Self-assembling of dry and cohesive non-Brownian spheres

Structural evolution of granular cubes packing during shear-induced ordering

Packings of granular particles may transform into ordered structures under external agitation, which is a special type of out-of-equilibrium self-assembly. Here, evolution of the internal packing structures of granular cubes under cyclic rotating shearing has been analyzed using magnetic resonance imaging techniques. Various order parameters, different types of contacts and clusters composed of face-contacting cubes, as well as the free volume regions in which each cube can move freely have been analyzed systematically to quantify the ordering process and the underlying mechanism of this granular self-assembly. The compaction process is featured by a first rapid formation of orientationally ordered local structures with faceted contacts, followed by further densification driven by free-volume maximization with an almost saturated degree of order. The ordered structures are strongly anisotropic with contacting ordered layers in the vertical direction while remaining liquid-like in the horizontal directions. Therefore, the constraint of mechanical stability for granular packings and the thermodynamic principle of entropy maximization are both effective in this system, which we propose can be reconciled by considering different depths of supercooling associated with various degrees of freedom.

Granular ionic crystals in a small nutshell

Ordered two-dimensional arrangements of triboelectrically oppositely charged granular particles have been reported several times, but observations of bulk ordered binary granular particle packings are singular. We attribute this suppression of triboelectrically induced order to the concurrent behaviour of granular particles to pack densest due to gravity. We show that triboelectrically induced order robustly emerges in a container that does not allow for crystallization into a dense packing under gravity. It turns out that the triboelectrically ordered structure follows Pauling's predictions for atomic ionic crystals in many aspects, but also exhibits systematic deviations. We discuss how the emergence of order in an incommensurate container, the deviations from Pauling's predictions and the gravitational potential energy of the particles are connected.

Bimodal self-assembly of granular spheres under vertical vibration

As granular particles in a packing are athermal, their self-assembly has to be realized with the input of energy via walls. But different manners of energy input, e.g., through tapping or shearing walls, have not been discriminated previously. We address this problem in the self-assembly of identical granular spheres in prism-like containers subjected to one-dimensional (1D) vertical vibration by numerical simulations. The edge lengths or diameter of the containers are the integer multiples of the particle diameter. When energy is input with the vibration, the particles can self-assemble into mainly mixed FCC (face-centred-cubic) and HCP (hexagonal-close-packed) structures from the bottom wall and/or the side walls. According to different movements of the walls, the shear-induced and tap-induced self-assemblies are distinguished. These two self-assembly modes can emerge solely or simultaneously, with different but overlapping regions in the vibration amplitude and frequency phase diagram. The structures of the self-assembly from the two modes also present different features, suggesting different formation mechanisms. Moreover, it is found that the close-packed planes of the ordered clusters formed from different walls are often misaligned, leading to conflicts in the self-assembly of the whole system. These findings are helpful for both the understanding and controlling of the self-assembly of granular particles and other similar athermal and low-thermal systems.

DEM simulation of the local ordering of tetrahedral granular matter

The formation and growth of local order clusters in a tetrahedral granular assembly driven by 3D mechanical vibration were captured in DEM (discrete element method) dynamic simulation using a multi-sphere model. Two important kinds of clusters, dimer and wagon wheel structures, were observed based on which the growth behavior and mechanism of each local cluster with different orientations/structures were investigated. The results show that during vibration, dimer clusters are formed first and then most of them grow into linear trimers and tetramers. Wagon wheel clusters are also frequently observed that grow into hexamers and, further, octamer and nonamer local clusters. Coordination number (CN) evolution indicates that the decrease of local mean CN can be regarded as the signal for the formation of local clusters in the tetrahedral particle packing system. Nematic order metric analysis shows that although the two basic structures (dimer and wagon wheel structures) grow into complex local clusters during packing densification, these local clusters are randomly distributed in the tetrahedral particle packing system. Stress analysis indicates that the dimer-based local clusters are mostly formed in the compaction state of the tetrahedral particle packing system during the vibrated packing densification process. In comparison, the wagon wheel-based local clusters need much stronger interaction forces from tetrahedral particles during vibrated packing densification.

Self-assembly of granular spheres under one-dimensional vibration

The self-assembly of uniform granular spheres is related to the fundamentals of granular matter such as the transitions of phases, order/disorder and jamming states. This paper presents a DEM (discrete element method) study of the continuous self-assembly of uniform granular spheres from random close packing (RCP) to partially and nearly fully ordered packings under one-dimensional (1D) sinusoidal vibration without other interventions. The effects of the vibration amplitude and frequency are investigated in a wide range. The structures of the packings are characterized in terms of packing fraction and other microscopic structural parameters, including the coordination number, bond-orientational orders, and, in particular, ordered clusters, by adaptive common neighbor analysis (a-CNA). It is shown that 1D vibrations can also lead to the self-assembly of uniform granular spheres with packing fractions exceeding the RCP limit, and FCC (face centered cubic) and HCP (hexagonal close packed) structures coexist in the self-assembled packings while their total fraction can reach nearly 100%. The structures of these packings can be better correlated with the vibration velocity amplitude rather than the commonly used vibration intensity. The dynamics of such self-assembly is also preliminarily analyzed. Our study not only presents the conditions for the self-assembly of uniform granular spheres under 1D vibration, but also characterizes the order-disorder transitions during the process, which can improve our understanding of the fundamentals of granular materials and jamming states.

Reversible Self-Assembly (fcc-bct) Crystallization of Confined Granular Spheres via a Shear Dimensionality Mechanism

By combining vibrational annealing and shear dimensionality, we experimentally show (1) a fast reversible crystallization fcc-bct (face-centered cubic-body-centered tetragonal) in a granular system that is composed of dissipative millimeter-sized dry spheres, (2) a two-dimensional (planar) shear promotes self-assembly into an fcc crystal, while one-dimensional shear produces a bct crystal, and (3) in analogy with heterogeneous nucleation, a granular temperature gradient leads to the formation of crystal domains showing competition of polymorphic phases in the cold regions. Our findings suggest that controlling the directionality of the interactions steers to reversible crystallization of hard spheres, adds clues for theoretical studies, and provides a novel mechanism for the technological development of the applications of self-assembling phononic crystals.

Dynamic self-assembly of non-Brownian spheres studied by molecular dynamics simulations

Granular self-assembly of confined non-Brownian spheres under gravity is studied by molecular dynamics simulations. Starting from a disordered phase, dry or cohesive spheres organize, by vibrational annealing, into body-centered-tetragonal or face-centered-cubic structures, respectively. During the self-assembling process, isothermal and isodense points are observed. The existence of such points indicates that both granular temperature and packing fraction undergo an inversion process that may be in the core of crystal nucleation. Around the isothermal point, a sudden growth of granular clusters having the maximum coordination number takes place, indicating the outcome of a first-order phase transition. We propose a heuristic equation that successfully describes the dynamic evolution of the local packing fraction in terms of the local granular temperature, along the entire crystallization process.

Scaling up self-assembly: bottom-up approaches to macroscopic particle organization

This review presents an overview of recent work in the field of non-Brownian particle self-assembly. Compared to nanoparticles that naturally self-assemble due to Brownian motion, larger, non-Brownian particles (d > 6 μm) are less prone to autonomously organize into crystalline arrays. The tendency for particle systems to experience immobilization and kinetic arrest grows with particle radius. In order to overcome this kinetic limitation, some type of external driver must be applied to act as an artificial "thermalizing force" upon non-Brownian particles, inducing particle motion and subsequent crystallization. Many groups have explored the use of various agitation methods to overcome the natural barriers preventing self-assembly to which non-Brownian particles are susceptible. The ability to create materials from a bottom-up approach with these characteristics would allow for precise control over their pore structure (size and distribution) and surface properties (topography, functionalization and area), resulting in improved regulation of key characteristics such as mechanical strength, diffusive properties, and possibly even photonic properties. This review will highlight these approaches, as well as discuss the potential impact of bottom-up macroscale particle assembly. The applications of such technology range from customizable and autonomously self-assembled niche microenvironments for drug delivery and tissue engineering to new acoustic dampening, battery, and filtration materials, among others. Additionally, crystals made from non-Brownian particles resemble naturally derived materials such as opals, zeolites, and biological tissue (i.e. bone, cartilage and lung), due to their high surface area, pore distribution, and tunable (multilevel) hierarchy.

Nucleation, aggregation, annealing, and disintegration of granular clusters

The processes of nucleation, aggregation, annealing, and disintegration of clusters of non-Brownian paramagnetic beads in a vibrofluidized system are experimentally investigated. The interaction among the beads is induced by a magnetic seed composed of two dipoles allocated outside the container cell. We observe a clearly differentiated nucleation stage, whose evolution (nucleation time versus acceleration strength) follows a power law. Thereafter, the beads aggregate forming 2D disordered clusters around the nucleus. Both processes (nucleation and aggregation) are determined by the competition between magnetic forces and the drag produced by a thermal bath created by glass particles. Once the agglomerates reach a final state (shape and length), they are annealed by increasing and decreasing the granular temperature. We found that the fractal dimension and the lacunarity index clearly describe the structural variations of the clusters. Our discussion on this phenomenon is addressed, making a rough analogy with the glass transition in a super-cooled liquid. Finally, we study the disintegration of the clusters as a function of time and the density of the surrounding gas. The question is not if, but how they disintegrate upon removing the external field; we find that the disintegration follows an exponential decay.

Free-energy landscapes of granular clusters grown by magnetic interaction

We experimentally study the aggregation of small clusters made of non-Brownian dipolar beads in a vibro-fluidized system. The particles are paramagnetic spheres that add around a fixed magnetic seed inside a granular gas of glass beads. We observe that under appropriate physical conditions symmetric and asymmetric cluster configurations are created and, as the number of particles increases, the aggregation time obeys a power law. We use an ensemble statistics to evaluate the free-energies and entropies landscapes of the granular clusters. The correspondence between such landscapes shows that, even if the system is of macroscopic scale and not in strict equilibrium, our approach to understand the relationship between the cluster structures and the interactions that create them is reliable.

Microstructure evolution in density relaxation by tapping

The density relaxation phenomenon is modeled using both Monte Carlo and discrete element simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the existence of a critical tap intensity which produces a maximum bulk solids fraction. We find that the mechanism responsible for the relaxation phenomenon is an evolving ordered packing structure propagating upwards from the plane floor.

Superheating in granular matter

Some materials remain solids even if they are heated beyond the temperature of their melting points. In condensed matter physics, this rare phenomenon is called superheating. Here we report the analogous phenomenon in granular matter: a strongly vibrated monolayer that instead of being a gas persists as a crystal for some time. Eventually, it spontaneously evaporates. We found that the system has thermodynamiclike features like coexistence and metastability. We show how the observed metastable phase is linked to energy dissipation.