Colloidal Crystal Structures Research Articles

Curvature-directed anchoring and defect structure of colloidal smectic liquid crystals in confinement

Abstract Rod-like objects at high packing fractions can exhibit liquid crystalline ordering. By controlling how the rods align near a boundary, i.e. the anchoring, the defects of a liquid crystal can be selected and tuned. For smectic phases, the rods break rotational and translational symmetry by forming lamellae. Smectic defects thereby include both discontinuities in the rod orientational order (disclinations), as well as in the positional order (dislocations). In this work, we use experiments and simulations to uncover the geometrical conditions necessary for a boundary to set the anchoring of a confined, particle-resolved, smectic liquid crystal. We confine a colloidal smectic within elliptical wells of varying size and shape for a smooth variation of the boundary curvature. We find that the anchoring depends upon the local boundary curvature, with an anchoring transition observed at a critical radius of curvature approximately twice the rod length. Surprisingly, the critical radius of curvature for an anchoring transition holds across a wide range of rod lengths and packing fractions. The anchoring controls the defect structure. By analyzing topological charges and networks composed of maximum density (rod centers) and minimum density (rod ends), we quantify disclinations and dislocations formed with varying confinement geometry. Circular confinements, characterized by planar anchoring, promote disclinations, whereas elliptical confinements, featuring antipodal regions of homeotropic anchoring, promote long-range smectic order and dislocations. Our findings demonstrate how geometrical constraints can control the anchoring and defect structures of liquid crystals—a principle that is applicable from molecular to colloidal length scales.

Core-softened colloid under extreme geometrical confinement.

Geometrical constraints offer a promising strategy for assembling colloidal crystal structures that are not typically observed in bulk or under 2D conditions. Core-softened colloids, in particular, have emerged as versatile chemical building blocks with applications across various scientific and technological areas. In this study, we investigate the behavior of a core-softened model confined between two parallel walls. Employing molecular dynamics simulations, we analyze the system's response under extreme confinement, where only one or two layers of colloids are permitted. The system comprises particles modeled by a ramp-like potential confined within slit nanoslits created by two flat, purely repulsive walls with a lateral side L separated by a distance Lz. Through a systematic analysis of the phase behavior as Lz increases, or as the system undergoes decompression, for different values of L, we identified a mono-to-bilayer transition associated with changes in the colloidal structure. In the monolayer regime, we observed solid phases at lower densities than those observed in the 2D case. Importantly, we demonstrated that confinement at specific Lz values, allowing particle arrangement into two layers, can lead to the emergence of the square phase, which was not observed under monolayer or 2D conditions. By correlating thermodynamic, translational, and orientational ordering, as well as the dynamics of this confined colloidal system, our findings offer valuable insights into the utilization of geometrical constraints to induce and manipulate structural changes.

Effect of Attapulgite Application on Aggregate Formation and Carbon and Nitrogen Content in Sandy Soil

Clay minerals are the main cementing substances for sandy soils to form aggregates. The clay mineral attapulgite clay is abundant in Northwest China, and its special colloidal properties and crystal structure make it excellent in improving soil physicochemical properties. Using attapulgite as soil conditioner, the effects of different application rates of attapulgite on the formation and stability of sandy soil aggregates were studied through field experiments for two consecutive years. The results showed that the application of 6000 kg·hm−2 attapulgite soil in sandy soil farmland for two consecutive years reduced the soil bulk density by 0–20 cm, from 1.55 g·cm−3 to 1.47 g·cm−3, a decrease of 3.6%; the soil pH was increased by 3.7% from 8.59 to 8.84. The soil organic carbon, inorganic carbon and total nitrogen in the whole soil increased by 4.52%, 5.23% and 6.22%, respectively. The mass fraction of macro-aggregates of 2–0.25 mm and micro-aggregates of 0.25–0.053 mm as well as the contents of organic carbon, inorganic carbon and total nitrogen increased by 3.5%, 5.2%, 8.7%, 5.6% and 6.7%, respectively, thus improving the stability of aggregates. However, low application rates (1500 kg·hm−2 and 3000 kg·hm−2) of attapulgite had no significant effect on soil physical and chemical properties. Attapulgite, as a kind of highly adsorptive clay mineral, can be directly applied to sandy soil to increase soil cementitious substances, promote the formation of soil aggregates and increase the carbon and nitrogen fixation capacity of sandy soil. The improvement effect on the formation and stability of aggregates will gradually accumulate with the years of application. Therefore, in the future, the effects of adding attapulgite on the growth of various crops under various types of soil and climatic conditions should be carried out to obtain more systematic conclusions.

Dewetting-Induced Hierarchical Self-Assembly of Block Copolymers Templated by Colloidal Crystals.

Recent advances in high-performance flexible electronic devices have increased the demand for more diverse and complex nanofabrication methods; high-resolution, high-efficiency, and low-cost patterning strategies for next-generation devices are therefore required. In this study, we demonstrate the formation of dewetting-induced hierarchical patterns using two self-assembled materials: block copolymers (BCPs) and colloidal crystals. The combination of the two self-assembly methods successfully generates multiscale hierarchical patterns because the length scales of the periodic colloidal crystal structures are suitable for templating the BCP patterns. Various concentric ring patterns were observed on the templated BCP films, and a free energy model of the polymer chain was applied to explain the formation of these patterns relative to the template width. Frequently occurring spiral-defective features were also examined and found to be promoted by Y-junction defects.

Efficient and Stable Perovskite Nanocrystal Light-Emitting Diodes with Sulfobetaine-Based Ligand Treatment

Perovskite nanocrystals (PNCs) possess outstanding optical properties such as narrow full-width at half-maximum (fwhm) emission and color tunability. However, the labile ionic nature and weakly bound surface ligands of PNCs result in colloidal instability and crystal structure deformation, thus degrading their optical properties. In this study, we treated CsPbBr3 PNCs with 3-(dodecyldimethyl-ammonio)propane-1-sulfonate (12-SBE) ligands and successfully stabilized the PNCs under ambient air and heat. Under optimum ligand exchange conditions, 12-SBE PNCs showed near 100% photoluminescence quantum yield (PLQY) without an increase in the size of the PNCs. After 12-SBE treatment, the agglomeration of PNCs in solution due to ligand loss was suppressed, and PNC size growth induced by moisture and oxygen under heating was reduced. Finally, we fabricated 12-SBE PNC LEDs exhibiting 6.7% external quantum efficiency (EQE). Moreover, the PL lifetime of 12-SBE PNC LEDs was enhanced 2-fold compared to oleylamine (OAM) PNC LEDs.

A Robust Method for the Elaboration of SiO2-Based Colloidal Crystals as a Template for Inverse Opal Structures.

Photonic crystals (PCs) are nanomaterials with photonic properties made up of periodically modulated dielectric materials that reflect light between a wavelength range located in the photonic band gap. Colloidal PCs (C-PC) have been proposed for several applications such as optical platforms for the formation of physical, chemical, and biological sensors based on a chromatic response to an external stimulus. In this work, a robust protocol for the elaboration of photonic crystals based on SiO2 particle (SP) deposition using the vertical lifting method was studied. A wide range of lifting speeds and particle suspension concentrations were investigated by evaluating the C-PC reflectance spectrum. Thinner and higher reflectance peaks were obtained with a decrease in the lifting speed and an increase in the SP concentrations up to certain values. Seven batches of twelve C-PCs employing a SP 3% suspension and a lifting speed of 0.28 µm/s were prepared to test the reproducibility of this method. Every C-PC fabricated in this assay has a wavelength peak in a range of 10 nm and a peak width lower than 90 nm. Inverse-opal polymeric films with a highly porous and interconnected morphology were obtained using the developed C-PC as a template. Overall, these results showed that reproducible colloidal crystals could be elaborated on a large scale with a simple apparatus in a short period, providing a step forward in the scale-up of the fabrication of photonic colloidal crystal and IO structures as those employed for the elaboration of photonic polymeric sensors.

Heteroepitaxial Growth of Colloidal Crystals: Dependence of the Growth Mode on the Interparticle Interactions and Lattice Spacing.

Epitaxial growth is one of the most important techniques for the control of crystal growth, especially for growing thin-film semiconductor crystals. Similarly, colloidal epitaxy, a template-assisted self-assembly method, is a powerful technique for controlling the structure of colloidal crystals. In this study, heteroepitaxial growth, which differs from homoepitaxial growth of conventional colloidal epitaxy, using foreign colloidal crystals as a substrate, was used to grow single-component colloidal crystal films. The Frank-van der Merwe (FM), Stranski-Krastanov (SK), and Volmer-Weber (VW) modes were observed, and the mode varied with the lattice-misfit ratio and interparticle interactions between the substrate and epitaxial phase. The transition of the growth mode (from SK to VW) and the coexistence of different growth modes (FM and VW) were observed, and their processes were revealed by in situ observation. Colloidal heteroepitaxy was confirmed to be useful for controlling structure, which will enable exploration of novel colloidal self-assembly structures.

A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures.

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of rA/rB = 0.8 to rA/rB = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Copper Ion Imprinted Hydrogel Photonic Crystal Sensor Film

An ion-imprinted photonic crystal (IIPC) sensor for visual detection of copper ions was prepared by the combination of ion-imprinting polymer and colloidal photonic crystal (CPC) structure. Monodisperse polystyrene (PS) colloidal nanospheres synthesized by the boiling soap-free emulsion polymerization method were used to prepare the CPC template by the solvent evaporation method. An ion-imprinted polymer based on poly(vinyl alcohol) and chitosan (PVA/CS) is infiltrated therein. The IIPC sensor film was then prepared by solvent-assisted freeze–thaw method while the CPC template was strengthened as the air pores of the template were replaced by PVA/CS hydrogel. The shift of the diffraction wavelength can be directly observed by the naked eye through the color change of the IIPCS according to the concentration change of copper ion. Such sensor film showed good selectivity and sensitivity with a lower detection limit of 10–4 M.

Small-Angle X-ray Scattering Analysis of Colloidal Crystals and Replica Materials Made from l-Arginine-Stabilized Silica Nanoparticles.

Colloidal crystals made from sub-100 nm silica nanoparticles have provided a versatile platform for the template-assisted synthesis of three-dimensionally interconnected semiconducting, metallic, and magnetic replicas. However, the detailed structure of these materials has not yet been characterized. In this study, we investigated the structures of colloidal crystalline films and germanium replicas by scanning electron microscopy and small angle X-ray scattering. The structures of colloidal crystals made by evaporative assembly depends on the size of l-arginine-capped silica nanoparticles. Particles smaller than ∼31 nm diameter assemble into non-close-packed arrangements (bcc) whereas particles larger than 31 nm assemble into random close-packed structures with disordered hexagonal phase. Polycrystalline films of these materials retain their structures and long-range order upon infiltration at high temperature and pressure, and the structure is preserved in Ge replicas. The shear force during deposition and dispersity of silica nanoparticles contributes to the size-based variation in the structure and to the size of crystal domains in the colloidal crystal films.

A theory of entropic bonding

Entropy alone can self-assemble hard nanoparticles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Molecular simulation is a powerful tool used extensively to study the self-assembly of ordered phases from disordered fluid phases of atoms, molecules, or nanoparticles. However, it is not yet possible to predict colloidal crystal structures a priori from particle shape as we can for atomic crystals from electronic valency. Here, we present such a first-principles theory. By calculating and minimizing excluded volume within the framework of statistical mechanics, we describe the directional entropic forces that collectively emerge between hard shapes, in familiar terms used to describe chemical bonds. We validate our theory by demonstrating that it predicts thermodynamically preferred structures for four families of hard polyhedra that match, in every instance, previous simulation results. The success of this first-principles approach to entropic colloidal crystal structure prediction furthers fundamental understanding of both entropically driven crystallization and conceptual pictures of bonding in matter.

Impact of free energy of polymers on polymorphism of polymer-grafted nanoparticles.

Colloidal crystals have gathered wide attention as a model material for optical applications because of their feasibility in controlling the propagation of light by their crystal structure and lattice spacing as well as the simplicity of their fabrication. However, due to the simple interaction between colloids, the colloidal crystal structures that can be formed are limited. It is also difficult to adjust the lattice spacing. Furthermore, colloidal crystals are fragile compared to other crystals. In this study, we focused on polymer-grafted nanoparticles (PGNP) as a possible solution to these unresolved issues. We expected that PGNPs, composed of two distinct layers (the hard core of a nanoparticle and the soft corona of grafted polymers on the surface), will demonstrate similar behaviors as star polymers and hard spheres. We also predicted that PGNPs may exhibit polymorphism because the interaction between PGNPs strongly depends upon their grafting density and the length of the grafted polymer chains. Moreover, we expected that crystals made from PGNPs will be structurally tough due to the entanglement of grafted polymers. From exploration of crystal polymorphs of PGNPs by molecular dynamics simulations, we found face-centered cubic (FCC)/hexagonal close-packed (HCP) and body-centered cubic (BCC) crystals, depending on the length of the grafted polymer chains. When the chains were short, PGNPs behaved like hard spheres and crystals were arranged in FCC/HCP structure, much like the phase transition observed in an Alder transition. When the chains were long enough, the increase in the free energy of grafted polymers was no longer negligible and crystals were arranged in BCC structure, which has a lower density than FCC/HCP. When the chains were not too short or long, FCC/HCP structures were first observed when the volume fraction of system was small, but a phase transition occurred when the system was further compressed and the crystals arranged themselves in a BCC structure. These results most likely have laid strong foundations for future simulations and experimental studies of PGNP crystals.

Nanocomposite tectons as unifying systems for nanoparticle assembly.

Nanocomposite tectons (NCTs) are nanocomposite building blocks consisting of nanoparticle cores functionalized with a polymer brush, where each polymer chain terminates in a supramolecular recognition group capable of driving particle assembly. Like other ligand-driven nanoparticle assembly schemes (for example those using DNA-hybridization or solvent evaporation), NCTs are able to make colloidal crystal structures with precise particle organization in three dimensions. However, despite the similarity of NCT assembly to other methods of engineering ordered particle arrays, the crystallographic symmetries of assembled NCTs are significantly different. In this study, we provide a detailed characterization of the dynamics of hybridizations through universal (independent of microscopic details) parameters. We perform rigorous free energy calculations and identify the persistence length of the ligand as the critical parameter accounting for the differences in the phase diagrams of NCTs and other assembly methods driven by hydrogen bond hybridizations. We also report new experiments to provide direct verification for the predictions. We conclude by discussing the role of non-equilibrium effects and illustrating how NCTs provide a unification of the two most successful strategies for nanoparticle assembly: solvent evaporation and DNA programmable assembly.

Rapid self-assembly preparation of p-nitrophenol-molecular imprinted photonic crystal sensors

To overcome the long period of three-dimension photonic crystal colloidal array preparation, a rapid self-assembly method is proposed. The effect of microspheres diameter and concentration, heating and nitrogen blowing have been also studied. According to the results, when the microspheres suspension concentration is 0.2 wt% and heating temperature of 70 °C, a highly regular 3D face-centered cubic colloidal crystal array structure self-assembles on the gas-liquid interface within 3 min. Then using this method, a p-nitrophenol-molecular (p-NP) imprinted photonic crystal sensor with high selectivity and sensitivity is prepared. The p-NP imprinted sensor presents twice signal intense than the non-imprinted sensor towards the target, and the structural color changes from blue to green. Meanwhile, the sensor responds in 3 min and can be reversible more than 9 times. This rapid self-assembly method provides a suitable way for large-area colloidal photonic crystal preparation with higher efficiency and good repeatability, which has a high value for practical applications.

Synthesizable nanoparticle eigenshapes for colloidal crystals.

The gulf between the complexity and diversity of colloidal crystal phases predicted to form in computer simulation and that realized to date in experiment is narrowing, but is still wide. Prior work shows that many synthesized particles are far from optimal "eigenshapes" for target superlattice structures. We use digital alchemy to determine eigenshapes for possible target colloidal crystal structures for eight families of polyhedral nanoparticle shapes already synthesized in the laboratory. Within each family we predict optimal building block shapes to obtain several target superlattice structures, as a guide for future experiments. For three target crystal structures common to multiple families, we identify which of the optimal shapes is most optimal under the same thermodynamic conditions.

Reversible solid-state phase transitions in confined two-layer colloidal crystals

Using a combination of fluorescence and bright-field optical imaging, the solid-state packing structures of semi-confined two-layer spherical colloidal crystals were observed during modulation of an external AC electric field. Upon increasing field strength, the bottom layer of colloids (layer 1) transitioned from the entropically favored hexagonal packing structure with p6m symmetry to a square-packing structure with p4m symmetry. The packing structure of layer 2 was determined by the packing structure of layer 1, with layer 2 particles resting in, and moving in registry with, the low-energy interstitial sites of layer 1. Modulation of the field strength thus resulted in a reversible transition between a face-centered cubic crystal structure and a body-centered cubic crystal structure at low and high field strengths, respectively. These structures were found to be sensitive to the particle density in the wells, with vacancies and insertions leading to the formation of mixed crystal phases at high field strengths.

Inverse design of compression-induced solid – solid transitions in colloids

ABSTRACT Ongoing developments in colloidal particle synthesis show promise for using colloids as building blocks for reconfigurable, functional materials, but their rational design remains a challenge. Recent efforts to inversely design a colloidal particle from a self-assembled target structure at a single state point have proven successful even for complex colloidal crystals, replacing trial-and-error searches. Can such approaches be used to design a particle capable of assembling into multiple target structures under multiple conditions, thereby designing a reconfigurable colloidal crystal? Here we present a computational approach for the design of colloids that exhibit distinct target behaviours under different thermodynamic conditions. By extending the digital alchemy inverse design framework to multiple state points, we design hard particle shapes that entropically self-assemble two different colloidal crystal structures at two different densities; upon a small density change, the system reliably reconfigures between the two solids. We also find that the optimal shape satisfying two constraints is not simply an average of the two optimal shapes from each state point, and therefore is not easily intuited.

Compression-Responsive Photonic Crystals Based on Fluorine-Containing Polymers.

Fluoropolymers represent a unique class of functional polymers due to their various interesting and important properties such as thermal stability, resistance toward chemicals, repellent behaviors, and their low refractive indices in comparison to other polymeric materials. Based on the latter optical property, fluoropolymers are particularly of interest for the preparation of photonic crystals for optical sensing application. Within the present study, photonic crystals were prepared based on core-interlayer-shell particles focusing on fluoropolymers. For particle assembly, the melt-shear organization technique was applied. The high order and refractive index contrast of the individual components of the colloidal crystal structure lead to remarkable reflection colors according to Bragg’s law of diffraction. Due to the special architecture of the particles, consisting of a soft core, a comparably hard interlayer, and again a soft shell, the resulting opal films were capable of changing their shape and domain sizes upon applied pressure, which was accompanied with a (reversible) change of the observed reflection colors as well. By the incorporation of adjustable amounts of UV cross-linking agents into the opal film and subsequent treatment with different UV irradiation times, stable and pressure-sensitive opal films were obtained. It is shown that the present strategy led to (i) pressure-sensitive opal films featuring reversibly switchable reflection colors and (ii) that opal films can be prepared, for which the written pattern—resulting from the compressed particles—could be fixed upon subsequent irradiation with UV light. The herein described novel fluoropolymer-containing photonic crystals, with their pressure-tunable reflection color, are promising candidates in the field of sensing devices and as potential candidates for anti-counterfeiting materials.

Gaussian beam sphere optics in condensed matter research

Transparent spheres in which the radius R of the sphere is larger than or equal to the wavelength λ of light have currently become of particular interest for quite a number of physical problems (2D colloidal crystal structures composed of transparent spheres, photonic crystals and meta-materials) and applications (laser lithography, fiber-optic systems, super resolution microscopy, biomedical applications, and others). The optical properties of a “full” sphere, when the light aperture r is of order R and the sphere is a natural spherical aberration, have not been investigated in ample detail yet. Strong spherical aberration makes focusing nontrivial. Usually, the exact solution of sphere optics is obtained using the Mie theory, the generalized Lorenz–Mie theory (GLMT), DFT, DDFT codes, which do not give much of a physical insight, as it requires summation of a large number of terms in a multipole expansion even for moderate sphere sizes. In this work we present an algorithm for describing the focusing properties of a transparent sphere using the Gaussian beam approximation that gives a good description of the field in the region of lens caustic. The algorithm developed for the spherical systems was used to create a code for calculating based on standard computation systems spheres with diameters ranging from ∼λ to thousands of λ. The results obtained were compared with the data of some authors obtained earlier by more sophisticated methods.

Entropy-Induced Self-Assembly of Colloidal Crystals with High Reflectivity and Narrow Reflection Bandwidth.

Cracks and defects, which could result in lower reflectivity and larger full width at half maximum (FWHM), are the major obstacles for obtaining highly ordered structures of colloidal crystals (CCs). The high-quality CCs with high reflectivity (more than 90%) and 9.2 nm narrow FWHM have been successfully fabricated using a fixed proportion of a soft matter system composed of silica particles (SPs), polyethylene glycol diacrylate (PEGDA), and ethanol. The influences of refractivity difference, volume fractions, and particle dimension on FWHM were illuminated. Firstly, we clarified the influences of the planar interface and the bending interface on the self-assembly. The CCs had been successfully fabricated on the planar interface and presented unfavorable results on the bending interface. Secondly, a hard sphere system consisting of SPs, PEGDA, and ethanol was established, and the entropy-driven phase transition mechanism of a polydisperse system was expounded. The FWHM and reflectivity of CCs showed an increasing trend with increasing temperature. Consequently, high-quality CCs were obtained by adjusting temperatures (ordered structure formed at 90 °C and solidified at 0 °C) based on the surface phase rule of the system. We acquired a profound understanding of the principle and process of self-assembly, which is significant for preparation and application of CCs such as optical filters.