Directing Liquid Crystalline Self-Organization of Rodlike Particles through Tunable Attractive Single Tips

M13-Phage-Based Star-Shaped Particles with Internal Flexibility

We report on the construction and the dynamics of monodisperse star-shaped particles, mimicking, at the mesoscale, star polymers. Such multiarm star-like particles result from the self-assembly of gold nanoparticles, forming the core, with tip-linked filamentous viruses (M13 bacteriophages) acting as spines in a sea urchin-like structure. By combining fluorescence and dark-field microscopy with dynamic light scattering, we investigate the diffusion of these hybrid spiny particles. We reveal the internal dynamics of the star particles by probing their central metallic core, which exhibits a hindered motion that can be described as a Brownian particle trapped in a harmonic potential. We therefore show that the filamentous viruses and specifically their tip proteins behave as entropic springs, extending the relevance of the study of such hybrid mesoscopic analogues of star polymers to phage biotechnology.

Uniform Colloidal Polymer Rods by Stabilizer-Assisted Liquid-Crystallization-Driven Self-Assembly

The synthesis of anisotropic colloidal building blocks is essential for their self-assembly into hierarchical materials. Here, a highly efficient stabilizer-assisted liquid-crystallization-driven self-assembly (SA-LCDSA) strategy was developed to achieve monodisperse colloidal polymer rods. This strategy does not require the use of block copolymers, but only homopolymers or random copolymers. The resulting rods have tunable size and aspect ratios, as well as well-defined columnar liquid crystal structures. The integrated triphenylene units enable the rods to exhibit unusual photo-induced fluorescence enhancement and accompanying irradiation memory effect, which, as demonstrated, are attractive for information encryption/decryption of paper documents. In particular, unwanted document decryption during delivery can be examined by fluorescence kinetics. This SA-LCDSA-based approach can be extended to synthesize other functional particles with desired π-molecular units.

Janus helices: From fully attractive to hard helices

The phase diagram of hard helices differs from its hard rods counterpart by the presence of chiral "screw" phases stemming from the characteristic helical shape, in addition to the conventional liquid crystal phases also found for rod-like particles. Using extensive Monte Carlo and Molecular Dynamics simulations, we study the effect of the addition of a short-range attractive tail representing solvent-induced interactions to a fraction of the sites forming the hard helices, ranging from a single-site attraction to fully attractive helices for a specific helical shape. Different temperature regimes exist for different fractions of the attractive sites, as assessed in terms of the relative Boyle temperatures, that are found to be rather insensitive to the specific shape of the helical particle. The temperature range probed by the present study is well above the corresponding Boyle temperatures, with the phase behaviour still mainly entropically dominated and with the existence and location of the various liquid crystal phases only marginally affected. The pressure in the equation of state is found to decrease upon increasing the fraction of attractive beads and/or on lowering the temperature at fixed volume fraction, as expected on physical grounds. All screw phases are found to be stable within the considered range of temperatures with the smectic phase becoming more stable on lowering the temperature. By contrast, the location of the transition lines do not display a simple dependence on the fraction of attractive beads in the considered range of temperatures.

Elastic response of colloidal smectic liquid crystals: Insights from microscopic theory

Elongated colloidal rods at sufficient packing conditions are known to form stable lamellar or smectic phases. Using a simplified volume-exclusion model, we propose a generic equation of state for hard-rod smectics that is robust against simulation results and is independent of the rod aspect ratio. We then extend our theory by exploring the elastic properties of a hard-rod smectic, including the layer compressibility (B) and bending modulus (K_{1}). By introducing weak backbone flexibility we are able to compare our predictions with experimental results on smectics of filamentous virus rods (fd) and find quantitative agreement between the smectic layer spacing, the out-of-plane fluctuation strength, as well as the smectic penetration length λ=sqrt[K_{1}/B]. We demonstrate that the layer bending modulus is dominated by director splay and depends sensitively on lamellar out-of-plane fluctuations that we account for on the single-rod level. We find that the ratio between the smectic penetration length and the lamellar spacing is about two orders of magnitude smaller than typical values reported for thermotropic smectics. We attribute this to the fact that colloidal smectics are considerably softer in terms of layer compression than their thermotropic counterparts while the cost of layer bending is of comparable magnitude.

Chiral Liquid Crystalline Properties of Cellulose Nanocrystals: Fundamentals and Applications

By using an independent self-assembly process that is occasionally controlled by evaporation, cellulose nanocrystals (CNCs) may create films (pure or in conjunction with other materials) that have iridescent structural colors. The self-forming chiral nematic structures and environmental safety of a new class of photonic liquid crystals (LCs), referred to as CNCs and CNC-embedded materials, make them simple to make and treat. The structure of the matrix interacts with light to give structural coloring, as opposed to other dye pigments, which interact with light by adsorption and reflection. Understanding how CNC self-assembly constructs structures is vital in several fields, including physics, science, and engineering. To constructure this review, the colloidal characteristics of CNC particles and their behavior during the formation of liquid crystals and gelling were studied. Then, some of the recognized applications for these naturally occurring nanoparticles were summarized. Different factors were considered, including the CNC aspect ratio, surface chemistry, concentration, the amount of time needed to produce an anisotropic phase, and the addition of additional substances to the suspension medium. The effects of alignment and the drying process conditions on structural changes are also covered. The focus of this study however is on the optical properties of the films as well as the impact of the aforementioned factors on the final transparency, iridescent colors, and versus the overall response of these bioinspired photonic materials. Control of the examined factors was found to be necessary to produce reliable materials for optoelectronics, intelligent inks and papers, transparent flexible support for electronics, and decorative coatings and films.

Structure of nematic tactoids of hard rods

We study by means of Monte Carlo simulations the internal structure of nematic droplets or tactoids formed by hard, rod-like particles in a gas of spherical ghost particles that act as depletion agents for the rods. We find that the shape and internal structure of tactoids are strongly affected by the size of the droplets. The monotonically increasing degree of nematic order with increasing particle density that characterizes the bulk nematic phase is locally violated and more so the smaller the tactoid. We also investigate the impact of an external quadrupolar alignment field on tactoids and find that this tends to make the director field more uniform, but not to very significantly increase the tactoid’s aspect ratio. This agrees with recent theoretical predictions yet is at variance with experimental observations and dynamical simulations. We explain this discrepancy in terms of competing relaxation times.

Blunt-End Driven Re-entrant Ordering in Quasi Two-Dimensional Dispersions of Spherical DNA Brushes

We investigate the effects of crowding on the conformations and assembly of confined, highly charged, and thick polyelectrolyte brushes in the osmotic regime. Particle tracking experiments on increasingly dense suspensions of colloids coated with ultralong double-stranded DNA (dsDNA) fragments reveal nonmonotonic particle shrinking, aggregation, and re-entrant ordering. Theory and simulations show that aggregation and re-entrant ordering arise from the combined effect of shrinking, which is induced by the osmotic pressure exerted by the counterions absorbed in neighbor brushes and of a short-range attractive interaction competing with electrostatic repulsion. An unconventional mechanism gives origin to the short-range attraction: blunt-end interactions between stretched dsDNA fragments of neighboring brushes, which become sufficiently intense for dense and packed brushes. The attraction can be tuned by inducing free-end backfolding through the addition of monovalent salt. Our results show that base stacking is a mode parallel to hybridization to steer colloidal assembly in which attractions can be fine-tuned through salinity and, potentially, grafting density and temperature.

Self-Assembly of All-DNA Rods with Controlled Patchiness

Double-stranded DNA (dsDNA) fragments exhibit noncovalent attractive interactions between their tips. It is still unclear how DNA liquid crystal self-assembly is affected by such blunt-end attractions. It is demonstrated that stiff dsDNA fragments with moderate aspect ratio can specifically self-assemble in concentrated aqueous solutions into different types of smectic mesophases on the basis of selectively screening of blunt-end DNA stacking interactions. To this end, this type of attractions are engineered at the molecular level by constructing DNA duplexes where the attractions between one or both ends are screened by short hairpin caps. All-DNA bilayer and monolayer smectic-A type of phases, as well as a columnar phase, can be stabilized by controlling attractions strength. The results imply that the so far elusive smectic-A in DNA rod-like liquid crystals is a thermodynamically stable phase. The existence of the bilayer smectic phase is confirmed by Monte-Carlo simulations of hard cylinders decorated with one attractive terminal site. This work demonstrates that DNA blunt-ends behave as well-defined monovalent attractive patches whose strength and position can be potentially precisely tuned, highlighting unique opportunities concerning the stabilization of nonconventional DNA-based lyotropic liquid crystal phases assembled by all-DNA patchy particles with arbitrary geometry and composition.

Hierarchical, Highly Open Microtubes and Columnar Liquid Crystals Self-Assembled from Symmetrical and Asymmetrical Colloidal Rings

The use of simple building blocks to produce hierarchical and porous structured materials is highly desired. Rings are simple colloidal particles but unique for their internal cavities. Here we report the self-assembly (SA) of colloidal rings with tunable asymmetry mediated by a depletion force and demonstrate that a variety of porous colloidal superstructures from microtubes, flexible chains, (plastic) crystals to highly open liquid crystals (LCs) can be formed along the predesigned SA paths. In particular, the SA is staged in binary or ternary systems. Large rings first form complex ring-in-ring and ring-in-ring-in-ring assemblies by capturing smaller rings, which, as new building blocks, can further form multi-walled microtubes and open columnar LCs. Moreover, a plastic columnar LC with alternating intracolumnar stacking is found from asymmetrical rings. The SA with colloidal rings opens a new avenue to construct hierarchical and porous ordered metamaterials.

When bigger is faster: A self-Van Hove analysis of the enhanced self-diffusion of non-commensurate guest particles in smectics

We investigate the anomalous dynamics in smectic phases of short host rods where, counter-intuitively, long guest rod-shaped particles diffuse faster than the short host ones due to their precise size mismatch. In addition to the previously reported mean-square displacement, we analyze the time evolution of the self-Van Hove functions G(r, t), as this probability density function uncovers intrinsic heterogeneous dynamics. Through this analysis, we show that the dynamics of the host particles parallel to the director becomes non-Gaussian and therefore heterogeneous after the nematic-to-smectic-A phase transition, even though it exhibits a nearly diffusive behavior according to its mean-squared displacement. In contrast, the non-commensurate guest particles display Gaussian dynamics of the parallel motion, up to the transition to the smectic-B phase. Thus, we show that the self-Van Hove function is a very sensitive probe to account for the instantaneous and heterogeneous dynamics of our system and should be more widely considered as a quantitative and complementary approach of the classical mean-squared displacement characterization in diffusion processes.

Growth transitions and critical behavior in the non-equilibrium aggregation of short, patchy nanorods

We have carried out Monte Carlo simulations to study the non-equilibrium aggregation of short patchy nanorods in two dimensions. Below a critical value of patch size ([Formula: see text]), the aggregates have finite sizes with small radii of gyration, [Formula: see text]. At [Formula: see text], the average radius of gyration shows a power law increase with time such that [Formula: see text], where [Formula: see text]. Above, [Formula: see text], the aggregates are fractal in nature and their fractal dimension depends on the value of patch size. These morphological differences are due to the fact that below the critical value of patch size ([Formula: see text]), the growth of the clusters is suppressed and the system reaches an 'absorbed state.' Above [Formula: see text], the system reaches an 'active state,' in which the cluster size keeps growing with a fixed rate at long times. Thus, the system encounters a non-equilibrium phase transition. Close to the transition, the growth rate scales as [Formula: see text], where [Formula: see text]. The long-time growth rate varies as [Formula: see text] where [Formula: see text]. These scaling exponents indicate that the transition belongs to the directed percolation universality class. The patchy nanorods also display a threshold patch size ([Formula: see text]), beyond which the long-time growth rate remains constant. We present geometric arguments for the existence of [Formula: see text]. The fractal dimension of the aggregates increases from 1.75, at [Formula: see text], to 1.81, at [Formula: see text]. It remains constant beyond [Formula: see text].

Phase behavior of hard cylinders

Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length (L) and diameter (D) using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate L/D > 1 and the oblate L/D < 1 phase diagrams are reported with no solution of continuity. In the prolate L/D > 1 case, we find intermediate nematic N and smectic SmA phases in addition to a low density isotropic I and a high density crystal X phase with I-N-SmA and I-SmA-X triple points. An apparent columnar phase C is shown to be metastable, as in the case of spherocylinders. In the oblate L/D < 1 case, we find stable intermediate cubatic (Cub), nematic (N), and columnar (C) phases with I-N-Cub, N-Cub-C, and I-Cub-C triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.

Hollow polymer microrods of tunable flexibility from dense amphiphilic block copolymer brushes

Polymer microrods of aspect ratio ∼10, and tunable flexibility are attractive model systems to study density and index matched liquid crystalline phases. However, the synthesis of anisotropic polymer particles is arduous, due to the lack of directional polymer growth mechanisms. In this work, non-cross-linked, hollow polymer microrods are developed from a dense block copolymer brush grown from the surface of micron-sized silica rods. The copolymer brush, comprising a hydrophobic inner block and a hydrophilic outer layer, is synthesized by surface-initiated atom transfer radical polymerization, and is exploited in the preparation of robust polymer rod particles in water, following etching of the inorganic core. The solvent-incompatible inner block is crucial for the synthesis of the rod-like polymer particles, in the absence of chemical cross-links, and the block copolymer composition affects the colloidal stability and flexibility of the hollow anisotropic colloids. For shorter hydrophobic block lengths, well-defined, yet flexible, hollow rods are obtained, whereas increasing the hydrophobic content of the copolymer results in rigid, tube-like particles. The approach is generic and could be easily employed to obtain polymer rod particles in any solvent medium, upon the appropriate selection of the solvent-incompatible inner block and the solvent-compatible outer block.

Self-organization of tip-functionalized elongated colloidal particles

Weakly attractive interactions between the tips of rodlike colloidal particles affect their liquid-crystal phase behavior due to a subtle interplay between enthalpy and entropy. Here we employ molecular dynamics simulations on semiflexible, repulsive bead-spring chains where one of the two end beads attract each other. We calculate the phase diagram as a function of both the volume fraction of the chains and the strength of the attractive potential. We identify a large number of phases that include isotropic, nematic, smectic-A, smectic-B, and crystalline states. For tip attraction energies lower than the thermal energy, our results are qualitatively consistent with experimental findings: We find that an increase of the attraction strength shifts the nematic to smectic-A phase transition to lower volume fractions, with only minor effect on the stability of the other phases. For sufficiently strong tip attraction, the nematic phase disappears completely, in addition leading to the destabilization of the isotropic phase. In order to better understand the underlying physics of these phenomena, we also investigate the clustering of the particles at their attractive tips and the effective molecular field experienced by the particles in the smectic-A phase. Based on these results, we argue that the clustering of the tips only affects the phase stability if lamellar structures ("micelles") are formed. We find that an increase of the attraction strength increases the degree of order in the layered phases. Interestingly, we also find evidence for the existence of an antiferroelectric smectic-A phase transition induced by the interaction between the tips. A simple Maier-Saupe-McMillan model confirms our findings.