A phenomenological model for predicting phase diagrams of a binary nematic mixture containing side chain liquid crystalline polymers and/or low molar mass liquid crystals has been proposed by combining Flory–Huggins free energy of isotropic mixing and Maier–Saupe free energy for nematic ordering of the nematogens. Two orientational order parameters, s1 and s2, of the two components in the mixtures having two different clearing temperatures are taken into consideration in the calculation. The Flory–Huggins interaction parameter, χ, and the nematic interaction parameter of the Maier–Saupe theory, ν11 and ν22, are assumed to be functions of inverse absolute temperature. Further the cross-nematic interaction is assumed to be proportional to the square root of the product of the nematic interaction parameters of the two mesogens, i.e., ν12=c (ν11⋅ν22)1/2. The theory predicts a variety of phase diagrams depending on a single parameter, c, which is a measure of a relative strength of interaction between two dissimilar mesogens to that in the same species. The predicted phase diagrams have been tested rigorously with experimental phase diagrams of various nematic mixtures reported by others as well as by us.

Dynamics of photopolymerization-induced phase separation (PIPS) and morphology development in mixtures of low molar mass nematic liquid crystal (LC) 4-n-heptyl-4′-cyanobiphenyl (designated K21) and photocuratives (designated NOA65) have been investigated by means of optical microscopy, light scattering, and differential scanning calorimetry. The equilibrium phase diagram of the LC/monomer (uncured NOA65) system was first established theoretically on the basis of the Flory-Huggins/Maier-Saupe theory. The calculated phase diagram displayed isotropic, liquid + liquid, liquid + nematic, and pure nematic coexistence regions in conformity with experiment. The effect of photopolymerization on the phase diagram was examined through comparison of the calculated phase diagrams of LC/linear polymer with LC/cross-linked polymer mixtures. Photopolymerization of the LC/monomer mixtures resulted in phase separation due to instability caused by an increase in molecular weight and subsequent network formation. Photopolymerization initiated in the isotropic phase gave uniformly distributed polygonal-shaped LC droplets in contrast to photopolymerization initiated in the two-phase region. Of particular interest is that the size of the phase-separated LC droplet increases with LC concentration. The network morphology is reminiscent of an interconnected thread seemingly running through the interstices of the polygonal droplets. Temporal evolution of structure factors was analyzed in the context of dynamical scaling law.

The spatiotemporal growth of single crystals in a crystalline polymer has been investigated theoretically based on a nonconserved time dependent Ginzburg-Landau equation (known as TDGL model A). In the description of the total free energy, a double-well local free energy density signifying metastability of crystal ordering is combined with a nonlocal free energy term representing an interface gradient. The resulting nonlinear reaction diffusion equation after renormalization possesses a solitary wave property. Two-dimensional numerical calculations were performed to elucidate the faceted single crystal growth including square, rectangular, diamond-shaped, and curved single crystals. A three-dimensional simulation was also undertaken for the emergence of diamond-shaped single crystals in polyethylene. Of particular importance is that the model field parameters can be linked directly to the material parameters of polyethylene single crystals. Simulation with various elements of the interface gradient coefficient tensor captures various topologies of polymer single crystals.

A theoretical investigation of the dynamics of photopolymerization-induced phase separation (PIPS) and morphology development in a nematic liquid crystal (LC) polymer network mixture has been undertaken by incorporating photopolymerization kinetics into the coupled time-dependent Ginzburg-Landau (TDGL–Model C) equations. The simulation on the spatio-temporal evolution of the coupled LC concentration and orientation order parameters reveals that both morphological and scattering patterns for the orientation order parameter initially lag behind those of the concentration order parameter. However, the two fields evolve to the same spatial topologies with the progression of time. The PIPS dynamics is characterized only by the late stage of phase separation. We also observed a subtle change in the curvature of the growth curve associated with the onset of nematic ordering. The growth behavior and the simulated morphology consisting of LC droplets dispersed in a matrix of polymer appears the same for all compositions, except that the size gets somewhat larger with increasing LC concentration. Decreasing the rate of reaction increases the size of droplets due to the dominance of structural growth driven by thermal relaxation. Of particular interest is that our simulation captures the observed domain topologies.

A theoretical simulation has been performed to elucidate the emergence of nematic domains during pattern photopolymerization-induced phase separation in holographic polymer-dispersed liquid crystals. We consider a reference system consisting of a single-component nematic, namely, 4-n-heptyl-4(')-cyanobiphenyl (T(NI)=42 degrees C), and a polymer network made from multifunctional monomers. To mimic pattern photopolymerization, the reaction rate was varied periodically in space through wave mixing. In the theoretical development, the photopolymerization kinetics was coupled with the time-dependent Ginzburg-Landau model C equations by incorporating the local free energy densities pertaining to isotropic liquid-liquid mixing, nematic ordering, and network elasticity. The simulated morphological patterns in the concentration and orientation order parameter fields show discrete layers of liquid-crystal droplets alternating periodically with polymer-network-rich layers. The Fourier transforms of these patterns show sharp diffraction spots arising from the periodic layers. As the layer thickness is reduced, the liquid-crystal molecules are confined in the narrow stripes. The liquid-crystal domains appear uniform along the stripes, which in turn gives rise to sharper diffraction spots in Fourier space. Of particular interest is that our simulated stratified patterns are in qualitative agreement with reported experimental observations.