Ezequiel R. Soulé

Thermodynamics, transition dynamics, and texturing in polymer-dispersed liquid crystals with mesogens exhibiting a direct isotropic/smectic-A transition

Experimental and modeling/simulation studies of phase equilibrium and growth morphologies of novel polymer-dispersed liquid crystal (PDLC) mixtures of PS (polystyrene) and liquid crystals that exhibit a direct isotropic/smectic-A (lamellar) mesophase transition were performed for PS/10CB (decyl-cyanobiphenyl) and PS/12CB (dodecyl-cyanobiphenyl). Partial phase diagrams were determined using polarized optical microscopy (POM) and differential scanning calorimetry (DSC) for different compositions of both materials, determining both phase separation (liquid/liquid demixing) and phase ordering (isotropic/smectic-A transition) temperatures. The Flory−Huggins theory of isotropic mixing and Maier−Saupe−McMillan theory for smectic-A liquid crystalline ordering were used to computationally determine phase diagrams for both systems, showing good agreement with the experimental results. In addition to thermodynamic observations, growth morphology relations were found depending on phase transition sequence, quench rat...

Phase equilibrium and structure formation in gold nanoparticles—nematic liquid crystal composites: experiments and theory

A theoretical and experimental study of mixtures of a calamitic nematic liquid crystal and gold nanoparticles capped with mixed monolayers (alkylic + mesogenic ligands) is presented. The effect of the ligand monolayer composition and nanoparticle concentration on the solubility in the isotropic phase and on the isotropic–nematic phase transition is studied. Mixed monolayers show the highest miscibility and lead to the formation of well-defined cellular networks. This behaviour is explained in terms of a mean-field thermodynamic model, in combination with a phenomenological expression for the isotropic interaction parameter that accounts for entropic and enthalpic effects of the mixed ligand monolayer. The final structure of the material is shown to be determined essentially by the phase equilibrium behaviour.

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.

Non-Isothermal Model for Nematic Spherulite Growth

A computational study of the growth of two-dimensional nematic spherulites in an isotropic phase was performed using a Landau-de Gennes-type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentylcyanobiphenyl). An energy balance, taking anisotropy into account, was derived and incorporated into the time-dependent model. Growth laws were determined for two different spherulite morphologies of the form t(n), with and without the inclusion of thermal effects. Results show that incorporation of the thermal energy balance correctly predicts the transition of the growth law exponent from the volume driven regime (n=1) to the thermally limited regime (approaching n = 1/2), agreeing well with experimental observations. An interfacial nematodynamic model is used to gain insight into the interactions that result in the progression of different spherulite growth regimes.

Thermodynamic Modelling of Phase Equilibrium in Nanoparticles – Nematic Liquid Crystals Composites

In this work, a theoretical study of phase equilibrium in mixtures of a calamitic nematic liquid crystal and hard spherical nanoparticles is presented. A mean-field thermodynamic model is used, where the interactions are considered to be proportional to the number of contacts, which in turn are proportional to the areas and area fractions of each component. It is shown that, as the radius of the particle is increased, the effect of the particles on the isotropic-nematic transition is less pronounced, and that for a large radius the miscibility increases as the particle radius increases.

Textures in polygonal arrangements of square nanoparticles in nematic liquid crystal matrices.

A systematic analysis of defect textures in faceted nanoparticles with polygonal configurations embedded in a nematic matrix is performed using the Landau-de Gennes model, homeotropic strong anchoring in a square domain with uniform alignment in the outer boundaries. Defect and textures are analyzed as functions of temperature T, polygon size R, and polygon number N. For nematic nanocomposites, the texture satisfies a defect charge balance equation between bulk and surface (particle corner) charges. Upon decreasing the temperature, the central bulk defects split and together with other -1/2 bulk defects are absorbed by the nanoparticles corners. Increasing the lattice size decreases confinement and eliminates bulk defects. Increasing the polygon number increases the central defect charge at high temperature and the number of surface defects at lower temperatures. The excess energy per particle is lower in even than in odd polygons, and it is minimized for a square particle arrangement. These discrete modeling results show for first time that, even under strong anchoring, defects are attached to particles as corner defects, leaving behind a low energy homogeneous orientation field that favors nanoparticle ordering in nematic matrices. These new insights are consistent with recent thermodynamic approaches to nematic nanocomposites that predict the existence of novel nematic/crystal phases and can be used to design nanocomposites with orientational and positional order.

Theory and computation of directional nematic phase ordering

A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau-de Gennes-type quadrupolar tensor order parameter model for the first-order isotropic-nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic-nematic interface. Thermal instabilities in both the linear and nonlinear regimes were observed and compared to past experimental and theoretical observations. A sharp-interface model for the study of linear morphological instabilities, taking into account additional complexity resulting from liquid-crystalline order, was derived. Results from the sharp-interface model were compared to those from full two-dimensional simulation identifying the specific limitations of simplified sharp-interface models for this liquid-crystal system. In the nonlinear regime, secondary instabilities were observed to result in the formation of defects, interfacial heterogeneities, and bulk texture dynamics.

Hedgehog defects in mixtures of a nematic liquid crystal and a non-nematogenic component

A theoretical study of the core structure and composition of a hedgehog defect in a mixture of a nematic liquid crystal and a second non-nematogenic component is presented. Fractionation of the components between the bulk and the defect core is rigorously considered by using solution thermodynamics. Two complementary approaches are used to analyze this problem: a multiscale model based on a Landau–de Gennes free energy functional that is solved numerically, and a macroscopic sharp interface phase-equilibrium model, which considers the defect core as an isotropic phase in equilibrium with a distorted nematic phase and that under certain limiting conditions yields equations that reveal the mechanisms that select defect core structure, geometry, and composition. It is found that the non-nematogenic component segregates preferentially to the defect core, and the defect radius increases as the concentration of the second component and the temperature are increased. As previously predicted for pure liquid crystals, close to saturation conditions the radius increases significantly, and a small range of supersaturation or superheating is observed.

A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy

A new computational strategy is proposed to approximate, with a simple but accurate expression, the Maier–Saupe free energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncated Taylor series, we employ a least-squares fitting to obtain the coefficients of a polynomial expression. Both methods are compared, and the fitting with at most five polynomial terms is shown to provide a satisfactory fitting, and to give much more accurate results than the traditional Taylor expansion. We perform the analysis in terms of the tensor order parameter, so the results are valid in uniaxial and biaxial states.

Formation and kinetics of transient metastable states in mixtures under coupled phase ordering and chemical demixing

We present theory and simulation of simultaneous chemical demixing and phase ordering in a polymer–liquid-crystal mixture in conditions where isotropic-isotropic phase separation is metastable with respect to isotropic-nematic phase transition. It is found that mesophase formation proceeds by a transient metastable phase that surround the ordered phase, and whose lifetime is a function of the ratio of diffusional-to-orientational mobilities. It is shown that kinetic phase ordering in polymer-mesogen mixtures is analogous to kinetic crystallization in polymer solutions.