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

Prismatic Confinement Induces Tunable Orientation in Plasmonic Supercrystals

Throughout history scientists have looked to Nature for inspiration and attempted to replicate intricate complex structures formed by self-assembly. In the context of synthetic supercrystals, achieving such complexity remains a challenge due to the highly symmetric nature of most nanoparticles (NPs). Previous works have shown intricate coupling between the self-assembly of NPs and confinement in templates, such as emulsion droplets (spherical confinement) or tubes (cylindrical confinement). This study focuses on the interplay between anisotropic NP shape and tunable "prismatic confinement" leading to the self-assembly of supercrystals in cavities featuring polygonal cross sections. A multiscale characterization strategy is employed to investigate the orientation and structure of the supercrystals locally and at the ensemble level. Our findings highlight the role of the mold interface in guiding the growth of distinct crystal domains: each side of the mold directs the formation of a monodomain that extends until it encounters another, leading to the creation of grain boundaries. Computer simulations in smaller prismatic cavities were conducted to predict the effect of an increased confinement. Comparison between prismatic and cylindrical confinements shows that flat interfaces are key to orienting the growth of supercrystals. This work shows a method of inducing orientation in plasmonic supercrystals and controlling their textural defects, thus offering insight into the design of functional metasurfaces and hierarchically structured devices.

Colloidal Rod-Like Particles with Temperature-Driven Tunable Interactions

Temperature-sensitive rod-like colloidal particles were synthesized by grafting a temperature-responsive polymer, poly(2-(dimethylamino)ethyl methacrylate) (PDMA), on the surface of high aspect ratio silica rods by surface-initiated atom transfer radical polymerization. The stability of the grafted polymer on the surface of the particles in aqueous solutions was found to deteriorate with time, leading to a gradual decrease of the polymer content of the hybrid colloids, which was attributed to the mechanically activated hydrolysis of the labile bonds at the polymer-silica interface. The polymer degrafting was significantly suppressed by first growing a hydrophobic poly(methyl methacrylate) block onto the particle surface to act as a barrier layer for the penetration of water molecules at the polymer-particle interface, followed by chain-extension with the hydrophilic PDMA chains. Dynamic light scattering, microscopy, and rheological measurements revealed that the PDMA block conferred a temperature-responsive behavior to the rod-like particles, which formed aggregates at temperatures above the lower critical solution temperature (LCST) of the polymer. However, in contrast to their spherical counterparts, the polymer-grafted rod-like particles did not exhibit complete thermo-reversibility upon lowering the solution temperature below the LCST of PDMA, which was reflected by different values of the diffusion coefficient for the heating and cooling cycles, indicating an irreversible rod particle aggregation upon increasing the temperature.

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.

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.

Topology of Orientational Defects in Confined Smectic Liquid Crystals

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.

Internal Microstructure Dictates Interactions of Polymer-grafted Nanoparticles in Solution

Understanding the effects of polymer brush architecture on particle interactions in solution is requisite to enable the development of functional materials based on self-assembled polymer-grafted nanoparticles (GNPs). Static and dynamic light scattering of polystyrene-grafted silica particle solutions in toluene reveals that the pair interaction potential, inferred from the second virial coefficient, A 2, is strongly affected by the grafting density, σ, and degree of polymerization, N, of tethered chains. In the limit of intermediate σ (∼0.3 to 0.6 nm-2) and high N, A 2 is positive and increases with N. This confirms the good solvent conditions and can be qualitatively rationalized on the basis of a pair interaction potential derived for grafted (brush) particles. In contrast, for high σ > 0.6 nm-2 and low N, A 2 displays an unexpected reversal to negative values, thus indicating poor solvent conditions. These findings are rationalized by means of a simple analysis based on a coarse-grained brush potential, which balances the attractive core-core interactions and the excluded volume interactions imparted by the polymer grafts. The results suggest that the steric crowding of polymer ligands in dense GNP systems may fundamentally alter the interactions between brush particles in solution and highlight the crucial role of architecture (internal microstructure) on the behavior of hybrid materials. The effect of grafting density also illustrates the opportunity to tailor the physical properties of hybrid materials by altering geometry (or architecture) rather than a variation of the chemical composition.

From n-layer planar ordering to the monolayer homeotropic structure of confined hard rods: The effect of shape anisotropy and wall-to-wall separation

Using the Parsons-Lee theory, we examined the effect of shape anisotropy and the wall-to-wall separation (H) on the phase behavior of the hard parallelepiped rods with dimensions L, D, and D (L>D) in such narrow slitlike pores which only one homeotropic layer can form. The phase structures, including biaxiality, planar nematic layering transition as well as planar to homeotropic, were studied for some separations in the range 2.5D≤H≤10.0D for H-D≤L<H.

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.

Rodlike molecules in extreme confinement

A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau-de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.

Nematic ordering of hard rods under strong confinement in a dense array of nanoposts

The effect of confinement on the behavior of liquid crystals is interesting from a fundamental and practical standpoint. In this work, we report Monte Carlo simulations of hard rods in an array of hard nanoposts, where the surface-to-surface separations between nanoposts are comparable to or less than the length of hard rods. This particular system shows promise as a means of generating large-scale organization of the nematic liquid by introducing an entropic external field set by the alignment of nanoposts. The simulations show that nematic ordering of hard rods is enhanced in the nanopost arrays compared with that in bulk, in the sense that the nematic order is significant even at low concentrations at which hard rods remain isotropic in bulk, and the enhancement becomes more significant as the passage width between two nearest nanoposts decreases. An analysis of local distribution of hard-rod orientations at low concentrations with weak nematic ordering reveals that hard rods are preferentially aligned along nanoposts in the narrowing regions between two curved surfaces of nearest nanoposts; hard rods are less ordered in the passages and in the centers of interpost spaces. It is concluded that at low concentrations the confinement in a dense array of nanoposts induces the localized nematic order first in the narrowing regions and, as the concentration further increases, the nematic order spreads over the whole region. The formation of a well-ordered phase at low concentrations of hard rods in a dense array of nanoposts can provide a new route to the low-concentration preparation of nematic liquid crystals that can be used as anisotropic dispersion media.

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.