Shape-Anisotropy-Induced Ordered Packings in Cylindrical Confinement

Orientational ordering and correlation in quasi-one-dimensional hard-body fluids due to close-packing degeneracy

We study the orientational ordering properties of some quasi-one-dimensional hard-body fluids, where the anisotropic particles are confined to a straight line, while they are free to rotate in a plane. We examine a class of models where the close-packing structure is degenerate, i.e., the highest possible density can be realized with different orientational ordering. We find that the close-packing degeneracy always gives rise to a diverging orientational correlation, which can be a marker of phase transition, glass formation, and jamming. In the case of isotropic or partially ordered phases at the close-packing density, the diverging orientational correlation indicates a tendency for being a strongly ordered nematic phase. However, the orientational divergence in the perfect nematic phase shows that the particles must rotate in concert to go from one closely packed structure to another.

Ordering properties of anisotropic hard bodies in one-dimensional channels

The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons-Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.

Chiral photonic crystals from sphere packing

Inspired by recent developments in self-assembled chiral nanostructures, we have explored the possibility of using spherical particles packed in cylinders as building blocks for chiral photonic crystals. In particular, we focused on an array of parallel cylinders arranged in a perfect triangular lattice, each containing an identical densest sphere packing structure. Despite the non-chirality of both the spheres and cylinders, the self-assembled system can exhibit chirality due to spontaneous symmetry breaking during the assembly process. We have investigated the circular dichroism effects of the system and have found that, for both perfect electric conductor and dielectric spheres, the system can display dual-polarization photonic band gaps for circularly polarized light at normal incidence along the axis of the helix. We have also examined how the polarization band gap size depends on the dielectric constant of the spheres and the packing fraction of the cylinders. Furthermore, we have explored the effects of non-ideality and found that the polarization gap persists even in the presence of imperfections and heterogeneity. Our study suggests that a cluster formed by spheres self-assembling inside parallel cylinders with appropriate material parameters can be a promising approach to creating chiral photonic crystals.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Shape-Mediated Oriented Assembly of Concave Nanoparticles under Cylindrical Confinement

This contribution describes the self-assembly of colloidal nanodumbbells (NDs) with tunable shapes within cylindrical channels. We present that the intrinsic concave geometry of NDs endows them with peculiar packing and interlocking behaviors, which, in conjunction with the adjustable confinement constraint, leads to a variety of superstructures such as tilted-ladder chains and crossed-chain superlattices. A mechanistic investigation, corroborated by geometric calculations, reveals that the phase behavior of NDs under strong confinement can be rationalized by the entropy-driven maximization of the packing efficiency. Based on the experimental results, an empirical phase diagram is generated, which could provide general guidance in the design of intended superstructures from NDs. This study provides essential insight into how the interplay between the particle shape and confinement conditions can be exploited to direct the orientationally ordered assembly of concave nanoparticles into unusual superlattices.

Densest packings from size segregation of particles in geometric confinement

A correlation between density maximization and size segregation for packings of polydisperse particles in geometric confinement has been discovered, through the derivation of a general solution for the densest-packed zigzag arrangements of polydisperse particles. This solution is a size-graded structure in which the larger a particle the closer it is located to either end of the system, such that the smaller particles in the interior are encapsulated by the larger ones away from it. Any pair of different-sized adjacent particles is a grain-boundary-like configuration that reduces the overall packing efficiency of the system, and this solution corresponds to a minimization of excess-volume contributions from grain-boundary-like configurations of different-sized particles as a result of the clustering of equal- or like-sized particles. Our findings provide new insights into how structural order of polydisperse particles emerges in confined settings.

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.

Entropy-Driven Unconventional Crystallization of Spherical Colloidal Nanocrystals Confined in Wide Cylinders

The densest packings of identical spherical colloidal nanocrystals in a thin cylinder generally give rise to confinement-induced chiral ordering. Here, we demonstrate that entropy can invalidate Pauling's packing rules for the nanocrystals confined in wide cylinders and novel ordered phases, where chiral ordering is broken, emerge. The nucleation and growth of spherical colloidal nanocrystals in the wide cylinders exhibit unique mechanisms which are distinctly different from that of thin ones. Furthermore, theoretical models which capture the essential physics of the ordering transitions are developed to reproduce the achiral ordering and reveal that the ordered phases are thermodynamically stable and stabilized through confinement-mediated entropic effect. These findings demonstrate that entropy arising from thermal motion can invalidate Pauling's packing rules of spherical colloidal nanocrystals confined in cylinders, which provides new insights into confinement physics of colloidal particles and might inspire nonintuitive design rules for the fabrication of novel ordered phases through confinement.

Curvature-assisted self-assembly of Brownian squares on cylindrical surfaces

HYPOTHESIS

We hypothesize that curved surfaces, including cylindrical surfaces, which go beyond prior experiments using flat surfaces, can significantly influence and alter the phase behavior and self-assembly of dense two-dimensional systems of Brownian colloids.

EXPERIMENTS

Here, we report a first experimental study regarding the self-assembly of Brownian square platelets with an edge length L = 2.3 μm on cylindrical surfaces having different curvatures; these platelets are subjected to a depletion attraction in order to form a monolayer above the cylindrical surface, yet have nearly hard interactions within the monolayer. Simulations are also performed to confirm and explain the experimental observations.

FINDINGS

Phase diagrams as a function of curvature are determined experimentally. Interestingly, hexagonal rotator crystal structures are observed for tubes having radii > 10.9L, but a tetratic phase is seen instead for the 10.9L tube at the corresponding platelet area fractions. We show that this transition is caused by the curvature-induced orientation-dependence of the depletion attraction between the squares and the underlying cylindrical surface. Brownian dynamics simulation results confirm the experimental observations and also illustrate helical structures formed by squares packing on cylinders. Our results demonstrate a way towards control over the self-assembly of anisotropic particles through curvature and depletion-attraction-induced orientational confinement.