceted NPs to link into strings and organise 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 are revealed by using theory, modelling, computation and visualisation.