Segregation of liquid crystal mixtures in topological defects

Elucidating Molecular-Scale Principles Governing the Anchoring of Liquid Crystal Mixtures on Solid Surfaces

Computational chemistry calculations are broadly useful for guiding the atom-scale design of hard-soft material interfaces including how molecular interactions of single-component liquid crystals (LCs) at inorganic surfaces lead to preferred orientations of the LC far from the surface. The majority of LCs, however, are not single-component phases but comprise of mixtures, such as a mixture of mesogens, added to provide additional functions such as responsiveness to the presence of targeted organic compounds (for chemical sensing). In such LC mixtures, little is understood about the near-surface composition and organization of molecules and how that organization propagates into the far-field LC orientation. Here, we address this broad question by using a multiscale computational approach that combines density functional theory (DFT)-based calculations and classical molecular dynamics (MD) simulations to predict the interfacial composition and organization of a binary LC mixture of 4'-cyano-4-biphenylcarbolxylic acid (CBCA) and 4'-n-pentyl-4-biphenylcarbonitrile (5CB) supported on anatase (101) titania surfaces. DFT calculations determine the surface composition and atomic-scale organization of CBCA and 5CB at the titania surface, and classical MD simulations build upon the DFT description to describe the evolution of the near-surface order into the bulk LC. A surprising finding is that the 5CB and CBCA molecules adopt orthogonal orientations at the anatase surface and that, above a threshold concentration of CBCA, this mixture of orientations evolves away from the surface to define a uniform far-field homeotropic orientation. These results demonstrate that molecular-level knowledge achieved through a combination of computational techniques permits the design and understanding of functional LC mixtures at interfaces.

Structures, thermodynamics and dynamics of topological defects in Gay-Berne nematic liquid crystals

Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay-Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K₃/K₁ using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient.

Transition kinetics of defect patterns in confined two-dimensional smectic liquid crystals

Topological defects in liquid crystals under confined geometries have attracted extensive research interests. Here, we perform molecular dynamics simulations to investigate the formation and transition of defect patterns in two-dimensional smectic Gay-Berne liquid crystals with a simple rectangular confinement boundary. Two typical types of defect patterns, bridge and diagonal defect patterns, are observed, which can be transformable continuously between each other over time. The transition usually starts from the line or point defect regions, and the competition between neighboring and opposite boundary effects induces the continuous realignments of the smectic layers to connect the neighboring or opposite walls. The relative stability of these two defect patterns can be controlled by changing the confinement conditions. These results deepen our understanding of transition kinetics of defect patterns in confined liquid crystals.

Derivation of coarse-grained force fields for buckling-induced topological defects of liquid crystals

Microscopic details of buckling-induced topological defects are required for molecular design of smectic liquid crystals to control buckling instability of the layers. In this study, we present a multiobjective optimization method to derive the coarse-grained (CG) force fields with sufficiently precise buckling characteristics including the molecular details for molecular dynamics (MD) simulations. We perform CGMD simulations of buckling deformation at sample points in the CG force field parameter space, from which the response surfaces of objective functions such as the scalar orientational order parameters, critical angles of layer collapse, and radial distribution functions are estimated. Since not all objective functions can be optimized simultaneously, we use a genetic algorithm to calculate the Pareto set of optimal solutions. We select the models with different molecular head-tail symmetries to study buckling deformation. The extracted CG model successfully reproduces the buckling deformation in terms of the collapse of smectic layers through the generation of dislocations with dipole disclinations. We also find that the molecular symmetry is a dominant factor to control the class of the buckling-induced dislocations.

Topics in the mathematical design of materials

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Temperature-induced liquid crystal microdroplet formation in a partially miscible liquid mixture

Liquid-in-liquid droplets are typically generated by the partitioning of immiscible fluids, e.g. by mechanical shearing with macroscopic homogenisers or microfluidic flow focussing. In contrast, partially miscible liquids with a critical solution temperature display a temperature-dependent mixing behaviour. In this work, we demonstrate how, for a blend of methanol (MeOH) and the thermotropic liquid crystal (LC) 4-Cyano-4'-pentylbiphenyl (5CB), cooling from a miscible to an immiscible state allows the controlled formation of microdroplets. A near-room-temperature-induced phase separation leads to nucleation, growth and coalescence of mesogen-rich droplets. The size and number of the droplets is tunable on the microscopic scale by variation of temperature quench depth and cooling rate. Further cooling induces a phase transition to nematic droplets with radial configuration, well-defined sizes and stability over the course of an hour. This temperature-induced approach offers a scalable and reversible alternative to droplet formation with relevance in diagnostics, optoelectronics, materials templating and extraction processes.

Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals

Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of dense hard needles as a model system for colloids suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte Carlo technique enables us to directly measure colloidal interactions in a microscopic simulation with explicit liquid crystal particles in the dense nematic phase. We find a directional short-range attraction for disks along the director, which triggers chaining parallel to the director and seemingly contradicts the standard liquid crystal field theory result of a quadrupolar attraction with a preferred [Formula: see text] angle. Our results can be explained by a short-range density-dependent depletion interaction, which has been neglected so far. Directionality and strength of the depletion interaction are caused by the weak planar anchoring of hard rods. The depletion attraction robustly dominates over the quadrupolar elastic attraction if disks come close. Self-assembly of many disks proceeds via intermediate chaining, which demonstrates that in lyotropic liquid crystal colloids depletion interactions play an important role in structure formation processes.

Topological-Defect-Induced Surface Charge Heterogeneities in Nematic Electrolytes

We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In particular, the location and type of the defect encodes the precise distribution of surface charges and the effect is enhanced when the liquid crystal is flexoelectric. We demonstrate the principle for patterned surfaces and charged colloidal spheres. More generally, our results indicate an interesting approach to control surface charges on external surfaces without changing the surface chemistry.

Machine learning-aided analysis for complex local structure of liquid crystal polymers

Elucidation of mesoscopic structures of molecular systems is of considerable scientific and technological interest for the development and optimization of advanced materials. Molecular dynamics simulations are a promising means of revealing macroscopic physical properties of materials from a microscopic viewpoint, but analysis of the resulting complex mesoscopic structures from microscopic information is a non-trivial and challenging task. In this study, a Machine Learning-aided Local Structure Analyzer (ML-LSA) is developed to classify the complex local mesoscopic structures of molecules that have not only simple atomistic group units but also rigid anisotropic functional groups such as mesogens. The proposed ML-LSA is applied to classifying the local structures of liquid crystal polymer (LCP) systems, which are of considerable scientific and technological interest because of their potential for sensors and soft actuators. A machine learning (ML) model is constructed from small, and thus computationally less costly, monodomain LCP trajectories. The ML model can distinguish nematic- and smectic-like monodomain structures with high accuracy. The ML-LSA is applied to large, complex quenched LCP structures, and the complex local structures are successfully classified as either nematic- or smectic-like. Furthermore, the results of the ML-LSA suggest the best order parameter for distinguishing the two mesogenic structures. Our ML model enables automatic and systematic analysis of the mesogenic structures without prior knowledge, and thus can overcome the difficulty of manually determining the specific order parameter required for the classification of complex structures.

Soft matter from liquid crystals

Liquid crystals (LCs) are fluids within which molecules exhibit long-range orientational order, leading to anisotropic properties such as optical birefringence and curvature elasticity. Because the ordering of molecules within LCs can be altered by weak external stimuli, LCs have been widely used to create soft matter systems that respond optically to electric fields (LC display), temperature (LC thermometer) or molecular adsorbates (LC chemical sensor). More recent studies, however, have moved beyond investigations of optical responses of LCs to explore the design of complex LC-based soft matter systems that offer the potential to realize more sophisticated functions (e.g., autonomous, self-regulating chemical responses to mechanical stimuli) by directing the interactions of small molecules, synthetic colloids and living cells dispersed within the bulk of LCs or at their interfaces. These studies are also increasingly focusing on LC systems driven beyond equilibrium states. This review presents one perspective on these advances, with an emphasis on the discovery of fundamental phenomena that may enable new technologies. Three areas of progress are highlighted; (i) directed assembly of amphiphilic molecules either within topological defects of LCs or at aqueous interfaces of LCs, (ii) templated polymerization in LCs via chemical vapor deposition, an approach that overcomes fundamental challenges related to control of LC phase behavior during polymerization, and (iii) studies of colloids in LCs, including chiral colloids, soft colloids that are strained by LCs, and active colloids that are driven into organized states by dissipation of energy (e.g. bacteria). These examples, and key unresolved issues discussed at the end of this perspective, serve to convey the message that soft matter systems that integrate ideas from LC, surfactant, polymer and colloid sciences define fertile territory for fundamental studies and creation of future transformative technologies.

Cardiolipin Alters Rhodobacter sphaeroides Cell Shape by Affecting Peptidoglycan Precursor Biosynthesis

The phospholipid composition of the cell membrane influences the spatial and temporal biochemistry of cells. We studied molecular mechanisms connecting membrane composition to cell morphology in the model bacterium Rhodobacter sphaeroides. The peptidoglycan (PG) layer of the cell wall is a dominant component of cell mechanical properties; consequently, it has been an important antibiotic target. We found that the anionic phospholipid cardiolipin (CL) plays a role in determination of the shape of R. sphaeroides cells by affecting PG precursor biosynthesis. Removing CL in R. sphaeroides alters cell morphology and increases its sensitivity to antibiotics targeting proteins synthesizing PG. These studies provide a connection to spatial biochemical control in mitochondria, which contain an inner membrane with topological features in common with R. sphaeroides.

Cardiolipin (CL) is an anionic phospholipid that plays an important role in regulating protein biochemistry in bacteria and mitochondria. Deleting the CL synthase gene (Δcls) in Rhodobacter sphaeroides depletes CL and decreases cell length by 20%. Using a chemical biology approach, we found that a CL deficiency does not impair the function of the cell wall elongasome in R. sphaeroides; instead, biosynthesis of the peptidoglycan (PG) precursor lipid II is decreased. Treating R. sphaeroides cells with fosfomycin and d-cycloserine inhibits lipid II biosynthesis and creates phenotypes in cell shape, PG composition, and spatial PG assembly that are strikingly similar to those seen with R. sphaeroides Δcls cells, suggesting that CL deficiency alters the elongation of R. sphaeroides cells by reducing lipid II biosynthesis. We found that MurG—a glycosyltransferase that performs the last step of lipid II biosynthesis—interacts with anionic phospholipids in native (i.e., R. sphaeroides) and artificial membranes. Lipid II production decreases 25% in R. sphaeroides Δcls cells compared to wild-type cells, and overexpression of MurG in R. sphaeroides Δcls cells restores their rod shape, indicating that CL deficiency decreases MurG activity and alters cell shape. The R. sphaeroides Δcls mutant is more sensitive than the wild-type strain to antibiotics targeting PG synthesis, including fosfomycin, d-cycloserine, S-(3,4-dichlorobenzyl)isothiourea (A22), mecillinam, and ampicillin, suggesting that CL biosynthesis may be a potential target for combination chemotherapies that block the bacterial cell wall.

The Assembling and Contraction Mechanisms of Striated Muscles

A novel approach to the description of the assembly mechanism of functional biological structures is presented. The approach is based on the identification of fundamental self-assembling processes to which an additional structurization "engineered" by Nature to optimize functions is superimposed. Application of the approach to the structure and contraction of the striated muscle evidences a key role of the residual liquid crystallinity of a constrained structure and the alteration of the compatibility between the thin and thick filaments driven by ionic interactions. ATP hydrolysis boosts the relaxation process. A strong protein scaffold, engineered during the evolutionary process and based on the selective anchoring of coordinated filaments, directs a demixing tendency of the two filaments toward a sliding motion along the fiber axis. The Huxley-Hanson sliding filament hypothesis aimed to explain the contraction-relaxation function of the striated muscle, but does not offer any clue on the overall assembling mechanism of the myofibril.

In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals

Experiments on confined droplets of the nematic liquid crystal 5CB have questioned long-established bounds imposed on the elastic free energy of nematic systems. This elasticity, which derives from molecular alignment within nematic systems, is quantified through a set of moduli which can be difficult to measure experimentally and, in some cases, can only be probed indirectly. This is particularly true of the surfacelike saddle-splay elastic term, for which the available experimental data indicate values on the cusp of stability, often with large uncertainties. Here, we demonstrate that all nematic elastic moduli, including the saddle-splay elastic constant k_{24}, may be calculated directly from atomistic molecular simulations. Importantly, results obtained through in silico measurements of the 5CB elastic properties demonstrate unambiguously that saddle-splay elasticity alone is unable to describe the observed confined morphologies.

Interplay of structure, elasticity, and dynamics in actin-based nematic materials

Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can be manipulated over a relatively wide range of elastic moduli. Specifically, thin films of actin filaments are assembled at an oil-water interface. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with [Formula: see text] topological defects, characteristic of a two-dimensional nematic system. As the average filament length increases, the defect morphology transitions from a U shape into a V shape, indicating the relative increase of the material's bend over splay modulus. Furthermore, through the sparse addition of rigid microtubule filaments, one can gain additional control over the liquid crystal's elasticity. We show how the material's bend constant can be raised linearly as a function of microtubule filament density, and present a simple means to extract absolute values of the elastic moduli from purely optical observations. Finally, we demonstrate that it is possible to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states. Despite the nonequilibrium nature of the system, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. Thus, we have experimentally realized a lyotropic liquid crystal system that can be truly engineered, with tunable mechanical properties, and a theoretical framework to capture its structure, mechanics, and dynamics.

Spherical nematic shells with a prolate ellipsoidal core

Liquid crystal shells have attracted considerable attention in recent years. In such systems, a combination of confinement and curvature generates topological defect structures that do not exist in the bulk. Past studies, however, have largely focused on perfectly spherical shells, and little attention has been devoted to the impact of core geometry on the configuration and arrangement of topological defects. In this work, a microfluidic glass capillary device is used to encapsulate spherical and prolate ellipsoidal particles in nematic liquid crystal (LC) droplets dispersed in aqueous media. Our experimental studies show that, when trapped inside a radial LC droplet, spherical particles with both homeotropic and planar anchoring are highly localized at the droplet's center. While the radial configuration of the LC droplets is not altered by a homeotropic particle, polystyrene particles with strong planar anchoring disturb the radial ordering, leading to a twisted structure. Experiments indicate that off-center particle positions can also arise, in which defects are displaced towards the vicinity of the droplet's surface. In contrast, when prolate ellipsoidal particles are encapsulated in a thick radial LC shell, the minimum free energy corresponds to configurations where the particle is positioned at the droplet center. In this case, defects arise at the two ends of the prolate ellipsoid, where the curvature of the particle is maximal, leading to the formation of peculiar hybrid and twisted structures.