Dynamic Simulation of the Packing of Ellipsoidal Particles

Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features

Boltzmann's H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann's H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling.

Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect

This study introduces a novel method for particle abrasion derived from fundamental natural phenomena and mechanical principles, allowing precise control over the degree of abrasion and more accurately mimicking natural processes. The method's validity is confirmed using a specific shape index. Through conventional triaxial tests, the mechanical behavior of granular aggregates with varying degrees of abrasion was analyzed. The findings indicate that increased particle abrasion leads to a decrease in the average coordination number and sliding amount, while the rotation amount increases. This suggests an inverse relationship between the degree of abrasion and the structural stability and interlocking of the particle aggregate. The fabric anisotropy of the system is mainly attributed to the anisotropy of the contact normal force, which decreases as particle abrasion increases. The partial stress ratio of the particle system is influenced by fabric anisotropy and remains independent of particle shape. Additionally, the internal friction angle may be overestimated in conventional triaxial tests.

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Probing Protein Corona Formation around Gold Nanoparticles: Effects of Surface Coating

There has been much interest in integrating various inorganic nanoparticles (nanoscale colloids) in biology and medicine. However, buildup of a protein corona around the nanoparticles in biological media, driven by nonspecific interactions, remains a major hurdle for the translation of nanomedicine into clinical applications. In this study, we investigate the interactions between gold nanoparticles and serum proteins using a series of dihydrolipoic acid (DHLA)-based ligands. We employed gel electrophoresis combined with UV-vis absorption and dynamic light scattering to correlate protein adsorption with the nature and size of the ligand used. For instance, we found that AuNPs capped with DHLA alone promote nonspecific protein adsorption. In comparison, capping AuNPs with polyethylene glycol- or zwitterion-appended DHLA essentially prevents corona formation, regardless of ligand charge and size. Our results highlight the crucial role of surface chemistry and core material in protein corona formation and offer valuable information for the design of colloidal nanomaterials for biological applications.

Random packing dynamics of [Formula: see text]-triplets

In this paper, we used a combination of DEM and the multi-sphere method to investigate the random packing dynamics of [Formula: see text]-triplets. These triplets consist of three overlapping primary spheres, forming a bent structure with a bond angle of [Formula: see text] and belonging to the [Formula: see text] symmetry group. The motivation for choosing such a structural arrangement is twofold: first, to understand how bent-shaped structures influence packing dynamics, and secondly, to investigate how mesoscopic or macroscopic particles possessing symmetry similar to that found in more elementary particles impact packing observables. To ensure non-overlapping particles at the beginning of the simulations, the confinement box was divided into basic cells. Each triplet was then inserted into a basic cell with a random orientation. After that, the system is allowed to settle under gravity toward the bottom of the box. An implicit leapfrog algorithm with quaternion acceleration was used to numerically integrate the rotational motion equations. Through a molecular approach, we consider the impact of long-range cohesive forces by employing a Lennard-Jones (LJ)-type potential. Packing processes are studied assuming different long-range interaction strengths. Different quantities are studied including packing density and orientation pair correlation function. In addition, the force probability distributions in the random packing structures have been analyzed.

Dense packings of geodesic hard ellipses on a sphere

Packing problems are abundant in nature and have been researched thoroughly both experimentally and in numerical models. In particular, packings of anisotropic, elliptical particles often emerge in models of liquid crystals, colloids, and granular and jammed matter. While most theoretical studies on anisotropic particles have thus far dealt with packings in Euclidean geometry, there are many experimental systems where anisotropically-shaped particles are confined to a curved surface, such as Pickering emulsions stabilized by ellipsoidal particles or protein adsorbates on lipid vesicles. Here, we study random close packing configurations in a two-dimensional model of spherical geodesic ellipses. We focus on the interplay between finite-size effects and curvature that is most prominent at smaller system sizes. We demonstrate that on a spherical surface, monodisperse ellipse packings are inherently disordered, with a non-monotonic dependence of both their packing fraction and the mean contact number on the ellipse aspect ratio, as has also been observed in packings of ellipsoids in both 2D and 3D flat space. We also point out some fundamental differences with previous Euclidean studies and discuss the effects of curvature on our results. Importantly, we show that the underlying spherical surface introduces frustration and results in disordered packing configurations even in systems of monodispersed particles, in contrast to the 2D Euclidean case of ellipse packing. This demonstrates that closed curved surfaces can be effective at introducing disorder in a system and could facilitate the study of monodispersed random packings.

Jamming of Nano-Ellipsoids in a Microsphere: A Quantitative Analysis of Packing Fraction by Small-Angle Scattering

The packing of particles is ubiquitous, and it is of fundamental importance, particularly in materials science in the nanometric length scale. It becomes more intriguing when constituent particles deviate from spherical symmetry owing to the inherent complexity in quantifying their positional and rotational correlation. For quantitative estimation of packing fraction, it requires a thorough analysis of the positional correlation of jammed particles. This article adopts a novel approach for determination of the packing fraction of strongly correlated nano-ellipsoids in a microsphere using small-angle scattering. The method has been elucidated through a quantitative analysis of structural correlation of nano-hematite ellipsoids in 3D micrometric granules, which are realized using rapid evaporative assembly. Owing to the deviation from spherical symmetry, the conventional analysis of scattering data fails to interpret the actual packing fraction of the anisotropic particles. The structural correlation gets smeared out because of orientation distribution among the packed anisotropic particles, which leads to an anomaly in the estimation of packing fraction using the conventional analysis approach. It is illustrated that consideration of an interparticle distance distribution function of the correlated nano-ellipsoids becomes indispensable in determining their packing fraction.

A kinematics-based model for the settling of gravity-driven arbitrary-shaped particles on a surface

A discrete model is proposed for settling of an arbitrary-shaped particle onto a flat surface under the gravitational field. In this method, the particle dynamics is calculated such that (a) the particle does not create an overlap with the wall and (b) reaches a realistic equilibrium state, which are not guaranteed in the conventional discrete element methods that add a repulsive force (torque) based on the amount of overlap between the particle and the wall. Instead, upon the detection of collision, the particle’s kinematics is modified depending on the type of contact, i.e., point, line, and surface types, by assuming the contact point/line as the instantaneous center/line of rotation for calculating the rigid body dynamics. Two different stability conditions are implemented by comparing the location of the projection of the center of mass on the wall along gravity direction against the contact points to identify the equilibrium (stable) state on the wall for particles with multiple contact points. A variety of simulations are presented, including smooth surface particles (ellipsoids), regular particles with sharp edges (cylinders and pyramids) and irregular-shaped particles, to show that the method can provide the analytically-known equilibrium state.

Vibration induced segregation of single large particles

The vibration-induced segregation (e.g., rising of one large intruder - so called Brazil Nut Effect (BNE)) is studied by discrete element method. Vibration frequency and amplitude are two dominating factors in the occurrence of BNE and a phase diagram is constructed. For fixed vibration amplitude, segregation only occurs when vibration frequency is within a certain range. Larger vibration amplitude can expand the range of vibration frequency for BNE. Size ratio and the intruder shape are studied under certain vibration conditions. Larger size ratio can enlarge the segregation intensity. The shape of the intruder influences the segregation process by the intruder′s orientation. Standing-like initial orientation can increase the time required for the intruder to reach the top while lying-like initial orientation cannot significantly affect the vertical segregation.

Granular flow of cylinder-like particles in a cylindrical hopper under external pressure based on DEM simulations

Granular flow is widely found in nature or industrial production. Although the external driving force significantly affects the dynamic behavior of a granular system, a large number of numerical simulations have been conducted to study granular flows driven by gravity. In this study, a superquadric equation was used to construct spherical and cylindrical elements, and the flow processes of granular materials under external pressure were simulated by the discrete element method. To examine the validity of the DEM model, the Janssen effect of spherical particles, the static packing of cylindrical particles and the flow process of spherical particles under external pressure are simulated and compared with the previous experimental and theoretical results. Subsequently, the effects of blockiness, orifice diameter, and particle friction on the flow characteristics are investigated. Results show that the flow rate of spherical particles increases as the external pressure and opening diameter increase or the particle friction decreases. However, the flow rate of cylindrical particles decreases as the blockiness parameter increases, and the external pressure has little effect on the flow rate of the cylindrical particles when the blockiness parameter is greater than 4. Furthermore, the external pressure causes a change in the flow pattern of granular systems. In a gravity-driven granular flow, cylindrical particles appear in funnel flow, and spherical particles in both mass and funnel flows. In a pressure-driven granular flow, spherical particles appear in mass flow, and cylindrical particles in both mass and funnel flows. The critical height of the transition between mass and funnel flows decreases with increasing external pressure and eventually reaches a steady state. Meanwhile, the critical height increases with the blockiness parameter, which indicates that more cylindrical than spherical particles appear in funnel flow. Finally, the basic flow characteristics of granular materials under external pressure are further analyzed by the velocity uniformity index, the normal contact force between particles, and the bottom pressure. Overall, the numerical results are useful for understanding the changes in the flow characteristics of spherical and cylindrical granular materials under external pressure, and further provide guidance for the appropriate design and optimization of cylindrical hoppers.