Defect structures mediate the isotropic-nematic transition in strongly confined liquid crystals

Defect-influenced particle advection in highly confined liquid crystal flows

We study the morphology of the Saturn ring defect and director structure around a colloidal particle with normal anchoring conditions and within the flow of the nematic host phase through a rectangular duct of comparable size to the particle. The changes in the defect structures and director profile influence the advection behaviour of the particle, which we compare to that in a simple Newtonian host phase. These effects lead to a non-monotonous dependence of the differential velocity of particle and fluid, also known as retardation ratio, on the Ericksen number.

Multistate Dynamic Pathways for Anisotropic Colloidal Assembly and Reconfiguration

We report the controlled interfacial assembly and reconfiguration of rectangular prism colloidal particles between microstructures of varying positional and orientational order including stable, metastable, and transient states. Structurally diverse states are realized by programming time dependent electric fields that mediate dipolar interactions determining particle position, orientation, compression, and chaining. We identify an order parameter set that defines each state as a combination of the positional and orientational order. These metrics are employed as reaction coordinates to capture the microstructure evolution between initial and final states upon field changes. Assembly trajectory manifolds between states in the low-dimensional reaction coordinate space reveal a dynamic pathway map including information about pathway accessibility, reversibility, and kinetics. By navigating the dynamic pathway map, we demonstrate reconfiguration between states on minute time scales, which is practically useful for particle-based materials processing and device responses. Our findings demonstrate a conceptually general approach to discover dynamic pathways as a basis to control assembly and reconfiguration of self-organizing building blocks that respond to global external stimuli.

External field induced defect transformation in circular confined Gay-Berne liquid crystals

Normally, defects in two-dimensional, circular, confined liquid crystals can be classified into four types based on the position of singularities formed by liquid crystal molecules, i.e., the singularities located inside the circle, at the boundary, outside the circle, and outside the circle at infinity. However, it is considered difficult for small aspect ratio liquid crystals to generate all these four types of defects. In this study, we use molecular dynamics simulation to investigate the defect formed in Gay-Berne, ellipsoidal liquid crystals, with small aspect ratios confined in a circular cavity. As expected, we only find two types of defects (inside the circle and at the boundary) in circular, confined, Gay-Berne ellipsoids under static conditions at various densities, aspect ratios, and interactions between the wall and liquid crystals. However, when introducing an external field to the system, four types of defects can be observed. With increasing the strength of the external field, the singularities in the circular, confined system change from the inside to the boundary and the outside, and the farthest position that the singularities can reach depends on the strength of the external field. We further introduce an alternating, triangular wave, external field to the system to check if we can observe the transformation of different defects within an oscillating period. We find that the position of the singularities greatly depends on the oscillating intensity and oscillating period. By changing the oscillating intensity and oscillating period of the external field, the defect types can be adjusted, and the transformation between different defects can be easily observed. This provides a feasible way to modulate liquid crystal defects and investigate the transformation between different defects.

Anomalous phase behavior of quasi-one-dimensional attractive hard rods

We study a two-state model of attractive hard rods using the transfer matrix method, where the centers of the particles are confined to a straight line, but the orientations of the rods can be parallel or perpendicular to the confining line. The rods are modeled as hard rectangles with length L and width D and decorated with attractive sites at both ends of the rectangles. We find that the particles align parallel to the line and form long chains at low densities, while they turn out of the line and form a Tonks gas at high densities. With increasing the stickiness between the rods, the structural change between parallel and perpendicular states becomes stronger and the pressure vs density curve becomes almost a horizontal line at the transition pressure. We show that such a behavior is reminiscent of the first-order phase transition. This manifests in the validity of the lever rule of the phase transitions for very sticky cases.

Defect patterns of two-dimensional nematic liquid crystals in confinement

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement

Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.

Highly confined mixtures of parallel hard squares: A density-functional-theory study

Using the fundamental-measure density-functional theory, we study theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting of two consecutive big squares, or three small squares, in the transverse direction, perpendicular to the walls, are forbidden. We analyze two different mixtures with edge lengths of species selected so as to allow or forbid one big plus one small square to fit into the channel. For the first mixture we obtain first-order transitions between symmetric and asymmetric packings of particles: Small and big squares are preferentially adsorbed at different walls. Asymmetric configurations are shown to lead to more efficient packing at finite pressures. We argue that the stability region of the asymmetric phase in the pressure-composition plane is bounded so that the symmetric phase is stable at low and very high pressure. For the second mixture, we observe strong demixing between phases which are rich in different species. Demixing occurs in the lateral direction, i.e., the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behavior (which in practical terms is precluded by jamming) in strictly two-dimensional systems is discussed. Finally, the phase behavior of a mixture with periodic boundary conditions is analyzed and the differences and similarities between the latter and the confined system are discussed. We claim that, although exact calculations exclude the existence of true phase transitions in (1+ε)-dimensional systems, density-functional theory is still successful in describing packing properties of large clusters of particles.

Colloidal Liquid Crystals Confined to Synthetic Tactoids

When a liquid crystal forming particles are confined to a spatial volume with dimensions comparable to that of their own size, they face a complex trade-off between their global tendency to align and the local constraints imposed by the boundary conditions. This interplay may lead to a non-trivial orientational patterns that strongly depend on the geometry of the confining volume. This novel regime of liquid crystalline behavior can be probed with colloidal particles that are macro-aggregates of biomolecules. Here we study director fields of filamentous fd-viruses in quasi-2D lens-shaped chambers that mimic the shape of tactoids, the nematic droplets that form during isotropic-nematic phase separation. By varying the size and aspect ratio of the chambers we force these particles into confinements that vary from circular to extremely spindle-like shapes and observe the director field using fluorescence microscopy. In the resulting phase diagram, next to configurations predicted earlier for 3D tactoids, we find a number of novel configurations. Using Monte Carlo Simulations, we show that these novel states are metastable, yet long-lived. Their multiplicity can be explained by the co-existence of multiple dynamic relaxation pathways leading to the final stable states.

Machine learning topological defects of confined liquid crystals in two dimensions

Supervised machine learning can be used to classify images with spatially correlated physical features. We demonstrate the concept by using the coordinate files generated from an off-lattice computer simulation of rodlike molecules confined in a square box as an example. Because of the geometric frustrations at high number density, the nematic director field develops an inhomogeneous pattern containing various topological defects as the main physical feature. We describe two machine-learning procedures that can be used to effectively capture the correlation between the defect positions and the nematic directors around them and hence classify the topological defects. First is a feedforward neural network, which requires the aid of presorting the off-lattice simulation data in a coarse-grained fashion. Second is a recurrent neural network, which needs no such sorting and can be directly used for finding spatial correlations. The issues of when to presort a simulation data file and how the network structures affect such a decision are addressed.

Topological defects in two-dimensional liquid crystals confined by a box

When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.

Nematic liquid crystal director structures in rectangular regions

We consider a shallow rectangular well of nematic liquid crystal subject to weak anchoring on the sides of the well. By considering weak anchoring instead of infinitely strong anchoring, we are able to analyze nematic equilibria in the well without the need to exclude point defects at the corners, as done in previous work in the area. For relatively weak anchoring, we are able to derive analytic expressions for the director alignment angle in terms of an infinite series of modes, involving roots of a transcendental equation. The analytic forms of the director configuration are then used to calculate critical anchoring strengths at which uniform and distorted director structures exchange stability. We also consider the asymptotic behavior of the director structure and energy for very strong anchoring. We show that in both cases-for the transitions from uniform to distorted states and the limit of infinitely strong anchoring-the approximate analytic expansions agree very well with corresponding numerical calculations of the full model.

Colloidal liquid crystals in square confinement: isotropic, nematic and smectic phases

We report on the confinement of colloidal liquid crystals in three dimensional chambers with a square footprint. To this end we use colloidal silica rods and exploit their relatively large density difference with respect to the dispersing solvent to study isotropic, nematic and smectic phases confined into a single chamber. Combining laser scanning confocal microscopy and soft-lithography techniques enables us to characterize the configurations down to the single particle level. We will focus on the smectic phase and compare to recent theories and simulations.

Finite particle size drives defect-mediated domain structures in strongly confined colloidal liquid crystals

When liquid crystals are confined to finite volumes, the competition between the surface anchoring imposed by the boundaries and the intrinsic orientational symmetry-breaking of these materials gives rise to a host of intriguing phenomena involving topological defect structures. For synthetic molecular mesogens, like the ones used in liquid-crystal displays, these defect structures are independent of the size of the molecules and well described by continuum theories. In contrast, colloidal systems such as carbon nanotubes and biopolymers have micron-sized lengths, so continuum descriptions are expected to break down under strong confinement conditions. Here, we show, by a combination of computer simulations and experiments with virus particles in tailor-made disk- and annulus-shaped microchambers, that strong confinement of colloidal liquid crystals leads to novel defect-stabilized symmetrical domain structures. These finite-size effects point to a potential for designing optically active microstructures, exploiting the as yet unexplored regime of highly confined liquid crystals.

Liquid crystals confined to micrometre-sized geometries can be well described by a continuum theory, where the size effect of constituent mesogens is negligible. Here, the authors show how the continuum theory breaks down in colloidal liquid crystal, leading to the formation of defect-mediated domains.

Analytical description of 2D magnetic Freedericksz transition in a rectangular cell of a nematic liquid crystal

We study the Freedericksz transition induced by a magnetic field in a rectangular cell filled with a nematic liquid crystal. In the initial state the director of the nematic liquid crystal is uniformly aligned in the cross section plane of the cell with rigid anchoring of the director at cell walls: planar on the top and bottom walls, and homeotropic on the left and right ones. The magnetic field is directed perpendicular to the cell cross section plane. We consider two-dimensional (2D) orientational deformations of the nematic liquid crystal in the rectangular cell and determine the critical value of the Freedericksz transition field above which these orientational deformations occur. The 2D expression for the director alignment profile above the threshold of Freedericksz transition is analytically found and the profile shapes as functions of cell sizes, values of the Frank elastic constants of the nematic liquid crystal and the magnetic field are studied.

Multi-particle collision dynamics algorithm for nematic fluids

Research on transport, self-assembly and defect dynamics within confined, flowing liquid crystals requires versatile and computationally efficient mesoscopic algorithms to account for fluctuating nematohydrodynamic interactions. We present a multi-particle collision dynamics (MPCD) based algorithm to simulate liquid-crystal hydrodynamic and director fields in two and three dimensions. The nematic-MPCD method is shown to successfully reproduce the features of a nematic liquid crystal, including a nematic-isotropic phase transition with hysteresis in 3D, defect dynamics, isotropic Frank elastic coefficients, tumbling and shear alignment regimes and boundary condition-dependent order parameter fields.