Particle Geometry Research Articles

3D polycatenated architected materials.

Architected materials derive their properties from the geometric arrangement of their internal structural elements. Their designs rely on continuous networks of members to control the global mechanical behavior of the bulk. In this study, we introduce a class of materials that consist of discrete concatenated rings or cage particles interlocked in three-dimensional networks, forming polycatenated architected materials (PAMs). We propose a general design framework that translates arbitrary crystalline networks into particle concatenations and geometries. In response to small external loads, PAMs behave like non-Newtonian fluids, showing both shear-thinning and shear-thickening responses, which can be controlled by their catenation topologies. At larger strains, PAMs behave like lattices and foams, with a nonlinear stress-strain relation. At microscale, we demonstrate that PAMs can change their shapes in response to applied electrostatic charges. The distinctive properties of PAMs pave the path for developing stimuli-responsive materials, energy-absorbing systems, and morphing architectures.

Nanoparticle adhesion at liquid interfaces.

Nanoparticle adhesion at liquid interfaces plays an important role in drug delivery, dust removal, the adsorption of aerosols, and controlled self-assembly. However, quantitative measurements of capillary interactions at the nanoscale are challenging, with most existing results at the micrometre to millimetre scale. Here, we combine atomic force microscopy (AFM) and computational simulations to investigate the adhesion and removal of nanoparticles from liquid interfaces as a function of the particles' geometry and wettability. Experimentally, AFM tips with controlled conical geometries are used to mimic the nano-asperities on natural nanoparticles interacting with silicone oil, a model liquid for many engineering applications including liquid-infused surfaces. Computationally, continuum modelling with the Surface Evolver software allows us to visualise the interface configuration and predict the expected force profile from energy minimisation. Quantitative agreement between the experimental measurements and the computational simulations validates the use of continuum thermodynamics concepts down to the nanoscale. We demonstrate that the adhesion of the nanoparticles is primarily controlled by surface tension, with minimum line tension contribution. The particle geometry is the main factor affecting the length of the capillary bridge before rupture. Both the particle geometry and liquid contact angle determine the shape of the adhesion force profile upon removal of the particle from the interface. We further extend our simulations to explore more complex geometries, rationalising the results from experiments with imperfect AFM tips. Our results could help towards the design of smart interfaces, for example, able to attract or repel specific particles based on their shape and chemistry.

Impacts of particle geometry on the characteristics of porous materials

Impacts of particle geometry on the characteristics of porous materials

Unit Load of Abrasive Grains in the Machining Zone During Microfinishing with Abrasive Films.

This work investigates the contact between abrasive particles and workpieces in microfinishing processes with special consideration given to the determination of unit force, unit pressure, and grain, the forces exerted by individual abrasive grains. A detailed methodology was established for measuring the contact area, penetration depth, and circumferences of grain imprints at depths corresponding to multiples of the total height of the abrasive film, represented by the parameter Sz. The following depths were analyzed: 0.05 Sz, 0.15 Sz, 0.25 Sz, and 0.35 Sz. Results show that the areas closer to the central microfinishing zone bear the highest unit pressures and forces and, thus, contribute dominantly to material removal. It was further found that near the edges of the contact zone, the pressure and force have been reduced to lower material removal efficiency. The non-uniform geometry of abrasive particles was found to significantly affect contact mechanics, more at shallow depths of penetration, whereas the shape of the apex defines the nature of the interaction. A parabolic force and pressure distribution were evident for the irregular load distribution of the microfinishing area. The result brings out the need for further refinement in the design of the abrasive film and pressure distribution in order to achieve improvement in uniformity and efficiency during microfinishing. It would bring out valuable insights on how to improve the effectiveness of an abrasive film and ways of optimizing the process conditions. The results provide a founding stone for further advancement of knowledge in the grain-workpiece interaction, enabling better surface quality and more reliable microfinishing processes.

Regulating socketed geometry of nanoparticles on perovskite oxide supports for enhanced stability in oxidation reactions.

Heterogeneous catalysts with highly dispersed active particles on supports often face stability challenges during high-temperature industrial applications. The ex-solution strategy, which involves in situ extrusion of metals to form socketed particles, shows potential for addressing this stability issue. However, a deeper understanding of the relationship between the socketed geometry of these partially embedded nanoparticles and their catalytic performance is still lacking. Here, in situ transmission electron microscopy and theoretical calculations are utilized to investigate the oxygen-induced ex-solution process of Pd-doped LaAlO3 with varying concentrations of La vacancies (LaxAl0.9Pd0.1O3-δ). We find that the socketed geometry of Pd-based particles can be tuned by manipulating the levels of La deficiencies in the oxide support, which in turn influences the catalytic performance in high-temperature oxidation reactions. As for the socketed particles, the balance between particle size and outcrop height is crucial for determining the oxidation activity and sinter-resistance behavior. Consequently, the optimized catalyst, La0.8Al0.9Pd0.1O3-δ, exhibits superior catalytic performances, particularly high stability (still working after aging at 1000 °C for 50 h) and water resistance in various combustion reactions (e.g., CH4 oxidation and C3H8 oxidation).

Differentiating PGM Ostwald Ripening from Catalyst Degradation Using Identical Location TEM and Controlled Potential Cycling

Nanoscale Platinum group metals (PGMs) over conductive supports with large specific area have been widely used as highly efficient catalysts for various reactions, including oxygen reduction reaction (ORR) (for fuel cells) and oxygen evolution reactions (OER) (for water electrolyers). However, these PGM nanoparticles (NPs) usually suffer from significant performance degradation over prolonged operation, primarily attributed to catalyst degradation, which remains a long-standing challenge. Two principal mechanisms, Ostwald ripening and particle migration, contribute to this degradation. Ostwald ripening is a process involves the first dissolution of smaller PGM NPs into PGM ions, followed by their diffusion and redeposition onto the surfaces of larger NP, where the driven force is surface energy. Particle migration, on the other hand, is a process of movement of PGM NPs leading to the formation of large agglomerates due to the weak interactions between NPs and supports. In general, both processes occurred simultaneously during catalyst degradation in the fuel cell/electrolyzer operation. However, addressing the PGM catalyst degradations caused by these mechanisms requires completely different strategies: enhancing intrinsic catalyst stability for overcoming Ostwald ripening and improving interactions between PGM NPs and supports for reducing particle migration. Hence, it is critically required to quantitatively differentiate between these two mechanisms during catalyst degradation. Here, we propose an innovative approach to distinguish the two mechanisms utilizing Identical Location Transmission Electron Microscope (IL-TEM) coupled with carefully designed experiments. Specifically, the IL-TEM grids with dispersed PGM catalysts, such as TKK 46%Pt/Kejten Black EC-300, would be imaged to characterized the particle geometry, size and interparticle distance of PGM NPs on before and after accelerated stress test (AST) for various cycles (i.e. 0, 5000, 10,000, 30,000 cycles, etc.) within an electrochemical cell. These PGM catalysts will undergo AST cycling among two potential regions: (1) 0.2 ~ 0.6V (vs. standard hydrogen electrode (SHE)) and (2) 0.6 ~ 0.95V (vs. SHE). PGM particles cycled within the potential region (1) should exhibit only particle migration, since potential below 0.6 V do not cause any oxidation of PGM, while those cycled within potential region (2) would experience both Ostwald ripening and particle migration. By comparing changes in particle geometry, size and interparticle distance for PGM NPs subjected to cycling within different potential regions, we could quantitively determine the contributive effect of each mechanism on the catalyst degradation. This study will shed the light on differentiation of these two different mechanisms and provide guidance for the design of highly active and stable PGM catalysts.

Modeling of laser beam absorption on rough surfaces, powder beds and sparse powder layers

The energy transfer from a laser beam source to material surfaces with arbitrary geometrical features and variable surface roughness is the crucial step in many high-end engineering applications. We propose two models capable of predicting this energy transfer, applicable in different scenarios. The first is a high-fidelity numerical framework for the simulation of laser beam interaction with rough surfaces, which includes meshed geometry of arbitrary shape and material Lagrangian particles. The method discretizes the laser source as a collection of photon-type immaterial Lagrangian particles (Discrete Element Method) and is able to capture the effects of multiple reflections, angle-dependent reflectivity, and polarization change. Simulations were performed on a geometry reconstructed from a rough copper sample to reveal the impact of the polarization effects. This method is generally applicable to any surface where the effects of inelastic light scattering are not expected to play a significant role. The second model is a novel phenomenological correlation specifically designed to predict the effective reflectivity of sparse powder layers, which occur for example when metal vapor is recondensed and redeposited on the substrate during laser welding. The correlation is compared to the predictions obtained from the simulation framework and has been favorably compared to experimental data in a separate publication.

Shape parameter of Weibull size statistics is a potential indicator of filler geometry in SiO2 reinforced polymer composites

In a previous study [Physica A, 625 (2023), 129026], a relationship between the filler size distribution and the filler geometry of SiO2 particle reinforced polymer composites has been reported. It has been experimentally demonstrated that the size of hollow and solid SiO2 particles disperse in polymer matrix follows Weibull statistics with shape parameter at 2 and 3, respectively. This mechanism has not yet been verified in the one-dimensional (1D) case. In this paper, we study the length distribution of glass fibers in polymer composites. Our results show that the previous theory still holds for the 1D case. Thus, shape parameter of Weibull size statistics could be a potential indicator of filler geometry in SiO2 reinforced polymer composites. This interesting mechanism can be explained by the scaling nature behind the Weibull statistics. Our study has thus shed new light on the evolution of filler geometry during the fabrication process of polymer composites, and should be useful for the related fields.

Effect of non-additive mixing on entropic bonding strength and phase behavior of binary nanocrystal superlattices.

Non-additive mixing plays a key role in the properties of molecular fluids and solids. In this work, the potential for athermal order-disorder phase transitions is explored in non-additive binary colloidal nanoparticles that form substitutionally ordered compounds, namely, for equimolar mixtures of octahedra + spheres, which form a CsCl lattice compound, and cubes + spheres, which form a NaCl crystal. Monte Carlo simulations that target phase coexistence conditions were used to examine the effect on compound formation of varying degrees of negative non-additivity created by component size asymmetry and by size-tunable indentations in the polyhedra's facets, intended to allow the nestling of neighboring spheres. Our results indicate that the stabilization of the compound crystal requires a relatively large degree of negative non-additivity, which depends on particle geometry and the packing of the relevant phases. It is found that negative non-additivity can be achieved in mixtures of large spheres and small cubes having no indentations and lead to the athermal crystallization of the NaCl lattice. For similarly sized components, athermal congruent transitions are attainable and non-additivity can be generated through indentations, especially for the cubes + spheres system. Increasing indentation leads to lower phase coexistence free energy and pressure in the cubes + spheres system but has the opposite effect in the octahedra + spheres system. These results indicate a stronger stabilizing effect on the athermal compound phase by the cubes' indentations, where a deeper nestling of the spheres leads to a denser compound phase and a larger reduction in the associated pressure-volume free-energy term.

Phenotypic Trait of Painting Cracks

ABSTRACT A painting, like human skin, develops cracks on the surface as it dries and ages. The painting cracks, also known as craquelure, are often considered analogous to human fingerprints; these have been regarded as a unique signature reflective of the painting’s characteristics and are important in art authentication. Intriguingly, studies in other fields, such as geology, have observed the presence of distinctive characteristics in soil desiccation cracks. These cracks exhibit self-similarity, forming patterns that suggest broader geological processes at work. In light of this connection, the primary objective of this study is to investigate whether the painting cracks also exhibit a self-similar nature. By delving into this, we seek to shed light on the underlying properties of the painting cracks. This study also aims to investigate whether the characteristic self-similar trait of the cracks can serve as an identifier in relation to the provenances of the paintings. To this end, this study adopts the methodology originally designed to characterize the phenotypic traits of 3D particle geometries in granular materials research. This study develops a 2D equivalent concept, focusing on the phenotypic traits of the individual islands enclosed by cracks within paintings. The results successfully demonstrate that the phenotypic trait of painting cracks exhibits a self-similar nature, which can reveal characteristics associated with the provenances of paintings. The findings will offer valuable insights into the scientific examination of artworks based on painting cracks.

Impact analysis of particle sphericity on the properties of porous materials via particle packing method for hydrogen fuel and electrolysis cells

This study focuses on the impacts of particle's sphericity on the properties of porous materials crucial to electrochemical devices. Three-dimensional structures with spherical and cylindrical particles were generated to simulate porous granular and fibrous materials. The constructed particle geometries are as follows: a sphere and cylinders with different aspect ratios (height-to-diameter) of 0.1, 0.5, 1.0, 2.5, 5.0, 10, and 20. Every model exhibits a porosity of 0.500 ± 0.001 to exclude the effects of porosity. The structures were binarized with 200×200×200 dimensionless voxels, which were analyzed with the specific surface area, grain and pore size distributions, geometrical tortuosity, conductivity, and diffusivity across the through- and in-planes. As a result, the particle geometry significantly impacts on tortuosity, conductivity, and diffusivity, with the absolute value of Spearman's correlation coefficient of up to 1. It may imply the necessity to consider particle geometry as an ex-situ characterization for better electrochemical performance.

Geometry Dependent Microwave Absorption Properties in Carbonaceous Materials over X-Band Frequencies (8.2-12.4 GHz) for Stealth Applications

: Carbonaceous materials of two different types, viz. spherical nano carbon black (NCB) powder (Brunauer-Emmett-Teller (BET) surface area ~1400 m2/g) and multiwalled carbon nanotube (MWCNT) (BET surface area ~75 m2/g), have been impregnated in room temperature vulcanized (RTV) silicon rubber matrix to study the effect of geometries of filler particles on microwave absorption characteristics, over X-band frequencies (8.2 -12.4 GHz). The rubber-based composites are prepared by dispersion of NCB and MWCNT fillers in the liquid rubber with loading fractions ranging from 0.3-0.9 wt% and 1.1-1.7 wt%, respectively. The dielectric loss tangent (tanδe) profiles were evaluated for the filler-loaded rubber composites at different concentrations. The calculated Reflection loss (RL) profiles suggest that NCB-based rubber provides maximum RL value, (RL)max ~ -20 dB (99.00 % absorption), at a lower filler concentration of 0.5 wt%, as compared to MWCNT. However, the MWCNT-based rubber composite shows enhanced (RL)min values of ~ -29 dB (~99.99% absorption) due to multiple scattering phenomena. The identified NCB and MWCNT-based rubber-based MW absorbers have potential stealth applications for military aerial vehicles.

Effect of isotropy and anisotropy: toward understanding the fracture behavior of magnetoactive elastomers

Magnetoactive elastomers (MAEs) exhibit magneto-mechanical coupling and typically contain micron-sized spherical ferromagnetic particles embedded in an elastomeric matrix. Anisotropic particle arrangement in MAEs, achieved by curing the material in a magnetic field, offers tailored and enhanced magneto-mechanical coupling compared to isotropic configurations. While tunable MAE properties such as the effective modulus and vibrational response have been relatively well studied, a thorough understanding of their fracture mechanisms, particularly in MAEs with microstructural anisotropy or composites with similar structures remains almost completely unexplored. Here, we characterize the fracture mechanisms of anisotropic and isotropic unmagnetized MAEs using experiments and simulations, focusing on the effects of spherical particles in anisotropic chain-like configurations. Specifically, we experimentally measure the fracture toughness of MAEs containing different volume fractions of particles, and with particles arranged both randomly and aligned at 0°, 45°, and 90° to the loading direction. Results show that anisotropic MAEs with particle chains aligned with the load direction can improve fracture toughness by up to almost 600%, whereas isotropic MAEs increase the fracture toughness by only 420%, compared to the pure elastomer. Scanning electron microscopy of the post-fractured surface reveals toughening mechanisms at micro-scale, such as chain waviness, particle agglomeration, and particle distribution. Simulations using a finite element method-based decoupled phase field-cohesive zone model on simplified geometries qualitatively support imaging interpretations. Overall, this work explains how internal geometry, including waviness in particle chains, chain alignment, and particle agglomerations affects fracture of MAEs and generally soft composites with chain-like geometries of spherical particles. These results have engineering applications in improving fracture properties of smart soft composites relevant to soft robotics, tunable vibration absorbers, and noise attenuators.

Determining the Soil Particle Shape by Use of Dynamic Image Analysis

In Soil Science, it is well established that the geometry of individual soil particles, including their shape and size, has a significant impact on a number of key physical properties of the soil and on the processes involved with it. The shape and size of soil particles directly impact aspects such as permeability, water retention, stability of soil aggregates and the availability of nutrients for plants. Therefore, accurate determination of these characteristics of soil particles becomes extremely important for understanding and effective soil management. Nowadays, dynamic image analysis (DIA) is emerging as an exceptionally versatile and effective technique that enables precise determination of particle characteristics, including shape and size, in a dynamic and non-invasive manner. DIA enables the automatic analysis of thousands of microscopic images, allowing rapid and accurate study of the morphology of soil particles at micro and macro scales. The use of dynamic image analysis in soil research provides insight into the complex structures of soil particles and better prediction of their impact on various soil processes. Moreover, DIA enables the examination of a large number of samples in a short time, which contributes to the efficiency and precision of soil testing. Therefore, dynamic image analysis is becoming a widely used technique for determining particles' characteristics, such as shape and size. In the context of an ever-increasing awareness of the sustainable use of natural resources and the need to optimize agricultural and engineering practices, dynamic image analysis is becoming an indispensable tool for soil scientists, environmental scientists and engineers. Its versatile use can contribute to further expanding our knowledge about soil and developing innovative solutions for sustainable soil and environmental management.

Surgical dissection of ignition behavior of aluminum nanoparticles using molecular dynamics

Aluminum nanoparticles (ANPs) show great promise in energy technology, yet their atomic behavior during ignition remains a puzzle. This study provides insights into atomic migration processes within ANPs of different chemical layers during ignition and combustion, inspired by surgical peeling techniques. The research reveals that cavity formation in ANPs is inevitable due to disparities in atomic migration rates between core and surface areas, with core aluminum atoms experiencing sudden and significant stress alterations crucial for cavity formation. A linear trend in atom counts across radial layers correlates with particle geometry, influencing reactivity and morphological changes. The proposed Bond Environment Change (BEC) analysis reveals that oxygen atoms in the ANP shell undergo a three-phase evolution: intensive bonding, gradual relaxation, and stable configuration, reflecting the dynamic transformation of the oxide layer during the reaction process. While this research provides a deeper understanding of ANP ignition and combustion mechanisms, it may serve as a reference for refining ANP synthesis and guiding further inquiries in the field of nanoparticle-based energy technologies.

Pore Network Modeling of Intraparticle Transport Phenomena Accompanied by Chemical Reactions.

In this work, a 3D pore network model (PNM) is introduced for modeling reaction-diffusion phenomena, with and without coupled heat transfer, in a spherical porous catalyst particle. The particle geometry is generated by packing thousands of microspheres inside a large sphere to represent the 3D geometry, porosity, and tortuosity of a spherical catalyst particle. A pore-network representation is extracted from this geometry, and a PNM for diffusion-reaction and heat conduction is constructed. This newly proposed particle-scale PNM allows for the application of realistic 3D nonuniform boundary conditions on the particle's surface, which is commonly encountered in slender packed-bed reactors. Concentration profiles inside the particle, and effectiveness of the reactions, is analyzed.

Numerical model of asphaltene deposition in vertical wellbores: Considerations of particle shape and drag force

Asphaltene deposition and plugging are common phenomena during crude oil production, significantly reducing production efficiency. Understanding the deposition behavior of asphaltene particles in vertical wellbores, particularly in relation to drag force interactions and settlement velocity, is imperative to mitigate these issues. Existing empirical models often fail due to their inherent inaccuracies and neglect of asphaltene particles' irregular shapes. This work established a quantitative method to describe irregular geometries of asphaltene particles. Shape coefficient, ∅, and shape coefficient influence factor, θ, are used to assess the impact of particle shape on the drag force coefficient and settling velocity. Experimental results from sedimentation experiments reveal particles with smaller shape coefficients encounter greater flow resistance and higher drag force coefficients. Moreover, the impact of shape coefficient on the drag coefficient gradually decreases as the Reynolds number increases. Based on these experimental findings, distinct models for the drag force coefficient and settling velocity of asphaltene particles are established, achieving a reduction in average error ranging between 2 % ∼ 25 % compared to existing models.

Engineering stress as a motivation for filamentous virus morphology

Many viruses are pleomorphic in shape and size, with pleomorphism often thought to correlate with infectivity, pathogenicity, or virus survival. For example, influenza and respiratory syncytial virus particles range in size from small spherical virions to filaments reaching many micrometers in length. We have used a pressure vessel model to investigate how the length and width of spherical and filamentous virions can vary for a given critical stress and fluorescence super-resolution microscopy along with image analysis tools to fit imaged influenza viruses to the model. We have shown that influenza virion dimensions fit within the theoretical limits of the model, suggesting that filament formation may be a way to increase an individual virus’s volume without particle rupture. We have also used cryoelectron microscopy to investigate influenza and respiratory syncytial virus dimensions at the extrema of the model and used the pressure vessel model to explain the lack of alternative virus particle geometries. Our approach offers insight into the possible purpose of filamentous virus morphology and is applicable to a wide range of other biological entities, including bacteria and fungi.

Unraveling the Origin of Reverse Plasmonic Circular Dichroism from Discrete Bichiral Au Nanoparticles.

Bichiral plasmonic nanoparticles exhibited intriguing geometry-dependent circular dichroism (CD) reversal; however, the crucial factor that dominates the plasmonic CD is still unclear. Combined with CD spectroscopy and theoretical multipole analysis, we demonstrate that plasmonic CD originates from the excitation of electric quadrupolar plasmons. Moreover, a comparative study of two distinct quadrupolar modes reveals the correlation between the sign of the CD and the local geometric handedness at the plasmonic hotspots, thereby establishing a structure-property relationship in bichiral nanoparticles. The reverse CD is attributed to the opposite directions of the wavelength shift of the two plasmon modes upon changing the particle geometry. By finely tuning the size of bichiral nanoparticles, we can further reveal that the dependence of plasmonic CD on the electric quadrupolar plasmons. Our work sheds light on the physical origin of plasmonic CD and provides important guidelines for the design of chiral plasmonic nanoparticles toward chirality-dependent applications.

Programmable 2D materials through shape-controlled capillary forces

In recent years, self-assembly has emerged as a powerful tool for fabricating functional materials. Since self-assembly is fundamentally determined by the particle interactions in the system, if we can gain full control over these interactions, it would open the door for creating functional materials by design. In this paper, we exploit capillary interactions between colloidal particles at liquid interfaces to create two-dimensional (2D) materials where particle interactions and self-assembly can be fully programmed using particle shape alone. Specifically, we consider colloidal particles which are polygonal plates with homogeneous surface chemistry and undulating edges as this particle geometry gives us precise and independent control over both short-range hard-core repulsions and longer-range capillary interactions. To illustrate the immense potential provided by our system for programming self-assembly, we use minimum energy calculations and Monte Carlo simulations to show that polygonal plates with different in-plane shapes (hexagons, truncated triangles, triangles, squares) and edge undulations of different multipolar order (hexapolar, octopolar, dodecapolar) can be used to create a rich variety of 2D structures, including hexagonal close-packed, honeycomb, Kagome, and quasicrystal lattices. Since the required particle shapes can be readily fabricated experimentally, we can use our colloidal system to control the entire process chain for materials design, from initial design and fabrication of the building blocks, to final assembly of the emergent 2D material.