Phase separations in liquid crystal-colloid mixtures

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

We review our recent contributions to anisotropic soft matter models for liquid crystal interfaces, drops and membranes, emphasizing validations with experimental and biological data, and with related theory and simulation literature. The presentation aims to illustrate and characterize the rich output and future opportunities of using a methodology based on the liquid crystal-membrane shape equation applied to static and dynamic pattern formation phenomena. The geometry of static and kinetic shapes is usually described with dimensional curvatures that co-mingle shape and curvedness. In this review, we systematically show how the application of a novel decoupled shape-curvedness framework to practical and ubiquitous soft matter phenomena, such as the shape of drops and tactoids and bending of evolving membranes, leads to deeper quantitative insights than when using traditional dimensional mean and Gaussian curvatures. The review focuses only on (1) statics of wrinkling and shape selection in liquid crystal interfaces and membranes; (2) kinetics and dissipative dynamics of shape evolution in membranes; and (3) computational methods for shape selection and shape evolution; due to various limitations other important topics are excluded. Finally, the outlook follows a similar structure. The main results include: (1) single and multiple wavelength corrugations in liquid crystal interfaces appear naturally in the presence of surface splay and bend orientation distortions with scaling laws governed by ratios of anchoring-to-isotropic tension energy; adding membrane elasticity to liquid crystal anchoring generates multiple scales wrinkling as in tulips; drops of liquid crystals encapsulates in membranes can adopt, according to the ratios of anchoring/tension/bending, families of shapes as multilobal, tactoidal, and serrated as observed in biological cells. (2) Mapping the liquid crystal director to a membrane unit normal. The dissipative shape evolution model with irreversible thermodynamics for flows dominated by bending rates, yields new insights. The model explains the kinetic stability of cylinders, while spheres and saddles are attractors. The model also adds to the evolving understanding of outer hair cells in the inner ear. (3) Computational soft matter geometry includes solving shape equations, trajectories on energy and orientation landscapes, and shape-curvedness evolutions on entropy production landscape with efficient numerical methods and adaptive approaches.

Particle-based mesoscopic model for phase separation in a binary fluid mixture

A mesoscopic simulation model to study the phase separation in a binary fluid mixture in three dimensions (3D) is presented here by augmenting the existing particle-based multiparticle collision dynamics (MPCD) algorithm. The approach describes the nonideal equation of the fluid state by incorporating the excluded-volume interaction between the two components within the framework of stochastic collision, which depends on the local fluid composition and velocity. Calculating the nonideal contribution to the pressure both from simulation and analytics shows the model to be thermodynamically consistent. A phase diagram to explore the range of parameters that give rise to phase separation in the model is investigated. The interfacial width and phase growth obtained from the model agree with the literature for a wide range of temperatures and parameters.

Ion-dependent DNA configuration in bacteriophage capsids

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Self-Organized, One-Dimensional Periodic Structures in a Gold Nanoparticle-Doped Nematic Liquid Crystal Composite

Composite structures exhibiting a periodic arrangement of building blocks can be found in natural systems at different length scales. Recreating such systems in artificial composites using the principles of self-assembly has been a great challenge, especially for 1D microscale systems. Here, we present a purposely designed composite material consisting of gold nanoparticles and a nematic liquid crystal matrix that has the ability to self-create a periodic structure in the form of a one-dimensional photonic lattice through a phase separation process occurring in a confined space. Our strategy is based on the use of a thermoswitchable medium that reversibly and quickly responds to both heating and cooling. We find that the period of the structure is strongly related to the size of the confining space. We believe that our findings will allow us to not only better understand the phase separation process in multicomponent soft/colloid mixtures with useful optical properties but also improve our understanding of the precise assembly of advanced materials into one-dimensional periodic systems, with prospective applications in future photonic technologies.

Thermodynamic modelling of acidic collagenous solutions: from free energy contributions to phase diagrams

Tropocollagen is considered one of the main precursors in the fabrication of collagen-based biomaterials. Triple helix acidic solutions of collagen I have been shown experimentally to lead to chiral plywood architectures found in bone and "cornea" like tissues. As these plywoods are solid analogues of liquid crystal architectures, bio-inspired processing and fabrication platforms based on liquid crystal physics and thermodynamics will continue to play an essential role. For tissue engineering applications, it has been shown that dilute isotropic collagen solutions need to be flow processed first and then dehydrated. Thus, a complete fundamental understanding of the thermodynamics and free energy contributions in acidic collagen aqueous solutions is necessary to avoid expensive trial-and-error fabrication. To achieve this goal, we analyze the microscopic mechanisms of ordering and interactions in solutions of triple helix collagen, namely mixing, attraction, excluded-volume and chirality. To capture the mentioned physics, we then incorporate and integrate the Flory-Huggins, Maier-Saupe, Onsager and Frank theories. Nonetheless, they together are incapable of providing an acceptable mesophasic description in acidic collagenous solutions because tropocollagen biomacromolecules are positively charged. We then explore a simple and accurate electrostatic mean-field potential. Our results on collagen are in good agreement with experiments and include phase diagrams, phase transition thresholds, and critical isotropic/cholesteric order parameters. The present extended theory is shown to properly converge to classical liquid crystal models and is used to express the phenomenological Landau-de Gennes parameters with more fundamental quantities. This study provides a platform to derive accurate process models for the fabrication of collagen-based materials, considering and benefitting from the full range of underlying interactions.

A comparative study of nematic liquid crystals doped with harvested and non-harvested ferroelectric nanoparticles: phase transitions and dielectric properties

Broadband dielectric spectroscopy is used to determine the dielectric properties and phase transitions of the 4-n-octyl-4′-cyanobiphenyl liquid crystal (8CB) doped with harvested and non-harvested ferroelectric nanoparticles.

Induced liquid-crystalline ordering in solutions of stiff and flexible amphiphilic macromolecules: Effect of mixture composition

Impact of mixture composition on self-organization in concentrated solutions of stiff helical and flexible macromolecules was studied by means of molecular dynamics simulation. The macromolecules were composed of identical amphiphilic monomer units but a fraction f of macromolecules had stiff helical backbones and the remaining chains were flexible. In poor solvents the compacted flexible macromolecules coexist with bundles or filament clusters from few intertwined stiff helical macromolecules. The increase of relative content f of helical macromolecules leads to increase of the length of helical clusters, to alignment of clusters with each other, and then to liquid-crystalline-like ordering along a single direction. The formation of filament clusters causes segregation of helical and flexible macromolecules and the alignment of the filaments induces effective liquid-like ordering of flexible macromolecules. A visual analysis and calculation of order parameter relaying the anisotropy of diffraction allow concluding that transition from disordered to liquid-crystalline state proceeds sharply at relatively low content of stiff components.

Electric field effects on phase transitions in the 8CB liquid crystal doped with ferroelectric nanoparticles

The influence of a low ac electric field on phase transitions is discussed in the case of a nematic liquid crystal 4-n-octyl-4^{'}-cyanobiphenyl (8CB) doped with Sn_{2}P_{2}S_{6} ferroelectric nanoparticles. The phase-transition temperatures obtained from temperature-dependent dielectric measurements were higher than those determined by the calorimetric method. This difference is explained by the presence of the measuring electric field which induces two effects. The first one is the amplification of the interactions between the nanoparticle polarization and the liquid-crystal order parameter. The second one is the field-induced disaggregation or aggregation process at high nanoparticle concentrations.

On the phase transitions of 8CB/Sn2P2S6 liquid crystal nanocolloids

Using differential scanning calorimetry measurements, the influence of Sn2P2S6 ferroelectric nanoparticles on the phase transition temperatures of the 8CB liquid crystal is studied. The spontaneous polarization, ionic and anchoring effects are discussed. For low concentration of dopant, the global effect leads to a decrease and an increase of the nematic-isotropic and the smectic A-nematic phase transition temperatures, respectively. For high concentrations, due to aggregates formation, the predominant anchoring effect induces a decrease of the both phase transition temperatures.

Dynamic arrest of nematic liquid-crystal colloid networks

We report interesting self-assembly structures of nematic liquid-crystal colloid (NLCC) networks, which are arrested during cooling from the isotropic temperature to room temperature. The NLCC is composed of sterically stabilized colloidal particles and a nematic liquid crystal (NLC) with nematic-isotropic transition temperature (T_{NI}) that is much higher than those of previously studied 4-Cyano-4'-pentylbiphenyl and N-(4-Methoxybenzylidene)-4-butylaniline. We find that the structure of NLCCs depends on T(NI), cooling rates, and boundary conditions, varying from cellular network to hierarchical fern structures in different length scales. Our time-lapse study shows that the transition from the cellular network to the fern structure directly corresponds to the transition from a spinodal demixing to a nucleation-and-growth mechanism.

A molecular and thermodynamic view of the assembly of gold nanoparticles in nematic liquid crystal

The molecular interactions driving the assembly of gold nanoparticles (AuNPs) in a nematic liquid crystal (LC) are directly detected by nuclear magnetic resonance (NMR) spectroscopy and thermodynamically analyzed. The orientational orders of the selectively deuterated LC matrix and AuNP ligands, each separately followed by variable temperature (2)H NMR as a function of particle concentration, were observed to be strongly correlated. The mechanism of the reversible formation of long-range, quasi-periodic nanoparticle structures is attributed to the coupling of the AuNP ligands to the LC matrix, inducing an isotropic-nematic biphasic state. Experimentally validated thermodynamic modeling shows that, in contrast to colloidal nematics that are dominated by elastic forces, nematic dispersions of nanoparticles self-organize through a subtle balance of entropic forces and excluded volume, interface-mediated mesogen and nanoparticle molecular interactions, and couplings between conserved and nonconserved order parameters. Fine-tuning of these interactions through ligand and mesogen chemistry, together with mesoscale modeling, provides a route for materials innovations by merging structured fluid physics and nanoscience.

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 nanoparticle's 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.

Phase separations in mixtures of a liquid crystal and a nanocolloidal particle

We present a mean field theory to describe phase separations in mixtures of a liquid crystal and a nanocolloidal particle. By taking into account a nematic, a smectic A ordering of the liquid crystal, and a crystalline ordering of the nanoparticle, we calculate the phase diagrams on the temperature-concentration plane. We predict various phase separations, such as a smectic A-crystal phase separation and a smectic A-isotropic-crystal triple point, etc., depending on the interactions between the liquid crystal and the colloidal surface. Inside binodal curves, we find new unstable and metastable regions, which are important in the phase ordering dynamics. We also find a crystalline ordering of the nanoparticles dispersed in a smectic A phase and a nematic phase. The cooperative phenomena between liquid-crystalline ordering and crystalline ordering induce a variety of phase diagrams.

Colloid-wall interaction in a nematic liquid crystal: the mirror-image method of colloidal nematostatics

The new area of nematic colloidal systems (or nematic emulsions) has been greatly guided by the fruitful analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V. M. Pergamenshchik and V. O. Uzunova, Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] develops this analogy at the level of charge density and Coulomb interaction. It shows, however, that the colloidal nematostatics in three dimensions substantially differs from the electrostatics both in its mathematical structure and physical implications: the elastic charge and multipoles are dyads; similar charges attract while opposite charges repel each other, and so on. In this paper we consider the interaction between an elastic charge and elastic dipole with a nematic surface (wall) at which the director alignment is fixed. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in the nematostatics for arbitrary director tilt at the wall. A wall is shown to induce a repulsive 1R{4} force on the elastic dipole which, in general, is accompanied by its reorientation. External torque on the colloid induces an elastic charge therein and triggers switching to the 1R{2} repulsion. The dyadic nature of an elastic dipole is shown to be essential: a particle-wall interaction potential cannot be obtained in phenomenological theories with a single component dipole. In the introductory sections we discuss connection between the director-mediated interaction in two and three dimensions and the electrostatic interaction and consider different symmetries of elastic dipoles. Conservation of the torque components exerted upon colloids is shown to play the role of Gauss' theorem and determines the elastic charge dyad.

Third-order thermodynamic perturbation theory for effective potentials that model complex fluids

We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.